{"id":"TagRoot","descr":{"en":"all tags","nl":"alle tags"},"tags":[],"collections":[{"id":"Algebra","descr":{"en":"Algebra","nl":"Algebra"},"tags":[{"id":"AlgebraRewriting","descr":{"en":"Rewriting algebraic expressions","nl":"Algebraïsch herleiden"},"stepType":"CONCEPT","errors":[{"id":"CompensateChange","type":["MISCONCEPTION"],"descr":{"en":"Not understanding how to compensate for a change in one number in a calculation, to give an equivalent calculation.","nl":"Niet begrijpen hoe je een verandering in een getal in een berekening kunt compenseren, om een gelijkwaardige berekening te krijgen."}},{"id":"Rearrange","type":["MISCONCEPTION"],"descr":{"en":"Not understanding how to rearrange an expression to find an equivalent statement that represents the information in a different way.","nl":"Niet begrijpen hoe je een uitdrukking kunt herschikken om een gelijkwaardige uitdrukking te krijgen die de informatie op een andere manier weergeeft."}}]}],"collections":[{"id":"ComplexNumbers","descr":{"en":"Complex numbers and their properties","nl":"Complexe getallen en hun eigenschappen"},"tags":[],"collections":[{"id":"ComplexNumberProperties","descr":{"en":"Properties of complex numbers","nl":"Eigenschappen van complexe getallen"},"tags":[{"id":"ComplexNumberAbsoluteValue","descr":{"en":"Calculating the absolute value of complex numbers","nl":"Absolute waarde van complexe getallen berekenen"},"stepType":"CALCULATE"},{"id":"ComplexNumberArgument","descr":{"en":"Calculating the argument of complex numbers","nl":"Het argument van complexe getallen berekenen"},"stepType":"CALCULATE"}],"collections":[]}]},{"id":"Expanding","descr":{"en":"Expanding brackets","nl":"Haakjes uitwerken"},"tags":[],"collections":[{"id":"ExpandingDoubleBrackets","descr":{"en":"Expanding double brackets","nl":"Dubbele haakjes uitwerken"},"tags":[{"id":"ExpandDoubleDifferenceSquares","descr":{"en":"Expanding into a differences of squares","nl":"Een product uitschrijven als het het verschil van twee kwadraten","en-SG":"Expand an expression into a difference of two squares"},"stepType":"ALGEBRA","errors":[{"id":"SignError","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Making a sign error when expanding into a difference of squares.","nl":"Een tekenfout maken bij het uitschrijven naar het verschil van twee kwadraten.","en-SG":"Sign error made when expanding the expression into a difference of two squares."}}]},{"id":"ExpandDoubleBracketsMultiplication","descr":{"en":"Expanding a product of two sums","nl":"Dubbele haakjes uitwerken","en-SG":"Expand the product of two algebraic expressions"},"stepType":"ALGEBRA","errors":[{"id":"NoCrossTerms","type":["MISCONCEPTION"],"descr":{"en":"Not including the cross terms when expanding double brackets.","nl":"De kruistermen niet opschrijven bij het uitwerken van dubbele haakjes.","en-SG":"Missing terms in the expansion."}},{"id":"MissingTerms","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"There are terms missing when expanding double brackets.","nl":"Er ontbreken termen bij het uitwerken van dubbele haakjes.","en-SG":"Missing terms in the expansion."}},{"id":"SignError","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Not writing the correct sign on the expanded terms.","nl":"Het teken van één of meer termen is niet correct.","en-SG":"Not writing the correct sign for the expanded terms."}}]},{"id":"ExpandDoubleBracketsSquare","descr":{"en":"Expanding a square of a sum of terms","nl":"Kwadraat van een tweeterm uitschrijven","en-SG":"Expand expression of the form $(a+b)^2$."},"stepType":"ALGEBRA","errors":[{"id":"NoCrossTerms","type":["MISCONCEPTION"],"descr":{"en":"Not including the cross terms when expanding the square of a sum.","nl":"De kruistermen niet opschrijven bij het uitwerken van het kwadraat van een tweeterm.","en-SG":"Missing terms in the expansion."}},{"id":"SignError","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Not writing the correct sign on the expanded terms.","nl":"Het teken van één of meer termen is niet correct.","en-SG":"Not writing the correct sign for the expanded terms."}}]}],"collections":[]},{"id":"ExpandingHigherPower","descr":{"en":"Expanding a power of an algebraic sum","nl":"Een macht van een algebraïsche som uitwerken"},"tags":[{"id":"BinomialExpansion","descr":{"en":"Expanding the power of a binomial","nl":"Een macht van een binomium uitwerken","en-SG":"Expand the power of a binomial"},"stepType":"ALGEBRA"},{"id":"RepeatedExpansion","descr":{"en":"Expanding more than two pairs of brackets by applying expansion repeatedly","nl":"Meer dan twee haakjesparen uitwerken door herhaaldelijk uit te werken","en-SG":"Expand more than two pairs of brackets by applying expansion repeatedly"},"stepType":"ALGEBRA"}],"collections":[]},{"id":"ExpandingSingle","descr":{"en":"Expanding single brackets","nl":"Enkele haakjes uitwerken"},"tags":[{"id":"ExpandSingleBrackets","descr":{"en":"Expanding a single pair of parentheses","nl":"Eén paar haakjes uitwerken","en-SG":"Expanding an expression with a single pair of brackets"},"stepType":"ALGEBRA","errors":[{"id":"DoubleMultiplication","type":["MISCONCEPTION"],"descr":{"en":"Multiplying all factors of a term by the coefficient.","nl":"Alle factoren van een term vermenigvuldigen met de coëfficiënt."}},{"id":"SkippingTerms","type":["MISCONCEPTION"],"descr":{"en":"Not multiplying all terms by the factored constant.","nl":"Niet alle termen vermenigvuldigen met de coëfficiënt."}},{"id":"SignError","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Making a sign error.","nl":"Een tekenfout maken."}},{"id":"MissingBrackets","type":["MISCONCEPTION"],"descr":{"en":"Not writing required parentheses in the resulting expression.","nl":"Geen haakjes schrijven in het resultaat, terwijl deze wel noodzakelijk zijn."}}]}],"collections":[]}]},{"id":"Factoring","descr":{"en":"Factoring polynomials","nl":"Veeltermen ontbinden in factoren"},"tags":[],"collections":[{"id":"FactoringDouble","descr":{"en":"Factoring polynomials in double brackets","nl":"Veeltermen ontbinden in dubbele haakjes"},"tags":[{"id":"FactorDoubleDifferenceSquares","descr":{"en":"Factoring differences of squares","nl":"Ontbinden van het verschil van twee kwadraten"},"stepType":"ALGEBRA","errors":[{"id":"SignError","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Making a sign error when factoring a difference of squares.","nl":"Een tekenfout maken bij het ontbinden van het verschil van twee kwadraten."}}]},{"id":"FactorIdentitySquare","descr":{"en":"Using the factoring identity 'square of a sum' when factoring a polynomial","nl":"Merkwaardig product 'kwadraat van som' gebruiken bij het ontbinden van een drieterm"},"stepType":"ALGEBRA","errors":[{"id":"SignError","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Making a sign error when using the factoring identity.","nl":"Een tekenfout maken bij het toepassen van het merkwaardig product."}}]},{"id":"FactorDoubleRegrouping","descr":{"en":"Using the regrouping method to factor polynomials with double brackets","nl":"De herschikking methode gebruiken om polynomen met dubbele haakjes te ontbinden"},"stepType":"ALGEBRA"},{"id":"FactorDoubleSumProduct","descr":{"en":"Factoring a quadratic expression using the Sum-Product Rule","nl":"Een kwadratische expressie ontbinden via de som-productmethode"},"stepType":"ALGEBRA","errors":[{"id":"SwitchedSumProduct","type":["MISCONCEPTION"],"descr":{"en":"Switching the values for sum and product.","nl":"De getallen voor de som en het product verwisselen."}}]}],"collections":[]},{"id":"FactoringHigherDegree","descr":{"en":"Factoring polynomials of higher degree","nl":"Veeltermen van hogere graad ontbinden"},"tags":[{"id":"FactorLinearFactor","descr":{"en":"Factoring a linear factor from a higher degree polynomial","nl":"Een lineaire factor ontbinden uit een polynoom van hogere graad"},"stepType":"ALGEBRA"},{"id":"FactorSubstitution","descr":{"en":"Using substitution to rewrite an expression into a polynomial that can be factored","nl":"Substitutie gebruiken om een expressie te herschrijven naar een polynoom die kan worden ontbonden"},"stepType":"ALGEBRA"}],"collections":[]},{"id":"FactoringSingleBrackets","descr":{"en":"Factoring single brackets","nl":"Ontbinden in enkele haakjes"},"tags":[{"id":"FactorSingleBrackets","descr":{"en":"Factoring a common factor","nl":"Een gemeenschappelijke factor buiten haakjes halen"},"stepType":"ALGEBRA","errors":[{"id":"SignError","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Making a sign error when factoring.","nl":"Een tekenfout maken bij het ontbinden."}},{"id":"SkippingTerms","type":["MISCONCEPTION"],"descr":{"en":"Not dividing all terms by the factor.","nl":"Niet alle termen delen door de factor bij het ontbinden."}}]}],"collections":[]}]},{"id":"AlgebraFactors","descr":{"en":"Factors","nl":"Factoren"},"tags":[{"id":"AlgebraFactorsConcept","descr":{"en":"Understanding multiplication","nl":"Vermenigvuldigen begrijpen"},"stepType":"CONCEPT","errors":[{"id":"MultiplicationAsRepeatedAddition","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that multiplication is repeated addition.","nl":"Niet begrijpen dat vermenigvuldiging herhaalde optelling is."}},{"id":"SubtractionInsteadOfMultiplication","type":["MISCONCEPTION"],"descr":{"en":"Thinking that $ab$ means $a - b$ instead of $a \\times b$.","nl":"Denken dat $ab$ betekent $a - b$ in plaats van $a \\times b$."}},{"id":"VariableInsteadOfMultiplication","type":["MISCONCEPTION"],"descr":{"en":"Thinking that $ab$ is a variable instead of $a \\times b$.","nl":"Denken dat $ab$ een variabele is in plaats van $a \\times b$."}},{"id":"NumberInsteadOfMultiplication","type":["MISCONCEPTION"],"descr":{"en":"Thinking that $ab$ is a two-digit number instead of $a \\times b$.","nl":"Denken dat $ab$ een getal met twee cijfers is in plaats van $a \\times b$."}}]},{"id":"AlgebraImplicitMultiplication","descr":{"en":"Understanding implicit multiplication","nl":"Impliciete vermenigvuldiging"},"stepType":"CONCEPT","errors":[{"id":"AdditionInsteadOfMultiplication","type":["MISCONCEPTION"],"descr":{"en":"Thinking that $ab$ means $a + b$ instead of $a \\times b$.","nl":"Denken dat $ab$ betekent $a + b$ in plaats van $a \\times b$."}},{"id":"SubtractionInsteadOfMultiplication","type":["MISCONCEPTION"],"descr":{"en":"Thinking that $ab$ means $a - b$ instead of $a \\times b$.","nl":"Denken dat $ab$ betekent $a - b$ in plaats van $a \\times b$."}},{"id":"VariableInsteadOfMultiplication","type":["MISCONCEPTION"],"descr":{"en":"Thinking that $ab$ is a variable instead of $a \\times b$.","nl":"Denken dat $ab$ een variabele is in plaats van $a \\times b$."}},{"id":"NumberInsteadOfMultiplication","type":["MISCONCEPTION"],"descr":{"en":"Thinking that $ab$ is a two-digit number instead of $a \\times b$.","nl":"Denken dat $ab$ een getal met twee cijfers is in plaats van $a \\times b$."}}]}],"collections":[]},{"id":"AlgebraFractions","descr":{"en":"Algebraic Fractions","nl":"Algebraïsche breuken"},"tags":[],"collections":[{"id":"AlgebraFractionsAddition","descr":{"en":"Adding Algebraic Fractions","nl":"Algebraïsche breuken optellen"},"tags":[{"id":"AlgebraFractionsAddProperCommonDenominator","descr":{"en":"Adding algebraïc fractions with common denominators","nl":"Gelijknamige algebraïsche breuken optellen"},"stepType":"ALGEBRA","errors":[{"id":"AddedDenominator","type":["MISCONCEPTION"],"descr":{"en":"Adding the denominators when adding algebraic fractions.","nl":"De noemers optellen bij het optellen van algebraïsche breuken."}},{"id":"SubtractedDenominator","type":["MISCONCEPTION"],"descr":{"en":"Subtracting the denominators when subtracting algebraic fractions.","nl":"De noemers aftrekken bij het aftrekken van algebraïsche breuken."}}]},{"id":"AlgebraFractionsAddProperUnlikeDenominator","descr":{"en":"Adding algebraïc fractions with unlike denominators","nl":"Ongelijknamige algebraïsche breuken optellen"},"stepType":"ALGEBRA","errors":[{"id":"AddedDenominator","type":["MISCONCEPTION"],"descr":{"en":"Adding the denominators when adding algebraic fractions.","nl":"De noemers optellen bij het optellen van algebraïsche breuken."}},{"id":"SubtractedDenominator","type":["MISCONCEPTION"],"descr":{"en":"Subtracting the denominators when subtracting algebraic fractions.","nl":"De noemers aftrekken bij het aftrekken van algebraïsche breuken."}}]}],"collections":[]},{"id":"FractionAlgebraDivision","descr":{"en":"Dividing algebraic fractions","nl":"Algebraïsche Breuken delen"},"tags":[{"id":"FractionAlgebracDivisionProperByExpression","descr":{"en":"Multiplying proper algebraic fractions","nl":"Algebraïsche breuken vermenigvuldigen"},"stepType":"CALCULATE"}],"collections":[]},{"id":"FractionAlgebraMultiplication","descr":{"en":"Multiplying algebraic fractions","nl":"Algebraïsche Breuken vermenigvuldigen"},"tags":[{"id":"FractionAlgebracMultiplicationProper","descr":{"en":"Multiplying proper algebraic fractions","nl":"Algebraïsche breuken vermenigvuldigen"},"stepType":"CALCULATE","errors":[{"id":"CreatingSimilarFractionsToMultiply","type":["MISCONCEPTION"],"descr":{"en":"Thinking that fractions need to be made similar before multiplying.","nl":"Denken dat breuken gelijknamig gemaakt moeten worden om ze te kunnen vermenigvuldigen."}},{"id":"CrossMultiplicationDone","type":["MISCONCEPTION"],"descr":{"en":"Applying cross multiplication instead of multiplying numerators and denominators.","nl":"Kruisgewijs vermenigvuldigen is toegepast."}}]}],"collections":[]},{"id":"AlgebraFractionsRewriting","descr":{"en":"Rewriting Algebraic Fractions","nl":"Algebraïsche breuken herleiden"},"tags":[{"id":"AlgebraFractionsNumeratorFactor","descr":{"en":"Rewriting algebraic fractions with a multiplication in the numerator into a product","nl":"Algebraïsche breuken met een vermenigvuldiging in de teller herleiden tot een product"},"stepType":"ALGEBRA"},{"id":"AlgebraFractionsDenominatorWithFraction","descr":{"en":"Rewriting fractions to remove a fraction from the denominator","nl":"Breuken herleiden om een breuk uit de noemer te halen"},"stepType":"ALGEBRA"},{"id":"AlgebraFractionsRemoveDecimal","descr":{"en":"Rewriting fractions to remove a decimal number from the numerator or denominator","nl":"Breuken herleiden om een decimaal getal uit de teller of noemer kwijt te raken"},"stepType":"ALGEBRA"},{"id":"AlgebraFractionsNumeratorSum","descr":{"en":"Rewriting algebraic fractions with a sum in the numerator into a sum of fractions","nl":"Algebraïsche breuken met een som in de teller herleiden tot een som van breuken"},"stepType":"ALGEBRA"}],"collections":[]}]},{"id":"AlgebraPowerRules","descr":{"en":"Algebraic manipulation of powers","nl":"Heleiden van machten"},"tags":[{"id":"AlgebraPowersConcept","descr":{"en":"Understanding powers","nl":"Machten begrijpen"},"stepType":"CONCEPT","errors":[{"id":"PowerAsRepeatedMultiplication","type":["MISCONCEPTION"],"descr":{"en":"Not understanding how to write repeated multiplication as a power.","nl":"Niet begrijpen hoe herhaalde vermenigvuldiging als een macht kan worden geschreven."}},{"id":"SwappedBaseExponent","type":["MISCONCEPTION"],"descr":{"en":"Mixing up the index and the base: writing $a^m$ as $m \\times m \\times \\ldots \\times m$ instead of $a \\times a \\times \\dots \\times a$.","nl":"De index en de basis door elkaar halen: $a^m$ schrijven als $m \\times m \\times \\ldots \\times m$ in plaats van $a \\times a \\times \\dots \\times a$."}},{"id":"ProductInsteadOfPower","type":["MISCONCEPTION"],"descr":{"en":"Writing $a^m$ as $a \\times m$ instead of $a \\times a \\times \\ldots \\times a$.","nl":"$a^m$ schrijven als $a \\times m$ in plaats van $a \\times a \\times \\ldots \\times a$."}},{"id":"ProductInsteadOfPowerReversed","type":["MISCONCEPTION"],"descr":{"en":"Thinking $a \\times a \\times \\ldots \\times a$ means $a\\times n$ instead of $a^n$.","nl":"Denken dat $a \\times a \\times \\ldots \\times a$ betekent $a\\times n$ in plaats van $a^n$."}},{"id":"SumInsteadOfPower","type":["MISCONCEPTION"],"descr":{"en":"Writing $a^m$ as $a + a + \\ldots + a$ instead of $a \\times a \\times \\ldots \\times a$.","nl":"$a^m$ schrijven als $a + a + \\ldots + a$ in plaats van $a \\times a \\times \\ldots \\times a$."}},{"id":"IncorrectExponent","type":["MISCONCEPTION"],"descr":{"en":"Not making the exponent equal to number of times the base is multiplied by itself.","nl":"De exponent niet gelijk maken aan het aantal keer dat de basis met zichzelf wordt vermenigvuldigd."}},{"id":"OneOff","type":["MISCONCEPTION"],"descr":{"en":"Not including the first occurrence of the base number when writing $a \\times a \\times \\ldots \\times a$ in index form.","nl":"Het eerste basisgetal niet opnemen bij het schrijven van $a \\times a \\times \\ldots \\times a$ als een macht."}}]},{"id":"AlgebraPowerNegativeExponent","descr":{"en":"Applying the power rule for negative exponents","nl":"De machtsregels voor negatieve exponenten toepassen"},"stepType":"ALGEBRA","errors":[{"id":"SignError","type":["MISCONCEPTION"],"descr":{"en":"Rewriting a negative exponent into a negative power function.","nl":"Een negatieve exponent herleiden naar een negatieve machtsfunctie."}}]},{"id":"AlgebraDivisionOfPowerFunctions","descr":{"en":"Applying the rule for dividing power functions","nl":"De regel voor delen van machtsfuncties toepassen"},"stepType":"ALGEBRA","errors":[{"id":"DividingExponents","type":["MISCONCEPTION"],"descr":{"en":"Dividing the exponents when dividing power functions.","nl":"De exponenten delen bij het delen van machtsfuncties."}},{"id":"DifferentBase","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Dividing power functions with different base.","nl":"Delen van machtsfuncties met verschillende basis."}}]},{"id":"AlgebraPowerOfProduct","descr":{"en":"Apply the rule for the power of a product of power functions","nl":"De regel toepassen voor de macht van een product van machtsfuncties"},"stepType":"ALGEBRA","errors":[{"id":"SignError","type":["MISCONCEPTION"],"descr":{"en":"Making a sign error when negating the base of a power function.","nl":"Een tekenfout maken bij het omdraaien van het teken van de basis van een machtsfunctie."}},{"id":"NotAllFactors","type":["MISCONCEPTION"],"descr":{"en":"Not applying the power to all factors.","nl":"De macht niet op alle factoren toepassen."}}]},{"id":"AlgebraProductOfPowerFunctions","descr":{"en":"Apply the rule for multiplying power functions","nl":"De machtsregels voor vermenigvuldigen van machtsfuncties toepassen"},"stepType":"ALGEBRA","errors":[{"id":"Concept","type":["MISCONCEPTION"],"descr":{"en":"Not understanding how to use index laws for multiplying powers.","nl":"Niet begrijpen hoe machtsregels moeten worden toegepast bij het vermenigvuldigen van machten."}},{"id":"MultiplyingExponents","type":["MISCONCEPTION"],"descr":{"en":"Multiplying the exponents when multiplying power functions.","nl":"De exponenten vermenigvuldigen bij het vermenigvuldigen van machtsfuncties."}},{"id":"DifferentBase","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Multiplying power functions with different base.","nl":"Vermenigvuldigen van machtsfuncties met verschillende basis."}}]},{"id":"AlgebraPowerRuleRoots","descr":{"en":"Apply the power rule for roots","nl":"De machtsregels voor wortels toepassen"},"stepType":"ALGEBRA"}],"collections":[]},{"id":"AlgebraRootRules","descr":{"en":"Algebraic manipulation of roots","nl":"Heleiden van wortels"},"tags":[{"id":"AlgebraRootsConcept","descr":{"en":"Understanding roots","nl":"Wortels begrijpen"},"stepType":"CONCEPT"},{"id":"AlgebraDivisionOfRoots","descr":{"en":"Applying the rule for dividing roots","nl":"De regel voor delen van wortels toepassen"},"stepType":"ALGEBRA"},{"id":"AlgebraProductOfRoots","descr":{"en":"Apply the rule for multiplying roots","nl":"De regels voor vermenigvuldigen van wortels toepassen"},"stepType":"ALGEBRA","errors":[{"id":"MultiplyingFactor","type":["MISCONCEPTION"],"descr":{"en":"Applying the factor on the radicand when multiplying a root.","nl":"De factor direct met de radicand vermenigvuldigen."}},{"id":"SignError","type":["MISCONCEPTION"],"descr":{"en":"Applying the sign of a root on the radicand.","nl":"Het teken van de wortel toepassen op de radicand."}}]}],"collections":[]},{"id":"AlgebraTerms","descr":{"en":"Terms in algebra","nl":"Termen in algebra"},"tags":[{"id":"AlgebraAddingLikeTerms","descr":{"en":"Adding like terms","nl":"Gelijksoortige termen optellen"},"stepType":"ALGEBRA","errors":[{"id":"NotAddingLikeTerms","type":["MISCONCEPTION"],"descr":{"en":"Not realising that like terms can be collected.","nl":"Niet beseffen dat gelijksoortige termen kunnen worden samengenomen."}},{"id":"UnlikeTerms","type":["MISCONCEPTION"],"descr":{"en":"Adding unlike terms.","nl":"Ongelijksoortige termen optellen."}},{"id":"ChangingTermType","type":["MISCONCEPTION"],"descr":{"en":"Changing the type when adding like terms.","nl":"De soort aanpassen bij optellen van gelijksoortige termen."}}]},{"id":"AlgebraTermsMinus","descr":{"en":"Understanding the negative sign","nl":"Het minteken begrijpen"},"stepType":"CONCEPT","errors":[{"id":"TwoMinusIsPlus","type":["MISCONCEPTION"],"descr":{"en":"Thinking that ‘two negatives make a positive’, so –m – n must be m + n.","nl":"Denken dat twee minnen een plus maken, dus –m – n moet m + n zijn."}},{"id":"MinusCommatative","type":["MISCONCEPTION"],"descr":{"en":"Thinking that subtraction from a positive number is commutative.","nl":"Denken dat aftrekken van een positief getal commutatief is."}},{"id":"MinusTermCorrespondence","type":["MISCONCEPTION"],"descr":{"en":"Not realising that the negative sign ‘belongs’ with the term it is immediately in front of.","nl":"Niet beseffen dat het minteken ‘hoort’ bij de term waar het direct voor staat."}},{"id":"TermOrder","type":["MISCONCEPTION"],"descr":{"en":"Thinking that changing the order of the terms means changing the signs.","nl":"Denken dat het veranderen van de volgorde van de termen betekent dat de tekens ook veranderen."}}]}],"collections":[]}]},{"id":"AnalyticGeometry","descr":{"en":"Analytic Geometry","nl":"Analytische Meetkunde"},"tags":[],"collections":[{"id":"AnalyticGeometryPolarVectors","descr":{"en":"Vectors in polar coordinates","nl":"Vectoren in poolcoördinaten"},"tags":[{"id":"CartesianVectorsToPolar","descr":{"en":"Convert Cartesian coordinates to polar coordinates","nl":"Cartesische coördinaten omschrijven naar poolcoördinaten"},"stepType":"CONCEPT"},{"id":"AnalyticGeometryPolarVectorsScale","descr":{"en":"Multiplying vectors in polar coordinates by a constant","nl":"Vermenigvuldigen van vectoren in poolcoördinaten met een constante"},"stepType":"CONCEPT"},{"id":"PolarVectorsToCartesian","descr":{"en":"Convert Polar coordinates to Cartesian coordinates","nl":"Poolcoördinates omschrijven naar Cartesische coördinaten"},"stepType":"CONCEPT"}],"collections":[]},{"id":"AnalyticGeometryVectors","descr":{"en":"Vectors in a coordinate system","nl":"Vectoren in een coördinatenstelsel"},"tags":[{"id":"AnalyticGeometryVectorsAddition","descr":{"en":"Adding vectors in a coordinate system by adding their coordinates","nl":"Vectoren in een coördinatenstelsel optellen door hun coordinaten op te tellen"},"stepType":"CONCEPT"},{"id":"AnalyticGeometryVectorDirection","descr":{"en":"Computing the direction of a vector","nl":"De hoek van een vector berekenen"},"stepType":"CONCEPT"},{"id":"AnalyticGeometryVectorLength","descr":{"en":"Computing the length of a vector using the Pythagorean theorem","nl":"De lengte van een vector berekenen met de stelling van Pythagoras"},"stepType":"CONCEPT"},{"id":"AnalyticGeometryVectorsMultiplication","descr":{"en":"Multiplying vectors by multiplying their coordinates","nl":"Vectoren vermenigvuldigen door hun coordinaten te vermenigvuldigen"},"stepType":"CONCEPT"}],"collections":[]}]},{"id":"Arithmetic","descr":{"en":"Arithmetic","nl":"Rekenen"},"tags":[],"collections":[{"id":"FractionArithmetic","descr":{"en":"Arithmetic with fractions","nl":"Rekenen met breuken"},"tags":[],"collections":[{"id":"FractionArithmeticAddition","descr":{"en":"Adding fractions","nl":"Breuken optellen"},"tags":[{"id":"FractionArithmeticAddMixed","descr":{"en":"Adding mixed fractions","nl":"Gemengde breuken optellen"},"stepType":"CALCULATE","errors":[{"id":"AddedDenominator","type":["MISCONCEPTION"],"descr":{"en":"Adding the denominators when adding mixed fractions.","nl":"De noemers optellen bij het optellen van gemengde breuken."}},{"id":"IncorrectFractionalPart","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Adding the fractional part incorrectly when adding mixed fractions.","nl":"Het breukgedeelte verkeerd optellen bij het optellen van gemengde breuken."}},{"id":"IncorrectIntegerPart","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Adding the fractional part correctly, but the integer part incorrectly when adding mixed fractions.","nl":"Het breukgedeelte juist optellen, maar de gehele getallen verkeerd optellen bij het optellen van gemengde breuken."}}]},{"id":"FractionArithmeticAddProperCommonDenominator","descr":{"en":"Adding proper fractions with common denominators","nl":"Gelijknamige echte breuken optellen"},"stepType":"CALCULATE","errors":[{"id":"AddedDenominator","type":["MISCONCEPTION"],"descr":{"en":"Adding the denominators when adding simple fractions.","nl":"De noemers optellen bij het optellen van echte breuken."}},{"id":"SubtractedDenominator","type":["MISCONCEPTION"],"descr":{"en":"Subtracting the denominators when subtracting simple fractions.","nl":"De noemers aftrekken bij het aftrekken van echte breuken."}}]},{"id":"FractionArithmeticAddProperUnlikeDenominator","descr":{"en":"Adding fractions with unlike denominators","nl":"Ongelijknamige breuken optellen"},"stepType":"CALCULATE","errors":[{"id":"AddedDenominator","type":["MISCONCEPTION"],"descr":{"en":"Adding the denominators when adding simple fractions.","nl":"De noemers optellen bij het optellen van echte breuken."}},{"id":"SubtractedDenominator","type":["MISCONCEPTION"],"descr":{"en":"Subtracting the denominators when subtracting simple fractions.","nl":"De noemers aftrekken bij het aftrekken van echte breuken."}}]},{"id":"FractionArithmeticSubtractMixed","descr":{"en":"Subtracting mixed fractions","nl":"Gemengde breuken aftrekken"},"stepType":"CALCULATE","errors":[{"id":"AddedDenominator","type":["MISCONCEPTION"],"descr":{"en":"Adding or subtracting the denominators when subtracting mixed fractions.","nl":"De noemers optellen of aftrekken bij het aftrekken van gemengde breuken."}},{"id":"AddedFractionalPart","type":["MISCONCEPTION"],"descr":{"en":"Adding the proper fractions when subtracting mixed fractions.","nl":"De echte breuken optellen bij het aftrekken van gemengde breuken."}}]},{"id":"FractionArithmeticSubtractWholeProper","descr":{"en":"Subtracting a fraction from a whole number","nl":"Een breuk aftrekken van een heel getal"},"stepType":"CALCULATE","errors":[{"id":"SubtractFromWhole","type":["MISCONCEPTION"],"descr":{"en":"Not knowing how to subtract a fraction from a whole number.","nl":"Niet weten hoe je een breuk van een heel getal aftrekt."}}]}],"collections":[]},{"id":"FractionArithmeticDivision","descr":{"en":"Dividing fractions","nl":"Breuken delen"},"tags":[{"id":"FractionArithmeticDivisionMixed","descr":{"en":"Dividing mixed fractions","nl":"Gemengde breuken delen"},"stepType":"CALCULATE","errors":[{"id":"DividingFractionalPartOnly","type":["MISCONCEPTION"],"descr":{"en":"Dividing the fractional part only, leaving the integer part unchanged.","nl":"Alleen het breukgetal delen. Het gehele deel ongewijzigd laten."}}]},{"id":"FractionArithmeticDivisionProperByNumber","descr":{"en":"Dividing a proper fraction by a number","nl":"Een echte breuk delen door een getal"},"stepType":"CALCULATE"},{"id":"FractionArithmeticDivisionProper","descr":{"en":"Dividing proper fractions","nl":"Echte breuken delen"},"stepType":"CALCULATE","errors":[{"id":"NotFlippingFraction","type":["MISCONCEPTION"],"descr":{"en":"Multiplying without flipping the fraction.","nl":"Niet vermenigvuldigen met het omgekeerde."}},{"id":"FlippingWrongFraction","type":["MISCONCEPTION"],"descr":{"en":"Flipping the wrong fraction.","nl":"De verkeerde breuk omkeren."}},{"id":"FlippingBothFractions","type":["MISCONCEPTION"],"descr":{"en":"Flipping both fractions.","nl":"Beide breuken omkeren."}},{"id":"SubtractionInsteadOfDivision","type":["MISCONCEPTION"],"descr":{"en":"Subtracting rather than dividing.","nl":"Aftrekken in plaats van delen."}}]}],"collections":[]},{"id":"FractionArithmeticEquivalent","descr":{"en":"Equivalent fractions","nl":"Gelijkwaardige breuken"},"tags":[{"id":"FractionArithmeticOrderCompare","descr":{"en":"Comparing fractions","nl":"Breuken onderling vergelijken"},"stepType":"CALCULATE","errors":[{"id":"SizeEquivalent","type":["MISCONCEPTION"],"descr":{"en":"Unable to recognise that equivalent fractions correspond to the same quantity.","nl":"Niet herkennen dat gelijkwaardige breuken even groot zijn."}},{"id":"SizeNumeratorDenominator","type":["MISCONCEPTION"],"descr":{"en":"Mistaking the fraction with the larger numerator and denominator as the larger fraction.","nl":"Denken dat een breuk met grotere teller en noemer de grotere breuk is."}},{"id":"SizeDenominator","type":["MISCONCEPTION"],"descr":{"en":"Mistaking the fraction with the larger denominator as the larger fraction.","nl":"Denken dat een breuk met grotere noemer de grotere breuk is."}}]},{"id":"FractionArithmeticEquivalentConcept","descr":{"en":"Understanding that fractions can be equivalent","nl":"Begrijpen dat breuken gelijkwaardig kunnen zijn"},"stepType":"CONCEPT","errors":[{"id":"EquivalentEqual","type":["MISCONCEPTION"],"descr":{"en":"Thinking that fractions are equivalent only when they look identical","nl":"Denken dat breuken alleen gelijkwaardig zijn als ze er hetzelfde uitzien"}},{"id":"EquivalentNumerator","type":["MISCONCEPTION"],"descr":{"en":"Thinking that fractions are equivalent if they have equal numerator","nl":"Denken dat breuken gelijkwaardig zijn als de teller gelijk is"}},{"id":"FractionAsNumberRatio","type":["MISCONCEPTION"],"descr":{"en":"Not understanding how to write one number as a fraction of another.","nl":"Niet begrijpen hoe je een getal als breuk van een ander getal schrijft."}},{"id":"EquivalentNumeratorDenominator","type":["MISCONCEPTION"],"descr":{"en":"Not understanding the relationship between size of numerator and denominator when comparing fractions","nl":"De relatie tussen teller en noemer niet begrijpen bij het vergelijken van breuken"}},{"id":"EquivalentOne","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that n/n = 1","nl":"Niet begrijpen dat n/n = 1"}},{"id":"EquivalentZero","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that a fraction with numerator zero is equal to zero","nl":"Niet begrijpen dat een breuk met teller nul gelijk is aan nul."}}]},{"id":"FractionArithmeticDecimalToFraction","descr":{"en":"Writing a decimal number into a fraction","nl":"Een decimaal getal als een breuk schrijven"},"stepType":"CALCULATE","errors":[{"id":"SwapNumeratorDenominator","type":["MISCONCEPTION"],"descr":{"en":"Swapping the numerator and denominator when writing a decimal in fraction form (for example writing 0.7 = 10/7).","nl":"De teller en noemer verwisselen bij het schrijven van een decimaal getal in breukvorm (bijvoorbeeld 0,7 = 10/7)."}}]},{"id":"FractionArithmeticFractionToDecimal","descr":{"en":"Writing a fraction into a decimal number","nl":"Een breuk als een decimaal getal schrijven"},"stepType":"CALCULATE","errors":[{"id":"DecimalNumerator","type":["MISCONCEPTION"],"descr":{"en":"Matching unit fraction with incorrect decimals by writing the denominator after the decimal point.","nl":"Een breuk als een verkeerd decimaal getal schrijven door de noemer achter de decimale komma te schrijven."}}]},{"id":"FractionArithmeticSimilarImproperToMixed","descr":{"en":"Writing an improper fraction into a similar mixed fraction","nl":"Een onechte breuk schrijven als een gemengde breuk"},"stepType":"CALCULATE"},{"id":"FractionArithmeticIntegerToFraction","descr":{"en":"Writing an integer number into a fraction","nl":"Een geheel getal als een breuk schrijven"},"stepType":"CALCULATE"},{"id":"FractionArithmeticSimilarMixed","descr":{"en":"Writing a similar mixed fraction","nl":"Een gelijkwaardige gemengde breuk schrijven"},"stepType":"CONCEPT","errors":[{"id":"MixedFractionConcept","type":["MISCONCEPTION"],"descr":{"en":"Misunderstanding mixed numbers. Treating whole parts and fractional parts as different entities.","nl":"Niet begrijpen wat samengestelde breuken zijn. Denken dat de helen en de breuk verschillende getallen zijn."}}]},{"id":"FractionArithmeticSimilarMixedToImproper","descr":{"en":"Writing a mixed fraction into a similar improper fraction","nl":"Een onechte breuk schrijven als een gemengde breuk"},"stepType":"CALCULATE"},{"id":"FractionArithmeticRewriteProper","descr":{"en":"Rewriting a proper fraction","nl":"Een breuk herleiden"},"stepType":"CALCULATE","errors":[{"id":"DenominatorHundred","type":["MISCONCEPTION"],"descr":{"en":"Not understanding how to convert a fraction to an equivalent fraction with denominator 100.","nl":"Niet begrijpen hoe je een breuk omzet naar een equivalente breuk met noemer 100."}}]},{"id":"FractionArithmeticSimplifyProper","descr":{"en":"Simplifying a proper fraction","nl":"Een breuk vereenvoudigen"},"stepType":"CALCULATE"}],"collections":[]},{"id":"FractionArithmeticMultiplication","descr":{"en":"Multiplying fractions","nl":"Breuken vermenigvuldigen"},"tags":[{"id":"FractionArithmeticMultiplicationMixed","descr":{"en":"Multiplying mixed fractions","nl":"Gemengde breuken vermenigvuldigen"},"stepType":"CALCULATE","errors":[{"id":"MultiplyingFractionalPartOnly","type":["MISCONCEPTION"],"descr":{"en":"Multiplying the fractional part only, leaving the integer part unchanged.","nl":"Alleen het breukgetal vermenigvuldigen. Het gehele deel ongewijzigd laten."}}]},{"id":"FractionArithmeticMultiplicationProper","descr":{"en":"Multiplying proper fractions","nl":"Echte breuken vermenigvuldigen"},"stepType":"CALCULATE","errors":[{"id":"CreatingSimilarFractionsToMultiply","type":["MISCONCEPTION"],"descr":{"en":"Thinking that fractions need to be made similar before multiplying.","nl":"Denken dat breuken gelijknamig gemaakt moeten worden om ze te kunnen vermenigvuldigen."}},{"id":"CrossMultiplicationDone","type":["MISCONCEPTION"],"descr":{"en":"Applying cross multiplication instead of multiplying numerators and denominators.","nl":"Kruisgewijs vermenigvuldigen is toegepast."}}]},{"id":"FractionArithmeticMultiplicationWholeProper","descr":{"en":"Multiplying whole numbers by proper fractions","nl":"Hele getallen vermenigvuldigen met echte breuken"},"stepType":"CALCULATE","errors":[{"id":"AssumeFraction","type":["MISCONCEPTION"],"descr":{"en":"Thinking that because there is a fraction in the question there must be a fraction in the answer.","nl":"Denken dat omdat er een breuk in de vraag staat, er ook een breuk in het antwoord moet staan."}},{"id":"MultiplyDenominator","type":["MISCONCEPTION"],"descr":{"en":"Multiplying the whole number by the denominator.","nl":"Het hele getal vermenigvuldigen met de noemer."}},{"id":"MultiplyNumeratorAndDenominator","type":["MISCONCEPTION"],"descr":{"en":"Multiplying the whole number by both the numerator and the denominator.","nl":"Het hele getal vermenigvuldigen met zowel de teller als de noemer."}},{"id":"MultiplyNoNumerator","type":["MISCONCEPTION"],"descr":{"en":"Dividing the whole number by the denominator, but not multiplying by the numerator.","nl":"Het hele getal delen door de noemer, maar niet vermenigvuldigen met de teller."}}]}],"collections":[]}]},{"id":"NumberArithmetic","descr":{"en":"Arithmetic with numbers","nl":"Rekenen met getallen"},"tags":[],"collections":[{"id":"NumberArithmeticAddition","descr":{"en":"Adding and subtracting numbers","nl":"Getallen optellen en aftrekken"},"tags":[{"id":"NumberArithmeticAdditionDecimal","descr":{"en":"Adding decimal numbers","nl":"Decimale getallen optellen"},"stepType":"CALCULATE"},{"id":"NumberArithmeticAdditionInteger","descr":{"en":"Adding integer numbers","nl":"Gehele getallen optellen"},"stepType":"CALCULATE"},{"id":"NumberArithmeticAddNegative","descr":{"en":"Adding a negative number","nl":"Een negatief getal optellen"},"stepType":"CALCULATE","errors":[{"id":"AddNegativeVsSubtraction","type":["MISCONCEPTION"],"descr":{"en":"Not knowing adding a negative number is the same as subtracting.","nl":"Niet weten dat optellen van een negatief getal neerkomt op aftrekken."}},{"id":"AddNegativeMoveSign","type":["MISCONCEPTION"],"descr":{"en":"Moving the negative sign to the starting number.","nl":"Het minteken verplaatsen naar het eerste getal."}},{"id":"AddNegativeStartingNumber","type":["MISCONCEPTION"],"descr":{"en":"Thinking that the additive number is negative, so the starting number must be negative.","nl":"Denken dat het eerste getal negatief is, omdat het tweede getal dat ook is."}},{"id":"AddNegativeIgnoreSign","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Ignoring the minus sign.","nl":"Het minteken negeren."}}]},{"id":"NumberArithmeticAddConcept","descr":{"en":"Understanding addition and subtraction","nl":"Optellen en aftrekken begrijpen"},"stepType":"CONCEPT","errors":[{"id":"AddvsSubtract","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Confusing addition and subtraction.","nl":"Optellen en aftrekken door elkaar halen."}},{"id":"AddForLess","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Thinking you need to add n to find n less.","nl":"Denken dat je n moeten optellen om n minder te vinden."}},{"id":"MoreVsLess","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Confusing ‘less than’ and ‘more than’.","nl":"‘Minder dan’ en ‘meer dan’ door elkaar halen."}},{"id":"IgnoreSign","type":["MISTAKE"],"descr":{"en":"Ignoring the negative sign and calculating n less than m instead of n less than –m.","nl":"Het minteken negeren en n minder dan m berekenen in plaats van n minder dan –m."}},{"id":"UnderstandingAdditionSubtraction","type":["MISTAKE"],"descr":{"en":"Not understanding the effect of adding or subtracting positive numbers of different sizes.","nl":"Niet begrijpen wat het effect is van optellen of aftrekken van positieve getallen van verschillende grootte."}}]},{"id":"NumberArithmeticSubtractionDecimal","descr":{"en":"Subtracting decimal numbers","nl":"Decimale getallen aftrekken"},"stepType":"CALCULATE","errors":[{"id":"SubtractDecimalFromWhole","type":["MISCONCEPTION"],"descr":{"en":"Not knowing how to subtract a decimal from a whole number.","nl":"Niet weten hoe je een decimaal van een heel getal aftrekt."}}]},{"id":"NumberArithmeticSubtractionInteger","descr":{"en":"Subtracting integer numbers","nl":"Gehele getallen aftrekken"},"stepType":"CALCULATE"},{"id":"NumberArithmeticSubtractNegative","descr":{"en":"Subtracting a negative number","nl":"Een negatief getal aftrekken"},"stepType":"CALCULATE","errors":[{"id":"SubtractNegativeAddition","type":["MISCONCEPTION"],"descr":{"en":"Not knowing subtraction of a negative number is the same as addition.","nl":"Niet weten dat aftrekken van een negatief getal neerkomt op optellen."}},{"id":"SubtractNegativeMoveSign","type":["MISCONCEPTION"],"descr":{"en":"Moving the negative sign to a different number.","nl":"Het minteken verplaatsen naar een ander getal."}},{"id":"SubtractNegativeStartingNumber","type":["MISCONCEPTION"],"descr":{"en":"Thinking that as the number being subtracted is negative, so the starting number is negative.","nl":"Denken dat als het getal dat afgetrokken wordt negatief is, het eeste getal dat ook is."}},{"id":"SubtractionVsNegativeNumber","type":["MISCONCEPTION"],"descr":{"en":"Confusing the subtraction symbol with a negative number.","nl":"Het teken voor aftrekken verwarren met het minteken voor negatieve getallen."}},{"id":"SubtractNegativeIgnoreSign","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Ignoring the minus sign.","nl":"Het minteken negeren."}}]}],"collections":[]},{"id":"NumberArithmeticDivision","descr":{"en":"Dividing numbers","nl":"Getallen delen"},"tags":[{"id":"NumberArithmeticDivsionConcept","descr":{"en":"Concept of division","nl":"Begrip van het concept delen"},"stepType":"CONCEPT"},{"id":"NumberArithmeticDivisionDecimal","descr":{"en":"Dividing decimal numbers","nl":"Decimale getallen delen"},"stepType":"CALCULATE"},{"id":"NumberArithmeticDivisionInteger","descr":{"en":"Dividing integer numbers","nl":"Gehele getallen delen"},"stepType":"CALCULATE"}],"collections":[]},{"id":"IntegerNumbers","descr":{"en":"Integer numbers","nl":"Gehele getallen"},"tags":[{"id":"IntegerPrimeFactorisation","descr":{"en":"Finding the prime factorisation of integer numbers","nl":"Priemontbinding bepalen van gehele getallen"},"stepType":"CONCEPT"}],"collections":[]},{"id":"NumberInverse","descr":{"en":"Inverses of numbers","nl":"Omgekeerden van getallen"},"tags":[{"id":"NumberInverseAdditive","descr":{"en":"Additive inverse of numbers","nl":"De additief inverse van getallen"},"stepType":"CALCULATE","errors":[{"id":"AddNegativeVsSubtraction","type":["MISCONCEPTION"],"descr":{"en":"Not knowing the additive inverse of numbers.","nl":"De additief inverse van een getal niet herkennen."}}]},{"id":"NumberInverseMultiplicative","descr":{"en":"Multiplicative inverse of numbers","nl":"Het multiplicatieve inverse van getallen"},"stepType":"CALCULATE","errors":[{"id":"MultiplicationVsDivision","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that in a multiplication calculation, multiplying one factor by a number and dividing the other factor by the same number gives an equivalent calculation.","nl":"Niet begrijpen dat in een vermenig-vuldiging, het vermenigvuldigen van een factor met een getal en het delen van de andere factor door hetzelfde getal een gelijkwaardige berekening oplevert."}}]}],"collections":[]},{"id":"NumberArithmeticMultiplication","descr":{"en":"Multiplying numbers","nl":"Getallen vermenigvuldigen"},"tags":[{"id":"NumberArithmeticMultiplicationConcept","descr":{"en":"Concept of multiplication","nl":"Begrip van het concept vermenigvuldigen"},"stepType":"CONCEPT","errors":[{"id":"Commutativity","type":["MISCONCEPTION"],"descr":{"en":"Not understanding commutativity of multiplication.","nl":"De commutatieve eigenschap van vermenigvuldiging niet kennen."}},{"id":"MultiplicationTable","type":["MISCONCEPTION"],"descr":{"en":"Not knowing the tables of multiplication.","nl":"De tafels van vermenigvuldiging niet kennen."}},{"id":"MultiplicationValue","type":["MISCONCEPTION"],"descr":{"en":"Not understanding value of simple products.","nl":"De waarde van eenvoudige vermenigvuldigingen niet begrijpen."}},{"id":"FactorVsMultiple","type":["MISCONCEPTION"],"descr":{"en":"Confusing the meaning of 'factor' and 'multiple'.","nl":"Het begrip 'factor' en 'veelvoud' met elkaar verwarren."}},{"id":"FactorZero","type":["MISCONCEPTION"],"descr":{"en":"Thinking zero is a factor of every number.","nl":"Denken dat nul een deler is van elk getal."}}]},{"id":"NumberArithmeticMultiplicationDecimal","descr":{"en":"Multiplying decimal numbers","nl":"Decimale getallen vermenigvuldigen"},"stepType":"CALCULATE"},{"id":"NumberArithmeticMultiplicationInteger","descr":{"en":"Multiplying integer numbers","nl":"Gehele getallen vermenigvuldigen"},"stepType":"CALCULATE"},{"id":"NumberArithmeticMultiplyNegative","descr":{"en":"Multiplying by negative numbers","nl":"Vermenigvuldigen met negatieve getallen"},"stepType":"CONCEPT","errors":[{"id":"General","type":["MISCONCEPTION"],"descr":{"en":"Not knowing the rules for multiplying by a negative number.","nl":"De regels voor vermenigvuldigen met een negatief getal niet kennen."}}]},{"id":"NumberArithmeticMultiplicationRepresentation","descr":{"en":"Representing multiplication","nl":"Vermenigvuldigen schematisch weergeven"},"stepType":"CONCEPT","errors":[{"id":"MultiplicationPattern","type":["MISCONCEPTION"],"descr":{"en":"Not understanding how array represents multiplication.","nl":"Niet weten hoe een rechthoek van objecten een vermenigvuldiging kan voorstellen."}},{"id":"MultiplicationDecompose","type":["MISCONCEPTION"],"descr":{"en":"Not understanding the distributive property of multiplication, e.g. 4x3 = 2x3+2x3.","nl":"De distributieve eigenschap van vermenigvuldiging niet kennen, zoals 4x3 = 2x3+2x3."}}]}],"collections":[]},{"id":"NumberParity","descr":{"en":"Even and odd numbers","nl":"Even en oneven getallen"},"tags":[{"id":"NumberParityConcept","descr":{"en":"Concept of even and odd numbers","nl":"Begrip van even en oneven getallen"},"stepType":"CONCEPT","errors":[{"id":"EvenDigit","type":["MISCONCEPTION"],"descr":{"en":"Thinking an even number anywhere in the number makes it even.","nl":"Denken dat een getal even is als er een even getal in voorkomt."}}]},{"id":"NumberParityRepresentation","descr":{"en":"Representation of even and odd numbers","nl":"Schematische weergave van even en oneven getallen"},"stepType":"CONCEPT","errors":[{"id":"EvenDigit","type":["MISCONCEPTION"],"descr":{"en":"Thinking an even number anywhere in the number makes it even.","nl":"Denken dat een getal even is als er een even getal in voorkomt."}},{"id":"EvenDivisibility","type":["MISCONCEPTION"],"descr":{"en":"Not knowing that even numbers are divisible by two.","nl":"Niet weten dat even getallen deelbaar zijn door twee."}},{"id":"OddDivisibility","type":["MISCONCEPTION"],"descr":{"en":"Not recognising odd numbers as numbers divisible by 2 with 1 remainder.","nl":"Niet weten dat oneven getallen gezien kunnen worden als getallen deelbaar door 2 met rest 1."}}]}],"collections":[]},{"id":"NumberArithmeticPowers","descr":{"en":"Powers of numbers","nl":"Machtsverheffen met getallen"},"tags":[{"id":"NumberArithmeticPower","descr":{"en":"Understanding the concept of powers of numbers","nl":"Het concept machtsverheffen begrijpen"},"stepType":"CONCEPT","errors":[{"id":"MultiplyVsPower","type":["MISCONCEPTION"],"descr":{"en":"Multiplying the base by the power instead of raising to the power.","nl":"Het grondtal en de exponent vermenigvuldigen in plaats van machtsverheffen."}},{"id":"AddVsPower","type":["MISCONCEPTION"],"descr":{"en":"Adding the base by the power instead of raising to the power.","nl":"Het grondtal en de exponent optellen in plaats van machtsverheffen."}},{"id":"BaseVsPower","type":["MISCONCEPTION"],"descr":{"en":"Confusing base and power.","nl":"De betekenis van het grondtal en de exponent verwisselen."}},{"id":"SignError","type":["MISCONCEPTION"],"descr":{"en":"Making a sign error when negating the base of a power function.","nl":"Een tekenfout maken bij het omdraaien van het teken van de basis van een machtsfunctie."}}]},{"id":"NumberArithmeticPowerSquare","descr":{"en":"Understanding the concept of squares","nl":"Het concept kwadraten begrijpen"},"stepType":"CONCEPT","errors":[{"id":"Parity","type":["MISCONCEPTION"],"descr":{"en":"Thinking all square numbers are even or all square numbers are odd.","nl":"Denken dat alle kwadraten even of alle kwadraten oneven zijn."}},{"id":"SquareVsCube","type":["MISCONCEPTION"],"descr":{"en":"Confusing squaring and cubing.","nl":"Kwadrateren verwarren met derde macht."}},{"id":"SignError","type":["MISCONCEPTION"],"descr":{"en":"Not realising that a square number is nonnegative.","nl":"Niet beseffen dat een kwadraat niet negatief kan zijn."}}]}],"collections":[]},{"id":"NumberValue","descr":{"en":"Value of decimal numbers","nl":"De waarde van decimale getallen"},"tags":[{"id":"NumberValueConcept","descr":{"en":"Understanding number values","nl":"Getalgroottes begrijpen"},"stepType":"CONCEPT","errors":[{"id":"NumberValueNegativeVsPositive","type":["MISCONCEPTION"],"descr":{"en":"Not knowing negative numbers are less than positive numbers.","nl":"Niet weten dat negatieve getallen kleiner zijn dan positieve getallen."}},{"id":"NumberValueSmallestVsLargest","type":["MISCONCEPTION"],"descr":{"en":"Confusing largest and smallest numbers.","nl":"Grootste en kleinste getallen met elkaar verwarren."}},{"id":"NumberOrderNegative","type":["MISCONCEPTION"],"descr":{"en":"Thinking that $-a > -b$, because $a > $. ","nl":"Denken dat $-a > -b$, omdat $a > b$."}},{"id":"PlaceValue","type":["MISCONCEPTION"],"descr":{"en":"Comparing the digits in decimals without considering their place value.","nl":"De decimalen in een decimaal getal vergelijken, zonder rekening te houden met hun plaatswaarde."}},{"id":"DecimalPlaceValue","type":["MISCONCEPTION"],"descr":{"en":"Not understanding place value to the right of the decimal point. Not understanding that 0.1 = 1/10 and 0.01 = 1/100.","nl":"De plaatswaarde rechts van de decimale punt niet begrijpen. Niet begrijpen dat 0,1 = 1/10 en 0,01 = 1/100."}},{"id":"DecimalPlaceValueAsFraction","type":["MISCONCEPTION"],"descr":{"en":"Thinking that the digits after the decimal point become the denominator of the equivalent fraction (for example thinking 0.2 = 1/2  or 0.02 = 1/20).","nl":"Denken dat de decimalen na de decimale punt de noemer van de equivalentie breuk worden (bijvoorbeeld denken dat 0,2 = 1/2 of 0,02 = 1/20)."}},{"id":"DigitsOnly","type":["MISCONCEPTION"],"descr":{"en":"Thinking that the number with the smallest digit in any decimal place is the lowest value number.","nl":"Denken dat het getal met de kleinste decimaal in een willekeurige decimaalplaats het kleinste getal is."}},{"id":"CountingDigits","type":["MISCONCEPTION"],"descr":{"en":"Thinking that a number with a smaller number of decimal places is a lower value number.","nl":"Denken dat een getal met minder decimalen een kleiner getal is."}},{"id":"AssumingDecimalPlaces","type":["MISCONCEPTION"],"descr":{"en":"Thinking that because there are n decimal places in the question there must be n decimal places in the answer.","nl":"Denken dat omdat er n decimalen in de vraag staan, er ook n decimalen in het antwoord moeten staan."}},{"id":"NumberOfPlaceValues","type":["MISCONCEPTION"],"descr":{"en":"Thinking that because there are n decimal places in the question there must be n decimal places in the answer.","nl":"Denken dat omdat er n decimalen in de vraag staan, er ook n decimalen in het antwoord moeten staan."}},{"id":"IgnoringDecimalPoint","type":["MISCONCEPTION"],"descr":{"en":"Ignoring the decimal point when working out the calculation and not inserting the decimal point in the answer.","nl":"De decimale komma negeren bij het berekenen en de decimale komma niet in het antwoord invoegen."}}]},{"id":"RoundingDecimals","descr":{"en":"Rounding to some number of decimals","nl":"Afronden op een aantal decimalen"},"stepType":"ROUND","errors":[{"id":"RoundErrorUpDown","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Set the last digit incorrectly when rounding.","nl":"De laatste decimaal verkeerd afronden."}}]}],"collections":[]}]},{"id":"ArithmeticOrder","descr":{"en":"Order of operations","nl":"Volgorde van bewerkingen"},"tags":[{"id":"ArithmeticOrderDivision","descr":{"en":"Order of operations with division","nl":"Volgorde van operaties met deling"},"stepType":"CALCULATE","errors":[{"id":"DivisionMultiplication","type":["MISCONCEPTION"],"descr":{"en":"Multiplying while division takes precedence.","nl":"Vermenigvuldigen terwijl deling voorrang heeft."}},{"id":"DivisionAddition","type":["MISCONCEPTION"],"descr":{"en":"Adding while division takes precedence.","nl":"Optellen terwijl deling voorrang heeft."}}]},{"id":"ArithmeticOrderMultiplication","descr":{"en":"Order of operations with multiplication","nl":"Volgorde van operaties met vermenigvuldiging"},"stepType":"CALCULATE","errors":[{"id":"MultiplicationAddition","type":["MISCONCEPTION"],"descr":{"en":"Adding while multiplication takes precedence.","nl":"Optellen terwijl vermenigvuldiging voorrang heeft."}}]}],"collections":[]},{"id":"Percentages","descr":{"en":"Percentages","nl":"Procenten"},"tags":[{"id":"PercentageAddition","descr":{"en":"Adding or subtracting with percentages","nl":"Met procenten optellen of aftrekken"},"stepType":"CALCULATE","errors":[{"id":"SubtractFromHundredPercent","type":["MISCONCEPTION"],"descr":{"en":"Not knowing how to subtract a percentage from 100%.","nl":"Niet weten hoe je een percentage van 100% aftrekt."}}]},{"id":"PercentageApplication","descr":{"en":"Using percentages in real-life contexts","nl":"Het gebruiken van procenten in reële contexten"},"stepType":"CONCEPT","errors":[{"id":"Not100Percent","type":["MISCONCEPTION"],"descr":{"en":"Incorrectly assuming the given value represents 100% in a real-life context.","nl":"Ten onrechte aannemen dat de gegeven waarde 100% vertegenwoordigt in een reële context."}},{"id":"Wrong100Percent","type":["MISCONCEPTION"],"descr":{"en":"Not identifying the right value with 100% in a real-life context.","nl":"Niet het juiste getal herkennen als 100% in een reële context."}}]},{"id":"PercentageCalculate","descr":{"en":"Calculating a percentage given a total and a part.","nl":"Een percentage berekenen gegeven een totaal en een deel."},"stepType":"CALCULATE","errors":[{"id":"MixingUpTotalAndPart","type":["MISCONCEPTION"],"descr":{"en":"Mixing up the total and the part when calculating the percentage.","nl":"Het verwarren van het totaal en het deel bij het berekenen van het percentage."}},{"id":"IncorrectRuleOfThree","type":["MISCONCEPTION"],"descr":{"en":"Applying the rule of three incorrectly when calculating the percentage.","nl":"Kruislings vermenigvuldigen verkeerd toepassen bij het berekenen van het percentage."}}]},{"id":"PercentageConcept","descr":{"en":"Understanding percentages","nl":"Het begrijpen van procenten"},"stepType":"CONCEPT","errors":[{"id":"EquivalenceFraction","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that a percentage is a fraction with denominator 100.","nl":"Niet begrijpen dat een percentage een breuk is met noemer 100."}},{"id":"EquivalenceWholeNumber","type":["MISCONCEPTION"],"descr":{"en":"Not knowing that a whole is 100%.","nl":"Niet weten dat een geheel 100% is."}}]},{"id":"PercentageMultiply","descr":{"en":"Multiplying by a percentage","nl":"Vermenigvuldigen met een percentage"},"stepType":"CONCEPT","errors":[{"id":"MissingPercentageSign","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Multiplying the two numbers but ignores the percentage sign.","nl":"De twee getallen vermenigvuldigen, maar het percentage teken negeren."}},{"id":"IncorrectMagnitude","type":["MISCONCEPTION"],"descr":{"en":"Multiplying the two numbers and then dividing by 10 or 1000 instead of by 100.","nl":"De twee getallen vermenigvuldigen en vervolgens delen door 10 of 1000 in plaats van door 100."}},{"id":"AssumewholeNumber","type":["MISCONCEPTION"],"descr":{"en":"Thinking a whole number multiplied by a percentage must give a whole number answer.","nl":"Denken dat een heel getal vermenigvuldigd met een percentage een heel getal als antwoord moet geven."}}]}],"collections":[]}]},{"id":"Calculus","descr":{"en":"Calculus","nl":"Calculus (Analyse)"},"tags":[],"collections":[{"id":"Limits","descr":{"en":"Limits","nl":"Limieten"},"tags":[],"collections":[{"id":"LimitsMethods","descr":{"en":"Methods to rewrite and compute limits","nl":"Methoden om limieten te herschrijven en berekenen"},"tags":[{"id":"LimitsMethodsCommonFactor","descr":{"en":"Compute the limit of a division by cancelling common factors from numerator and denominator","nl":"De limiet van een deling bepalen door gemeenschappelijke factoren weg te delen"},"stepType":"STRATEGY"},{"id":"LimitsMethodsConjugate","descr":{"en":"Use the conjugate method to evaluate the limit of a division","nl":"De limiet van een deling bepalen door vermenigvuldigen met de geconjungeerde"},"stepType":"STRATEGY"}],"collections":[]},{"id":"LimitsProperties","descr":{"en":"General properties of limits","nl":"Algemene eigenschappen van limieten"},"tags":[{"id":"LimitsPropertiesDivision","descr":{"en":"Compute the limit of a division by evaluating the limit of the numerator and denominator","nl":"De limiet van een deling bepalen door de limiet van teller en noemer te bepalen"},"stepType":"STRATEGY"},{"id":"LimitsPropertiesPlus","descr":{"en":"Compute the limit of an addition by evaluating the limit of the terms","nl":"De limiet van een optelling bepalen door de limiet van de termen te bepalen"},"stepType":"STRATEGY"},{"id":"LimitsPropertiesTimes","descr":{"en":"Compute the limit of a multiplication by evaluating the limit of the factors","nl":"De limiet van een vermenigvuldiging bepalen door de limiet van de factoren te bepalen"},"stepType":"STRATEGY"}],"collections":[]}]}]},{"id":"Equations","descr":{"en":"Equations and inequalities","nl":"Gelijkheden en ongelijkheden"},"tags":[{"id":"EquationsConcept","descr":{"en":"Understanding equations and their solutions","nl":"Vergelijkingen en oplossingen begrijpen"},"stepType":"STRATEGY","errors":[{"id":"IntegerSolution","type":["MISCONCEPTION"],"descr":{"en":"Thinking that the solution to an equation must be an integer.","nl":"Denken dat de oplossing van een vergelijking een geheel getal moet zijn."}}]}],"collections":[{"id":"EquationsBalanceMethod","descr":{"en":"Solving linear equations using the balance method","nl":"Lineaire vergelijkingen oplossen met de balansmethode"},"tags":[{"id":"EquationsBalanceMethodArrangeTerms","descr":{"en":"Arrange terms with variable to the left and other terms to the right.","nl":"Termen met de variabele naar links en andere termen naar rechts halen."},"stepType":"STRATEGY","errors":[{"id":"ArrangeToZero","type":["MISCONCEPTION"],"descr":{"en":"Arranging all terms to one side.","nl":"Alle termen zijn naar dezelfde kant gebracht."}}]},{"id":"EquationsBalanceMethodDivideCoefficient","descr":{"en":"Divide by the coefficient of the variable to get the solution.","nl":"Delen door de coëfficiënt voor de variabele om de oplossing te krijgen."},"stepType":"STRATEGY"},{"id":"EquationsBalanceMethodRemoveFractions","descr":{"en":"Multiply an equation to remove the fractions.","nl":"Een vergelijking vermenigvuldigen om breuken weg te werken."},"stepType":"STRATEGY"}],"collections":[]},{"id":"EquationsFactoring","descr":{"en":"Solving equations by factoring","nl":"Vergelijkingen oplossen door ontbinden"},"tags":[{"id":"EquationsSplitFactors","descr":{"en":"Equating each factor to zero","nl":"Elke factor gelijkstellen aan nul"},"stepType":"STRATEGY","errors":[{"id":"SplitFactorOnNonzeroRHS","type":["MISCONCEPTION"],"descr":{"en":"Equating factors to a non-zero right hand side.","nl":"Factoren gelijkstellen aan de rechterzijde van de vergelijking die niet gelijk is aan nul."}}]},{"id":"EquationsFactorLHS","descr":{"en":"Factor the expression","nl":"Een vergelijking ontbinden"},"stepType":"STRATEGY","errors":[{"id":"FactorDivide","type":["MISCONCEPTION"],"descr":{"en":"Dividing an equation instead of factoring.","nl":"Een factor wegdelen in plaats van ontbinden in factoren."}}]},{"id":"EquationsWriteToZero","descr":{"en":"Write one side of an equation to zero","nl":"Een vergelijking op nul herleiden"},"stepType":"STRATEGY"}],"collections":[]},{"id":"EquationsInverting","descr":{"en":"Solving an equation by inverting operations","nl":"Een vergelijking oplossen door operaties te inverteren"},"tags":[{"id":"EquationsInvertingConcept","descr":{"en":"Understanding how to use operation inverses to solve equations","nl":"Begrijpen hoe inverse operaties gebruikt worden om vergelijkingen op te lossen"},"stepType":"STRATEGY","errors":[{"id":"InvalidInverseOperation","type":["MISCONCEPTION"],"descr":{"en":"Not using the correct inverse operation to calculate an unknown number in an expression.","nl":"Niet de juiste inverse operatie gebruiken om een onbekend getal in een uitdrukking te berekenen."}},{"id":"CompensateChange","type":["MISCONCEPTION"],"descr":{"en":"Not knowing how to solve one-step equations using inverse operations.","nl":"Niet weten hoe je vergelijkingen met één stap kunt oplossen met inverse operaties."}},{"id":"CompensateTwoStepEquations","type":["MISCONCEPTION"],"descr":{"en":"Not knowing how to apply inverse operations in the correct order to solve two-step equations.","nl":"Niet weten hoe je inverse operaties in de juiste volgorde kunt toepassen om tweestapsvergelijkingen op te lossen."}},{"id":"FunctionMachines","type":["MISCONCEPTION"],"descr":{"en":"Not knowing how to draw function machines and inverses.","nl":"Niet weten hoe je functiemachines en inverse functies kunt tekenen."}}]},{"id":"EquationsInvertingPower","descr":{"en":"Inverting power functions with integer exponents","nl":"Een machtsfunctie met geheeltallige exponent inverteren"},"stepType":"STRATEGY","errors":[{"id":"IncorrectOrder","type":["MISCONCEPTION"],"descr":{"en":"Inverting a power function while another operation should be inverted first.","nl":"Een machtsfunctie inverteren terwijl een andere operatie eerst geïnverteerd moet worden."}},{"id":"MissingSecondSolution","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Leaving out the second solution when inverting a power with even exponent.","nl":"De tweede oplossing weglaten bij inverteren van een machtsfuntie met een even exponent."}},{"id":"ExtraSecondSolution","type":["MISCONCEPTION"],"descr":{"en":"Adding an incorrect second solution when inverting power functions with uneven exponent.","nl":"Ten onrechte twee oplossingen geven bij het inverteren van een machtsfunctie met oneven macht."}},{"id":"InvalidSecondSolution","type":["MISCONCEPTION"],"descr":{"en":"Writing the second solution incorrectly when inverting power functions with even exponent.","nl":"De tweede oplossing verkeerd genoteerd bij het inverteren van een machtsfunctie met even macht."}}]},{"id":"EquationsInvertingProduct","descr":{"en":"Inverting multiplication","nl":"Vermenigvuldiging inverteren"},"stepType":"STRATEGY","errors":[{"id":"MultiplyInsteadOfDivide","type":["MISCONCEPTION"],"descr":{"en":"Thinking that $ax = b$ is solved by multiplying by $a$ instead of dividing by $a$.","nl":"Denken dat $ax = b$ wordt opgelost door te vermenigvuldigen met $a$ in plaats van te delen door $a$."}},{"id":"SubtractInsteadOfDivide","type":["MISCONCEPTION"],"descr":{"en":"Thinking that $ax = b$ is solved by subtracting by $a$ instead of dividing by $a$.","nl":"Denken dat $ax = b$ wordt opgelost door $a$ af te trekken in plaats van te delen door $a$."}},{"id":"AddInsteadOfDivide","type":["MISCONCEPTION"],"descr":{"en":"Thinking that $ax = b$ is solved by adding by $a$ instead of dividing by $a$.","nl":"Denken dat $ax = b$ wordt opgelost door $a$ op te tellen in plaats van te delen door $a$."}}]},{"id":"EquationsInvertingSum","descr":{"en":"Inverting summation","nl":"Optelling inverteren"},"stepType":"STRATEGY","errors":[{"id":"AddInsteadOfSubtract","type":["MISCONCEPTION"],"descr":{"en":"Thinking that the first step to solve e.g. $ax + c = b$ is to add $c$.","nl":"Denken dat de eerste stap om bijvoorbeeld $ax + c = b$ op te lossen is om $c$ op te tellen."}},{"id":"SubtractInsteadOfAdd","type":["MISCONCEPTION"],"descr":{"en":"Thinking that the first step to solve e.g. $ax - c = b$ is to subtract $c$.","nl":"Denken dat de eerste stap om bijvoorbeeld $ax - c = b$ op te lossen is om $c$ af te trekken."}},{"id":"PlusMinus","type":["MISCONCEPTION"],"descr":{"en":"Carrying out only the additive step when attempting to solve $ax \\pm c = b$.","nl":"Alleen de optelling uitvoeren bij het proberen op te lossen van $ax \\pm c = b$."}}]}],"collections":[]},{"id":"EquationsOperations","descr":{"en":"Operations on equations and inequalities","nl":"Bewerkingen uitvoeren op gelijkheden en ongelijkheden"},"tags":[{"id":"EquationsOperationsAdd","descr":{"en":"Add or subtract terms using the balance method","nl":"Termen optellen of aftrekken via de balansmethode"},"stepType":"STRATEGY","errors":[{"id":"AddSubtract","type":["MISCONCEPTION"],"descr":{"en":"Adding on one side and subtracting on the other side of the equation.","nl":"Optellen aan één kant en aftrekken aan de andere kant van de vergelijking."}}]},{"id":"EquationsOperationsMultiply","descr":{"en":"Multiply or divide an equation using the balance method","nl":"Vermenigvuldigen of delen van een vergelijking via de balansmethode"},"stepType":"STRATEGY","errors":[{"id":"MultiplyDivide","type":["MISCONCEPTION"],"descr":{"en":"Multiplying on one side and dividing on the other side of the equation.","nl":"Vermenigvuldigen aan één kant en delen aan de andere kant van de vergelijking."}},{"id":"MultiplyOneSide","type":["MISCONCEPTION"],"descr":{"en":"Multiplying or dividing one side, but not the other side of an equation.","nl":"Vermenigvuldigen of delen aan één kant van een vergelijking, maar niet de andere kant."}},{"id":"MultiplyAllTerms","type":["MISCONCEPTION"],"descr":{"en":"Not multiplying or dividing all terms of the equation.","nl":"Niet alle termen van de vergelijking vermenigvuldigen of delen."}},{"id":"SignError","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Making a sign error.","nl":"Een tekenfout maken."}},{"id":"FlipSign","type":["MISCONCEPTION","MISTAKE"],"descr":{"en":"Not flipping the sign of the inequality when multiplying or dividing by a negative factor.","nl":"De richting van de ongelijkheid niet omklappen bij vermenigvuldigen met of delen door een negatieve factor."}},{"id":"MissingBrackets","type":["MISCONCEPTION"],"descr":{"en":"Not writing parentheses when multiplying a sum of terms.","nl":"Geen haakjes schrijven wanneer een som van termen wordt vermenigvuldigd."}}]},{"id":"EquationsOperationsPower","descr":{"en":"Applying a power to both sides of an equation","nl":"Een macht toepassen op een vergelijking"},"stepType":"STRATEGY","errors":[{"id":"PowerDivide","type":["MISCONCEPTION"],"descr":{"en":"Applying multiplication or division instead of a power.","nl":"Vermenigvuldigen of delen in plaats van een macht toepassen."}},{"id":"MissingSolutions","type":["MISCONCEPTION"],"descr":{"en":"Not realising that there are multiple solutions to the power equation.","nl":"Zich niet realiseren dat er meerdere oplossingen zijn van de machtsvergelijking."}}]}],"collections":[]},{"id":"QuadraticEquations","descr":{"en":"Quadratic Equations and Inequalities","nl":"Kwadratische gelijkheden en ongelijkheden"},"tags":[{"id":"EquationsQuadraticCompleteSquare","descr":{"en":"Completing the Square for Quadratic Expressions","nl":"Een kwadraat afsplitsen van een kwadratische expressie"},"stepType":"STRATEGY"}],"collections":[{"id":"EquationsQuadraticFormula","descr":{"en":"Solving Quadratic Equations using the Quadratic Formula","nl":"Kwadratische vergelijkingen oplossen met de abc-formule"},"tags":[{"id":"EquationsQuadraticFormulaDiscriminant","descr":{"en":"Calculating the discriminant of a quadratic equation","nl":"De discriminant berekenen van een tweedegraads vergelijking"},"stepType":"STRATEGY","errors":[{"id":"MixedCoefficients","type":["MISCONCEPTION"],"descr":{"en":"Mixing-up the values for a, b and c.","nl":"De waarden van a, b en c verwisselen."}}]},{"id":"EquationsQuadraticFormulaEvaluate","descr":{"en":"Write and evaluate the Quadratic Formula","nl":"De abc-formule opschrijven en evalueren"},"stepType":"STRATEGY"},{"id":"EquationsQuadraticFormulaNumberSolutions","descr":{"en":"Identify the number of solutions from the sign of the discriminant","nl":"Het aantal oplossingen bepalen aan de hand van het teken van de discriminant"},"stepType":"STRATEGY"}],"collections":[]}]}]},{"id":"Functions","descr":{"en":"Functions","nl":"Functies"},"tags":[{"id":"FunctionRules","descr":{"en":"Finding Rules for Relations","nl":"Rekenregels voor verbanden vinden"},"stepType":"CONCEPT","errors":[{"id":"FirstCoordinatePairOnly","type":["MISCONCEPTION"],"descr":{"en":"Giving a rule that works for the first coordinate pair only.","nl":"Een regel geven die alleen voor het eerste coördinatenpaar werkt."}},{"id":"SingleCoordinatePairOnly","type":["MISCONCEPTION"],"descr":{"en":"Giving a rule that works for a single coordinate pair only.","nl":"Een regel geven die alleen voor een enkel coördinatenpaar werkt."}},{"id":"InverseXY","type":["MISCONCEPTION"],"descr":{"en":"Giving a rule to get from y-coordinate to x-coordinate (inverse of rule required).","nl":"Een regel geven om van de y-coördinaat naar de x-coördinaat te gaan (inverse van de gevraagde regel)."}},{"id":"OnlyY","type":["MISCONCEPTION"],"descr":{"en":"Giving a rule that connects the y-coordinates.","nl":"Een regel geven die de y-coördinaten verbindt."}},{"id":"OnlyX","type":["MISCONCEPTION"],"descr":{"en":"Giving a rule that connects the x-coordinates.","nl":"Een regel geven die de x-coördinaten verbindt."}},{"id":"AdditiveAndMultiplicative","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that two numbers can be connected by both an additive and a multiplicative rule.","nl":"Niet begrijpen dat twee getallen met zowel een optellings- als een vermenigvuldigingsregel kunnen worden verbonden."}},{"id":"ReversedOrder","type":["MISCONCEPTION"],"descr":{"en":"Finding the rule that connects numbers in reverse order.","nl":"De regel geven die getallen in omgekeerde volgorde verbindt."}}]}],"collections":[{"id":"FunctionGraphs","descr":{"en":"Function Graphs","nl":"Grafieken"},"tags":[{"id":"ReadingGraphs","descr":{"en":"Reading and Interpreting Graphs","nl":"Grafieken lezen en interpreteren"},"stepType":"CONCEPT","errors":[{"id":"ErrorConcept","type":["MISCONCEPTION"],"descr":{"en":"Not understanding how to read values from a graph.","nl":"Niet begrijpen hoe waarden van een grafiek af te lezen."}},{"id":"HorizontalInsteadOfVerticalAxisIntersection","type":["MISCONCEPTION"],"descr":{"en":"Giving value of $x$ when $y = 0$ instead of the value of $y$ when $x= 0$.","nl":"De waarde van $x$ geven wanneer $y = 0$ in plaats van de waarde van $y$ wanneer $x = 0$."}},{"id":"VerticalInsteadOfHorizontalAxisIntersection","type":["MISCONCEPTION"],"descr":{"en":"Giving value of $y$ when $x = 0$ instead of the value of $x$ when $y = 0$.","nl":"De waarde van $y$ geven wanneer $x = 0$ in plaats van de waarde van $x$ wanneer $y = 0$."}},{"id":"HorizontalInteractionSign","type":["MISCONCEPTION"],"descr":{"en":"Giving value of $x$ when $y = 0$ but ignoring the negative sign.","nl":"De waarde van $x$ geven wanneer $y = 0$ maar het minteken negeren."}},{"id":"VerticalAxisFormula","type":["MISCONCEPTION"],"descr":{"en":"Not realising that $x = 0$ is the y-axis. ","nl":"Niet beseffen dat $x = 0$ de y-as is."}},{"id":"HorizontalAxisFormula","type":["MISCONCEPTION"],"descr":{"en":"Not realising that $y = 0$ is the x-axis.","nl":"Niet beseffen dat $y = 0$ de x-as is."}},{"id":"EqualXY","type":["MISCONCEPTION"],"descr":{"en":"Thinking $x$ and $y$ must have the same value.","nl":"Denken dat $x$ en $y$ dezelfde waarde moeten hebben."}},{"id":"MaxAxisCoordinate","type":["MISCONCEPTION"],"descr":{"en":"Giving the largest value marked on an axis.","nl":"De grootste waarde geven die op een as is aangegeven."}},{"id":"FractionValues","type":["MISCONCEPTION"],"descr":{"en":"Not being able to read fractional values from graphs.","nl":"Niet in staat zijn om breukwaarden van grafieken af te lezen."}}]}],"collections":[]},{"id":"LinearFunctions","descr":{"en":"Linear and Proportional Functions","nl":"Lineaire en evenredige Functies"},"tags":[{"id":"LinearFunctionRules","descr":{"en":"Finding Rules for Linear Relations","nl":"Rekenregels voor lineaire verbanden vinden"},"stepType":"CONCEPT","errors":[{"id":"FindMultiplicativeConstant","type":["MISCONCEPTION"],"descr":{"en":"Not recognising which number to multiply/divide the first number by to give the second.","nl":"Niet herkennen welk getal bij het eerste getal moet worden vermenigvuldigd/gedeeld om het tweede getal te geven."}},{"id":"FindAdditiveConstant","type":["MISCONCEPTION"],"descr":{"en":"Not recognising which number to add to / subtract from the first number to give the second.","nl":"Niet herkennen welk getal bij het eerste getal moet worden opgeteld / afgetrokken om het tweede getal te geven."}},{"id":"AdditiveInsteadOfMultiplicative","type":["MISCONCEPTION"],"descr":{"en":"Using an additive rule when a multiplicative rule is asked for.","nl":"Een optellingsregel gebruiken wanneer om een vermenigvuldigingsregel wordt gevraagd."}},{"id":"MultiplicativeInsteadOfAdditive","type":["MISCONCEPTION"],"descr":{"en":"Using a multiplicative rule when an additive rule is asked for.","nl":"Een vermenigvuldigingsregel gebruiken wanneer om een optellingsregel wordt gevraagd."}}]},{"id":"LinearFunctionSubstitution","descr":{"en":"Substituting values in linear formules","nl":"Waarden substitueren in lineaire formules"},"stepType":"CONCEPT","errors":[{"id":"MissingConstant","type":["MISCONCEPTION"],"descr":{"en":"Correctly substituting for $x$, but not adding/subtracting the constant.","nl":"Correct substitueren voor $x$, maar de constante niet optellen/aftrekken."}},{"id":"ShiftMinusSign","type":["MISCONCEPTION"],"descr":{"en":"Correctly substituting for $x$, but moving the negative sign to make the calculation 'larger number - smaller number' (to give a positive answer).","nl":"Correct substitueren voor $x$, maar het minteken verplaatsen om de berekening 'groter getal - kleiner getal' te maken (om een positief antwoord te geven)."}},{"id":"VariableX","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that $kx$ has different values, depending on the value of $x$.","nl":"Niet begrijpen dat $kx$ verschillende waarden heeft, afhankelijk van de waarde van $x$."}}]}],"collections":[]}]},{"id":"General","descr":{"en":"Non-mathematical skills","nl":"niet-wiskundige vaardigheden"},"tags":[],"collections":[{"id":"GeneralReading","descr":{"en":"Skills related to reading","nl":"Leesvaardigheden"},"tags":[{"id":"GeneralReadingIdentifyMath","descr":{"en":"Identifying math concepts or properties in a text.","nl":"Wiskundige concepten of eigenschappen herkennen in een tekst."},"stepType":"CONCEPT","errors":[{"id":"IncorrectRelation","type":["MISCONCEPTION"],"descr":{"en":"Incorrectly identifying the relationship between math concepts from the text.","nl":"Niet de juiste relatie tussen wiskundige concepten uit de tekst halen."}},{"id":"TranslateToAlgebra","type":["MISCONCEPTION"],"descr":{"en":"Incorrectly translating written statements into algebra. ","nl":"Geschreven uitspraken onjuist vertalen naar algebra."}}]},{"id":"GeneralReadingComprehension","descr":{"en":"Reading comprehension skills","nl":"Algemene leesvaardigheid"},"stepType":"ALGEBRA"}],"collections":[]},{"id":"SelfRegulation","descr":{"en":"Skills related to self-regulation","nl":"Vaardigheden gerelateerd aan zelfregulatie"},"tags":[{"id":"SelfRegulationEvaluation","descr":{"en":"Evaluating the solution","nl":"Het evalueren van de oplossing"},"stepType":"CONCEPT","errors":[{"id":"NoInterpretation","type":["MISCONCEPTION"],"descr":{"en":"Not interpreting whether the solution makes sense in the given context.","nl":"Niet interpreteren of de oplossing logisch is in de gegeven context."}},{"id":"ConfirmResponse","type":["MISCONCEPTION"],"descr":{"en":"Not checking if the answer addresses the question asked.","nl":"Niet controleren of het antwoord de gestelde vraag beantwoordt."}}]},{"id":"SelfRegulationMonitoring","descr":{"en":"Monitoring the problem-solving process","nl":"Het monitoren van het probleemoplossingsproces"},"stepType":"CONCEPT","errors":[{"id":"NoErrorDetection","type":["MISCONCEPTION"],"descr":{"en":"Not realizing that an error was made during the problem-solving process.","nl":"Niet beseffen dat er een fout is gemaakt tijdens het probleemoplossingsproces."}},{"id":"IgnoringFeedback","type":["MISCONCEPTION"],"descr":{"en":"Ignoring feedback or hints that indicate a mistake was made.","nl":"Feedback of hints negeren die aangeven dat er een fout is gemaakt."}}]},{"id":"SelfRegulationPlanning","descr":{"en":"Orienting and planning the solving of a problem","nl":"Orienteren op en plannen van het oplossen van een probleem"},"stepType":"CONCEPT","errors":[{"id":"ProblemUnderstanding","type":["MISCONCEPTION"],"descr":{"en":"Not understanding what the problem is asking before starting to solve it.","nl":"Niet begrijpen wat het probleem vraagt voordat je begint met oplossen."}},{"id":"GettingStarted","type":["MISCONCEPTION"],"descr":{"en":"Not knowing how to get started with solving the problem.","nl":"Niet weten hoe te beginnen met het oplossen van het probleem."}},{"id":"Rushing","type":["MISCONCEPTION"],"descr":{"en":"Rushing into answering or guessing without taking intermediate steps.","nl":"Overhaast antwoorden of gokken zonder tussenstappen te maken."}}]}],"collections":[]}]},{"id":"Geometry","descr":{"en":"Geometry","nl":"Meetkunde"},"tags":[],"collections":[{"id":"Angles","descr":{"en":"Angles","nl":"Hoeken"},"tags":[{"id":"AnglesConcept","descr":{"en":"Understanding the concept of angles","nl":"Het concept van hoeken begrijpen"},"stepType":"CONCEPT","errors":[{"id":"ErrorAnglesConceptTurn","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that angle describes a turn, and that the sizes of these turns can be compared.","nl":"Niet weten dat een hoek een draai beschrijft en dat de groottes van draaiingen kunnen worden vergeleken."}},{"id":"ErrorAnglesConceptSizeShort","type":["MISCONCEPTION"],"descr":{"en":"Thinking that shorter ‘arms’ on an angle mean the angle is smaller.","nl":"Denken dat als de benen van een hoek korter zijn, de hoek kleiner is."}},{"id":"ErrorAnglesConceptSizeLong","type":["MISCONCEPTION"],"descr":{"en":"Thinking that longer ‘arms’ on an angle mean the angle is larger.","nl":"Denken dat als de benen van een hoek langer zijn, de hoek groter is."}},{"id":"ErrorAnglesConceptArms","type":["MISCONCEPTION"],"descr":{"en":"Thinking that ‘measuring an angle’ means measuring the arms of the angle.","nl":"Denken dat het meten van een hoek betekent dat de lengte van de benen moet worden gemeten."}},{"id":"ErrorAnglesConceptDegrees","type":["MISCONCEPTION"],"descr":{"en":"Not knowing that angles are measured in degrees.","nl":"Niet weten dat een hoek wordt uitgedrukt in graden."}},{"id":"ErrorAnglesDegree","type":["MISCONCEPTION"],"descr":{"en":"Not having an understanding of the size of a degree.","nl":"Niet weten wat de grootte is van één graad."}}]}],"collections":[{"id":"AnglesArithmetic","descr":{"en":"Calculating with Angles","nl":"Rekenen met hoeken"},"tags":[{"id":"AnglesArithmeticPeriodic","descr":{"en":"Rewriting and angle to the first period","nl":"Herschrijven van een hoek naar de eerste periode"},"stepType":"CALCULATE"}],"collections":[]},{"id":"AnglesClassifying","descr":{"en":"Classifying angles","nl":"Hoeken herkennen"},"tags":[{"id":"ClassifyingAcuteAngles","descr":{"en":"Recognising acute angles","nl":"Scherpe hoeken herkennen"},"stepType":"CONCEPT","errors":[{"id":"ErrorAcuteAngleSize","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that an acute angle is less than 90°.","nl":"Niet weten dat een scherpe hoek kleiner is dan 90°."}}]},{"id":"ClassifyingFullAngles","descr":{"en":"Recognising full angles","nl":"Volledige hoeken herkennen"},"stepType":"CONCEPT","errors":[{"id":"ErrorFullAngleSize","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that a full angle measures 360°.","nl":"Niet weten dat een volledige hoek gelijk is aan 360°."}}]},{"id":"ClassifyingAngles","descr":{"en":"Classifying angles","nl":"Soorten hoeken herkennen"},"stepType":"CONCEPT","errors":[{"id":"ErrorClassifyingAngles","type":["MISCONCEPTION"],"descr":{"en":"Not recognising the different types of angles.","nl":"De verschillende soorten hoeken niet herkennen."}}]},{"id":"ClassifyingObtuseAngles","descr":{"en":"Recognising obtuse angles","nl":"Stompe hoeken herkennen"},"stepType":"CONCEPT","errors":[{"id":"ErrorObtuseAngleSize","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that an obtuse angle measures between 90° and 180°.","nl":"Niet weten dat een stompe hoek tussen 90° en 180° is."}}]},{"id":"ClassifyingReflexAngles","descr":{"en":"Recognising reflex angles","nl":"Reflexhoeken herkennen"},"stepType":"CONCEPT","errors":[{"id":"ErrorObtuseAngleSize","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that a reflex angle measures between 180° and 360°.","nl":"Niet weten dat een reflexhoek tussen 180° en 360° is."}}]},{"id":"ClassifyingRightAngles","descr":{"en":"Recognising right angles","nl":"Rechte hoeken herkennen"},"stepType":"CONCEPT","errors":[{"id":"ErrorRightAngle","type":["MISCONCEPTION"],"descr":{"en":"Not recognising a right angle.","nl":"Een rechte hoek niet herkennen."}},{"id":"ErrorRotatedRightAngle","type":["MISCONCEPTION"],"descr":{"en":"Not recognising a right angle in an unfamiliar orientation.","nl":"Een rechte hoek in een onverwachte oriëntatie niet herkennen."}},{"id":"ErrorRightAngleVerticalLine","type":["MISCONCEPTION"],"descr":{"en":"Thinking that one line of a right angle must be vertical.","nl":"Denken dat één van de benen van een rechte hoek verticaal moet zijn."}},{"id":"ErrorRightAngleHorizontalLine","type":["MISCONCEPTION"],"descr":{"en":"Thinking that one line of a right angle must be horizontal.","nl":"Denken dat één van de benen van een rechte hoek horizontaal moet zijn."}},{"id":"ErrorRightAngleIntersect","type":["MISCONCEPTION"],"descr":{"en":"Thinking that all intersecting lines meet at right angles.","nl":"Denken dat de hoek tussen twee snijdende lijnen altijd recht is."}},{"id":"ErrorRightAngleSize","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that a right angle measures 90°.","nl":"Niet weten dat een rechte hoek gelijk is aan 90°."}}]},{"id":"ClassifyingStraightAngles","descr":{"en":"Recognising straight angles","nl":"Gestrekte hoeken herkennen"},"stepType":"CONCEPT","errors":[{"id":"ErrorStraightAngleSize","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that a straight angle measures 180°.","nl":"Niet weten dat een gestrekte hoek gelijk is aan 180°."}}]},{"id":"ClassifyingThreeQuarterAngles","descr":{"en":"Recognising three-quarter angles","nl":"Driekwart-hoeken herkennen"},"stepType":"CONCEPT","errors":[{"id":"ErrorThreeQuarterAngleSize","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that a three-quarter angle measures 270°.","nl":"Niet weten dat een driekwart-hoek gelijk is aan 270°."}}]}],"collections":[]},{"id":"AnglesMeasuring","descr":{"en":"Measuring angles","nl":"Hoeken meten"},"tags":[{"id":"MeasuringAnglesProtractor","descr":{"en":"Measuring angles with a protractor","nl":"Hoeken meten met een kompasroos"},"stepType":"CONCEPT","errors":[{"id":"ErrorProtractorConcept","type":["MISCONCEPTION"],"descr":{"en":"Not recognising a protractor as the tool to measure an angle.","nl":"Niet weten dat een kompasroos gebruikt wordt om hoeken te meten."}},{"id":"ErrorProtractorWrongScale","type":["MISCONCEPTION"],"descr":{"en":"Reading off the wrong scale on a protractor.","nl":"De verkeerde schaal van een kompasroos aflezen."}},{"id":"ErrorProtractorVsSetSquare","type":["MISCONCEPTION"],"descr":{"en":"Confusing a protractor with a set square, used to draw right angles.","nl":"Een kompasroos verwarren met een geodriehoek, bedoeld voor het tekenen van rechte hoeken."}},{"id":"ErrorProtractorVsCompasses","type":["MISCONCEPTION"],"descr":{"en":"Confusing a protractor with a pair of compasses.","nl":"Een kompasroos verwarren met een passer."}}]}],"collections":[]},{"id":"AnglesNotation","descr":{"en":"Angle notation","nl":"Hoeknotatie"},"tags":[{"id":"AnglesNotationsGraphical","descr":{"en":"Graphical notations of angles","nl":"Grafische notaties van hoeken "},"stepType":"CONCEPT","errors":[{"id":"ErrorAngleArc","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that the angle arc shows the angle being considered.","nl":"Niet begrijpen dat de cirkelboog een hoek aangeeft."}}]},{"id":"AnglesNotationsWritten","descr":{"en":"Written notations of angles","nl":"Geschreven notaties van hoeken "},"stepType":"CONCEPT","errors":[{"id":"ErrorAngleNotationThreeLetters","type":["MISCONCEPTION"],"descr":{"en":"Not correctly interpreting 3-letter angle names.","nl":"De drieletterige notatie van hoeken niet juist interpreteren."}},{"id":"ErrorAngleNotationAlphabetical","type":["MISCONCEPTION"],"descr":{"en":"Thinking that the letters in the angle name must be in alphabetical order.","nl":"Denken dat de letters van de hoek in alfabetische volgorde geschreven moeten worden."}},{"id":"ErrorAngleNotationVertexName","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that the single letter name for an angle is the letter at the vertex of the angle.","nl":"Niet weten dat het symbool van een hoek de naam is van het bijbehorende punt."}},{"id":"ErrorAngleNotationAllVertices","type":["MISCONCEPTION"],"descr":{"en":"Thinking that all the letters on the shape should be used in the angle name.","nl":"Denken dat je alle punten van een figuur moet schrijven om een hoek te noteren."}},{"id":"ErrorAngleNotationSame","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that angles identified by the same algebraic letter are equal.","nl":"Niet weten dat hoeken met dezelfde algebraïsche notatie gelijk zijn."}}]}],"collections":[]},{"id":"AnglesReasoning","descr":{"en":"Reasoning with angles","nl":"Redeneren met hoeken"},"tags":[{"id":"AnglesReasoningDiagram","descr":{"en":"Reasoning with angles in a diagram","nl":"Redeneren met hoeken in een figuur"},"stepType":"CONCEPT","errors":[{"id":"ErrorAngleDiagramStraightLines","type":["MISCONCEPTION"],"descr":{"en":"Thinking that as the diagram contains straight lines, the angles must add up to 180°.","nl":"Denken dat omdat een figuur rechte lijnen heeft, de hoeken optellen tot 180°."}},{"id":"ErrorCorrespondingAngles","type":["MISCONCEPTION"],"descr":{"en":"Not recognising corresponding angles in a diagram.","nl":"Overeenkomstige hoeken niet herkennen in een figuur."}}]},{"id":"AnglesReasoningPoint","descr":{"en":"Reasoning with angles at a point or vertex","nl":"Redeneren met hoeken van een punt"},"stepType":"CONCEPT","errors":[{"id":"ErrorAnglePointMissing","type":["MISCONCEPTION"],"descr":{"en":"Not including all the angles in calculations involving 'angles at a point add to 360°'.","nl":"Niet alle deelhoeken meenemen bij het optellen tot een volledige hoek."}},{"id":"ErrorRighAngleMissing","type":["MISCONCEPTION"],"descr":{"en":"Not including right angles in angle calculations because they are not labelled with the value 90°.","nl":"Rechte hoeken niet meenemen in berekeningen omdat deze niet een label van 90° hebben."}},{"id":"ErrorOppositeAngles","type":["MISCONCEPTION"],"descr":{"en":"Not correctly identifying vertically opposite angles.","nl":"Overstaande hoeken niet herkennen."}},{"id":"ErrorAlternatingAngles","type":["MISCONCEPTION"],"descr":{"en":"Not recognising alternate angles.","nl":"Alternerende hoeken niet herkennen."}},{"id":"ErrorAnglePart","type":["MISCONCEPTION"],"descr":{"en":"Identifying the whole angle rather than the size of an individual angle that forms part of a right angle, a straight line, or a complete turn.","nl":"Uitgaan van de hele hoek in plaats van een deelhoek dat."}},{"id":"ErrorAngleHalf","type":["MISCONCEPTION"],"descr":{"en":"Thinking that an angle divided into two must be halved, so the angles are equal.","nl":"Denken dat dat als een hoek in tweeën wordt gedeeld, de hoeken van beide helften gelijk zijn."}},{"id":"ErrorAngleRightStraight","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that two right angles can be arranged to make a straight line.","nl":"Niet weten dat twee rechte hoeken samen een gestrekte hoek kunnen vormen."}},{"id":"ErrorEstimatingRight","type":["MISCONCEPTION"],"descr":{"en":"Not comparing an angle to a right angle when estimating its size.","nl":"Een hoek verkeerd inschatten door deze niet te vergelijken met een rechte hoek."}}]},{"id":"AnglesReasoningTriangle","descr":{"en":"Reasoning with angles in a triangle","nl":"Redeneren met hoeken in een driehoek"},"stepType":"CONCEPT","errors":[{"id":"ErrorTriangeAngleSum","type":["MISCONCEPTION"],"descr":{"en":"Not knowing that angles in a triangle add to 180°.","nl":"Niet weten dat de hoeken van een driehoek optellen tot 180°."}},{"id":"ErrorTriangeExteriorAngle","type":["MISCONCEPTION"],"descr":{"en":"Not knowing exterior angle theorem for triangles.","nl":"De regel voor buitenhoeken van driehoeken niet kennen."}},{"id":"ErrorTriangeInnerExterior","type":["MISTAKE"],"descr":{"en":"Calculating the angle in the triangle, not the exterior angle.","nl":"De binnenhoek en niet de buitenhoek berekenen in de driehoek."}}]}],"collections":[]}]},{"id":"GeometryLines","descr":{"en":"Lines","nl":"Lijnen"},"tags":[],"collections":[{"id":"GeometryStraightLines","descr":{"en":"Straight Lines","nl":"Rechte lijnen"},"tags":[{"id":"StraightLinesOrientation","descr":{"en":"Orientation of straight lines","nl":"Richting van rechte lijnen"},"stepType":"CONCEPT","errors":[{"id":"ConfuseVerticalHorizontal","type":["MISCONCEPTION"],"descr":{"en":"Confusing vertical with horizontal.","nl":"Verticaal en horizontaal door elkaar halen."}},{"id":"MeaningVertical","type":["MISCONCEPTION"],"descr":{"en":"Not understanding the meaning of 'vertical'.","nl":"De betekenis van 'verticaal' niet begrijpen."}},{"id":"MeaningHorizontal","type":["MISCONCEPTION"],"descr":{"en":"Not understanding the meaning of 'horizontal'.","nl":"De betekenis van 'horizontaal' niet begrijpen."}}]},{"id":"StraightLinePairs","descr":{"en":"Describing pairs of straight lines","nl":"Beschrijven van paren van rechte lijnen"},"stepType":"CONCEPT","errors":[{"id":"ConceptParallel","type":["MISCONCEPTION"],"descr":{"en":"Not recognising parallel lines.","nl":"Parallelle lijnen niet herkennen."}},{"id":"ConceptPerpendicular","type":["MISCONCEPTION"],"descr":{"en":"Not recognising perpendicular lines.","nl":"Loodrechte lijnen niet herkennen."}},{"id":"ConfusePerpendicularParallel","type":["MISCONCEPTION"],"descr":{"en":"Confusing perpendicular with parallel.","nl":"Verticaal en horizontaal door elkaar halen."}},{"id":"ConfuseIntersectParallel","type":["MISCONCEPTION"],"descr":{"en":"Thinking that two lines that intersect are parallel.","nl":"Denken dat twee lijnen die elkaar snijden parallel zijn."}},{"id":"ConfuseIntersectPerpendicular","type":["MISCONCEPTION"],"descr":{"en":"Thinking that two lines that intersect are perpendicular.","nl":"Denken dat twee lijnen die elkaar snijden loodrecht zijn."}}]}],"collections":[]}]},{"id":"GeometryMeasurement","descr":{"en":"Measurement in geometry","nl":"Maten in meetkunde"},"tags":[{"id":"GeometryMeasurementArea","descr":{"en":"Concept of area","nl":"Het begrip oppervlakte"},"stepType":"CONCEPT","errors":[{"id":"AreaUnit","type":["MISCONCEPTION"],"descr":{"en":"Using incorrect units of measurement of area","nl":"De verkeerde eenheid gebruiken voor oppervlakte"}}]},{"id":"GeometryMeasurementPerimeter","descr":{"en":"Concept of perimeter","nl":"Het begrip omtrek"},"stepType":"CONCEPT","errors":[{"id":"PartialError","type":["MISCONCEPTION"],"descr":{"en":"Taking only partial number of edges to calculate perimeter","nl":"Niet alle zijden gebruiken bij het berekenen van de omtrek"}},{"id":"PerimeterVsArea","type":["MISCONCEPTION"],"descr":{"en":"Confusing area with perimeter","nl":"Omtrek en oppervlakte met elkaar verwarren"}},{"id":"PerimeterParallel","type":["MISCONCEPTION"],"descr":{"en":"Thinking parallel side lengths equal perimeter","nl":"Denken dat evenwijdige lijnen de omtrek zijn"}},{"id":"PerimeterOperation","type":["MISCONCEPTION"],"descr":{"en":"Using the wrong operation to calculate the perimeter, e.g. subtraction","nl":"De verkeerde bewerking gebruiken om de omtrek te bereken, zoals bijvoorbeeld aftrekken"}}]}],"collections":[]},{"id":"GeometryPoints","descr":{"en":"Points","nl":"Punten"},"tags":[{"id":"PointCoordinates","descr":{"en":"Coordinates of a point","nl":"Coördinaten van een punt"},"stepType":"CONCEPT","errors":[{"id":"ConfuseSigns","type":["MISCONCEPTION"],"descr":{"en":"Confusing the signs in one or both coordinates.","nl":"De tekens in één of beide coördinaten door elkaar halen."}},{"id":"SwappedOrder","type":["MISCONCEPTION"],"descr":{"en":"Confusing the order of coordinates.","nl":"De volgorde van de coördinaten door elkaar halen."}}]}],"collections":[{"id":"GeometryPointTypes","descr":{"en":"Point Types","nl":"Soorten punten"},"tags":[{"id":"GeometryMidpoints","descr":{"en":"Understanding Midpoints","nl":"Middens begrijpen"},"stepType":"CONCEPT","errors":[{"id":"MeaningMidpoint","type":["MISCONCEPTION"],"descr":{"en":"Not understanding the meaning of 'midpoint'.","nl":"De betekenis van 'midden' niet begrijpen."}},{"id":"MidpointOfPart","type":["MISCONCEPTION"],"descr":{"en":"Giving the midpoint of the part of the line segment that is on one side of an axis.","nl":"Het midden geven van het deel van het lijnstuk dat aan één kant van een as ligt."}},{"id":"MidpointOnAxis","type":["MISCONCEPTION"],"descr":{"en":"Thinking that if a line segment crosses an axis, the midpoint must be on the axis.","nl":"Denken dat als een lijnstuk een as kruist, het midden op de as moet liggen."}},{"id":"ConfuseMidpointEndpoint","type":["MISCONCEPTION"],"descr":{"en":"Confusing the meaning of 'midpoint' and 'end point'.","nl":"De betekenis van 'midden' en 'eindpunt' door elkaar halen."}}]}],"collections":[]}]},{"id":"GeometryShape","descr":{"en":"Geometrical shapes","nl":"Meetkundige figuren"},"tags":[{"id":"GeometryShapeCompound","descr":{"en":"Compound shapes","nl":"Samengestelde figuren"},"stepType":"CONCEPT","errors":[{"id":"Decompose","type":["MISCONCEPTION"],"descr":{"en":"Unable to decompose a compound shape into basic shapes","nl":"Niet kunnen splitsen van een samengesteld figuur in basisfiguren"}}]},{"id":"GeometryShapeRectangle","descr":{"en":"Properties of rectangles","nl":"Eigenschappen van rechthoeken"},"stepType":"CONCEPT","errors":[{"id":"RectangleDefinition","type":["MISCONCEPTION"],"descr":{"en":"Using an incorrect definition of a rectangle","nl":"Een onjuiste definitie van een rechthoek gebruiken"}},{"id":"RectangleArea","type":["MISCONCEPTION"],"descr":{"en":"Calculating the area of a rectangle incorrectly","nl":"De oppervlakte van een rechthoek verkeerd berekenen"}}]},{"id":"GeometryShapeTriangle","descr":{"en":"Properties of triangles","nl":"Eigenschappen van driehoeken"},"stepType":"CONCEPT","errors":[{"id":"TriangleArea","type":["MISCONCEPTION"],"descr":{"en":"Calculating the area of a triangle incorrectly","nl":"De oppervlakte van een driehoek verkeerd berekenen"}},{"id":"TriangleProperties","type":["MISCONCEPTION"],"descr":{"en":"Misunderstanding of properties of a triangle.","nl":"De eigenschappen van een driehoek niet kennen"}}]}],"collections":[]}]},{"id":"Measurement","descr":{"en":"Measurement","nl":"Meten"},"tags":[],"collections":[{"id":"MeasurementUnits","descr":{"en":"Units of measurement","nl":"Eenheden"},"tags":[{"id":"UnitConversion","descr":{"en":"Converting between units of measurement","nl":"Omrekenen tussen eenheden"},"stepType":"CALCULATE","errors":[{"id":"UnitsConvertNumberSteps","type":["MISCONCEPTION"],"descr":{"en":"Applying an incorrect number of steps when converting metric units.","nl":"Een verkeerd aantal stappen toepassen bij het omrekenen van eenheden."}}]},{"id":"UnitConversionPower","descr":{"en":"Converting between units of area or volume","nl":"Omrekenen tussen eenheden van oppervlakte of volume"},"stepType":"CALCULATE","errors":[{"id":"UnitsConvertDirection","type":["MISCONCEPTION"],"descr":{"en":"Converting in the opposite direction. For example, converting from 100 m to 1 cm.","nl":"Omrekenen in de verkeerde richting. Bijvoorbeeld van 100 m naar 1 cm."}},{"id":"UnitsConvertNoDimension","type":["MISCONCEPTION"],"descr":{"en":"Not shifting two or three decimal places for area or volume.","nl":"Geen twee of drie decimalen verschuiven bij oppervlakte of volume."}},{"id":"UnitsConvertOrder","type":["MISCONCEPTION"],"descr":{"en":"Shifting an incorrect number of decimal places","nl":"De komma een verkeerd aantal plaatsen verschuiven"}}]}],"collections":[]}]},{"id":"Probability","descr":{"en":"Probability","nl":"Kansrekening"},"tags":[],"collections":[{"id":"ProbabilityConcept","descr":{"en":"Understanding the concept of probability","nl":"Het concept van kansrekening begrijpen"},"tags":[{"id":"ProbabilityConceptRatio","descr":{"en":"Definition of probability as a ratio","nl":"Definitie van kans als een verhouding"},"stepType":"CONCEPT","errors":[{"id":"NotOutcome","type":["MISCONCEPTION"],"descr":{"en":"Giving the probability of *not* the desired outcome","nl":"De breuk geven die *niet* het verwachte resultaat is"}},{"id":"InvertOutcome","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that ‘not outcome’ includes all the other outcomes","nl":"Niet begrijpen dat 'niet de uitkomst' alle andere uitkomsten omvat"}},{"id":"MultipleOutcome","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that ‘A or B or C' means counting all the outcomes of A, B and C","nl":"Niet begrijpen dat 'A of B of C' betekent dat alle uitkomsten van A, B en C worden geteld"}},{"id":"IncorrectDenominator","type":["MISCONCEPTION"],"descr":{"en":"Thinking the probability is (number of expected outcomes) / (number of other outcomes) instead of (number of expected outcomes) / (total number of outcomes)","nl":"Denken dat de kans (aantal verwachte uitkomsten) / (aantal andere uitkomsten) is in plaats van (aantal verwachte uitkomsten) / (totaal aantal uitkomsten)"}},{"id":"UnequalWeighting","type":["MISCONCEPTION"],"descr":{"en":"Thinking that as there are n outcomes the fraction of each outcome is one nth","nl":"Denken dat als er n uitkomsten zijn, de breuk van elke uitkomst één n-de is"}},{"id":"ProbabilityZero","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that zero is a valid probability","nl":"Niet begrijpen dat nul een geldige kans is"}}]},{"id":"ProbabilityConceptValue","descr":{"en":"Understanding the value of a probability","nl":"Het begrijpen van de waarde van een kans"},"stepType":"CONCEPT","errors":[{"id":"MeaningOfLikely","type":["MISCONCEPTION"],"descr":{"en":"Not understanding the meaning of ‘likely’ in terms of probability","nl":"De betekenis van 'waarschijnlijk' in termen van kans niet begrijpen"}},{"id":"ComparingLikely","type":["MISCONCEPTION"],"descr":{"en":"Not being able to compare likelihoods using ‘least likely’ or 'most likely'","nl":"Niet in staat zijn om waarschijnlijkheden te vergelijken met 'minst waarschijnlijk' of 'meest waarschijnlijk'"}},{"id":"EquallyLikely","type":["MISCONCEPTION"],"descr":{"en":"Not understanding the meaning of ‘equally likely’","nl":"De betekenis van 'even waarschijnlijk' niet begrijpen"}},{"id":"LeastMostLikely","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that the least common item is the least likely and the most common item is the most likely’","nl":"Niet begrijpen dat het minst voorkomende item het minst waarschijnlijk is en het meest voorkomende item het meest waarschijnlijk is"}}]}],"collections":[]}]},{"id":"Sequences","descr":{"en":"Sequences and series","nl":"Rijen en reeksen"},"tags":[],"collections":[{"id":"SequencesFormulas","descr":{"en":"Sequence formulas","nl":"Rijformules"},"tags":[{"id":"SequenceRules","descr":{"en":"Recognizing sequence rules","nl":"Rijregels herkennen"},"stepType":"CONCEPT","errors":[{"id":"ReversedOrder","type":["MISCONCEPTION"],"descr":{"en":"Finding the rule that connects the terms of a sequence in reverse order.","nl":"De regel geven die de termen van een rij in omgekeerde volgorde verbindt."}},{"id":"TwoTermsOnly","type":["MISCONCEPTION"],"descr":{"en":"Giving a rule that connects two of the numbers in the sequence instead of the rule that works for all terms in the sequence.","nl":"Een regel geven die twee van de getallen in de rij verbindt in plaats van de regel die voor alle termen in de rij werkt."}},{"id":"FirstTwoTermsOnly","type":["MISCONCEPTION"],"descr":{"en":"Giving a rule that works for first two terms only.","nl":"Een regel geven die alleen voor de eerste twee termen werkt."}},{"id":"AdditiveAndMultiplicative","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that two numbers can be connected by both an additive and a multiplicative rule.","nl":"Niet begrijpen dat twee getallen met zowel een optellings- als een vermenigvuldigingsregel kunnen worden verbonden."}}]}],"collections":[{"id":"ArithmeticSequenceFormulas","descr":{"en":"Arithmetic sequence formulas","nl":"Arithmetic rijformules"},"tags":[{"id":"ArithmeticSequenceExplicitFormula","descr":{"en":"Explicit formulas for arithmetic sequences","nl":"Expliciete formules voor rekenkundige rijen"},"stepType":"CONCEPT","errors":[{"id":"CommonDifferenceIncorrectNumber","type":["MISCONCEPTION"],"descr":{"en":"Adding incorrect number of common differences.","nl":"Het verkeerde aantal gemeenschappelijke verschillen toevoegen."}},{"id":"OneOff","type":["MISCONCEPTION"],"descr":{"en":"Finding the nth term of an arithmetic sequence by adding '$n \\times$ common difference' to the first term instead of adding '$(n - 1) \\times$ common difference'.","nl":"De $n$-de term van een rekenkundige rij vinden door '$n \\times$ gemeenschappelijk verschil' op te tellen bij de eerste term in plaats van '$(n - 1) \\times$ gemeenschappelijk verschil'."}},{"id":"PowerInsteadOfProduct","type":["MISCONCEPTION"],"descr":{"en":"Finding the nth term of an arithmetic sequence by adding a power of the common difference to the first term instead of adding a multiple of the common difference.","nl":"De $n$-de term van een rekenkundige rij vinden door een macht van het gemeenschappelijk verschil op te tellen bij de eerste term in plaats van een product van het gemeenschappelijk verschil."}}]},{"id":"ArithmeticSequenceRules","descr":{"en":"Recognizing arithmetic sequence rules","nl":"Rekenkundige rijregels herkennen"},"stepType":"CONCEPT","errors":[{"id":"FindAdditiveConstant","type":["MISCONCEPTION"],"descr":{"en":"Not recognising which number to add to / subtract from the first number to give the second.","nl":"Niet herkennen welk getal bij het eerste getal moet worden opgeteld / afgetrokken om het tweede getal te geven."}},{"id":"FindCommonDifference","type":["MISCONCEPTION"],"descr":{"en":"Not understanding how to find the common difference in an arithmetic sequence. ","nl":"Niet weten hoe het gemeenschappelijk verschil in een rekenkundige rij te vinden."}},{"id":"MultiplicativeInsteadOfAdditive","type":["MISCONCEPTION"],"descr":{"en":"Using a multiplicative rule when an additive rule is asked for.","nl":"Een vermenigvuldigingsregel gebruiken wanneer om een optellingsregel wordt gevraagd."}}]},{"id":"ArithmeticSequenceSubstitution","descr":{"en":"Substituting values in arithmetic sequence formulas","nl":"Waarden substitueren in rekenkundige rijformules"},"stepType":"CONCEPT","errors":[{"id":"MissingConstant","type":["MISCONCEPTION"],"descr":{"en":"Correctly substituting for n, but not adding/subtracting the constant.","nl":"Correct substitueren voor n, maar de constante niet optellen/aftrekken."}},{"id":"ShiftMinusSign","type":["MISCONCEPTION"],"descr":{"en":"Correctly substituting for n, but moving the negative sign to make the calculation 'larger number - smaller number' (to give a positive answer).","nl":"Correct substitueren voor n, maar het minteken verplaatsen om de berekening 'groter getal - kleiner getal' te maken (om een positief antwoord te geven)."}},{"id":"VariableN","type":["MISCONCEPTION"],"descr":{"en":"Not understanding that kn has different values, depending on the value of n.","nl":"Niet begrijpen dat kn verschillende waarden heeft, afhankelijk van de waarde van n."}}]}],"collections":[]},{"id":"GeometricSequencesFormulas","descr":{"en":"Geometric sequence formulas","nl":"Meetkundige rijformules"},"tags":[{"id":"GeometricSequenceExplicitFormula","descr":{"en":"Explicit formulas for geometric sequences","nl":"Expliciete formules voor meetkundige rijen"},"stepType":"CONCEPT","errors":[{"id":"CommonRatioIncorrectNumber","type":["MISCONCEPTION"],"descr":{"en":"Multiplying incorrect number of times by the common ratio.","nl":"Het verkeerde aantal keer vermenigvuldigen met de gemeenschappelijke ratio."}},{"id":"FindCommonRatio","type":["MISCONCEPTION"],"descr":{"en":"Not understanding how to find the common ratio in a geometric sequence. ","nl":"Niet weten hoe de gemeenschappelijke factor in een meetkundige rij te vinden."}},{"id":"OneOff","type":["MISCONCEPTION"],"descr":{"en":"Finding the nth term of a geometric sequence by multiplying the first term by the common ration $n$ times, not $(n-1)$ times.","nl":"De $n$-de term van een meetkundige rij vinden door de eerste term $n$ keer te vermenigvuldigen met de gemeenschappelijke ratio, niet $(n-1)$ keer."}}]},{"id":"GeometricSequenceRules","descr":{"en":"Recognizing geometric sequence rules","nl":"Meetkundige rijregels herkennen"},"stepType":"CONCEPT","errors":[{"id":"FindMultiplicativeConstant","type":["MISCONCEPTION"],"descr":{"en":"Not recognising which number to multiply/divide the first number by to give the second.","nl":"Niet herkennen welk getal het eerste getal moet worden vermenigvuldigd / gedeeld om het tweede getal te geven."}},{"id":"AdditiveInsteadOfMultiplicative","type":["MISCONCEPTION"],"descr":{"en":"Using an additive rule when a multiplicative rule is asked for.","nl":"Een optellingsregel gebruiken wanneer om een vermenigvuldigingsregel wordt gevraagd."}}]}],"collections":[]}]},{"id":"SequenceTables","descr":{"en":"Sequence tables","nl":"Rijtabellen"},"tags":[{"id":"SequenceTablesConcept","descr":{"en":"Understanding sequence tables","nl":"Rijtabellen begrijpen"},"stepType":"CONCEPT","errors":[{"id":"General","type":["MISCONCEPTION"],"descr":{"en":"Not understanding how to use a table of values.","nl":"Niet begrijpen hoe een tabel met waarden te gebruiken."}}]}],"collections":[]}]},{"id":"Statistics","descr":{"en":"Statistics","nl":"Statistiek"},"tags":[],"collections":[{"id":"StatisticsIntepreting","descr":{"en":"Interpreting data","nl":"Data interpreteren"},"tags":[{"id":"StatisticsDataTypes","descr":{"en":"Understanding the different types of data","nl":"De verschillende soorten data begrijpen"},"stepType":"CONCEPT","errors":[{"id":"ContinuousDiscrete","type":["MISCONCEPTION"],"descr":{"en":"Not knowing the difference between continuous and discrete data.","nl":"Het verschil tussen continue en discrete data niet kennen."}},{"id":"UnitMeansContinuous","type":["MISCONCEPTION"],"descr":{"en":"Thinking that any data given with units (for example, price or waist size of a pair of jeans) must be continuous.","nl":"Denken dat alle data met een eenheid (bijvoorbeeld prijs of taillemaat van een spijkerbroek) continue data is."}},{"id":"NoUnitMeansContinuous","type":["MISCONCEPTION"],"descr":{"en":"Thinking that any data with non-unit values (for example, child's shoe size) must be continuous.","nl":"Denken dat alle data zonder eenheid (bijvoorbeeld schoenmaten) continue data is."}}]},{"id":"StatisticsInterpretGeneral","descr":{"en":"Interpreting diagrams and tables","nl":"Diagrammen en tabellen gebruiken"},"stepType":"CONCEPT","errors":[{"id":"CountingMissedClasses","type":["MISCONCEPTION"],"descr":{"en":"Not including all classes that satisfy the criterion when counting the data.","nl":"Niet alle klassen die aan het criterium voldoen meetellen."}},{"id":"CountingMissedFrequencies","type":["MISCONCEPTION"],"descr":{"en":"Not including all frequencies when calculating the total frequency.","nl":"Niet alle frequenties meetellen bij het berekenen van de totale frequentie."}},{"id":"WrongScale","type":["MISCONCEPTION"],"descr":{"en":"Misreading the scale on a pictogram.","nl":"De schaal op een pictogram verkeerd lezen."}},{"id":"ProportionOrValue","type":["MISCONCEPTION"],"descr":{"en":"Confusing proportion and number of items.","nl":"Verhouding en aantal items door elkaar halen."}}]}],"collections":[{"id":"StatisticsBarCharts","descr":{"en":"Working with bar charts","nl":"Werken met staafdiagrammen"},"tags":[{"id":"StatisticsBarChartsInterpret","descr":{"en":"Interpreting bar charts","nl":"Staafdiagrammen interpreteren"},"stepType":"CONCEPT"}],"collections":[]},{"id":"FrequencyTables","descr":{"en":"Working with frequency tables","nl":"Werken met frequentietabellen"},"tags":[{"id":"StatisticsTablesFrequencyInterpret","descr":{"en":"Interpreting frequency tables","nl":"Frequentietabellen gebruiken"},"stepType":"CONCEPT","errors":[{"id":"CountingTalliesFourFive","type":["MISCONCEPTION"],"descr":{"en":"Thinking that each group of tallies represents four instead of five.","nl":"Denken dat elke groep streepjes vier in plaats van vijf vertegenwoordigt."}},{"id":"CountingTallies","type":["MISCONCEPTION"],"descr":{"en":"Counting only the groups of five in the tallies instead of counting all the data.","nl":"Alleen de groepen van vijf streepjes tellen in plaats van alle data."}},{"id":"CountingClassesInsteadOfTallies","type":["MISCONCEPTION"],"descr":{"en":"Counting the number of classes instead of the number of tallies to find the total number of pieces of data.","nl":"Het aantal klassen tellen in plaats van het aantal streepjes om het totaal aantal data te vinden."}},{"id":"InclusiveIsteadOfExclusiveMore","type":["MISTAKE","MISCONCEPTION"],"descr":{"en":"Calculating the frequency of ‘n or more’ when asked for ‘more than n’.","nl":"De frequentie van ‘n of meer’ berekenen wanneer gevraagd wordt naar ‘meer dan n’."}},{"id":"InclusiveIsteadOfExclusiveLess","type":["MISCONCEPTION"],"descr":{"en":"Calculating the frequency ‘n or fewer’ when asked for ‘fewer than n’.","nl":"De frequentie van ‘n of minder’ berekenen wanneer gevraagd wordt naar ‘minder dan n’."}},{"id":"LessInsteadOfMore","type":["MISTAKE","MISCONCEPTION"],"descr":{"en":"Calculating the frequency of ‘fewer than n ’ when asked for ‘more than n ’.","nl":"De frequentie van ‘minder dan n ’ berekenen wanneer gevraagd wordt naar ‘meer dan n ’."}},{"id":"MoreInsteadOfLess","type":["MISTAKE","MISCONCEPTION"],"descr":{"en":"Calculating the frequency of ‘more than n’ when asked for ‘fewer than n’.","nl":"De frequentie van ‘meer dan n’ berekenen wanneer gevraagd wordt naar ‘minder dan n’."}},{"id":"FrequencyInsteadOfClass","type":["MISTAKE"],"descr":{"en":"Giving the highest frequency, rather than the name of the class with that frequency, when asked for the most common class.","nl":"De hoogste frequentie geven, in plaats van de naam van de klasse met die frequentie, wanneer gevraagd wordt naar de meest voorkomende klasse."}},{"id":"WrongColumnTotal","type":["MISCONCEPTION"],"descr":{"en":"Finding the total of the wrong column when asked for the total frequency.","nl":"Het totaal van de verkeerde kolom vinden wanneer gevraagd wordt naar de totale frequentie."}}]}],"collections":[]},{"id":"StatisticsPieCharts","descr":{"en":"Working with pia charts","nl":"Werken met cirkeldiagrammen"},"tags":[{"id":"StatisticsPieChartsInterpret","descr":{"en":"Interpreting pie charts","nl":"Cirkeldiagrammen interpreteren"},"stepType":"CONCEPT","errors":[{"id":"AngleAndValue","type":["MISCONCEPTION"],"descr":{"en":"Not understanding the relationship between the angle of a sector on a pie chart and the number of items represented.","nl":"De relatie tussen de hoek van een sector in een cirkeldiagram en het aantal items dat deze sector vertegenwoordigt niet begrijpen."}}]}],"collections":[]},{"id":"StatisticsTablesTwoWay","descr":{"en":"Working with two-way tables","nl":"Werken met tabellen"},"tags":[{"id":"StatisticsTablesTwoWayCreate","descr":{"en":"Creating two-way tables","nl":"Tabellen maken"},"stepType":"CONCEPT","errors":[{"id":"CalculateOverallTotal","type":["MISCONCEPTION"],"descr":{"en":"Not knowing how to calculate the overall total.","nl":"Niet weten hoe de totaalwaarde berekend moet worden."}},{"id":"SplitIntoClasses","type":["MISCONCEPTION"],"descr":{"en":"Not knowing how to split the information into classes for the rows and columns.","nl":"Niet weten hoe de informatie in klassen voor de rijen en kolommen verdeeld moet worden."}},{"id":"WrongCells","type":["MISCONCEPTION"],"descr":{"en":"Not writing the data in the correct cells.","nl":"De data niet in de juiste cellen schrijven."}}]},{"id":"StatisticsTablesTwoWayInterpret","descr":{"en":"Interpreting two-way tables","nl":"Tabellen interpreteren"},"stepType":"CONCEPT","errors":[{"id":"WrongColumn","type":["MISCONCEPTION"],"descr":{"en":"Reading from the wrong column of a two-way table.","nl":"Uit de verkeerde kolom van een tabel lezen."}},{"id":"WrongRow","type":["MISCONCEPTION"],"descr":{"en":"Reading from the wrong row of a two-way table.","nl":"Uit de verkeerde rij van een tabel lezen."}},{"id":"TotalInsteadOfCell","type":["MISCONCEPTION"],"descr":{"en":"Reading the total for the row or column instead of the correct cell in the row or column.","nl":"De totaalwaarde van de rij of kolom lezen in plaats van de juiste cel in de rij of kolom."}},{"id":"CellInsteadOfTotal","type":["MISCONCEPTION"],"descr":{"en":"Reading a particular value from a row or column instead of the total for the row or column.","nl":"Een bepaalde waarde uit een rij of kolom lezen in plaats van de totaalwaarde van de rij of kolom."}},{"id":"AddingInsteadOfReadingTotal","type":["MISCONCEPTION"],"descr":{"en":"Adding together the totals in the bottom row or the final column instead of reading the overall total value.","nl":"De totaalwaarden van de onderste rij of de laatste kolom bij elkaar optellen in plaats van de totaalwaarde van de tabel lezen."}},{"id":"AddingRowColumnTotals","type":["MISCONCEPTION"],"descr":{"en":"Adding all the totals from the bottom row and final column instead of reading the overall total value.","nl":"Alle totaalwaarden van de onderste rij en de laatste kolom bij elkaar optellen in plaats van de totaalwaarde van de tabel lezen."}},{"id":"AddingCellInsteadOfReadingTotal","type":["MISCONCEPTION"],"descr":{"en":"Adding all the numbers in all the cells instead of reading the overall total value.","nl":"Alle getallen in alle cellen bij elkaar optellen in plaats van de totaalwaarde van de tabel lezen."}},{"id":"WrongTotalCellForClass","type":["MISCONCEPTION"],"descr":{"en":"Not correctly identifying the cell for the total of a particular class.","nl":"De cel voor de totaalwaarde van een bepaalde klasse niet correct identificeren."}},{"id":"WrongTotalCell","type":["MISCONCEPTION"],"descr":{"en":"Not correctly identifying the cell for the overall total.","nl":"De cel voor de totaalwaarde niet correct identificeren."}},{"id":"InterpretTotalColumn","type":["MISCONCEPTION"],"descr":{"en":"Not knowing that the final column shows the total of each row.","nl":"Niet weten dat de laatste kolom de totaalwaarde van elke rij weergeeft."}},{"id":"InterpretTotalRow","type":["MISCONCEPTION"],"descr":{"en":"Not knowing that the final row shows the total of each column.","nl":"Niet weten dat de onderste rij de totaalwaarde van elke kolom weergeeft."}}]}],"collections":[]}]}]}]}