TY - JOUR

T1 - University students' grasp of inflection points

AU - Tsamir, Pessia

AU - Ovodenko, Regina

PY - 2013/7

Y1 - 2013/7

N2 - This paper describes university students' grasp of inflection points. The participants were asked what inflection points are, to mark inflection points on graphs, to judge the validity of related statements, and to find inflection points by investigating (1) a function, (2) the derivative, and (3) the graph of the derivative. We found four erroneous images of inflection points: (1) f ′ (x) = 0 as a necessary condition, (2) f ′ (x) ≠ 0 as a necessary condition, (3) f ″ (x) = 0 as a sufficient condition, and (4) the location of "a peak point, where the graph bends" as an inflection point. We use the lenses of Fischbein, Tall, and Vinner and Duval's frameworks to analyze students' errors that were rooted in mathematical and in real-life contexts.

AB - This paper describes university students' grasp of inflection points. The participants were asked what inflection points are, to mark inflection points on graphs, to judge the validity of related statements, and to find inflection points by investigating (1) a function, (2) the derivative, and (3) the graph of the derivative. We found four erroneous images of inflection points: (1) f ′ (x) = 0 as a necessary condition, (2) f ′ (x) ≠ 0 as a necessary condition, (3) f ″ (x) = 0 as a sufficient condition, and (4) the location of "a peak point, where the graph bends" as an inflection point. We use the lenses of Fischbein, Tall, and Vinner and Duval's frameworks to analyze students' errors that were rooted in mathematical and in real-life contexts.

KW - Concept image

KW - Definition

KW - Inflection point

KW - Intuition

KW - Representation

UR - http://www.scopus.com/inward/record.url?scp=84878499698&partnerID=8YFLogxK

U2 - 10.1007/s10649-012-9463-1

DO - 10.1007/s10649-012-9463-1

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AN - SCOPUS:84878499698

SN - 0013-1954

VL - 83

SP - 409

EP - 427

JO - Educational Studies in Mathematics

JF - Educational Studies in Mathematics

IS - 3

ER -