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We design, validate, and administer a 24-item test to study student understanding of linear functions in 1D kinematics [xðtÞ] and mathematics [yðxÞ] in the 9th grade. The items assess identification and comparison of initial position and velocity in 1D kinematics and of the y intercept and slope in mathematics using a graph or an algebraic formula. Results show that students’ performance on most mathematics items is significantly better than on their isomorphic kinematic counterparts, but also that most of the easiest as well as the most difficult items are kinematics items. Students achieve the highest accuracies on graphical questions in which they must compare two positive slopes, and they achieve the lowest accuracies on questions in which they must determine or compare a negative slope. We find that students have more difficulties with the y intercept in mathematics and with the slope in kinematics. Furthermore, questions in symbolic representation result in far lower accuracies compared to questions in graphical representation, particularly when the y intercept or the slope has to be determined instead of compared. We also analyze the results qualitatively by categorizing the students’ strategies and errors. We find frequent confusion between the x intercept and the y intercept in mathematics, but far less in kinematics. Negative velocities in kinematics are by far the largest pitfall, whereas negative slope in mathematics is rarely an issue. The results also show a significant frequency of interval or point confusions in kinematics but very little in mathematics. We reaffirm the occurrence of the interval or point confusion in questions with graphs and discuss three different cases of interval or point confusions in questions with algebraic expressions: numerical, algebraic, and unit based. Our results indicate a weak link between kinematics and mathematics and we suggest that closer integration between these two contexts during education could benefit student understanding of linear functions and linear phenomena in kinematics.

physical review. physics education research

9th grade students’ understanding and strategies when solving <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> problems in 1D kinematics and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>y</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> …

9th grade students’ understanding and strategies when solving x(t) problems in 1D kinematics and y(x) …