9th grade students’ understanding and strategies when solving x(t) problems in 1D kinematics and y(x) problems in mathematics
9th grade students’ understanding and strategies when solving
x(t)
problems in 1D kinematics and
y(x)
problems in mathematics
复制标题
九年级学生解决一维运动学中的x(t)问题和数学中的y(x)问题时的理解和策略
DOI：
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发表时间：
2019
影响因子：
3.1
通讯作者：
M. Cock
中科院分区：
文献类型：
--
作者：
S. Ceuppens;L. Bollen;J. Deprez;W. Dehaene;M. Cock
我们设计，验证，并管理一个24项测试，以研究学生在9年级的一维运动学[xuzhou]和数学[yuzhou xuzhou]的线性函数的理解。这些项目使用图形或代数公式评估1D运动学中的初始位置和速度以及数学中的y截距和斜率的识别和比较。结果表明，学生在大多数数学项目上的表现明显优于同构运动学项目，但大多数最简单和最困难的项目是运动学项目。学生在必须比较两个正斜率的图形问题上的准确率最高，在必须确定或比较负斜率的问题上的准确率最低。我们发现学生在数学中的y截距和运动学中的斜率方面有更多的困难。此外，与图形表示中的问题相比，符号表示中的问题的准确性要低得多，特别是当必须确定y截距或斜率而不是比较时。我们还对学生的学习策略和错误进行了定性分析。我们经常在数学中发现x截距和y截距之间的混淆，但在运动学中却少得多。运动学中的负速度是迄今为止最大的陷阱，而数学中的负斜率很少成为问题。结果还表明，一个显着的频率区间或点混淆运动学，但很少在数学。我们重申发生的区间或点混淆的问题与图形和讨论三种不同的情况下的区间或点混淆的问题与代数表达式：数值，代数和单位为基础的。我们的研究结果表明，运动学和数学之间的联系薄弱，我们建议，这两个背景之间的紧密结合，在教育过程中，可以有利于学生的线性函数和线性现象的运动学的理解。
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.