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Exploring Shanghai students’ mathematics learning as related to content presentation in textbooks: the case of the commutative property of addition

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Abstract

Properties of arithmetic operations are important in mathematics and play a significant role in elementary school students’ learning of mathematics. At the same time, it is quite challenging to help students learn arithmetic operational properties beyond memorization, so that they know when and how to use a specific arithmetic property. This paper reports a study containing two parts to explore students’ learning of the Commutative Property of Addition (CPA) as related to the content presentation in textbooks. Part one is to assess selected students’ performance on CPA at the end of Grade two, and part two is to explore possible contributions of textbooks to students’ performance in Shanghai. Firstly, we evaluated the performance of 41 second-graders on CPA by collecting data through a paper-and-pencil test, which was followed up with individual interviews. Through analyzing how textbooks present and organize this topic, we sought to better understand from a curriculum standpoint how students’ performance on CPA is impacted by textbooks. Results revealed that Shanghai textbooks make a positive contribution to students’ learning performance. The findings from this study help to shed light on how those textbooks aid student learning, and provide an example for further reflection on student learning of arithmetic operational properties in different curricula.

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Authors and Affiliations

  1. Research Institute for International and Comparative Education, Shanghai Normal University, Shanghai, China

    Xingfeng Huang

  2. Texas A&M University, College Station, USA

    Yu Xiao, Joseph S. Webster, Roger E. Howe & Yeping Li

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  1. Xingfeng Huang
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Correspondence to Yeping Li.

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Appendix

Appendix

 

Textbook

Unit

Contents

Page

Code

Grade one

First semester

Addition and subtraction within 10

Split and combine

21

(P1, C1)

22

(P1, C1)

Addition

23

(P3, C1)

24

(P3, C1)

25

(P3, C1)

List number sentences

60

(P3, C1)

Mathematical amusement

62

(P3, C1)

Second semester

Addition and subtraction within 100

Adding or subtracting a multiple of ten

26

(P1, C2)

(P2, C2)

(P4, C2)

27

(P1, C2)

(P2, C2)

(P4, C2)

Adding or subtracting two-digit numbers

32

(P2, C2)

(P4, C2)

33

(P2, C2)

(P4, C2)

34

(P2, C2)

37

(P2, C2)

(P4, C2)

38

(P2, C2)

Review and improvement

Review addition and subtraction with two-digit

61

(P4, C2)

62

(P4, C2)

64

(P4, C2)

65

(P4, C2)

Exchange

67

(P1, C1)

(P3, C1)

68

(P4, C3)

Grade two

First semester

Review and improvement

Review addition and subtraction with two-digit

2

(P5, C3)

Miss numbers in box

6

(P4, C3)

Second semester

Addition and subtraction with three-digit

Addition with three-digit

28

(P1, C2)

(P4, C2)

Subtraction with three-digit

33

(P1, C2)

(P4, C2)

Review and improvement

Simplifying operation

69

(P5, C3)

70

(P5, C3)

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Huang, X., Xiao, Y., Webster, J.S. et al. Exploring Shanghai students’ mathematics learning as related to content presentation in textbooks: the case of the commutative property of addition. ZDM Mathematics Education 54, 595–609 (2022). https://doi.org/10.1007/s11858-022-01362-6

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