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Capturing Diversity in the Classroom: Uncovering Patterns of Difficulty with Simple Addition

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Diversity in Mathematics Education

Part of the book series: Mathematics Education Library ((MELI))

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Abstract

In this chapter, we draw attention to a common problem encountered in mathematics classrooms, poor number fluency with simple addition. We believe poor number fluency restricts children’s ability to learn mathematics and that a different type of research is needed to inform teachers’ practice to improve number fluency. We used a variety of techniques to capture differences in how children performed simple addition at a time when curriculum documents suggest that proficiency is expected. The findings illustrate marked diversity in performance and reveal varied patterns of difficulty, including the use of highly inefficient counting strategies, inconsistent counting errors and low retrieval on key problem types. The research approach described here provides clear pointers for where teachers need to target instruction for individual children. We propose that inclusive teaching practices are those that are matched to children’s individual patterns of difficulty and suggest how this may be achieved.

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Author information

Authors and Affiliations

  1. Faculty of Education, Monash University, Berwick, Australia

    Sarah Hopkins

  2. Graduate School of Education, University of Western Australia, Crawley, Australia

    Celéste de Villiers

Authors
  1. Sarah Hopkins
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  2. Celéste de Villiers
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Corresponding author

Correspondence to Sarah Hopkins .

Editor information

Editors and Affiliations

  1. Faculty of Education, Monash University, Clayton, Victoria, Australia

    Alan Bishop

  2. Faculty of Education, Monash University, Clayton, Victoria, Australia

    Hazel Tan

  3. School of Education, RMIT University, Bundoora, Victoria, Australia

    Tasos N Barkatsas

Appendix

Appendix

Reaction times to min-counting trials separated by the number of counts required

Minimum addend

Study 1

Study 2

Study 3

Mean (SD)

N

Mean (SD)

N

Mean (SD)

N

2

3.55s (2.11)

86

3.85s (1.96)

103

4.62s (2.18)

190

3

3.89s (1.49)

146

4.28s (1.68)

206

5.59s (2.57)

211

4

4.77s (2.12)

119

4.94s (1.96)

254

7.26s (3.33)

200

5

5.78s (2.27)

70

5.48s (2.13)

190

7.99s (3.71)

156

6

6.30s (3.74)

41

6.15s (2.58)

180

10.05s (5.42)

131

7

6.53s (2.22)

46

6.83s (2.48)

125

10.51s (4.89)

105

8

6.38s (2.35)

17

7.57s (3.75)

65

10.29s (4.59)

63

9

8.62s (2.84)

12

6.06s (2.87)

8

11.72s (5.72)

24

  1. Note: The size of the standard deviation associated with mean RTs is likely to be influenced by trials where the counting procedure is interrupted and/or counts are repeated due to self-correction, as documented in Hopkins and Lawson (2002). This argument is supported by the general pattern that standard deviations increased as the minimum addend increased (children are more likely to lose track when making more counts) and that the highest standard deviations were recorded in Study 3 where children were more likely to lose track and make errors during the min-counting procedure

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Hopkins, S., de Villiers, C. (2015). Capturing Diversity in the Classroom: Uncovering Patterns of Difficulty with Simple Addition. In: Bishop, A., Tan, H., Barkatsas, T. (eds) Diversity in Mathematics Education. Mathematics Education Library. Springer, Cham. https://doi.org/10.1007/978-3-319-05978-5_13

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