Abstract
What neuropsychological processes underlie mathematics performance? What cognitive strategies should we teach to boost mathematics performance? Undoubtedly, both questions lie at the heart of mathematics research and are critical for many teachers and practitioners. In this chapter, we aim to provide an answer to both questions by drawing readers’ attention to four separate but interrelated neuropsychological processes: Planning, Attention, Simultaneous, and Successive (PASS) processing. In the first section of this chapter, we review the literature on PASS neuropsychological processes and their relation to mathematics performance. In the second section, we present evidence on how information from assessing children on these neuropsychological processes (see Cognitive Assessment System; [Naglieri, J. A., Das, J. P., & Goldstein, S., Cognitive Assessment System—Second Edition: Brief, 2014]) can be used to describe children with mathematics difficulties or superior mathematics performance in three countries (Canada, China, and Cyprus) representing three different cultures (Western, East Asian, and European). These profiles clearly show that children have weaknesses (in the case of children with mathematics difficulties) or strengths (in the case of high achievers) in Planning and, to a lesser extent, Simultaneous processing, and this is irrespective of the cultural background of the participants. Finally, in the last section, we discuss the role of planning facilitation that can be used to enhance cognitive planning and mathematics performance.
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Notes
- 1.
The acronym PASS does not follow the order of the three functional units. Das et al. (1994) chose PASS because it is easy to remember.
- 2.
Broad Math is a cluster score derived from three subtests (Calculations, Math Fluency, and Applied Problems) from the Woodcock Johnson III (WJ-III; Woodcock et al., 2001).
- 3.
The children’s standard score in WJ-III Broad Math was as follows: George scored 142, Kate scored 134, Jiao scored 148, and Ming-tun scored 136. In Cyprus, the children’s z score for the mathematics achievement test was 1.4 (Gabriel) and 1.5 (Andreas), whereas their score in logits for the mathematics reasoning test was 1.8 (Gabriel) and 1.6 (Andreas).
- 4.
The children’s standard score in WJ-III Broad Math was as follows: Jasper scored 83, Alice scored 80, Chiu scored 84 and Zhan scored 78. In Cyprus, the children’s z score for the mathematics performance test was −0.61 (Gregory) and − 0.55 (Anna); for the mathematics reasoning test, their score in logits was −0.69 (Gregory) and − 0.60 (Anna).
- 5.
Students were first asked to solve a task or a sub-task silently, and immediately after finishing, articulate their thinking. We preferred a retrospective as opposed to a concurrent think-aloud approach, because of the possibility of reactivity when students articulate their thinking as they work on a task and the excessive cognitive load often involved in this approach, as students try to both think and articulate their thinking (see more in Jaaskelainen, 2010; Someren et al., 1994; van den Haak et al., 2003). As suggested (Ericsson & Simon, 1993), the limitations of the retrospective approach can be minimized when students are asked to articulate their thinking immediately after having worked on a task.
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Georgiou, G.K., Charalambous, C.Y., Sergiou, S. (2023). The Role of Neuropsychological Processes in Mathematics: Implications for Assessment and Teaching. In: Robinson, K.M., Dubé, A.K., Kotsopoulos, D. (eds) Mathematical Cognition and Understanding. Springer, Cham. https://doi.org/10.1007/978-3-031-29195-1_6
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