Is counting hindering learning? An investigation into children’s proficiency with simple addition and their flexibility with mental computation strategies

Hopkins, Sarah; Russo, James; Siegler, Robert S.

doi:10.1080/10986065.2020.1842968

Cited by 14 publications

(15 citation statements)

References 63 publications

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“…As noted by White et al (2007), while an addend slope of about 400 ms/addend undoubtedly reflects the use of counting and an addend slope of 0 indicates the use of memory retrieval, addend slopes of intermediate values most probably reflect the use of mixed strategies. This mixture of strategies has been well-described in mental arithmetic by Siegler (1987) and recently by Hopkins et al (2020) who found that, despite the fact that in young children, the minimum operand is the best predictor of solution times, the frequency of reported use of this strategy was only 36%, similar to the reported use of retrieval (i.e., in 35% of trials).…”

Section: Discussionmentioning

confidence: 61%

Individual Differences in the Evolution of Counting

Dewi

Thévenot

2022

Experimental Psychology

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Abstract. The alphabet–arithmetic paradigm, in which adults are asked to add a numeral addend to a letter augend (e.g., D + 3 = G), was conceived to mimic the way children learn addition. Studies using this paradigm often conclude that procedural learning leads to the memorization of associations between operands and answers. However, as recently suggested, memorization might only be used by a minority of participants and only for problems with the largest addend. In the present paper, we aim at investigating these individual differences through transfer effects from trained problems to new ones. Participants were trained over 12 learning sessions, followed by 3 transfer sessions. A group of participants, that we called the nonbreakers, showed a linear function associating solution times and addends throughout the experiment. In this group, transfer was observed during the first transfer session, suggesting that a procedural strategy, transferable to new items, was still used at the end of training. In another group of participants, that we called the breakers, we observed a decrease in solution times for problems with the largest addend. In this group, transfer was only observed after two transfer sessions, suggesting that procedural strategies were not used as often in this group than in the other group. This was especially true for problems with the largest addend because transfer effects were stronger when they were excluded. Therefore, during learning and for breakers, the answers to problems with larger addends are retrieved first and, as for non-breakers, the answers to problems with very small operands remain computed.

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Section: Discussionmentioning

confidence: 61%

Individual Differences in the Evolution of Counting

Dewi

Thévenot

2022

Experimental Psychology

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“…Gaidoschik (2012) found that up to 27% of children continued to favor counting strategies for sums and minuends to 10 at the end of Grade 1; only one third were able to fully automatize operations to 10. Hopkins et al (2022) reported that third graders used the min-counting strategy (counting on from the lager summand) in 17% of trials when performing basic addition. These children often made mistakes when forced to use a retrieval strategy.…”

Section: Highlightsmentioning

confidence: 99%

Assessment of computation competence and non-count strategy use in addition and subtraction in Grade 1

Leuenberger,

Moser Opitz,

Gloor

2024

J. Numer. Cogn.

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Computation competence (CC) in simple addition and subtraction using non-counting (NC) strategies is an important learning objective in Grade 1 mathematics but many children, especially low achievers in mathematics, struggle to acquire these skills. To provide these students with the support they need, it is important to have valid and reliable tools for assessing progress in CC and NC strategy use. Developing an assessment instrument for use in Grade 1, when some children start the year unable to solve any problems, is challenging, as is ensuring measurement invariance over a school year when children generally make large achievement gains. This paper presents a new assessment tool for CC and NC strategy use in Grade 1 that was tested in a longitudinal study with N = 1,017 children. Analyses using the Rasch model revealed acceptable mean square scores (MNSQ 0.83 – 1.20). Warm’s Weighted Likelihood Estimate (WLE) reliability scores were acceptable (pre-test .77; post-test .87). Measurement invariance over time was given. The instrument is promising for assessing CC and NC strategy use efficiently and accurately in Grade 1.

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“…Still regarding resolution strategies, and as Boavida et al (2008) and Dante (2009) emphasise, the teacher must provide tasks that enhance the emergence of strategies, underlining the importance of the typology of problems used, leaving it to the students to discover and build new action schemes. As they become familiar with the effectiveness of a series of strategies, they are more likely to choose the strategy that has worked best for them to solve a similar problem in the past, becoming more proficient (Hopkins, Russo & Siegler, 2020). However, the final role of identification and systematisation to cement the learning developed cannot be devalued.…”

Section: Problem-solvingmentioning

confidence: 99%

Appealing to Creativity Through Solving and Posing Problems in Mathematics Class

Miranda

Mamede

2022

Acta Sci.

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Background: Creativity should be a key issue in mathematics learning. However, mathematics class rarely provides opportunities for students to experience it. Problem solving and posing can play a leading role in promoting creative thinking in mathematics. Objectives: This study aims to have an insight into 6 th -graders understanding of problem solving and posing, analyse their solving strategies, their ability to pose problems, and their difficulties when doing so. Design: Qualitative methods were used in a case study approach. An intervention of five sessions comprising five problem-solving and four problem-posing tasks was implemented in mathematics class. Setting and Participants: Participants were thirty 6 th -graders (11-12-year-olds) from a public supported school in Braga (Portugal). Data collection and analysis: Data collection used photographs, audio recordings, students' written productions, and researcher field notes. Results: Students conceptualised strategies such as building schemas and tables, solving from the end to the beginning, making attempts, and reducing to a simpler problem. Students faced problem posing positively, creating problems adjusted to the requirements, with a wide variety of creative contexts. Students' difficulties in problem solving rely on the interpretation of statements, recognition of previous similar problems, and mathematical communication; on problem posing, difficulties regarding the complexity of the formulated problems and a weak diversity of problems were identified. Conclusions: Problem solving and posing tasks can promote mathematical creativity and knowledge, therefore should be used more often in mathematics class, allowing the construction of solid mathematical skills and enthusiasm.

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Is counting hindering learning? An investigation into children’s proficiency with simple addition and their flexibility with mental computation strategies

Cited by 14 publications

References 63 publications

Individual Differences in the Evolution of Counting

Individual Differences in the Evolution of Counting

Assessment of computation competence and non-count strategy use in addition and subtraction in Grade 1

Appealing to Creativity Through Solving and Posing Problems in Mathematics Class

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