Learning multiplication: An integrated analysis of the multiplication ability of primary school children and the difficulty of single digit and multidigit multiplication problems

Ven, Sanne H. G. van der; Straatemeier, Marthe; Jansen, Brenda R.J.; Klinkenberg, Sharon; Maas, Han L. J. van der

doi:10.1016/j.lindif.2015.08.013

Cited by 26 publications

(31 citation statements)

References 46 publications

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“…In line with the results of van der Ven et al (2015), the tie-effect was more prominent in the fast responses.…”

supporting

confidence: 90%

Fast and Slow Strategies in Multiplication

Hofman¹,

Visser²,

Jansen³

et al. 2017

Preprint

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In solving multiplication problems, children use both fast, retrieval-based, processes, and, slower computational processes. In the current study, we explore the possibility of disentangling these strategies using information contained in the observed response latencies using a method that is applicable in large data sets.We used a tree-based item response-modeling framework to investigate whether the proposed qualitative distinctions in fast and slow strategies can be detected. We analyzed responses to two sets of multiplication items, totalling more than 500.000 responses, collected with an online computer-adaptive training environment for mathematics.Results showed qualitative differences between the fast and the slow strategies. Building on these results, both item and person characteristics were differently related to fast and slow processes. These characteristics, resulting from substantive models of multiplication, allowed us to further describe the fast and slow strategies. Results emphasize the quantitative and qualitative differences between strategies used for solving multiplication problems, and provide possibilities for tailored feedback on learning multiplication.

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“…In line with the results of van der Ven et al (2015), the tie-effect was more prominent in the fast responses.…”

supporting

confidence: 90%

Fast and Slow Strategies in Multiplication

Hofman¹,

Visser²,

Jansen³

et al. 2017

Preprint

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“…For more details on the Math Garden and its psychometric properties, see Appendix A. In this study we focus on two basic skills: counting (Jansen et al, 2014) and addition, and two more advanced skills: multiplication (van der Ven et al, 2015;Hofman et al, 2017) and division. Each skill is measured by a separate game.…”

Section: Instrumentsmentioning

confidence: 99%

The dynamics of the development of mathematics skills: A comparison of theories of developing intelligence.

Hofman¹,

Kievit²,

Stevenson³

et al. 2018

Preprint

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This study investigates why children who are good at one math skill also perform well on other math tasks and seeks a solution by comparing two influential theories of general intelligence. The g-factor theory (g for 'general intelligence') implies a general math ability that steers all math-related development. In contrast, mutualism theory states that different math skills co-develop, positively influencing each others growth. We examined this with a large longitudinal data set (N ≈ 12.000) that tracked the development of basic (counting ↔ addition) and more advanced (multiplication ↔ division) math skills for a full school year. We used bivariate latent change score models to investigate whether g-factor or mutualism theory provides a better explanation of their co-development. We found that basic and more advanced math skills become more strongly related over time and that co-development is mutually beneficial. Both results support mutualism theory, a dynamic network perspective of cognitive development, where, in this case, growth in a particular math domain positively influences that of other math skills. Our results perhaps reveal the tip of the iceberg when it comes to the intricacies of co-developing math abilities. We discuss the implications of mutualism theory for understanding the dynamics of learning mathematics.

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“…As one of the four basic mathematical operations, multiplication is an important skill learnt in primary education. Especially mastery of the single-digit multiplication table is an important aim of primary education, as it forms the basis for other operations such as division and multi-digit multiplication (van der Ven, Straatemeier, Jansen, Klinkenberg, & van der Maas, 2015). The teaching of multiplication provides some particular challenges for teachers in order to help pupils develop a conceptual understanding of these operations (Bicknell, Young-Loveridge & Nguyen, 2016).…”

Section: Problem Statementmentioning

confidence: 99%

“…Arithmetic facts, in particular multiplication tables to be organized in an interrelated network in long-term memory, which allows individuals to quickly retrieve the answers to simple arithmetic problems such as 3 x 4 (Visscher, Noel, & Smedt, 2016). Single-digit multiplication mental calculation is considered important, as in most countries children learn to memorize the multiplication tables (ven der Ven et al, 2015). Multiplication facts are stored in a verbal form and the retrieval of multiplication facts relies more on verbal modality.…”

Section: Multiplicationmentioning

confidence: 99%

DEVELOPMENT AND EVALUATION OF DoCtor WoRM’S MODULE IN IMPROVING MULTIPLICATION SKILLS AMONG YEAR FOUR LOW ACHIEVERS

May¹,

Ahmad²

2019

Preprint

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The purpose of this study is to develop and evaluate the effectiveness of DoCtor WoRM’s Module in improving multiplication skills among Year Four low achievers in National-Type Chinese Primary School (SJKC). DoCtor WoRM’s Module had been designed based on Constructivist Theory, mastery learning, and game-based learning. The module was developed based on Sidek’s Module Development Model. Quantitative approaches with quasi-experimental design were used for this study. A number of 60 Year Four low achievers from Manjung District were selected using random sampling. The sample was divided into the treatment and control groups. The former went through a teaching and learning process using DoCtor WoRM’s Module, while the latter learnt through traditional teaching. After the pre-test, three months of intervention was carried out to both groups of sample, followed by a post-test. Data was analysed using descriptive and inferential statistics. Dependent t-test showed that there was a significant increase in the achievement of treatment group from pre-test (M = 59.47, SD = 27.242) to post-test (M = 91.53, SD = 12.566), t(29) = 6.254, p < .001. The independent t-test had shown that the achievement of multiplication skills in post-test of treatment group (M = 91.53, SD = 12.566) is higher than the post-test of control group (M = 79.17, SD = 22.588), t(58) = 2.621, p < .012. As a conclusion, DoCtor WoRM’s Module has improved the multiplication skills among Year Four low achievers in SJKC. This study implicates that DoCtor WoRM’s Module should be applied to the low achievers in Malaysia in order to improve their Mathematics achievement particularly in multiplication skills.

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Learning multiplication: An integrated analysis of the multiplication ability of primary school children and the difficulty of single digit and multidigit multiplication problems

Cited by 26 publications

References 46 publications

Fast and Slow Strategies in Multiplication

Fast and Slow Strategies in Multiplication

The dynamics of the development of mathematics skills: A comparison of theories of developing intelligence.

DEVELOPMENT AND EVALUATION OF DoCtor WoRM’S MODULE IN IMPROVING MULTIPLICATION SKILLS AMONG YEAR FOUR LOW ACHIEVERS

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