Are Physical Experiences with the Balance Model Beneficial for Students’ Algebraic Reasoning? An Evaluation of two Learning Environments for Linear Equations

Otten, Mara; Heuvel–Panhuizen, Marja van den; Veldhuis, Michiel; Boom, Jan; Heinze, Aiso

doi:10.3390/educsci10060163

Cited by 8 publications

(4 citation statements)

References 42 publications

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“…A recent study by Freina et al (2018) found that digital games supported the development and consolidation of visuospatial abilities in students of the last 2 years of the primary school, and such a training would have a positive impact on their mathematics performance. Similar results were obtained by Otten et al (2020) . Fifth-grader students in primary school who worked with the physical balance model more often used advanced algebraic strategies and made a larger improvement in their algebraic reasoning.…”

Section: Introductionsupporting

confidence: 90%

Improving middle school students’ geometry problem solving ability through hands-on experience: An fNIRS study

Shi

Dong²,

Zhao³

et al. 2023

Front. Psychol.

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Hands-on learning is proposed as a prerequisite for mathematics learning in kindergarten and primary school. However, it remains unclear that whether hands-on experience aids understanding of geometry knowledge for middle school students. We also know little about the neural basis underlying the value of hands-on experience in math education. In this study, 40 right-handed Chinese students (20 boys and 20 girls) with different academic levels were selected from 126 seventh-grade students in the same school, who learnt “Axisymmetric of an Isosceles Triangle” in different learning style (hands-on operation vs. video observation). Half of them operated the concrete manipulatives while the other half watched the instructional videos. The learning-test paradigm and functional near-infrared spectroscopy (fNIRS) technique were used to compare the differences in geometry reasoning involved in solving well-structured problems and ill-structured problems. Behavioral results showed that hands-on experience promoted students’ performances of geometry problem-solving. Students with lower academic level were more dependent on hands-on experience than those with higher academic level. The fNIRS results showed that meaningful hands-on experience with concrete manipulatives related to learning contents increased reactivation of the somatosensory association cortex during subsequent reasoning, which helped to improve the problem-solving performance. Hands-on experience also reduced students’ cognitive load during the well-structured problem-solving process. These findings contribute to better understand the value of hands-on experience in geometry learning and the implications for future mathematics classroom practices.

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Section: Introductionsupporting

confidence: 90%

Improving middle school students’ geometry problem solving ability through hands-on experience: An fNIRS study

Shi

Dong²,

Zhao³

et al. 2023

Front. Psychol.

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“…The difficulties dealing with absolute value function graphs show a lack of symbol sense, i.e., a lack of ability in recognizing function families and graph features from the structure of functions [22,29]. In other studies [30,31], the ability to switch from symbolic algebra to geometrical ideas, showing versatile thinking of different representations, which also shows symbol sense behavior, concerns the ability to intertwine between mathematical topics. Taking this finding into account, we recommend further investigation into the relationship between pre-service teachers' ability in drawing absolute value function graphs and their symbol sense ability.…”

Section: Discussion On Absolute Value Inequalitiesmentioning

confidence: 99%

Pre-Service Teachers’ Strategies in Solving Absolute Value Equations and Inequalities

2022

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Many secondary school students have encountered difficulties when dealing with absolute value equations and inequalities. This condition might be brought to higher education, including by pre-service mathematics teachers in teacher training colleges. The difficulties in dealing with absolute value equations and inequalities, which can be observed from solution strategies, indicate the lack of symbol sense. This study aims to investigate strategies that pre-service teachers used while solving absolute value equations and inequalities from the perspective of symbol sense. To investigate this, we conducted a qualitative case study through two written tests followed by interviews involving 36 pre-service mathematics teachers in one of the state universities in Bandung, Indonesia. The results revealed three different solution strategies for solving either absolute value equations or inequalities. Also, difficulties that occurred during the solution processes of equations and inequalities were addressed. We conclude that the symbol sense characteristics are fruitful for interpreting the selection of solution strategies used by pre-service teachers in solving absolute value equations and inequalities.

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“…There are many reasons that could explain the observed differences in students' understanding of equivalence across the countries. For example, classroom instruction could contribute to students' understanding of equivalence, such as feedback, perceptual support, physical experiences with the balance model, use of relational words, use of inequality symbols with the equals sign, support for students' self-explanation, support for students' use of different solution strategies; nonsymbolic instruction (see Alibali et al, 2009Alibali et al, , 2018Bajwa & Perry, 2019;Chesney et al, 2018;Chow & Wehby, 2019;Fyfe et al, 2012;Hattikudur & Alibali, 2010;Otten et al, 2020;Rittle-Johnson, 2006). Moreover, differences in understanding of equivalence across the countries could partly be explained by curricula and their implementation (e.g., Cai et al, 2011;Grouws et al, 2013), the length of an average school day ("School Years around the World," 2017), the differences between parent-related factors such as parents' education and support and expectation from their children (e.g., Ahn & Baek, 2013;Kim & Bang, 2017;Ma et al, 2013;Xu & LeFevre, 2018), and family socioeconomic status (e.g., Hu et al, 2018).…”

Section: Answers To the Research Questionsmentioning

confidence: 99%

Factors associated with children’s understanding of mathematical equivalence: An investigation across six countries.

Şimşek¹,

Xenidou-Dervou²,

Hunter³

et al. 2022

Journal of Educational Psychology

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Many primary school students have difficulties understanding mathematical equivalence with considerably poorer performance in some countries than in others. However, students’ formal understanding of equivalence has significant and long-lasting effects, as it predicts arithmetic and algebra achievement throughout school years. Currently, little is known about the factors influencing students’ understanding of mathematical equivalence particularly across different countries. We have conducted the first large-scale study to explore the factors associated with primary school students’ understanding of mathematical equivalence across six countries (China, England, New Zealand, South Korea, Turkiye, and the United States). Participants were 2,760 primary school students and their teachers (N = 108). Using multilevel structural equation modeling, we found that students’ knowledge of definitions of the equals sign relates to their equation-solving performance. We also found that while teachers’ knowledge of students’ relational strategies does relate to students’ understanding of equivalence, teachers’ knowledge of students’ operational strategies, and the format of arithmetic practice presented in the students’ current year textbooks do not. Using England as the reference country, we found that this pattern was similar across the samples from all the participating countries. Taken together, our findings have important theoretical and practical implications, providing a more complete picture of the individual and classroom-level factors associated with students’ understanding of equivalence.

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Are Physical Experiences with the Balance Model Beneficial for Students’ Algebraic Reasoning? An Evaluation of two Learning Environments for Linear Equations

Cited by 8 publications

References 42 publications

Improving middle school students’ geometry problem solving ability through hands-on experience: An fNIRS study

Improving middle school students’ geometry problem solving ability through hands-on experience: An fNIRS study

Pre-Service Teachers’ Strategies in Solving Absolute Value Equations and Inequalities

Factors associated with children’s understanding of mathematical equivalence: An investigation across six countries.

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