Sources of Differences in Children's Understandings of Mathematical Equality: Comparative Analysis of Teacher Guides and Student Texts in China and the United States

Li, Xiaobao; Ding, Meixia; Capraro, Mary Margaret; Capraro, Robert M.

doi:10.1080/07370000801980845

Cited by 99 publications

(115 citation statements)

References 9 publications

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“…For example, textbook analysis was applied to the distributive property (Ding & Li, 2010), the equal sign (Li, Ding, Capraro, & Capraro, 2008;McNeil et al, 2006), fractions (Charalambous, Delaney, Hsu, & Mesa, 2010), subtraction up to 100 (Van Zanten & Van den Heuvel-Panhuizen, 2014), non-routine problem solving (Kolovou, Van den Heuvel-Panhuizen, & Bakker, 2009;Xin, 2007), and mathematical modeling (Gatabi, Stacey, & Gooya , 2012).…”

Section: Opportunity-to-learn and The Role Of Textbooksmentioning

confidence: 99%

“…Similarly, Stein and Smith (1998) reported that students' lack of prior experience with open-ended tasks leads to difficulties when solving tasks in which the mathematical procedure is implicit. A lack of particular experience is also directly related to a missing OTL in textbooks as shown in the studies by Li et al (2008) and McNeil et al (2006), which revealed that students have difficulties in interpreting the equal sign as a relation because the textbooks they use rarely provide equal signs with operations on both sides. A specific characteristic of context-based tasks that we found missing in the three Indonesian textbooks is the use of incomplete or irrelevant information, which, according to Forman and Steen (2001), and Greer, Verschaffel, and Mukhopadhyay (2007), is crucial for developing students' ability to apply mathematics in real-world problems.…”

Section: Opportunity-to-learn and Students' Difficultiesmentioning

confidence: 99%

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Opportunity-to-learn context-based tasks provided by mathematics textbooks

2015

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Based on the findings of an error analysis revealing that Indonesian ninth-and tenthgraders had difficulties in solving context-based tasks, we investigated the opportunity-to-learn offered by Indonesian textbooks for solving context-based mathematics tasks and the relation of this opportunity-to-learn to students' difficulties in solving these tasks. An analysis framework was developed to investigate the characteristics of tasks in textbooks from four perspectives: the type of context used in tasks, the purpose of context-based tasks, the type of information provided in tasks, and the type of cognitive demands of tasks. With this framework, three Indonesian mathematics textbooks were analyzed. Our analysis showed that only about 10 % of the tasks in the textbooks are context-based tasks. Moreover, at least 85 % of these tasks provide exactly the information needed to solve them and do not leave room for students to select relevant information by themselves. Furthermore, of the context-based tasks, 45 % are reproduction tasks requiring performing routine mathematical procedures, 53 % are connection tasks requiring linking different mathematical curriculum strands, and only 2 % are reflection tasks, which are considered as tasks with the highest level of cognitive demand. A linkage between the findings of the error analysis and the textbook analysis suggests that the lacking opportunity-to-learn in Indonesian mathematics textbooks may cause Indonesian students' difficulties in solving context-based tasks. Based on the results of this study, recommendations are given for improving the opportunities-tolearn to solve context-based tasks as well as for doing further research on this topic.

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Section: Opportunity-to-learn and The Role Of Textbooksmentioning

confidence: 99%

Section: Opportunity-to-learn and Students' Difficultiesmentioning

confidence: 99%

Opportunity-to-learn context-based tasks provided by mathematics textbooks

2015

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“…Students' misunderstanding of the equal sign that has been being studied for more than thirty years shows that students have long had difficulties in relational thinking (Bernstein, 1974;Ginsburg, 1989;Hiebert, 1984;Kieran, 1981;Li et al, 2008). Ability to define the meaning of the symbol of the equal sign is important, and it has been related to some success in algebra and further success in the courses of advanced mathematics (Usiskin, 1995).…”

Section: Introductionmentioning

confidence: 99%

Mathematics Education Students’ Understanding of Equal Sign and Equivalent Equation

Baiduri¹

2015

ASS

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The objective of this paper is to analyse matemathics education students' understanding of the equal sign, their strategies in solving the equivalent equations and the relationship between the two. Data were collected through responses from 167 first year students of mathematics education in University of Muhammadiyah Malang, East Java, Indonesia to the assigned tasks and the data were descriptively analysed using a Chi-square statistics. The results of the analysis showed that their operational understanding of the equal sign is more dominant than their relational conception. In solving equivalent equations, they tended to adopt operational procedures by making solutions, comparisons and substitutions, instead of paying attention to the existing relations in equivalence, called a strategy to recognize equivalence. No significant relations exist between students' understanding of the equal sign and their strategies in solving equivalent equations. Then gender and repondents' origin of areas are also discussed.

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“…The fact that so many learners have difficulty interpreting the equals sign with a relational meaning may be a consequence of the nature of the way learners are taught. In a comparative study, Li et al (2008) found that there was a significant difference between Chinese and US Grade 6 students where a large percentage of US learners appeared to view the equals sign operationally whilst almost none of the Chinese learners did so. When comparing text books they found that the US text books rarely portrayed the equals sign relationally whereas this was very common with the Chinese text books.…”

Section: Equals Signmentioning

confidence: 99%

Designing Educational Software: The Case of Grid Algebra

Hewitt

2016

Digit Exp Math Educ

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To be successful educational software needs to be carefully designed in order to provide constraints and freedoms (Greeno 1994) which relate to its educational aims, restrict or enable learners and teachers to carry out certain actions, and be based upon a clear set of beliefs related to the complex dynamic of teaching and learning. This paper seeks to show the contraints and freedoms built in to the design of Grid Algebra; software which offers an intuitive and novel approach to early algebraic learning, and how they have been informed by a clear set of beliefs and frameworks. The paper shows how the design has taken into consideration known misconceptions that many learners exhibit with early algebra work and how the three frameworks of arbitrary and necessary, subordination and embodied cognition have been fundamental to the design of both the software and some of the activities used with the software. The paper finishes off with considering limitations of the software as well as some strengths that its design offers, and poses questions to consider about the design of this and other resources.

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Sources of Differences in Children's Understandings of Mathematical Equality: Comparative Analysis of Teacher Guides and Student Texts in China and the United States

Cited by 99 publications

References 9 publications

Opportunity-to-learn context-based tasks provided by mathematics textbooks

Opportunity-to-learn context-based tasks provided by mathematics textbooks

Mathematics Education Students’ Understanding of Equal Sign and Equivalent Equation

Designing Educational Software: The Case of Grid Algebra

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