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In this note we describe the mathematics that emerges from the construction of an origami box. We first construct a simple origami box from two rectangular sheets and then discuss some of the mathematical questions that arise in the context of algebra, geometry and calculus. [ABSTRACT FROM AUTHOR]

This study reports the academic benefits of peer tutoring in algebra for middle school students. A total of 380 students enrolled in grades 7th and 8th participated in the study. Two peer tutoring sessions took place during each week (10 weeks). Interactions between peers lasted 20 to 25 minutes for each session. The typology of tutoring was fixed and same-age. A pretest posttest with control group design was used. Statistical significant improvements were reported in the academic achievement variable after the implementation of the peer tutoring program for 7th and 8th grade courses separately and altogether. Over 87% of the students in the experimental group improved their marks. The overall effect size for the experience was reported to be medium (Hedge's g = 0.48). The main conclusion of this study is that fixed and same-age peer tutoring in algebra may be very beneficial for middle school students. [ABSTRACT FROM AUTHOR]

In this paper, we highlight examples from school mathematics in which invariance did not receive the attention it deserves. We describe how problems related to invariance stimulated the interest of both teachers and students. In school mathematics, invariance is of particular relevance in teaching and learning geometry. When permitted change leaves some relationships or properties invariant, these properties prove to be inherently interesting to teachers and students. [ABSTRACT FROM PUBLISHER]

There is a growing consensus that algebra is an important aspect of mathematics teaching and learning and several abilities are required in order students to have successful performance in algebra. The present study uses insights from the domain of psychology to enrich what is currently known in the domain of mathematics education about the relationship of algebraic thinking with abilities involved in fundamental cognitive processes. In total, 190 students between the ages of 13–17 years old were tested through two tests. The first test addressed four types of cognitive systems which are responsible for the representation and processing of different types of relations in the environment: the spatial-imaginal, the causal-experimental, the qualitative-analytic and the verbal-propositional. The second test addressed algebraic thinking. The results support the key role of the four types of cognitive processes in students’ algebraic thinking. The results also suggest that abilities involved in the four types of cognitive processes predict algebraic thinking abilities, irrespective of the age of the students. [ABSTRACT FROM PUBLISHER]

This paper contains a discussion of how the concept of critical aspects and the principle of compositionality can provide a powerful tool to analyse and understand the communications that occur in the classroom. It is grounded in data collected in a longitudinal study. The content chosen is algebra. It is argued that the critical aspects and the principle of compositionality should be considered as a methodological principle that describes how communication in the classroom should be designed. Here, I present the power of using variation theory whose main purpose is to generate an understanding of critical aspects and compositionality in practice. [ABSTRACT FROM AUTHOR]

This note presents demonstrations of quadratic expressions that come about when particular problems are posed with respect to matchsticks that form regular triangles, squares, pentagons and so on. Usually when such ‘matchstick’ problems are used as ways to foster algebraic thinking, the expressions for the number of matchstick quantities are linear and not quadratic. It will be shown that a pedagogy of ‘summing all the matchsticks’ is central to the emergence of quadratic expressions. This pedagogy involves generational and transformational activities which are considered as some of the main activities of algebra. Key elements to these activities are processes such as recognizing and extending patterns, and specializing and generalizing particular functional relationships. Implications of these processes in terms of algebraic thinking are considered. [ABSTRACT FROM PUBLISHER]

Although research has shown that self-efficacy beliefs predict academic achievement across all academic subjects and levels, little is known about the effect of using spreadsheets on self-efficacy beliefs in mathematics. This study is an investigation of the effect of instruction that includes spreadsheet-based purposeful activities on secondary school students' self-efficacy beliefs for algebra. The context of the study is a 10th grade mathematics course in a public secondary school. Analysis of the data indicated that students who received spread-sheet-based instruction had significantly higher self-efficacy for algebra than those who received conventional instruction. [ABSTRACT FROM AUTHOR]

This note presents demonstrations of mathematics that emerges when problems are posed with respect to a combined 12 × 12 multiplication table showing multiplier and multiplicand. Through processes such as recognizing and extending patterns, specializing and generalizing particular functional relationships between the diagonal and row sequences are compressed. Insights obtained from the various methods can be used to deepen teachers' and students' understandings of possible ways to bridge arithmetic and algebra. [ABSTRACT FROM AUTHOR]

In this article, the author explores the "algebra for all" issue to raise awareness about the many facets of this dilemma facing educators at the middle and high school levels. She discusses both sides of this controversial issue, especially regarding its impact on students' futures relative to higher education and employment. The author concludes that unless dramatic reform occurs in the delivery of algebra so that all students benefit from such instruction, students must make the decision to take algebra based on individual needs, interests, and desires. [ABSTRACT FROM AUTHOR]

ABSTRACT: This article presents essential principles for mathematics instruction for students with disabilities and those who are at risk for school failure. These students have great difficulty in applying algorithmic knowledge to solve problems and even greater difficulty with abstract problem solving associated with higher level mathematics. A procedural and cognitive model of problem solving at the algebraic level is presented. [ABSTRACT FROM AUTHOR]

Much of the neuroimaging research has focused on how mathematical operations are performed. Although this body of research has provided insight for the refinement of pedagogy, there are very few neuroimaging studies on how mathematical operations should be taught. In this article, we describe the teaching of algebra in Singapore schools and the imperatives that led us to develop two neuroimaging studies that examined questions of curricular concerns. One of the challenges was to condense issues from classrooms into tasks suitable for neuroimaging studies. Another challenge, not particular to the neuroimaging method, was to draw suitable inferences from the findings and translate them into pedagogical practices. We describe our efforts and outline some continuing challenges. [ABSTRACT FROM AUTHOR]