The aim of the study was to determine and compare 7th, 8th, and 9th grades students' level of use and interpret the literal symbols. In addition, students' responses to questions that require use of different roles of literal symbol were examined to identify the errors. For this purpose, Chelsea Diagnostics Algebra test developed by The Concepts…

Learning to write formal mathematical proofs presents a major challenge to undergraduates. Students who have succeeded in algorithm-intensive courses such as calculus often find the abstract logic and nonprocedural nature of proof writing to be technically difficult, ambiguous and "filled" with potential errors and misconceptions. This…

In this article, Garcia and Davis describe problem analysis as the process of examining a given mathematics exercise to find ways in which the problem can be modified and extended to create a richer learning opportunity for students. Students are often reluctant to attempt what they perceive to be higher-order thinking problems, but problem…

Complex numbers are essential in many fields of engineering, but students often fail to have a natural insight of them. We present a learning object for the study of complex polynomials that graphically shows that any complex polynomials has a root and, furthermore, is useful to find the approximate roots of a complex polynomial. Moreover, we…

The primary aim of this article is to bring the work of Deleuze and Guattari to bear on the question of communication in the classroom. I focus on the mathematics classroom, where agency and subjectivity are highly regulated by the rituals of the discipline, and where neoliberal psychological frameworks continue to dominate theories of teaching…

In 2008, president-elect Barack Obama declared that preparing the nation for the "21st-century economy" required making "math and science education a national priority." Encouraging more students to take advanced classes seems laudable, but concerns have arisen about the ability of many students to complete such course work…

Students who engage in mathematical arguments in classrooms take part in an important practice involving reasoning and justification. As a mathematical practice, argumentation involves using both conceptual and procedural reasoning to justify a claim. Even though argumentation can occur in discussions where one asserts and defends their claim…

This paper describes the implementation of the online and f2f summer algebra courses that were delivered in summers 2011 and 2012. These data will be used to frame the impact results presented in an earlier paper. In particular, the paper will provide a detailed picture of how the online course was structured and the types of supports provided to…

Over decades and across grade levels, deaf/hard-of-hearing (d/hh) student performance in mathematics has shown a gap in achievement. It is unclear, however, exactly when this gap begins to emerge and in what areas. This study describes preschool d/hh children's knowledge of early mathematics concepts. Both standardized and nonstandardized measures…

Introduction: In this study, the effectiveness of two different interventions was investigated. The effects of a concrete abstract intervention and a regular method of teaching intervention were compared. Both interventions were designed in line with the specifications of classical principles of instructional design for learning mathematics in the…

This study examined 361 Chinese and 345 Singaporean sixth-grade students' performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies…

The complementary use of the theories of instrumental genesis and shifts of attention enabled me to obtain insights into students' understandings of the concepts of eigenvector and eigenvalue. My analysis suggests that the use of different dragging modalities can provide evidence of shifts in structure of a student's attention and consequently can…

Pattern blocks are inexpensive wooden, foam, or plastic manipulatives developed in the 1960s to help students build an understanding of shapes, proportions, equivalence, and fractions (EDC 1968). The colorful collection of basic shapes in classic pattern block kits affords opportunities for amazing puzzle-like problem-solving tasks and for…

This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.

At a time when the debate continues over whether homework is overused, optional, or essential or favors well-off students over those with little home support, teachers must understand ways in which effective homework strategies can help narrow the achievement gap. Vatterott (2009, p. 94) argues convincingly that the "old paradigm" of…