Background: A key learning outcome in problem-solving domains is the development of procedural flexibility, where learners know multiple procedures and use them appropriately to solve a range of problems (e.g., Verschaffel, Luwel, Torbeyns, & Van Dooren, 2009). However, students often fail to become flexible problem solvers in mathematics. To…

Blackwell et al. (Child Development 78(1):246-263, 2007) tested a motivational model of achievement in which an incremental theory of intelligence leads to learning goals and positive effort beliefs, which leads to fewer ability-based, helpless attributions, and more positive strategies, which leads to improved grades. In the present study, we…

Visualization is mostly despised although it complements and--sometimes--guides the analytical process. This study mainly investigates teachers' preferences concerning the use of the visualization method and determines the extent to which they encourage their students to make use of it within the problem-solving process. This study was conducted…

Mathematics is an important educational component for students with visual impairments, and technology to support the access to and success of students with visual impairments in mathematics is essential. However, little research exists. This particular paper explores one aspect of technology and mathematics education for students with visual…

In a recent paper by Wilamowsky et al. [6], an intuitive proof of the area of the circle dating back to the twelfth century was presented. They discuss challenges made to this proof and offer simple rebuttals to these challenges. The alternative solution presented by them is simple and elegant and can be explained rather easily to non-mathematics…

The Common Core State Standards (CCSS) for Mathematics are organized by grade level in Grades K-8. At the high school level, the standards are organized by conceptual category (number and quantity, algebra, functions, geometry, modeling and probability and statistics), showing the body of knowledge students should learn in each category to be…

This study seeks to demonstrate a method for treatment effect estimation in a multisite observational study where the treatment is highly selective and the assignment mechanism varies across sites. The method is demonstrated by addressing three primary research questions about the effect of 8th grade algebra: (1) For students who take algebra in…

This quasi-experimental study focused on the initiatives undertaken by a community college's Academic Skills Enhancement Program (ASEP) commonly known as the Developmental Education Department to find an alternative delivery method to aid its students in learning developmental mathematics. Moreover, this study (1) conducted a comparative…

To implement current reforms regarding proof and reasoning in secondary school mathematics successfully, pre-service secondary mathematics teachers must have adequate understandings of concepts across mathematical domains for their future teaching. This paper examined the strategies that pre-service secondary mathematics teachers had for…

Dynamic/interactive graphing applets can be used to supplement standard computer algebra systems such as Maple, Mathematica, Derive, or TI calculators, in courses such as Calculus, Differential Equations, and Dynamical Systems. The addition of this type of software can lead to discovery learning, with students developing their own conjectures, and…

The purpose of this study was to investigate the pre-service teachers' conceptions about the limit of same partial functions given in the form of both graphical and symbolic, the misconception that the pre-service teachers have the concept of limit, and whether there were any differences between pre-service teachers' algebraic performance and…

This article describes a laboratory module on Fourier series and Gibbs phenomenon which was undertaken by 32 Year 12 students. It shows how the use of CAS played the role of an "amplifier" by making higher level mathematical concepts accessible to students of year 12. Using Mathematica students were able to visualise Fourier series of…

An online testing system developed for entry-skills testing of first-year university students in algebra and calculus is described. The system combines the open-source computer algebra system "Maxima" with computer scripts to parse student answers, which are entered using standard mathematical notation and conventions. The answers can…

This article describes the impact of starting with gases in an introductory chemistry course at a community college. Students in the author's class frequently are very weak in algebra skills, and this has a cumulative impact over time that culminates in student struggles when moles and reaction stoichiometry are discussed. The rationale behind…

Linear algebra has become one of the most useful fields of mathematics since last decade, yet students still have trouble seeing the connection between some of the abstract concepts and real-world applications. In this article, we propose the use of thought-provoking questions in lesson designs to allow two-way communications between instructors…