General education placement of students with autism spectrum disorders (ASD) has increased at a rate faster than all other disability categories combined. As more children are diagnosed with ASD and expected to meet the same academic standards as their neurotypical peers, there is a demand for effective educational strategies. Using a…

A problem-solving capstone course for mathematics and mathematics education majors can help majors synthesize material learned in the major, create a basis for lifelong learning in the discipline, develop confidence, and promote interest in graduate study. Such a course may also play a role in departmental assessment of the major. This article…

This research study was specifically concerned with the development, testing, and revision to an instructional theory for studying the mathematical concepts of equivalence and equation solving with multiple representations and multiple tools. Following a design research approach, a collaborative teaching experiment was conducted with a ninth-grade…

This article argues for a shift in how researchers discuss and examine students' uses of representations during their calculus problem solving. An extension of Zazkis, Dubinsky, and Dautermann's (1996) Visualization/Analysis-framework to include physical modes of reasoning is proposed. An example that details how transitions between visual,…

The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers' knowledge. It is aimed at exploring the development of teachers' mathematical and pedagogical conceptions…

The article gives an account of an experiment in which sixty-eight high school students of age 16 - 19 developed spreadsheet applications that simulated fall and projectile motion in the air. The students applied the Euler method to solve the governing differential equations. The aim was to promote STEM to the students and motivate them to study…

Confidence assessment (CA), in which students state alongside each of their answers a confidence level expressing how certain they are, has been employed successfully within higher education. However, it has not been widely explored with school pupils. This study examined how school mathematics pupils (N?=?345) in five different secondary schools…

This article describes how to teach fraction and percentage word problems using a model-drawing strategy. This cognitive strategy places emphasis on explicitly teaching students how to draw a schematic diagram to represent the qualitative relations described in the problem, and how to formulate the solution based on the schematic diagram. The…

In many scientific contexts, students need to be able to use mathematical knowledge in order to engage in scientific reasoning and problem-solving, and their understanding of scientific concepts relies heavily on their ability to understand and use mathematics in often new or unfamiliar contexts. Not only do science students need high levels of…

The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. These kinds of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school, problems are solved by using basic…

The present study investigated (a) whether the perceived cognitive load was different when geometry problems with various levels of configuration comprehension were solved and (b) whether eye movements in comprehending geometry problems showed sources of cognitive loads. In the first investigation, three characteristics of geometry configurations…

This paper investigates the possible influence of attitude on seven Year 11 students' use of a Computer Algebra System (CAS) during a class activity where students could choose to use CAS or pen-and-paper in solving a range of problems. Investigation of anxiety, confidence, liking and usefulness through a survey and interview revealed that these…

This paper reports the findings of research into an educational intervention featuring open-ended mathematical problems situated in "real life" contexts and associated pedagogies. "Money and financial mathematics" is the topic in focus, with tasks termed "financial dilemmas" being trialled by 35 teachers in 16…

Over the past decade, research has shown that problem solving skills and students' achievement in mathematics have been a primary focus for mathematics instruction at all grade levels. Despite this persistent focus on cognitive development and children's thinking processes, some teachers fail to help students use these cognitive…

Math achievement in elementary school is mediated by performance and growth in number sense during kindergarten. The aim of the present study was to test the effectiveness of a targeted small-group number sense intervention for high-risk kindergartners from low-income communities. Children were randomly assigned to 1 of 3 groups (n = 44 in each…