This article describes what is often referred to as the dog, beetle, mice, ant, or turtle problem. Solutions to this problem exist, some being variations of each other, which involve mathematics of a wide range of complexity. Herein, the authors describe the intuitive solution and the calculus solution and then offer a completely new solution…

This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage…

Conversations as moments for interpersonal and intimate turning round of ideas for the purpose of growth are well-defined within curriculum inquiry. Interactions among grade 12 students in this study demonstrate the possibility of learning to learn mathematics through conversation. Attending to opportunities for learning-based conversations,…

This study aims to develop a realistic mathematics learning model using cooperative strategy. This study applies research and development approach conducted at Junior High School "Laboratorium," State University of Malang. The implementation of this model is conducted through five stages: 1) previous study phase; 2) model planning phase;…

Teachers' critical thinking skills are essential for fostering the development of the same skills in their students. To demonstrate how teachers' ability to examine solutions critically can be developed and supported, we analyse a classroom activity performed by a group of pre-service secondary school mathematics teachers (N = 37) who were asked:…

While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts,…

When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…

"Mathematical modeling of the physical world should be the central theme of physics instruction" (Hestenes 1987). Science teachers know this, but because of standardized state testing, many math teachers and some science teachers feel the need to focus on memorizing facts that will be on a multiple-choice test (Volante 2004). As a…

Problem Statement: So far, there have been many problems in maths education in the world; negative attitudes and low self-efficacy perceptions towards mathematics are the two important reasons for these problems. Though there are several studies regarding the topic, choosing random students from secondary school for the sample group of the study…

Noting the benefits of mathematics in students' future educational attainment and labor market success, there is considerable interest in high school requirements in terms of course-taking in mathematics at the national, state, and school district level. Previous research indicates that taking advanced math courses in high school leads to positive…

It is generally said in Pakistani classrooms that students face problems in recalling facts in mathematics and it brings hardship for students to understand mathematics meaningfully. Thus, most of the concepts and procedures of mathematics are difficult to understand for many students because rules and algorithms dominate. The purpose is to…

This study on the mental solving of systems of linear equations is part of a larger research program, aimed to gain a better understanding of the potential of mental mathematics activities with topics/objects other than numbers. Through outlining the study details and the activities engaged with, the paper reports on the variety of strategies…

This paper explores teaching mathematics for spatial justice (Soja, 2010), as an extension of teaching mathematics for social justice (Gutstein, 2006). The study is contextualized in a 10-session curricular module focused on the spatial justice of a city's two-tiered system of personal finance institutions (mainstream vs. alternative), piloted…

This study investigated the effects of test-wiseness training in Mathematics on adolescent secondary school students' test anxiety. The research study adopted for the study was an experimental research that involved pretest, posttest and control groups design. One hundred and twenty (120) adolescent senior secondary school class three students of…

We examined the use of balance and inverse methods in equation solving. The main difference between the balance and inverse methods lies in the operational line (e.g. +2 on both sides vs -2 becomes +2). Differential element interactivity favours the inverse method because the interaction between elements occurs on both sides of the equation for…