"Probability is a difficult concept to teach, because children and adults find it counterintuitive." This is impetus to consider the detailed planning of a set of lessons with a "mixed", in many senses, group of fourth graders. Can the use of prior experience, and the knowledge associated with that experience, make probability a concept that is…

Learners are all different and teachers are all different, so why do we often ignore this reality when trying to explain, or demystify, some aspect of mathematics in the classroom? Enabling learning can be challenging, demanding of creativity, and needy of alternatives if understanding is the real goal. Here the authors offer ideas that are aimed…

In this article, we describe how using prediction during instruction can create learning opportunities to enhance the understanding and doing of mathematics. In doing so, we characterize the nature of the predictions students made and the levels of sophistication in students' reasoning within a middle school algebra context. In this study, when…

Teachers have used graphic organizers successfully in teaching the writing process. This paper describes graphic organizers and their potential mathematics benefits for both students and teachers, elucidates a specific graphic organizer adaptation for mathematical problem solving, and discusses results using the "four-corners-and-a-diamond"…

Twenty middle grades students were interviewed to gain insights into their reasoning about problem-solving strategies using a Problem Solving Justification Scheme as our theoretical lens and the basis for our analysis. The scheme was modified from the work of Harel and Sowder (1998) making it more broadly applicable and accounting for research…

The topic of the magic knight's tour, discussed by Martin Gardner in one of his books, is here brought up to date in the light of modern computer discoveries.

This study examines whether creating a mathematics-based digital story increases pre-service teachers' understanding of the problem solving process, the relationship among visual, auditory and verbal representation in critical thinking/problem solving in mathematics. Survey results indicated that pre-service teachers were unfamiliar with the uses…

Mathematical representation is an important skill in mathematics learning that enables students to interpret and solve problems with ease. However, building confidence in such a skill can be difficult for some students, especially for those who lack self-motivation skills. Therefore, this study examines the effects of the think-talk-write strategy…

Collaborative problem-solving in the classroom is a student-centred pedagogical practice that looks to improve learning. However, collaboration does not occur spontaneously; instead it needs to be guided by appropriate scaffolding. In this study we explore whether a script that explicitly incorporates constructing arguments in collaborative…

The senior school Mathematics syllabus is often restricted to the study of single variable differential equations of the first order. Unfortunately most real life examples do not follow such types of relations. In addition, very few differential equations in real life have exact solutions that can be expressed in finite terms. Even if the solution…

During Mathematics Teaching Course-I (MT-I), the author was given the opportunity to teach a primary mathematics class at a Government school in Karachi, Pakistan while on teaching practice. The author was lucky to be able to share the lesson planning with a friend, and they found the sharing of ideas a supportive process. The focus of the lesson…

This qualitative study considers middle grades mathematics teachers' reasoning about drawn representations of fractions and decimals. We analyzed teachers' strategies based on their response to multiple-choice tasks that required analysis of drawn representations. We found that teachers' flexibility with referent units played a significant role in…

In this article, the authors discuss how acknowledging and embracing that the sample space is one of many ways to partition the set of all possible outcomes impacts the teaching and learning of sample space and probability. After recounting an exchange surrounding two viable answers to a probability question, the authors detail how developments…

The purpose of this study was to provide preliminary results on the use of schema-based strategy instruction to teach addition and subtraction word problem solving to a fourth grade student with autism. The student was taught to use schematic diagrams to solve three types of addition and subtraction word problems. A multiple probes across…

There is continuing interest in the identification of student and instructional factors associated with the mathematics achievement of students in Japan. The Trends in International Mathematics and Science Study (TIMSS) assessments have provided opportunities to examine factors associated with mathematics achievement. The purpose of this study was…