Learning the concept of fractions is among the most challenging topics in school mathematics. One of the main sources of difficulties in learning fractions is related to "natural number bias" (Van Hoof, Verschaffel & Van Dooren, 2015). Applying properties of the natural numbers incorrectly in situations involving rational numbers can…

The goal of the paper is to pay attention to some important techniques and approaches including adequate designations as a tool for unambiguous understanding and a key to success in solving problems, vivid visual images as a mnemonic techniques, and special formulas as a universal tool for solving typical problems, when teaching medical students…

In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore- and junior-level students' reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved…

The current study was conducted with the goal of helping to address the research gap of improving preservice teachers' pedagogical knowledge about probability by investigating how preservice teachers explored concepts of probability during aleatoric music composition, as well as their contemplation process during follow-up reflections focused on…

As the number of independent tosses of a fair coin grows, the rates of heads and tails tend to equality. This is misinterpreted by many students as being true also for the absolute numbers of the two outcomes, which, conversely, depart unboundedly from each other in the process. Eradicating that misconception, as by coin-tossing experiments,…

We explore the transition from school to university through a commognitive (Sfard 2008) analysis of twenty-two students' examination scripts from the end of year examination of a first year, year-long module on Sets, Numbers, Proofs and Probability in a UK mathematics department. Our analysis of the scripts relies on a preliminary analysis of the…

Many view mathematics as a rich and wonderfully elaborate game. In turn, games can be used to illustrate mathematical ideas. Fibber's Dice, an adaptation of the game Liar's Dice, is a fast-paced game that rewards gutsy moves and favors the underdog. It also brings to life concepts arising in the study of probability. In particular, Fibber's Dice…

This study is motivated by the desire to address some of the enormous challenges faced by the students as well as the lecturer in fulfilling their respective expectations and duties demanded by the process of learning--teaching of mathematics and statistics within the framework of the constraining schedules laid down by the academic institutions…

The theme of this year's conference is "Sin Fronteras: Questioning Borders with(in) Mathematics Education." This theme is intended to encourage research presentations, discussion, and reflection on the variety of borders within mathematics education, as well as those that might be probed, challenged, explained, enhanced and/or…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

In the present research, we evaluated the effectiveness of a multi-year professional development program in mathematics for elementary teachers. Each year the program focused on a different domain of mathematics. We found the program increased teachers' knowledge of (a) number and operations, (b) measurement and geometry, and (c) probability and…

The purpose of this causal-comparative study was to examine whether differences exist in the mathematics achievement of fifth grade gifted students based on the instructional delivery model used for mathematics instruction, cluster or collaborative, as defined by the Georgia Department of Education. The content area of mathematics, an area…

This second edition of the bestselling book "The Young Child and Mathematics" reflects recent developments in math education in a wealth of vignettes from classrooms, activity ideas, and strategies for teaching young children about math processes and concepts. Using standards and guidelines from the National Council of Teachers of Mathematics…

This paper summarises part of a longitudinal study to investigate the possibility of establishing an Index that would indicate the appropriate starting point for instruction for students entering high school and reports on the first group of students to sit the Index tests in 2005, comparing the predictive nature of the tests with other state and…

The authors describe a collection of dynamic interactive simulations for teaching and learning most of the important ideas and techniques of introductory statistics and probability. The modules cover such topics as randomness, simulations of probability experiments such as coin flipping, dice rolling and general binomial experiments, a simulation…