The authors explore how one teacher uses play and enacts the Effective Teaching Practices as a way to increase student engagement and autonomy and to meet learning goals when teaching mathematics with interactive simulations.

Asking effective questions has been considered to be one of the most important indicators of good teaching since questioning is an important instructional tool and the ability to ask effective questions requires sophisticated pedagogical reasoning. Teachers can facilitate students' higher-level thinking through effective questions. However,…

A Number Talk is a brief activity (10-15 minutes in length) that is designed to support students' mathematical sense making and promote flexible thinking. During a Number Talk, students engage in mental computations. Number Talks help students do the following: (1) Develop number sense focused on making sense of quantity and mathematical…

Background: Prior studies on fraction magnitude understanding focused mainly on students with relatively sufficient formal instruction on fractions whose fraction magnitude understanding is relatively mature. Aim: This study fills a research gap by investigating fraction magnitude understanding in the early stages of fraction instruction. It…

The purpose of this study is to show the differences in problem-solving ability between first-year University students who received culture-based contextual learning and conventional learning. This research is a quantitative research using quasi-experimental research design. Samples were the First-year students of mathematics education department;…

This study explored the design and implementation of the Cover-up and Un-cover games, two manipulative-based fraction games, in 14 fifth-grade classrooms. We examined how the fraction concepts were integrated into the game design and explored the nature of teacher-student interactions during games using lesson videos. Our examination showed that…

A considerable amount of evidence supports the value of teaching physical education (PE) and the Common Core in unison. This study investigated mathematics concepts taught during fitness segments in elementary PE. Specifically, we studied student perceptions about linking PE activities and mathematics. We wanted to determine if math concepts could…

Nationally, student performance in math has been flat, and achievement gaps persist. And with a growing economy driven by industries in the science, technology, engineering, and math (STEM) fields, educators are tasked with instilling interest in and preparing students for college studies and careers that will supply these in-demand jobs. Now,…

Although national interest has been focused on increasing STEM graduates, calculus courses still pose a challenge for most STEM major students. As recent statistics show, only half of the students are successful in calculus courses. Many times, students in these courses do not see the relevancy of the material to their future careers and this…

This work is an exploration of upper elementary students' sense making around four conventional representations of function: equations with algebraic notation, Cartesian graphs, function tables, and natural language. The cornerstone to the empirical work is a task called the Function Puzzle, where students are given 16 cards representing four…

In this study I explore the construction of algebraic structure sense through engaging students in task sequences designed to elicit the development of competencies related to this understanding. The primary task-design principle employed in this study is strategic variation, in which certain components of items within task sequences vary while…

Practicing teachers as well as researchers, mathematicians, and teacher educators have offered opinions and theoretical critiques of the multiple models used to teach integer arithmetic. Few studies, however, have investigated what students learn with models or empirically compared affordances and constraints of integer models. This led me to…

The present study evaluated the effects and interaction of item set size and instructional time on students' fluency growth rates with multiplication facts over time when using an Explicit Timing intervention. The first goal was to determine an interaction between set size and instructional time across time that would influence the fluency growth…

This book is inspired by Roger E. Howe's contributions to the international communities of mathematics and mathematics education. Renowned for his research contributions in the fields of representation theory, automorphic forms, harmonic analysis, and invariant theory, Dr. Howe has also fundamentally deepened our understanding of the mathematics…

This project tested the effects of adding instruction of trios of children in patterning, mathematics, early literacy, or social studies to ongoing instruction in kindergartens. Children were randomly assigned to trios which were randomly assigned to one of four kinds of instruction. A quarter of the trios received patterning instruction with a…