In this study we investigated the development of 245 kindergarteners' mathematics problem solving (MPS) at two time points within 7 months using a cognitive diagnostic test, which measured three cognitive components (mathematical knowledge and skills, semantic understanding, and quantitative reasoning) with eleven cognitive attributes. The effects…

In this study, it was aimed to determine the geometry problem posing performance of eighth grade students in different problem posing situations. For this purpose, the convergent parallel mixed model accepted as one of the mixed method designs was preferred. The participants consisted of 151 eighth grade students from the same school. The…

The balance model is often used for teaching linear equation solving. Little research has investigated the influence of various representations of this model on students' learning outcomes. In this quasi-experimental study, we examined the effects of two learning environments with balance models on primary school students' reasoning related to…

Educational literature indicates that solving open mathematical tasks (OTs) is a powerful creativity-directed activity. However, the use of these tasks with school students on an everyday basis is extremely limited. To promote implementation of OTs in middle school, we manage a large-scale R&D project, Math-Key, which makes open mathematical…

Assistive technology supports students with disabilities in a variety of ways, including serving as a means of instruction. Although virtual manipulatives can serve as an assistive technology tool, limited research examines virtual manipulatives in-and-of-themselves to support students with disabilities. This study explored app-based virtual…

Many secondary students with specific learning disabilities (SLD) struggle with mathematics problem solving. When students with SLD are taught to use effective problem-solving strategies, their ability to solve mathematics word problems improves. The purpose of this article is to provide a guide for secondary teachers to implement self-regulated…

One of the most fundamental strategies in mathematics instruction is practice problems because teachers know that practicing a skill improves performance. At the same time, teachers also know that just because students can correctly answer practice problems does not mean they fully understand the concept or how to apply a formula--especially not…

The aim of this study was to examine 6th-grade students' mathematical abstraction processes related to the concept of variable by using the teaching experiment method and to reveal their learning trajectories in the context of the RBC+C model. A teaching experiment was administered to a class of 29 middle school students for 3 weeks. Observations,…

This paper studies students engagement in e-learning environments in which students work independently and solve problems without external supervision. We propose a new method to infer engagement patterns of users in such self-directed environments. We view engagement as a continuous process in time, measured along chosen axes that are derived…

Creating an enjoyable atmosphere and fostering creativity are the two most required components in learning mathematics. Hence, creativity would enable students to formulate something new. In addition, creativity is one of the most important and highest competencies in Bloom's latest taxonomy. Furthermore, it is necessary to be possessed by…

Elementary standards include multiplication of single-digit numbers and students advance to solve complex problems and demonstrate procedural fluency in algorithms. The ability to illustrate procedural fluency in algorithms is dependent on the development of understanding and reasoning in multiplication. Development of multiplicative reasoning…

How can we design mathematical lessons that spark student interest? To answer this, we analyzed teacher-designed and enacted lessons that students described as interesting for how the content unfolded. When compared to those the same students describe as uninteresting, multiple distinguishing characteristics are evident, such as the presence of…

We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions. This method does not involve differentiation or solving linear equations for obtaining the unknown partial fraction coefficients, which is very suitable for either…

Building students' understanding of cardinality is fundamental for working with numbers and operations. Without these early mathematical foundations in place, students will fall behind. Consequently, it is imperative to build on students' strengths to address their weaknesses with the notion of cardinality.

This paper presents some critical perspectives regarding pedagogical approaches to the method of reversing the order of integration in double integrals from prevailing educational literature on multivariable calculus. First, we question the message found in popular textbooks that the traditional process of reversing the order of integration is…