Understanding how students learn is important for both researchers and teachers. In terms of mathematics, constructing a new mathematical structure depends on conceptual understanding and connection with previous construct and they needs to be consolidated. A construct can be consolidated when the construct is recognized and used in the further…

In this article, the authors summarize results from 5 randomized controlled trials assessing the effects of intervention to improve the fraction performance of fourth-grade students at risk for difficulty in learning about fractions. The authors begin by explaining the importance of competence with fractions and why an instructional focus on…

The traditional method of teaching math--showing students how to do a procedure, then assigning problems that require them to use that exact procedure--leads to adults who don't know how to approach problems that don't look like those in their math book. Seeley describes an alternative teaching method (upside-down teaching) in which teachers give…

Measurement is an important component of K-grade 12 mathematics curricula. The concepts of area and perimeter of polygons are first introduced in third grade and serve as the basis for teaching in the upper grades. Without a strong understanding of measurement, students will struggle to meaningfully grasp three-dimensional measurement concepts…

In this descriptive study, the goal was to determine teachers' preferred pedagogical methods and techniques in mathematics. Qualitative research methods were employed, primarily case studies. 40 teachers were randomly chosen from various secondary schools in Kirsehir during the 2015-2016 educational terms, and data were gathered via…

In this study, we investigated how Grade 3 and 4 students' organizational structure for volume units develops through repeated experiences with a virtual manipulative for building prisms. Our data consist of taped clinical interviews within a micro-genetic experiment. We report on student strategy development using a virtual manipulative for…

Amid the implementation of new curriculum standard regarding statistics and new recommendations for preservice secondary mathematics teachers [PSMTs] to teach statistics, there is a need to examine the current state of PSMTs' common statistical knowledge. This study reports on the statistical knowledge 217 PSMTs from a purposeful sample of 18…

There is increasing realization that mathematics-related self-efficacy expectations are a strong predictor of an array of significant mathematics outcomes. It is also evident that the curricular practice in schools largely neglects development of a student understanding in the unique language of mathematics. Consequently, this study probes how…

The purpose of this study was to understand the relationship between teacher discourse around social norms, student mathematical roles, and student mathematical explanations in the classroom. Mathematical explanations are important for learning mathematics and professional organizations encourage their use in the classroom. This study sought to…

It is known that difficulties are often experienced in conceptual learning of mathematics, which is an abstract lesson. For this reason, it is difficult for students to conceptually learn inequalities, one of the difficult subjects of mathematics. The aim of this study is to investigate the effect of dialogic teaching to overcome the general…

The paper reports a research study aimed at investigating the appeal and pedagogical efficacy of animated teaching avatars. Specifically, the goal of the study was to determine whether animated characters could be effective and engaging teachers in the context of undergraduate surveying mathematics. The study included two forms of evaluation:…

This study focuses on how prospective teachers learn about students' mathematical thinking when (1) anticipating secondary students' answers reflecting different characteristics of understanding, and (2) propose new activities in relation to the classification of quadrilaterals. The data were collected from forty-eight prospective secondary school…

Are there differential benefits of training sequential number knowledge versus spatial skills for children's numerical and spatial performance? Three- to five-year-old children (N = 84) participated in 1 session of either sequential training (e.g., what comes before and after the number 5?) or non-numerical spatial training (i.e., decomposition of…

The study presents an introductory idea of using mathematical averages as a tool for enriching mathematical problem solving. Throughout students' activities, a research was conducted on their ability to solve mathematical problems, and how to cope with a variety of mathematical tasks, in a variety of ways, using the skills, tools and experiences…

Interesting and engaging mathematics problems can come from anywhere. Sometimes great problems arise from interesting contexts. At other times, interesting problems arise from asking "what if" questions while appreciating the structure and beauty of mathematics. The intriguing problem described in this article resulted from the second…