With the Common Core State Standards' emphasis on transformations, teachers need a variety of approaches to increase student understanding. Teaching matrix transformations by focusing on row vectors gives students tools to create matrices to perform transformations. This empowerment opens many doors: Students are able to create the matrices for…

Over the course of her teaching career, this author learned to create environments in which both the teacher and learners embrace understanding. She introduced new concepts with a general question or word problem and encouraged students to find solutions with a strategy of their choice. By using this instructional method, she allowed her students…

This paper focuses on children's number fact knowledge from a study that explored the impact of using multiplication and division contexts for developing number understanding with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. After a series of focused lessons, children's knowledge of number facts, including…

Many rules taught in mathematics classrooms "expire" when students develop knowledge that is more sophisticated, such as using new number systems. For example, in elementary grades, students are sometimes taught that "addition makes bigger" or "subtraction makes smaller" when learning to compute with whole numbers,…

Instructional applications (apps) are educational software programs that can be accessed via mobile technologies (e.g., iPad, smartphone) and used to help students acquire various academic skills, including mathematics. Although research suggests that app-based instruction (AI) can be effective, there is a paucity of research comparing AI, to…

For centuries, the basic operations of school mathematics have been identified as addition, subtraction, multiplication, and division. Notably, these operations are "basic," not because they are foundational to mathematics knowledge, but because they were vital to a newly industrialized and market-driven economy several hundred years…

Students with Autism Spectrum Disorders (ASD) have unique educational needs. The concrete representational abstract (CRA) instructional sequence has been shown effective in teaching students with mathematical difficulties. The purpose of this study was to examine the effects of the CRA sequence in teaching students with ASD. A multiple baseline…

This study aimed to create a constructivist learning environment wherein third-grade students talk to problem solve, which is different from traditional approaches to math learning. The study focused on the group talk and discussions to understand the students' actions and interactions during the process of problem-solving. Fifteen students and…

South Africa participated in TIMSS from 1995 to 2015. Over these two decades, some positive changes have been reported on the aggregated mathematics performance patterns of South African learners. This paper focuses on the achievement patterns of South Africa's high-performing Grade 9 learners (n = 3378) in comparison with similar subsamples of…

There are 3 questions that will be answered in this study, namely (1) what are the contexts that can be used to introduce the meaning of multiplication of two fractions and to find the result of multiplying two fractions, (2) how to use these contexts to help students construct the understanding of the meaning of multiplication of two fractions…

"That was the day I decided I was bad at math." Countless times, preservice and in-service teachers make statements such as this after sharing vivid memories of learning multiplication facts. Timed tests; public competitive games, such as Around the World; and visible displays of who has and has not mastered groups of facts still…

In this article, Lorraine Jacob and Joanne Mulligan discuss how arrays can be used to promote students' early learning in relation to multiplication and division. They provide examples of activities that can be used from Foundation to Year 5.

Several studies on learning mathematics for rural area's student indicate that students have difficulty in understanding the concept of division operation. Students are more likely to be introduced by the use of the formula without involving the concept itself and learning division separate the concrete situation of learning process. This…

This study examined 361 Chinese and 345 Singaporean sixth-grade students' performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies…

The aim of the study is to examine prospective mathematics teachers' pedagogical content knowledge in terms of knowledge of understanding students and knowledge of instructional strategies which are the subcomponents of pedagogical content knowledge. The participants of this research consist of 98 prospective teachers who are studying in two…