Computational models of learning can be powerful tools to test educational technologies, automate the authoring of instructional software, and advance theories of learning. These mechanistic models of learning, which instantiate computational theories of the learning process, are capable of making predictions about learners' performance in…

The aim of the current study is to investigate the effects of digital teaching materials on 4th graders' academic achievement on fractions subject and attitudes towards mathematics and computers. The study was planned with a pretest and posttest control group design. The participants of the study were 60 students studying in a public elementary…

We analyzed item responses provided by a nationwide sample of 990 in-service U.S. middle grades mathematics teachers to a novel survey focused on fraction arithmetic. The survey targeted four components of reasoning in terms of measured quantities: "Referent units," "Reversibility," "Partitioning and iterating," and…

Background: Within the ambit of the Fourth Industrial Revolution (4IR), the use of technology-based tools within teaching and learning is advancing rapidly at education institutions globally, including the teaching and learning of mathematics. Learners and teachers have challenges with teaching and learning fractions in mathematics. A learner's…

This study investigated relations between the distribution of practice problems in textbooks and students' learning of decimal arithmetic. In Study 1, we analyzed the distributions of decimal arithmetic practice problems that appeared in 3 leading math textbook series in the United States. Similar imbalances in the relative frequencies of decimal…

Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.

To provide effective fractions instruction, teachers need deep understanding of fraction concepts (i.e., content knowledge) and skill in using visual representations of fractions to support student learning (i.e., pedagogical content knowledge); yet, research indicates that many pre- and in-service teachers lack knowledge in both areas. The…

There is anecdotal evidence that many elementary teachers integrate mathematics lessons and art activities by having students first make colorful, rich material that is subsequently used in an instructional activity. However, it is unclear whether such activities effectively promote learning and transfer of mathematical concepts. The goal of the…

Students show deficient understanding on fraction division and supporting that understanding remains a challenge for mathematics educators. This article aims to describe primary students' understanding of partitive fraction division (PFD) and explore ways to support their understanding through the use of sequenced fractions and context-related…

A solid foundation in mathematics is beneficial not only for individuals' concurrent and later academic achievement, but also for future career success and financial stability. Rational number knowledge plays a pivotal role in mathematical success, yet it is often regarded as a challenging area to grasp comprehensively. The dissertation aims to…

Students enrolled in post-secondary developmental mathematics courses hold mathematical misunderstandings that begin before their college careers. Specifically, these students struggle with conceptual understanding of fractions, ratios, and proportions. The Common Core State Standards in Mathematics outline standards for K-12 mathematics…

When designing professional development for math teachers, teacher confidence, math anxiety, and student performance are factors to consider. St. Lucie Public Schools in Florida has seen a decline in performance in fifth-grade mathematics, where students are first asked to showcase their knowledge on operations for fractions. As a curriculum…

This study investigates college students' understanding of arithmetic fraction operations as defined by the Common Core State Standards in grades three through six Mathematics. This study is meant to extend upon an extensive body of research regarding elementary and middle grades students' understanding of fraction operations and see if recognized…

This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Common factors, common multiples, strip diagrams, and double number lines are discussed in this, the third installment in the series. [For the second installment in this series see "Connecting the Dots: Building…

This article provides results from a study examining the impact of a self-regulated strategy development (SRSD) intervention on the fraction calculations of three Grade 5 male students with or at-risk for emotional or behavioral disorders using a multiple-baseline across students, single-case design. The teacher-led SRSD Fractions intervention…