There is a large body of research on how to improve student learning through active learning and metacognition. However, without well-structured guidelines, students do not tend to actively engage with the taught material, peers, and the instructor at a desirable metacognitive level (Deslauriers et al., 2019). To address this problem, a…

We previously (Gantt et al., 2023; Paoletti et al., 2021) identified items from the publicly released TIMSS 2011 assessments that had potential for students to employ covariational reasoning as a solution strategy. In this report, we explore the extent to which fourth-grade students' performance on such items in mathematics differed among 26…

This study investigated how 155 pre-service teachers solved three pattern generalization problems in a two-part written test and sequenced them for teaching purposes to demonstrate their curricular noticing. Participants' solutions were analyzed using inductive content analysis, which showed that only 8.4% of PSTs produced correct answers to all…

Teaching and learning of differential equations (DEs) have a prominent role in all the fields of education. In spite of its prominence and frequent applications, teaching and learning of DEs is still considered as one of the most difficult, particularly at pre-university level. This is because, the topic of differential equation along with…

Mental skills are required for individuals to think quickly and make correct decisions. It can be said that mental skills, which play an important role in the acquisition of thinking and questioning skills, are only possible with creative, critical, and other high-level thinking skills. In this regard, the PISA exam, which reveals the mathematics…

These notes discuss several related propositions in geometry that can be explored in a dynamic geometry environment. The propositions involve an unexpected property of quadrilaterals.

Understanding related to fraction concepts is a critical prerequisite for advanced study in mathematics such as algebra. Therefore, it is important that elementary students form conceptual and procedural understanding of fractional numbers, allowing for advancement in mathematics. The concrete-representational-abstract (CRA) instructional sequence…

The low performance of Grade 4 learners in the mathematical concept of word problems involving multiplication remains a concern for many researchers in mathematics education. Several studies conducted have largely focused on improving learners' performance on bare problems involving multiplication, with little focus on contextual problems. The…

The purpose of this study was to measure the mathematics-vocabulary performance of 3rd graders to determine if performance differences existed among English learners (ELs) and non-ELs with and without mathematics difficulty (MD). Using screening data from a large-scale intervention study, we categorized students into four groups based on equation…

The purpose of this study was to measure the mathematics-vocabulary performance of 3rd graders to determine if performance differences existed among English learners (ELs) and non-ELs with and without mathematics difficulty (MD). Using screening data from a large-scale intervention study, we categorized students into four groups based on equation…

"Math Expressions" is a curriculum for students in prekindergarten through sixth grade that aims to build students' conceptual understanding of mathematics and to develop fluency in mathematical problem solving and computation. The curriculum encourages student learning of mathematics through real-world situations, visual supports such…

"Math Expressions" is a curriculum for students in prekindergarten through sixth grade that aims to build students' conceptual understanding of mathematics and to develop fluency in mathematical problem solving and computation. The curriculum encourages student learning of mathematics through real-world situations, visual supports such…

Teachers in kindergarten, primary, and secondary schools use hands-on manipulatives to help students grasp concepts in areas such as numbers, operations, geometry, algebra, measurement, data analysis, and probability. These manipulatives and interactive games are essential for fostering mathematical understanding, enabling students to build,…

When researchers code behavior that is undetectable or falls outside of the validated ordinal scale, the resultant outcomes often suffer from informative missingness. Incorrect analysis of such data can lead to biased arguments around efficacy and effectiveness in the context of experimental and intervention research. Here, we detail a new…

Mathematics and technology serve the health sciences as demonstrated in this article, cowritten by one of our calculus students. Creating a lesson based on dosing an antibiotic allows teachers and students to see the immediate value of high school calculus and technology.