Algebraic thinking in children can bridge the cognitive gap between arithmetic and algebra. This quantitative study aimed to develop and test a cognitive model that examines the cognitive factors influencing algebraic thinking among Year Five pupils. A total of 720 Year Five pupils from randomly selected national schools in Malaysia participated…

We implemented a STEM task that highlights the engineering cycle and engages students in productive struggle. Students problem solved in productive ways and saw tangible benefits of revising their work to achieve mathematical goals.

This study investigated the ways in which college algebra students watch mathematics instructional videos about completing the square with the goal of identifying student responsibilities within a particular video and across different videos. Guided by the theory of didactic situations that has defined implicit teacher and student responsibilities…

Recent scholarship around teaching elementary mathematics supports the learning of early algebra with 5- to 12-year olds. However, in spite of the recognition of the affordances of early algebra, issues about how to introduce it remain open. Within this context, Davydov's work is often cited as a source of impressive demonstration of young…

Generalisation is a key feature of learning algebra, requiring all four proficiency strands of the Australian Curriculum: Mathematics (AC:M): Understanding, Fluency, Problem Solving and Reasoning. From a review of the literature, we propose a learning progression for algebraic generalisation consisting of five levels. Our learning progression is…

Purpose: Currently, in the education data use literature, there is a lack of research and examples that consider the early steps of filtering, organizing and visualizing data to inform decision-making. The purpose of this study is to describe how school leaders and researchers visualized and jointly made sense of data from a common learning…

Prior work exploring preschool-aged children's reasoning with repeating patterns has shown that patterning ability is an important predictor of math achievement; however, there is limited research exploring older children's growing pattern task performance. The current study tested whether presentation format impacts performance on growing pattern…

This paper drills deeper into the documented effects of the Cognitive Tutor Algebra I and ASSISTments intelligent tutoring systems by estimating their effects on specific problems. We start by describing a multilevel Rasch-type model that facilitates testing for differences in the effects between problems and precise problem-specific effect…

The purpose of this study was to examine the relationship between grit, mathematics self-efficacy, students' career interest in STEM, and student achievement in Algebra I. The study was intentional in examining the concepts of self-efficacy, achievement, and career interest as part of STEM education research. The research was completed during the…

Students at Century High School (CHS), a Catholic all-boys high school on Long Island, New York, who started ninth grade with Algebra 1 instead of Geometry demonstrated less obvious career interest in science, technology, engineering, and mathematics (STEM) and lower mathematics achievement, as typically evidenced by Iowa Tests of Educational…

The paper describes active learning strategies used in undergraduate college algebra and business calculus courses. There are a variety of active learning strategies described in the literature. We wanted to implement a few that together, satisfy the key characteristics of active learning strategies. The active learning strategies described in…

Does the timing of children's formal understanding of mathematical equivalence matter for algebra readiness? A change-resistance account (McNeil & Alibali, 2005) predicts that it is beneficial for children to construct a formal understanding of mathematical equivalence in the early grades before overly narrow operational patterns become…

This analysis uses the case of the Better Math Teaching Network (BMTN) to explore whether individuals participating in a networked improvement community (NIC) experienced common developmental trajectories on known dimensions of engagement. The analysis included quantitative data from annual network member surveys and qualitative data from annual…

Strong mathematics achievement is lacking in the United States, with motivation waning especially among mathematics and online students. Online mathematics students, in particular, struggle with self-regulation and self-efficacy (Kim, 2012; Sun & Rueda, 2012). Ryan and Deci (2017), in their well-established and empirical self-determination…

Federal legislation requires every student receive access to and make progress in the general curriculum. Teachers have reported difficulties in meeting this requirement for students with extensive support needs (ESN) who do not yet demonstrate foundational academic skills, such as in the areas of literacy and numeracy. Once students enter high…