Proportional reasoning has been greatly influencing the development of students' mathematical abilities. Along with the area conservation ability, it helps elementary students comprehend area measurement. This exploratory study aimed to produce qualitative-descriptive data on elementary students' proportional reasoning in solving the conservation…

This article makes a case for introducing moving averages into introductory statistics courses and contemporary modeling/data-based courses in college algebra and precalculus. The authors examine a variety of aspects of moving averages and draw parallels between them and similar topics in calculus, differential equations, and linear algebra. The…

This article aims to delve into the meaning of school mathematical concepts by their semantic analysis. Concretely, this paper aimed primarily to describe and characterize the meaning of derivative of a function at a point expressed by mathematics pre-service teachers. In order to achieve this goal, we use a semantic framework, in which the…

Given the relevance of graphs of functions, we consider their inclusion in primary education from the functional approach to early algebra. The purpose of this article is to shed some light on the students' production and reading of graphs when they solved generalization problems from a functional thinking approach. We aim to explore how 3rd and…

The paper examined the relations among problem solving, automaticity, and working memory load (WML) by changing the difficulty level of task characteristics through two applications. In Study 1, involving 68 engineering students, a 2 (automaticity) x 2 (WML) design was utilized for arithmetic problems. In Study 2, involving 76 engineering…

This research aims to describe students' level of algebraic reasoning based on the adversity quotient types of climber, camper, and quitter in solving PISA model mathematics problems. This research is descriptive research with a qualitative approach. The research began by administering a questionnaire to determine the student's adversity quotient…

While the lion's share of mathematics education research in linear algebra has been concerned with the conceptual aspects of students' learning, this study focuses on procedural knowledge that undergraduates can develop in a typical first-year course. The study analyzes the methods that a large cohort of second-semester students applied in a final…

Algebra has been identified as a gatekeeper to careers in STEM, but little research exists on how algebra appears for practitioners in the workplace. Surveys and interviews were conducted with 77 STEM practitioners from a variety of fields, examining how they reported using algebraic functions in their work. Survey and interview reports suggest…

The law of conservation of momentum is a fundamental law of nature. It states that the momentum of an isolated system is conserved. In high school or introductory-level physics courses, for simplicity, teachers and textbooks always use collisions in one dimension as the examples to introduce the concept of conservation of momentum. To solve simple…

Teachers need ways to efficiently assess students' cognitive understanding. One promising approach involves easily adapted and administered item types that yield quantitative scores that can be interpreted in terms of whether or not students likely possess key understandings. This study illustrates an approach to analyzing response process…

Understanding of the equal sign is associated with early algebraic competence in the elementary grades and equation-solving success in middle school. Thus, it is important to find ways to build foundational understanding of the equal sign as a relational symbol. Past work promoted a conception of the equal sign as meaning "the same as".…

This study investigated the effects of (1) proximal grouping of numbers; (2) problem-solving goals to make 100; and (3) prior knowledge on students' initial solution strategies in an interactive online mathematics game. In this game, students transformed an initial expression into a perceptually different but mathematically equivalent goal state.…

This study investigated the effects of: (1) proximal grouping of numbers; (2) problem-solving goals to make 100; and (3) prior knowledge on students' initial solution strategies in an interactive online mathematics game. In this game, students transformed an initial expression into a perceptually different but mathematically equivalent goal state.…

The use of the algebraic method for solving word problems is a challenging topic for secondary school students. Students' difficulties are usually associated with extracting the problem's network of relationships between quantities and with formalizing these relationships into algebraic language in a problem model. Both sources can coexist and…

In light of the recent interest in mathematical competencies and the ways in which students communicate their ideas, this study aims to explore how undergraduate students communicate their ideas about mathematical tasks through written texts. Forty-three first-year undergraduate students participated in this study. They were given a graph of a…