In an undergraduate analysis course taught by one of the authors, three prompts are regularly given: (i) What do we know? (ii) What do we need to show? (iii) Let's draw a picture. We focus on the third prompt and its role in helping students develop their confidence in learning how to construct proofs. Specific examples of visual models and their…

Research indicates that standards-based mathematics instruction positively supports students' academic development. Although standards documents identify accepted best practices, they do not speak to the impact that students' expectations of the mathematics classroom has on the successful implementation of standards-based instruction at the…

What do nonroutine algebra problems look like for a second-year algebra course, and where can such problems be found? Starting from the belief that even challenging, nonroutine problems should be solvable with the resources that students possess, Benjamin Dickman proceeded to formulate a small collection of tasks to push students into integrating…

This study was conducted to examine the effects of modality across gender on undergraduate student achievement when learning Algebra concepts. Cognitive Load Theory (CLT) and Cognitive Theory of Multimedia Learning (CTML) provided a framework for this study to describe in depth the concept of the modality principle. Participants were undergraduate…

Advancement of self-regulation during complex problem solving and the development of strategical reasoning are among the central educational goals linked to 21st century skills. In this paper we introduce the notion of "Stepped Tasks", which are specially designed in Top-Down structure to achieve these goals in mathematics instruction.…

This study explored the cognitive mechanism behind information integration in the test anxiety judgments in 140 engineering students. An experiment was designed to test four factors combined (test goal orientation, test cognitive functioning level, test difficulty and test mode). The experimental task required participants to read 36 scenarios,…

in this paper we focus on the link between the use of dynamic geometry software and student understanding for the solution of systems of linear equations from an instrumental genesis perspective. Three task-based interviews were conducted with an undergraduate linear algebra student majoring in mathematics education and proficient in using dynamic…

We investigated how the opportunity to learn (OTL) with different types of mathematics tasks are related to mathematical literacy and the role of perceived control in the relationship between OTL and mathematical literacy. The structural equation modeling was applied to the data of 1,649 Korean students from the PISA 2012 database. OTL with the…

The purpose of this study was to examine the effects of using GeoGebra software in a computer-supported collaborative learning (CSCL) environment on seventh grade students' geometry achievement, retention of learning, and attitudes toward geometry. The study was designed using a quasi-experimental research method with pretest, post-test and…

This paper presents an analysis of fractions errors displayed by learners due to deficient mastery of prerequisite concepts. Fractions continue to pose a critical challenge for learners. Fractions can be a tricky concept for learners although they often use the concept of sharing in their daily lives. 30 purposefully sampled learners participated…

The issue of higher-order thinking skills in Indonesia began to be raised in line with the changing goals of mathematics learning. The efforts have been made to be able to produce improved thinking skills, one of which is the PINTER model. This study aimed to see if there are any differences in higher-order thinking skills and mathematical…

Too often, high school algebra students encounter topics in a discrete, disconnected fashion. In the authors' first years of teaching, they found students to be adept at solving problems they were currently studying; for instance, they could solve quadratics during a quadratics unit. Too often, however, students struggled with that same content…

Studies examining gender differences in introductory physics show a consensus when it comes to a gender gap on conceptual assessments; however, the story is not as clear when it comes to differences in gendered performance on exams. This study examined whether gendered differences exist on midterm and final exams in introductory physics courses…

Due to the COVID-19 global pandemic, educators and school administrators need to understand the available distance learning models and programs that may assist students who attend school from a remote location. To meet this need, this rapid evidence review sought to identify and report on what works in distance learning educational programming.…

The capacity to recognise, represent, and reason about relationships between different quantities, that is, to think multiplicatively, has long been recognised as critical to success in school mathematics in the middle years and beyond. Building on recent research that found a strong link between multiplicative thinking and algebraic, geometrical,…