Background: One criterion of adaptive learning is appropriate generalization to new instances based on the original learning context and avoiding overgeneralization. Appropriate generalization requires understanding what features of a solution are applicable in a new context and whether the new context requires modifications or a new approach. In…

We describe 24 third (8-9 years old) and 24 fifth (10-11 years old) graders' generalization working with the same problem involving a function. Generalizing and representing functional relationships are considered key elements in a functional approach to early algebra. Focusing on functional relationships can provide insights into how students…

The mathematical representation ability is essential in solving mathematical problems, especially in algebraic expressions problems. Therefore, it is crucial to have a valid design of learning activities to support students' mathematical representation ability. Several previous studies claimed that realistic mathematics education is one of the…

The aim of this study is to examine the argumentation-based problem solving processes of 10th grade students in the context of quadratic equations. The study was carried out in a public high school in Istanbul. The study group consists of three male students selected by the method of "homogeneous sampling". In the research, special case…

Using the High School Longitudinal Study of 2009, we examine the association between taking Algebra I by the eighth grade and students' later achievements and advanced mathematics course-taking. To explore our research questions, we employ three distinct methods--regression analysis, fixed effects models, and propensity score matching. In all our…

The present paper describes beautiful conservation relations between areas formed by different geometrical shapes and area relations formed by algebraic functions. The conservation properties were investigated by students at an academic college of education using a computerized technological tool and were subsequently accompanied by justified…

One of the fundamental topics taught in the microeconomics class is minimizing economic costs. It includes understanding the concept of derivatives and applying them. However, most of the first-year undergraduate students find calculus difficult to understand, which also results in poor knowledge of optimization. We use the method based on the…

Prior work on teachers' mathematical knowledge has contributed to our understanding of the important role of teachers' knowledge in teaching and learning. However, one aspect of teachers' mathematical knowledge has received little attention: "strategic competence for word problems." Adapting from one of the most comprehensive…

In this paper we discuss students' opportunities to learn to pose mathematical problems, based on a historical analysis of problem posing in the area of number and algebra in six series of Chinese primary school mathematics textbooks published since the 1950s. We examine changes in the proportion and distribution of the problem-posing tasks, and…

Prior research showed a gender effect on spatial ability, math anxiety, and math achievement. Lacking, however, is a comprehensive study that tested the mediation effects of spatial ability and math anxiety between gender and math achievement in a sequential mediation model. To fill this gap, this pilot study tested two mediation relationships,…

Purpose: Metacognitive awareness plays an important role in assisting students to solve problems because it affects their reasoning in assessing their thinking results. This research aims to investigate students' metacognitive awareness failures about solving absolute value problems in Mathematics Education. Methodology: It is qualitative research…

The authors present mathematics problems related to the packaging of sporting goods which they used to motivate and engage their students in the USA. This article reports on a series of questions/problems that were explored in groups by the students in a college class designed for sophomores, as part of a program to prepare them to be teachers at…

Achieving the Dream (ATD) is one of 12 higher education and digital learning organizations that make up the Every Learner Everywhere (Every Learner) Network, whose mission is to help higher education institutions improve and ensure more equitable student outcomes through advances in digital learning, particularly among poverty-impacted, racially…

Generalizing, conjecturing, representing, justifying, and refuting are integral parts of algebraic thinking and mathematical thinking in general (Lannin et al., 2011). The activity described in this article makes a case for generalizing as an overall mindset for any introductory algebra or geometry class by illustrating how generalization problems…

Algebraic Thinking Skills (ATS) are one of the skills that students need to master in order to solve nonroutine problems. These skills are also necessary as a foundation for students preparing to enter university studies and fields of work that require logical and analytical thinking. However, Malaysian students' performance in solving algebraic…