The success or failure of education systems in promoting student problem-solving skills depends on attitudinal, political, and pedagogical variables. Among these variables, the design of mathematics textbooks is thought to partially explain why students from high-achieving countries show better problem-solving ability in international assessments.…

In recent decades, there has been considerable research that explores the teaching and learning of combinatorics. Such work has highlighted the fact that understanding and justifying combinatorial formulas can be challenging for students, and there is a need to identify ways to support students' combinatorial reasoning. In this paper, we…

Internationally, mathematics education reform has been directed toward characterizing educational goals that go beyond topic/content/skill descriptions and develop students' problem solving. The Revised Bloom's Taxonomy and MATH (Mathematical Assessment Task Hierarchy) Taxonomy characterize such goals. University entrance examinations have been…

We investigate the beliefs that influence middle and high school algebra teachers' appraisals of contextual problems having diverse mathematical and pedagogical features. We asked six teachers to analyze six contextual algebra tasks and indicate how they would apportion instructional time among the six tasks based on their structure, pedagogical…

A solid foundation in mathematics is beneficial not only for individuals' concurrent and later academic achievement, but also for future career success and financial stability. Rational number knowledge plays a pivotal role in mathematical success, yet it is often regarded as a challenging area to grasp comprehensively. The dissertation aims to…

This study reports the findings from a year-long randomized evaluation assessing the impact of assigning 62 classrooms in Nigeria to receive either blocked or interleaved math problem sets. Blocked practice sessions focused on a single skill at a time. Interleaved problem sets alternated between different skills within a practice session. On tests…

We present a type of arithmetic called Proportional Arithmetic. The main properties and objects that emerge with this way of operating quantities are exposed. Finally, the antiderivative and the indefinite integral are defined in order to calculate the primitive of [equation omitted] in the Proportional context.

Many U.S. students possess only a weak knowledge of fraction arithmetic. I hypothesize that textbooks are a critical reason for students' poor performance on fraction arithmetic. This is not because of what textbooks contain but rather because of what they lack. Distributions of fraction arithmetic problems in textbooks are imbalanced, with…

In recent decades, research has stressed the prominence of mathematics classroom discussions in productive instructional practices in mathematics instruction. In this context, problem-solving activities have been a common focus of research. Research shows that teachers need to deal with prerequisites and challenges such as norms, design of tasks,…

Intelligent tutoring systems (ITSs) aim to deliver personalized learning support to each learner, aligning with the educational aspiration of many countries, including China. ITSs' personalized support is mainly achieved by providing individual prompts to learners when they encounter difficulties in problem-solving. The guiding principles and…

This study examined the engagement of preservice elementary teachers (PSTs) with mathematics tasks that were open in various ways and to varying extents. In K-12 settings, practitioners who have implemented recently popular open tasks report increased engagement and from a wider variety of students. While these anecdotal reports and related…

Collaborative problem-solving (CPS) has been widely used in K-12, higher education, and informal learning to enhance the quality of student learning. Understanding the relationship between learning engagement and group performance is crucial for CPS pedagogy and analytics. However, few empirical studies investigated individual engagement role…

The purpose of this intervention study was to develop and evaluate a support model for teachers, designed to assist them in diagnosing students' (age 16-19 years) difficulties and providing feedback to support students' mathematical problem solving. Reporting on an iteration in a design research project, the results showed that the support helped…

Coordinate geometry is an important part of mathematics. It helps students develop thinking, logic, and problem-solving skills. This study was conducted to test the effectiveness of the CORE learning model in promoting students' mathematical problem-solving skills when they learn the method of coordinates in a plane. Consequently, this study used…

In this dissertation I explore instructors' work with instructional tasks as they plan to introduce various representations of derivatives. Drawing on the notion of "framing" from sociology, I adopt a situative lens to study calculus instructors' planning of instructional tasks. I rely on Herbst and Chazan's (2012) notion of…