Flexibility in transforming algebraic expressions is recognized as fundamental for a rich procedural knowledge. Here, flexibility in-depth is proposed as the ability to apply one strategy to a wide range of unfamiliar expressions. In this study, design experiments with four groups of students were conducted to support students' flexibility…

This study analyzed children's use of mental computation strategies and the standard algorithm on multi-digit subtractions. Fifty-eight Flemish 4th graders of varying mathematical achievement level were individually offered subtractions that either stimulated the use of mental computation strategies or the standard algorithm in one choice and two…

Derivatives and integrals are two important concepts of calculus which are precondition topics for most of mathematics courses and other courses in different fields of studies. A majority of students at the undergraduate level have to master derivatives and integrals if they want to be successful in their studies However, students encounter…

Research suggests that inquiry-based strategies are the most effective modes of delivery in working with the gifted students. The characteristics of the gifted reveal a strong basis for understanding the power of question-asking as a part of differentiating curriculum. This article describes three different models of questioning--Guilford, Bloom,…

In this research, we examined how 200 students in seventh grade (around 12 years old) solved simple addition problems. A cluster approach revealed that less than half of the cohort displayed proficiency with simple addition: 35% predominantly used min-counting and were accurate, and 16% frequently made min-counting errors. Students who frequently…

This study's purpose was to determine the effect of instruction in self-regulated learning (SRL) strategies on low-achieving fourth-grade students' perseverance in solving mathematics problems. This study was conducted with fourth-grade students who had been ability-grouped based on prior low achievement and testing data in math. Students were…

This article looks at writing tasks as a methodology to support learners' mathematical problem-solving strategies in the South African Foundation Phase context. It is a qualitative case study and explores the relation between the use of writing in mathematics and development of learners' problem-solving strategies and conceptual understanding. The…

This study investigated effects of feedback and exposure to alternative strategies on strategy change in children (N = 106, age range = 7;3-10;0) learning about mathematical equivalence. Children's strategies were evaluated before and after a brief instructional intervention. During the intervention, children either were exposed to a set of 4…

The aim of this research is to study the fundamental elements used to broaden mathematical knowledge and to establish guidelines for its development using Intercultural Bilingual Education (IBE) framework. This study is an experimental quantitative research. Problem solving pretest and posttest were given to the students of Carti Tupile School…

Organic synthesis problems require the solver to integrate knowledge and skills from many parts of their courses. Without a well-defined, systematic method for approaching them, even the strongest students can experience difficulties. Our research goal was to identify the most successful problem-solving strategies and develop associated teaching…

Proportional reasoning is important to students' future success in mathematics and science endeavors. More specifically, students' fluent and flexible use of scalar and functional relationships to solve problems is critical to their ability to reason proportionally. The purpose of this study is to investigate the influence of systematically…

The main goal of this study is to find out the effect of the instructional design method on the enhancement of problem solving abilities of students. Teaching sessions were applied to ten students who are in 11th grade, to teach them problem solving strategies which are working backwards, finding pattern, adopting a different point of view,…

This paper explores young children's drawings (6 years old) in early number and addition activities in Malaysia. Observation, informal interviews and analysis of drawings revealed two types of drawing, and gave insight into the transitional process required for children to utilise drawings in problem solving. We argue the importance of valuing and…

The ability to self-regulate learning (SRL) is a skill theorized to transfer across learning environments. Students with this ability can consider a learning task, identify a goal, develop a plan to achieve it, execute that plan, and monitor and adapt learning until the goal is met. This paper examines the educational implications of developing…

Owing to the popularity of tablet computers and smart phones, e-books have become an important medium for both formal and informal learning. However, conventional e-books are mainly designed to provide information in the form of multimedia, implying that students spend most of their time memorizing and comprehending what they read from e-books,…