In this article we review the research on the flexible or adaptive use of solution strategies in school mathematics, with a focus on the most recent work in the field. After a short introduction, we provide an overview of the various ways in which strategy flexibility has been conceptualized and investigated in the research literature. Then we…

This single-case study assessed the effectiveness of a mnemonic pegword strategy designed to enhance the multiplication fact fluency of three 6th-grade students who demonstrated persistent learning difficulties in mathematics. A nonconcurrent multiple baseline across subjects design was utilized, incorporating 3-5 baseline sessions followed by…

This study examined a 6-week intervention in which fourth grade students either played fluency games or used pictorial flashcards to develop fluency with their basic multiplication facts. Students who played fluency games showed more growth than the pictorial flashcards, but an analysis of variance showed that there was no statistically…

Geometry education is an important aspect of science, technology, engineering, and mathematics (STEM) education, but it is often overlooked in K-12 education in the United States. Chunking strategy reduces the cognitive load demanded in the processing of information, and it has been applied as a testing accommodation for high school students with…

This single-subject design study examines the effectiveness of a Tier 3 math intervention designed to address the academic challenges of three fifth-grade students not meeting minimum proficiency standards in long division. Using the self-regulated strategy development (SRSD) model, the intervention targeted procedural fluency and conceptual…

This case study was undertaken to characterise the interventions made by a kindergarten teacher during a multiplicative structure problem-solving lesson. The study findings show that when she realised the children were having difficulty, she provided assistance to enable them to find the right answer. When the children gave an incorrect response,…

As students develop understanding and fluency in single-digit operations such as addition, they develop sophisticated strategies and number sense (magnitude, number order, and composition). Deficits in number sense and reliance on inefficient approaches can lead to struggle in mathematics. Intervention research in this area reported effects on…

Prior short-term studies have shown the effectiveness of worked examples and self-explanation prompts in improving elementary students' mathematics knowledge. However, year-long classroom-based interventions have been tested only with older students. The purpose of the current study was to explore the effectiveness of a year-long classroom…

Research on fraction knowledge has revealed that prospective teachers' (PSTs) often lack fraction proficiency. The aim of this dissertation was to develop and test an intervention intended to increase PSTs' fraction proficiency by focusing on fraction comparison. I first adopted a five-dimensional framework to define PSTs' fraction proficiency. I…

The aim of the study reported in this article was to reveal how instruction, enriched with reasoning about students' thought processes and strategies, regulates prospective teacher's noticing skills in the context of whole number multiplication. In addition, the study examined the evidence of the prospective teacher's (Matt) knowledge that…

In this paper, we report how 5-year-olds' arithmetic skills developed through participation in an 8-month-long intervention. The intervention program aimed to enhance the children's ways of experiencing numbers' part-part-whole relations as a basis for arithmetic skills and was built on principles from the variation theory of learning. The report…

We investigated how students' strategic knowledge about situational (pictorial) drawings and mathematical (schematic) drawings affects drawing accuracy and modeling competencies in the domain of geometry. We conducted a pre-posttest experimental study with 473 students in grade 9. Students were randomly assigned to one of three treatment…

Mathematical learning is to produce a high competence individual with multiple skills in line with the needs of the 21st century. However, mathematical education is still plagued with problem of mastery of mathematical concepts. In addressing this problem, various initiatives and interventions need to be implemented to ensure that mathematical…

Background: Base-ten thinking (BTT) -- children's ability to reason in tens and ones is a crucial measure of Foundation Phase learners' mathematical performance in South Africa. Aim: The study looks at the six learners using BTT to solve additive tasks through two different assessments. Setting: Six purposely selected Grade 3 learners in…

In the present study, the impact of formative assessment on secondary school students' mathematics achievement and their metacognitive awareness was examined. The participants included 164 (84 boys) grade 11 students and four mathematics teachers from four secondary schools in Kenya. A quasi-experimental pretest-posttest non-equivalent group…