Math problem solving frequently involves choices among alternative strategies. Strategy choices, and effects of problem features on strategy choices, both vary among individuals. We propose that individual differences in strategy choices can be well characterized in terms of parametric variation in three types of influence: global bias, relevant…

Arithmetic fluency is regarded as a foundational math skill, typically measured as a single construct with pencil-and-paper-based timed assessments. We introduce a tablet-based assessment of single-digit fluency that captures individual trial response times across several embedded experimental contrasts of interest. A large (n = 824) cohort of…

Procedural flexibility is an important skill for algebra. Although prior work has focused on measuring students' procedural flexibility using arithmetic problems, word problems may also capture students' flexibility because of their open-ended nature. To date, no published study has examined the use of word problems as another measure of…

This article addresses argumentation in middle-school students' group work with conjectures in arithmetic with different epistemic states. Twenty-five episodes were analysed using G. J. Stylianides' framework for reasoning and proving, which comprised a mathematical, psychological, and pedagogical component. The mathematical component was studied…

In this study, the effectiveness of a learning management plan using the think-pair-share technique on students' learning of decimal multiplication and division was investigated. The quasi-experimental study involved 42 grade 7 students in a public school in Thailand, who were simple random sampling. The study used a learning management plan, a…

A theoretical model describing Grade 7 students' rational number sense was formulated and validated empirically (n = 360), hypothesizing that rational number sense is a general construct consisting of three factors: basic rational number sense, arithmetic sense, and flexibility with rational numbers. Data analysis suggested that rational-number…

We present a case study of proving by three 12-13-year-old students with different levels of mathematical giftedness. After analysing students' proofs, we conclude that: there was a relation on the consistency and the students' levels of mathematically giftedness, being the least consistent the student not mathematically gifted and the most…

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…

Students' difficulties in algebra are generally caused by the use of algebraic notation, the meaning of letters, as well as the types of relationships or methods used. Therefore, interpreting letters in algebra is one of the critical points in the transition from arithmetic to algebra. However, many students have misconceptions in interpreting…

Diagnostic tests have been developed previously to measure algebraic thinking skills; however, the tests do not specifically address algebraic problem-solving. Thus, an Algebraic Thinking Test (ATT) Instrument was developed to measure algebraic thinking skills in problem-solving involving linear equations. ATT comprises nine open-ended questions…

The integration of technology in entrepreneurship arithmetic that uses realistic mathematic education as the basis into learning processes is instrumental in creating understanding and problem-solving abilities among students. However, until recently only a few technology-based learning media have been developed to accommodate the aforementioned…

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…

The long-term negative consequences of learning difficulties have been acknowledged. Nonetheless, research is still scarce regarding the prediction of adolescent difficulties in reading and arithmetic skills. The present study examines at which age phase and with what kind of constellation of parent- and child-related factors can adolescent…

This article explores three attributes of teachers' understanding of fraction magnitude: the accuracy and reasonableness of teachers' estimations in response to fraction arithmetic tasks as well as the alignment of the estimation strategies they used with the concept of fraction magnitude. The data were collected from a national sample of…

This study investigated the role of the bar model method, a significant aspect of the Singapore mathematics curriculum, in the remediation of seventh-grade students' errors on algebra word problems. To accomplish this purpose, we first assessed students' errors on a written test involving algebra problems and identified ten students based on the…