Children of 10-11 years of age were interviewed while undertaking a range of mathematic problems, most of which embedded mathematical operations in textually represented realistic settings. One problem, concerning a lift moving people in the morning rush, comprised a division-with-remainder problem in which children are required, conventionally,…

This paper shows how inequalities can be utilized in reducing dimensionality of problems associated with the partition of unit fractions into the sums of two, three, and four like fractions. The need for such a reduction in this context stems from using a spreadsheet as a modelling tool. Activities described in this paper are grounded in standards…

"Saxon Math" focuses on fundamental mathematics skills, targeting children from kindergarten through grade 12. This report focuses on middle school math, defined as grades 6 through 9. The 6th grade curriculum covers simplifying expressions containing parentheses, graphing functions, and understanding ratios and proportions. The 7th…

The academic silos that house mathematics, science, and language skills must be broken down to better replicate how those disciplines mix in the real world. This article discusses the benefits of linking writing with mathematics, the challenges of integrating mathematics and writing, and the strategies for mathematics writing. Combining…

This article will share results from research that investigated how sixth-, seventh-, and eighth-grade students who had not been exposed to formal algebraic methods approached word problems of an algebraic nature. Student use of systematic guess and check, the predominate approach taken by these students, is the focus. The goal is to consider the…

This article deals with the investigation of the psychometric quality and constructs validity of algebra word problems generated by means of a schema-based version of the automatic min-max approach. Based on review of the research literature in algebra word problem solving and automatic item generation this new approach is introduced as a…

Changing perspectives on mathematics teaching and learning resulted in a new generation of mathematics textbooks, stressing among others the importance of mathematical reasoning and problem-solving skills and their application to real-life situations. The article reports a study that investigates to what extent the reform-based ideas underlying…

The author examined the potential influence of learning opportunities provided in 1 U.S. and 1 Chinese mathematics textbook series on students' problem-solving performance. Also, the author studied learning opportunities provided in the textbooks by analyzing word problem distribution across various problem types, as well as the potential…

Borrowing the concept of story grammar from reading comprehension literature, the purpose of this study was to examine the effect of teaching "word problem (WP) story grammar" on arithmetic WP solving that emphasizes the algebraic expression of mathematical relations in conceptual models. Participants were five students in Grades 4 and 5 with or…

Students "doing" mathematics ultimately results in students reading mathematics. This reading of mathematics is manifested in students reading words, symbols (including numerals), and visuals such as diagrams and graphs. Furthermore, students' successful response to word problems engages them in reading mathematics in the context of real-life or…

This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…

The purpose of this study was to examine the tenability of a curriculum-based mathematical word problem-solving (WPS) measure as a progress-monitoring tool to index students' rate of growth or slope of achievement over time. Participants consisted of 58 third-grade students, who were assessed repeatedly over 16 school weeks. Students were measured…

Writing can provide opportunities for students to construct their own knowledge of mathematics. The student work that appears in this book shows learners interpreting unfamiliar texts, constructing arguments, struggling to understand complex systems, and developing new approaches to problems. The chapters are entitled: (1) "Writing to Learn"; (2)…

In this study, children (ages 7-12) of average intelligence who had learning disabilities (LD) (n=29) and typical children (n=30) were individually tested in a task that investigated the development of proportional structures of thought. In addition, mathematical knowledge was assessed on the Woodcock-Johnson Tests of Achievement-Revised (WJTA-R).…

In this book, 10 strategies that are widely used in problem-solving both in mathematics and real-life situations are examined. Approximately 200 problems are selected to illustrate these strategies. Chapters include: (1) Introduction To Problem-Solving Strategies; (2) Working Backwards; (3) Finding a Pattern; (4) Adopting a Different Point of…