Despite the introduction of Common Core State Standards and the National Council of Teachers of Mathematics urging educators to explore fundamental concepts in mathematics at a deeper level, the majority of mathematics education has remained aimed at initial skill acquisition. The result has led to students learning to mimic a standard set of…

Representing repeating nonterminating decimals as rational numbers is a topic introduced in the seventh-grade Common Core State Standards for Mathematics. According to Content Standard 7.NS.2.D., students should be able to represent a rational number as a decimal and understand that the decimal will either end in zeros or eventually repeat (NGO…

In this meta-analysis of single-case designs, the researchers investigated the effects of word-problem instruction for students with learning disabilities in Grades 1 through 12, as reported in 20 peer-reviewed articles published between 1975 and 2020. A two-level multilevel model with a robust variance estimation method was implemented to…

This paper details an exploratory study of ten elementary preservice teachers (PSTs) involvement in the problem-solving process in a mathematics methods course. The dynamic, messy and nonlinear nature of this process was demonstrated by discussing PSTs' solution process of an open box construction problem. Effective approaches to solve this…

Improving children's "number sense" has been a core component of recent mathematics curricular and instructional reforms (CCSS, 2010; NCTM, 2000, 2014) in the United States. Students with mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient…

A key debate in computer science education is whether and how computational thinking (CT) is used within disciplines other than computer science. Broad definitions provide many avenues for developing integrated instruction, as practices within existing activities can simply be reframed in terms of CT. But such general use of the term CT may…

This study explores six item-reduction methodologies used to shorten an existing complex problem-solving non-objective test by evaluating how each shortened form performs across three sources of validity evidence (i.e., test content, internal structure, and relationships with other variables). Two concerns prompted the development of the present…

This article details a high school classroom activity in which algebra tiles are used to help students gain a conceptual understanding of completing the square. The activity utilises the eight elements of effective mathematics education suggested in the National Council of Teacher of Mathematics' (NCTM's) "Principles to action: Ensuring…

Students often have the misconception that mathematics involves reading the problem, staring at the page, and then writing down an answer. With more than twenty years of experience working with students in eighth-grade math through college calculus, the author has been increasingly interested in how she can foster problem-solving skills in her…

The Common Core State Standards in Mathematics outline both the content and practices students must engage in at each grade level to become mathematically proficient. Mathematical processes include problem solving, reasoning and proof, communication, and procedural fluency, which includes flexible thinking. The purpose of this study was to…

Problem solving has long been a priority in mathematics education, and the first Common Core mathematical practice (SMP1) focuses on this priority through the language of "Make sense of problems and persevere in solving them." We present findings from a survey about how prospective elementary teachers' (PTs) make sense of potential…

Science, Technology, Engineering, and Mathematics (STEM) education initiatives have placed pressure on teachers to bring technology tools into classroom, including three-dimensional (3D) printing. Yet, little research has examined what specific math skills are required for 3D printing technology. This article describes a follow-up analysis of…

Moving among levels of abstraction is an important skill in mathematics and computer science, and students show similar difficulties when applying abstraction in each discipline. While computer science educators have examined ways to explicitly teach students how to consciously navigate levels of abstraction, these ideas have not been explored in…

The Common Core State Standards (CCSSI 2010) for Mathematical Practice have relevance even for those not in CCSS states because they describe the habits of mind that mathematicians--professionals as well as proficient school-age learners--use when doing mathematics. They provide a language to discuss aspects of mathematical practice that are of…

With rigor outlined in state and Common Core standards and the addition of constructed-response test items to most state tests, math constructed-response questions have become increasingly popular in today's classroom. Although constructed-response problems can present a challenge for students, they do offer a glimpse of students' learning through…