Despite problem posing's prominence in mathematics education research, its implementation in classrooms is limited. Therefore, teacher educators should incorporate problem posing tasks into preparation programs to help prospective teachers gain confidence in their abilities. One approach to teaching problem posing includes providing examples. The…

In this article, the author describes strategies to support students in conjecturing in ways that promote their agency. Conjecturing involves justifying (i.e., a practice that promotes epistemic agency and engages students in mathematical reasoning to defend their claims; Bieda & Staples, 2020) by which a conjecture becomes proven, modified,…

A new classification for semantic structures of one-step word problems is proposed in this paper. The classification is based on illustrations of word problem situations in Common Core State Standards (CCSSM, 2010) and related historical studies (e.g. Weaver, 1973, 1979, 1982), as well as conceptual elaborations of embodied and grounded nature in…

Changes in U.S. textbooks indicate that U.S. first-grade students in the Common Core era were exposed to a wider variety of word problem types than students in previous generations were. We compared the performance of U.S. first graders in the Common Core era with that of previous generations in solving 11 types of additive word problems to…

This research examined how three middle school mathematics teachers who were supported by their district to use the Teaching Through Problem Solving approach interpreted and implemented the Standards for Mathematical practices (SMPs) developed by the Common Core State Standards (2010) and the Mathematics Teaching Practices (MTPs) developed by the…

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…

While contemporary mathematics education literature argues that curricular resources, such as textbooks, play a significant role guiding mathematics teachers in what and how they teach, it also shows that these resources often do not do what they say they will do, nor adhere to the standards they claim to further. When it comes to the most…

A Common Core expectation of high school mathematics students is to analyze functions using different representations. One type of function to be analyzed is piecewise-defined functions. The author has found most approaches to the study of piecewise functions to be abstract, disconnected from any context, and difficult for students to understand.…

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…

The instructional decisions made by classroom teachers impact the learning acquired by students. The Common Core Mathematics Standards and the history of mathematics education in the United States create a background for how geometry standards are taught in one Midwest middle school. A study of the pacing guides, lesson plans, and naturalistic…

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…

There is little empirical research related to how elementary students develop computational thinking (CT) and how students apply CT in problem-solving. To address this gap in knowledge, this study made use of learning trajectories (LTs; hypothesized learning goals, progressions, and activities) in CT concept areas such as sequence, repetition,…

The Common Core State Standards for Mathematics emphasize the importance of developing students' conceptual understanding, mathematical reasoning, and problem solving skills. This is a shift from the traditional approach to teaching mathematics and many teachers rely on curriculum resources to help them meet these new standards and expectations.…

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…

The adoption of the Common Core State Standards has necessitated a change in the instructional practices used by many mathematics teachers. The new standards encourage problem solving and the development of conceptual understanding rather than rote memorization of formulas and rules. Researchers have demonstrated that formative assessment is a…