This paper reports on 73 Grades 3 to 6 students' written responses to equal groups, arrays, multiplicative comparison and Cartesian product word problems. It is part of a larger study relating to students' development of multiplicative thinking (MT). The potential of using multiplicative word problems as a diagnostic assessment to reveal students'…

Problem decomposition into sub-problems or subgoals and recomposition of the solutions to the subgoals into one complete solution is a common strategy to reduce difficulties in structured problem solving. In this study, we use a datadriven graph-mining-based method to decompose historical student solutions of logic-proof problems into Chunks. We…

In this study, it is aimed to examine the text-based questions in the secondary school Turkish textbooks according to the revised Bloom's Taxonomy and to evaluate these questions according to the cognitive domain steps. In the research, the text-based questions in the Turkish textbooks approved by the Ministry of National Education were examined…

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…

Past research has identified factors that help maintain the cognitive demand of tasks, including "drawing conceptual connections." We investigated whether teachers who were engaging in the teaching practice of "building"--and thus focusing the class on collaboratively making sense of their peers' high-leverage mathematical…

Learning progressions have become an important construct in educational research, in part because of their ability to inform the design of coherent standards, curricula, assessments, and instruction. In this paper, I discuss how a learning progressions approach has guided our development of an early algebra innovation for the elementary grades and…

Access to body-based resources has been shown to augment cognitive processes, but not all movements equally aid reasoning. Interactive technologies, like dynamic geometry systems (DGS), potentially amplify the link between movement and geometric representation, thereby deepening students' understanding of geometric properties. This study…

Society has increasingly looked upon science education to prepare the public for Industrial Revolution 4.0, as scientific reasoning and practices can hone 21st century skills, including scientific literacy. However, the COVID-19 pandemic has changed how science is taught and learned. Hence, this mixed methods study seeks to determine if there…

The purpose of this study was to characterize variations in how teachers enacted an approach to ambitious mathematics teaching: "rough draft math." We also examined teachers' motivations for their enactments. Thirty-two teachers from five states in the U.S.A. were recruited to participate in interviews based on recommendations from…

This study presents an extension of the validity argument for the PCK-Fractions measure. PCK-Fractions is designed to assess the effectiveness of professional experiences in facilitating teachers' pedagogical content knowledge (PCK) for children's fraction reasoning in grades 3-5. We examined data across 101 participants from two Midwest…

The didactic strategy is given by the set of methods and techniques by which the cooperation between the teacher and students, between students and teacher, between students and students is achieved to obtain the anticipated results. For a positive result of the didactic approach, there must be a good didactic strategy capable of leading to the…

Block building activities help develop students' spatial reasoning, but few studies focus on the development of block building skills beyond preschool. We worked with four kindergarten, four first grade, and four second grade students to learn more about their Lego block building. We compared students' accuracy, building strategies, and spatial…

The purpose of this paper is to investigate students' engagement in computational thinking (CT) and programming with MATLAB when solving a mathematical task in a programming course at the undergraduate level. The data collection method is participant observation of three groups of three students presented with a mathematical task to solve. The…

The National Council of Teachers of Mathematics (NCTM) has been emphasizing the importance of teachers' pedagogical communication as part of mathematical teaching and learning for decades. Specifically, NCTM has provided guidance on how teachers can foster mathematical communication that positively impacts student learning. A teacher may have…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…