Constructing multiplicative reasoning is critical for students' learning of mathematics, particularly throughout the middle grades and beyond. Tzur, Xin, Si, Kenney, and Guebert [American Educational Research Association, ERIC No. ED510991, (2010)] conclude that an assimilatory composite unit is a conceptual spring to multiplicative reasoning.…

A converging body of evidence from neuroimaging, behavioral, and neuropsychology studies suggests that different arithmetic operations rely on distinct neuro-cognitive processes: while addition and subtraction may rely more on visuospatial reasoning, multiplication would depend more on verbal abilities. In this paper, we tested this hypothesis in…

Previous research suggests that the Approximate Number System (ANS) allows people to approximate the cardinality of a set. This ability to discern numerical quantities may explain how meaning becomes associated with number symbols. However, recently it has been argued that ANS representations are not directly numerical, but rather are formed by…

The subject of this study is to investigate if, and to what extent the performance of third-grade students' multiplication fact proficiency differs in a hybrid learning setting as compared to in-person instruction. These differences were questioned by researching if there was a change in student proficiency due to the instructional modality, if…

This study aims to analyze and to describe, in terms of information processing theory, the thinking processes of junior high school students as they solved problems involving direct and inverse proportions. This study design is qualitative and exploratory-descriptive in nature. 26 students in the seventh grade of SMP Negeri 1 Kota Ternate were…

This case study investigated the relationship between five undergraduate interior design students' reasoning with numerical units and reasoning about length and area. The multiplicative concepts frame participants' coordination of numerical units. Differences were found between participants' reasoning about length and area, based on their…

Students encounter mathematics word problems as early as kindergarten and continue to see them throughout their schooling experience. Schema instruction with an attack strategy can support students to successfully navigate word-problem solving. Schemas help students categorize word problems by similar characteristics. To better support students…

There is broad consensus on the assumption that adults solve single-digit multiplication problems almost exclusively by fact retrieval from memory. In contrast, there has been a long-standing debate on the cognitive processes involved in solving single-digit addition problems. This debate has evolved around two theoretical accounts. Proponents of…

In this article, I argue that the common practice across many school mathematics curricula of using a variety of different representations of number may diminish the coherence of mathematics for students. Instead, I advocate prioritising a single representation of number (the number line) and applying this repeatedly across diverse content areas.…

This article provides a task that can be used effectively for exploring arrays in middle and upper primary schools, and the notion of prime and composite numbers in particular. As students are engaging in these activities, teachers can encourage them to record their arrays both diagrammatically and as number sentences.

Through a constructivist lens, this dissertation research (a case study) examines the problem of how elementary teachers' MKT might be related to their ways of implementing and adapting mathematical tasks to promote students' construction of multiplicative reasoning. In particular, this study addresses the following four research questions: 1.…

Multiplication fluency math interventions are utilized in elementary schools, but a dearth in scholarship exists on the effects of these interventions on fifth grade math students' performance and final grades. This scholarship gap may have an adverse effect on informing administrators and educators on best practices in helping fifth grade math…

Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely…

This research study sought to identify a solution for building fact fluency for middle school aged students identified with LD. After analyzing a 1st-12th grade independent school for students with LD's math curriculum, it was noted that basic fact fluency is not taught after grade five. This has shown to be problematic for students who enroll in…

The paper examined the relations among problem solving, automaticity, and working memory load (WML) by changing the difficulty level of task characteristics through two applications. In Study 1, involving 68 engineering students, a 2 (automaticity) x 2 (WML) design was utilized for arithmetic problems. In Study 2, involving 76 engineering…