The purpose of this research was to investigate students' mathematical understandings of fraction division with an ethnomathematics/STEM framework. A small group teaching study (Cobb et al., 2003) was conducted using design research methodology to examine how students interacted with the curriculum. The researcher served as interventionist and…

This study's purpose was to examine the effects of the concrete-representational-abstract integrated (CRA-I) sequence on the performance of students who struggled with rational number concepts. Three students in southeastern U.S. fifth grade class participated in the study. The CRA-I intervention was grounded in the principles of explicit…

Recent solar eclipses provide relevant real-world contexts for learning about the scientific phenomena of the lunar phases. News coverage of the phenomenon may have raised questions such as, "Why does the Moon look different at different times, and sometimes as if it is not there?," and "What patterns can be found in the lunar…

The paper presents findings from a study that examined, through the lens of the Image Having layer of the Pirie-Kieren model, the qualitative characteristics of the images that different children formed when engaging with eight, novel partitive quotient tasks. The Image Having layer is the first point of abstraction within the Pirie-Kieren model.…

In many schools across the world, students experience mathematical concepts as ideas empty of wisdom and possibility. In this paper the authors analyze a philosophical conversation in which fifth-grade students were caught up in the animacy of the concept of space. Challenging the common view of mathematics as dealing with absolute truths and…

After years of noticing the challenge our students have with fraction operations, we decided to implement a scaffold approach that focuses on using benchmarks to better develop both students' understanding of a fraction as a quantity and their ability to think about fraction operations meaningfully. While we found this approach supported students…

When educators started incorporating the letter A into the STEM acronym to form STEAM some science educators had reservations. Seen from a western, rationalistic way of knowing (Colucci-Gray et al. 2017, 23) the STEM community had detractors regarding the idea of integrating art into science. Hence, scientific language is often thought of as being…

Generalization is one of the core aspects of algebraic thinking, and research literature points to the importance of objectification when generalizing mathematical discourses. To increase the field's understanding of the objectification process in various algebra discourses, our study analyses Grade 6 teachers' use of words, symbols, routines and…

Mathematical coherence is a goal within the Common Core State Standards for Mathematics. One aspect of this coherence is how student mathematical thinking is developed across concepts. Unfortunately, mathematics is often taught as isolated ideas across grades. The multiplicative field is an area of study that needs to be examined as a space to…

Competence with rational numbers is essential for mathematics proficiency in secondary mathematics. However, many students struggle with rational number concepts, and students with mathematics difficulties struggle even more. The purpose of this study was to examine the effects of an intervention that incorporated the use of explicit instruction…

Instructional designs that include two or more artifacts (digital manipulatives, tables, graphs) have shown to support students' development of reasoning about covarying quantities. However, research often neglects how this development occurs from the student point of view during the interactions with these artifacts. An analysis from this lens…

In this article, we address a call by Thompson and Carlson to directly contribute to defining the variation of students' reasoning about varying quantities. We show that students as young as in sixth grade can engage in complex forms of reasoning about multiple quantities in contexts that involve exploring science phenomena using interactive…

The concept of fractions given in learning is the concept of part of whole and part of unit. The development of student's concepts of fractions can be built through fraction schemes. A partitive fraction scheme is a scheme that estimates the size of the fraction in the form of non-units to the whole that is not partitioned. The concept of…

Numerous studies (Anwar et al., 2016; Carpenter et al., 1980; Huang & Witz, 2013; Outhred & Mitchelmore, 1996; Machaba, 2016; Van de Walle, Karp & Bay-Williams, 2014; Winarti et al., 2012) have shown that students need help understanding the concept of area and perimeter. This study aimed to investigate what students know about finding…

The association or relationship between two variables, also known as covariation, has been identified as one of the fundamental statistical concepts. This article details a statistical investigation that was used to informally introduce Grade 6 students to this concept.