This study investigated the noticing of teachers who teach mathematics at different grade levels in the context of lesson study. The study specifically focused on teachers' noticing during the planning phase of the lesson. For this, the lesson planning phase of a group of four teachers consisting of kindergarten and primary school 1st grade…

Ensuring students correctly understand the notion of equality is a fundamental problem in teaching mathematics. Is it possible to teach arithmetic in such a way that students do not misinterpret the equal sign "=" as indicating the result of an arithmetic operation and, consequently, viewing the arithmetic operation symbols (+, -, or x)…

This study examined the effects of embodied learning experiences on students' understanding of computational thinking (CT) concepts and their ability to solve CT problems. In a mixed-reality learning environment, students mapped CT concepts, such as sequencing and loops, onto their bodily movements. These movements were later applied to robot…

Drawing on research around the utility of worked examples, we examine how 29 first- and 27 third-grade students made sense of integer subtraction worked examples and used those examples to solve similar problems. Students first chose which of three worked examples correctly represented an integer subtraction problem and used the example to solve a…

Pictorial representations are often used to help children understand the situation described in a given number-sentence scheme. These static pictorial problems essentially attempt to depict a dynamic situation (e.g., one bird flies away while there are three birds still sitting on the fence). Previous research suggested that such pictorial…

Do you work tirelessly to make your math lessons meaningful, challenging, accessible, and engaging? Do you spend hours you don't have searching for, adapting, and creating tasks to provide rich experiences for your students that supplement your mathematics curriculum? Help has arrived! "Classroom Ready-Rich Math Tasks for Grades K-1"…

The National Council of Teachers of Mathematics (2000) emphasizes the importance of communication in mathematics and mathematics education. Effective mathematical communication is essential in mathematics instruction, as it is a collaborative and social activity between teachers and students (Moschkovich, 2002; Khairunnisa et al., 2020). This…

The "Next Generation Science Standards" call for engaging students in practices that scientists and engineers use (NGSS Lead States 2013), but it's also important to explicitly teach thinking approaches that scientists and engineers use. One way to help children think and act like scientists and engineers is to engage them with…

This chapter focuses on the interaction of two first graders as they attempt to make sense of a particular instructional context for learning negative numbers. The context is one where they move an elevator to a building's floors above and below ground in order to model integer addition and subtraction problems. In particular, the focus of the…

Mastering the ability for learning to learn is the most ambitious goal of modern educators. A distinction is made between two relatively independent components of this expertise: (a) the reflective component of the learning to learn ability that allows a person comprehend what knowledge and skills he or she lacks to act in the new situation; (b)…

Our paper builds on the construct of the zone of proximal development (ZPD) (Vygotsky in Mind in society: the development of higher psychological processes, Harvard University Press, Cambridge, 1978) to analyze the relationship between students' answers and the help they receive as they construct them. We report on a secondary analysis of…

In this article, the authors describe how their first-grade class used the book "Inch by Inch" (Lionni 1960)--the story of an inchworm that escapes from a hungry robin by proving he is useful for measuring--as inspiration for a lesson focused on exploring length measurement through examining the meaning of an inch. The authors designed a…

In this article, we analyze a first grade classroom episode and individual interviews with students who participated in that classroom event to provide evidence of the variety of understandings about variable and variable notation held by first grade children approximately six years of age. Our findings illustrate that given the opportunity,…

The distinction between procedural and conceptual learning has long been a topic of discussion in mathematics education and the idea of compression into thinkable concepts that enable the individual make links between them (Tall, 2007). In addition to, the compression to thinkable concept was to be thinking mechanism arising naturally and…

Number and operations serve as the "cornerstone" of the K-12 mathematics curriculum in many countries. Solving problems in the mathematical domains of algebra, geometry, measurement, and statistics is often closely connected to student knowledge of number and operation (Griffin, 2005). Although considerable knowledge exists regarding the…