This article aims to illustrate how the collective resolution of routine mathematical tasks can give rise to uncertainties, fostering and supporting a rich and authentic mathematical activity. While solving routine tasks may not typically be classified as problem-solving, the research presented in this paper shows that, at the collective level,…

This study examines the solutions of 34 kindergarten children as they create equal groups from n bottle caps, where n was equal to 8, 9, 22, and 23. For each n, children were asked to find as many different solutions as possible. The number of solutions they found, i.e., children's fluency, as well as the strategies used to create equal groups,…

Metacognition supports students in successfully working through struggle by equipping them with the tools to maintain an awareness of what they are doing and to change directions when needed to overcome obstacles. Thus, it is of little surprise that effective problem solvers spend a significant amount of time analyzing tasks relative to the amount…

Open tasks are mathematical problems "that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies" (National Council of Teachers of Mathematics [NCTM], 2014, p. 17). Open tasks can have more than one right answer, solution, or outcome. Facilitation of open tasks offers learning…

The ability to recognize one's learning processes is important for learning mathematics as it helps learners to practice the thinking process of how each element works in solving mathematics problems. The K-W-D-L technique has emerged as a technique that could bring about metacognition in learning and it could be beneficial in elementary school…

Textbooks are one of the learning mediums. The activities in mathematics textbooks and qualities of these activities are of paramount importance. Problem-posing is one of the activities in these textbooks. Many researchers emphasize that examination of textbooks is important in explaining student success. The purpose of this study was to examine…

Use of algorithmic thinking in education has received significant attention as it is grounded on thinking and performing the necessary action in line with a clearly defined purpose. The current study aimed to probe prospective classroom teachers' views on algorithmic thinking skills and use of these skills in education. The research data were…

Rich and challenging tasks can be the vehicle to bring mathematical challenge in classroom. Challenge emerges when you don't know how to solve the task at first but you can figure out, that is when the solvers are not aware of certain tools to solve the tasks and they have therefore to invent some mathematical actions to proceed. Some challenging…

This article aims to describe the mathematical identity of elementary school students during studying mathematics. When studying mathematics, the students often face difficulties in understanding the concepts which results the decrease in their learning motivation. It will lead to the lack of development of their mathematical identity. The…

This research brief discusses the benefits of teachers using mathematical discourse--allowing students to explain, justify, and debate their individual techniques for solving math problems--to enhance learning. Using this strategy requires educators to discard traditional teacher-centered modes of instruction and adopt new student-centered modes…

This study examined the effects of comparison and game-challenge strategies on sixth graders' learning achievement of algebra variable, learning attitude towards algebra variable learning, and meta-cognitive awareness of algebra variable learning. A 2 × 2 factorial design was used, and 86 students were invited to participate in the experimental…

In this article, associate professor Chrystal Dean describes how teachers can challenge their upper elementary students' understanding of area beyond a memorized formula. Herein she describes an activity that will show students the "why" behind using A = l × w to solve rectangular area problems. The activity will help deepen…

In this article, authors Jordan T. Hede and Jonathan D. Bostic present a classroom activity that challenges upper elementary students' understanding of area beyond a memorized formula and explores the meaning behind students using A = l × w to solve rectangular area problems. This activity will deepen students' understanding of the area…

The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…

Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally explaining how…