Purpose: This paper aimed to present the design of a teaching module on mathematical problem solving for the upper primary mathematics. Method: The module used Pólya's and Schoenfeld's problem solving models as the theoretical framework. The researchers introduced problem-solving processes through specialized mathematics "practical"…

This chapter identifies the ways in which 15 prospective teachers engage the strands of mathematical proficiency as they solve word problems involving integer addition and subtraction. The prospective teachers, through think-aloud interviews, demonstrated a strong focus on solving problems using procedures, which some did not explain and others…

In this study, the elements of the design and results of the implementation of a Massive Open Online Course (MOOC) based on the problem solving and the use of digital technology are analyzed and discussed. The results show that the design of the activities, the intervention of the MOOC design team in the discussion forums and the interaction among…

Researchers have proposed a variety of methods to make a connection between real life and mathematics so that it can be learned in a practical way and enable people to utilise mathematics in their daily lives. Model-eliciting activities (MEAs) were developed to fulfil this need and are very capable of serving this purpose. The reason MEAs are so…

The Smarties-Box Challenge encourages students to apply several different mathematical capabilities and concepts--such as, estimation, multiplication, and the notion of being systematic--to solve a complex, multistep problem. To effectively engage in the Smarties-Box Challenge, students are required to demonstrate aspects of all four proficiency…

This exploratory study examined how pre-service teachers (PSTs) pose mathematical problems for free and structured mathematical problem-posing conditions. It was hypothesized that PSTs would pose more complex mathematical problems under structured posing conditions, with increasing levels of complexity, than PSTs would pose under free posing…

Mathematical games are widely used in the primary classroom; however, not all games are equally valuable. How might teachers decide which specific games to introduce? The authors present five principles of educationally-rich games to help teachers address this issue. In so doing, they provide teachers with a usable framework to stimulate…

The purpose of this research was to determine strategies used by 8th grade students in Number Sense problems. This was a case study of 28 8th grade students at three similar secondary schools in a city centre south of Turkey. A Number Sense test consisting of 25 items designed according to five main Number Sense components was used as a data…

The present study explored the relationships between student engagement and mathematics achievement for 295,416 15-year-old students from 11,767 secondary schools in 34 countries who participated in the Program for International Student Assessment (PISA) 2012. Affective engagement was measured by students' mathematics interest (InterestMath) and…

Mathematical skills are essential for young people to attain academic results needed for further study and employment. Recent changes to the English National Curriculum have put an increased emphasis on pupils explaining the reasoning behind answers in maths. This is a skill that can be developed by improving metacognitive skills. The authors…

Using memorized rules and algorithms without coherence and understanding is a perennial problem for teachers and students especially in the teaching and learning of fraction operations. I present data in which prospective middle school teachers explain a commonly used rule for fraction division--keep-change-flip. I argue that using both strip…

This article concerns student sense making in the context of algebraic activities. We present a case in which a pair of middle-school students attempts to make sense of a previously obtained by them position formula for a particular numerical sequence. The exploration of the sequence occurred in the context of two-month-long student research…

Clock Buddies is our favorite first-day-of-class activity. It starts as a nonthreatening icebreaker activity that helps students learn one another's names, but it soon asks students to find their own strategies for solving a real-world scheduling problem. Even highly math phobic students work with others and succeed. Students gain insight from…

This study proposes a framework for investigating how preservice mathematics teachers notice students' reasoning about comparing distributions, including preservice teachers' attention to statistical elements used by students, interpretation of students' understanding, and decision about how to respond to students' statistical reasoning. The…

In this article, we use a two-dimensional assessment to examine the experimental impacts of a mathematics learning trajectory-oriented formative assessment program on student strategies for problems involving multiplication and division. Working from the theory that the development of students' multiplicative reasoning involves improvements in…