Physical distancing, which is widely practiced limiting the spread of COVID-19, is recognized to contain mathematical thoughts that can be harnessed as a context for prospective teachers' practices of mathematical problem posing. The goal of this study is to investigate the profile of mathematical tasks posed by prospective mathematics teachers…

This explanatory sequential mixed methods study, which consisted of QUAN [right arrow] to qual investigated the impact of mathematics word problems among African American students in the seventh grade. This study applied a culturally relevant education (CRE) lens to examine how students solve mathematics word problems. Ladson-Billings (1997) and…

This study sought to compare the effectiveness of teaching with manipulatives versus algorithms and procedures. Assessment data were collected before instruction, after instruction with algorithms and procedures, and after instruction with modeling and manipulatives. Data were collected from 113 students from the 5th, 6th, and 7th grades within…

Scholars propose that contextual problems can be used to ground students' understanding of mathematical ideas, and recent curricular trends have resulted in a plethora of resources that introduce and develop new mathematical ideas through contextual problems (CPs). Given the tension between this approach and the traditional role of CPs as…

The present study aims to describe and characterize the insights of elementary school students during the collaborative solving of mathematics problems. A total of 10 elementary school 60-min math classes were analyzed, with each session documented by videotaping the interaction of groups of 3 to 6 children. The study included 41 students in total…

This paper discusses the mathematical and didactical problems of teaching indefinite integral in the context of the ubiquitous availability of online integral calculators. The symbol of indefinite integral introduced by Leibniz, unfortunately, does not contain an indication of the interval on which the antiderivatives should be calculated. This…

What comes to mind when one thinks about building? One may envision constructions with blocks or engineering activities. Yet, constructing and building a number system requires the same sort of imagination, creativity, and perseverance as building a block city or engaging in engineering design. We know that children invent their own notation for…

Various features have been found hidden in the Pascal triangle. In this paper, some very well-known properties of the Pascal triangle will be presented, as well as the properties related to different extensions of the triangle, namely the Pascal pyramid. Given that in the textbooks of the tenth grade, respectively in the school, where we realised…

Discrete mathematics brings interesting problems for teaching and learning proof, with accessible objects such as integers (arithmetic), graphs (modeling, order) or polyominoes (geometry). Many problems that are still open can be explained to a large public. The objects can be manipulated by simple dynamic operations (removing, adding, 'gluing',…

While helping proofread a book during my doctoral studies, I came across a chapter that included (among other things) a discussion of a set of problems and tasks involving the building of towers using only two (or three) colours of cubes (Maher & Ahluwali, 2014). Later that year, as I started my tenure track position at the University of…

The present study attempted to explore the relationship between computational estimation and problem solving in a sample of Year 6 children and adults (N=72). For this purpose, participants were presented with two tasks which asked them to estimate the computational result in eight arithmetic operations (Computational Estimation Task) as well as…

Teachers are continually in search of tasks that balance the dual priorities of rigorous thinking and fluency development. These often-competing priorities are emphasized by national-level organizations as well as by state-level standards and assessments. The National Council of Teachers of Mathematics (NCTM) calls for school mathematics…

Geometry mastery is a must for high school students, affected by several factors such as learning approach (LA), gender, level of basic geometry competencies (BGC) and level of mathematical self-efficacy (MSE) among others. The purpose of this study is to examine those factors that affect the geometry problem solving (GPS) abilities of the…

The transition to tertiary mathematics requires students to use definitions of mathematical objects instead of intuitions. However, routines of defining and of proving with definitions are difficult to engage in, as they are not familiar to students who come from secondary school mathematics. Defining is highly complex because of its underlying…

Informal strategies reflecting the representation of a situation described in an arithmetic word problem mediate students' solving processes. When the informal strategies are inefficient, teaching students to make way for more efficient ways to find the solution is an important educational issue in mathematics. The current paper presents a…