In this study, we share our broad and deep search for what is known from blind-peer-reviewed research publications about the efficacy of the instructional practice of Number Talks. We describe our process for literature review and the subsequent analysis that revealed a shallow depth of articles for which one can discern the factors of quality of…

Mathematics is presented in non-STEM disciplines as a subject that helps students acquire tools they will need in their future careers. Therefore, the need for instruction in mathematics demands content, oriented not only towards fundamental principles and techniques, but also towards their application in a specific context. By directing the…

This paper leverages an intrinsic approach to the conception of mathematical knowledge for teaching (MKT) to show how it can be used to examine teachers' MKT. In this qualitative study, I interviewed eight practicing teachers using tasks designed to generate data regarding their (a) personal interpretations of slope, (b) understanding of how…

In this article, the authors present an inquiry activity presented to Year 7 students in a mathematics excellence class at a P-12 school in regional Queensland. Different students solved the activity (comparing the sugar content of fruit) using decimals, percentages, ratio and rates. By asking the students to solve a problem they were much more…

As educators of students with autism, many teachers recognize that the day-to-day instruction is helping students learn skills to improve their quality of life, for today and in the long term. For those who teach young students, it may be difficult to project that far into the future; however, the reality is that educators want students with…

This paper examines three elementary school mathematics textbooks (one textbook from each of 6th, 7th, and 8th grade) to determine to what extent these textbooks present questions with multiple outcomes and multiple solution methods. Document analysis as a qualitative research method is adopted. The findings reveal that only 8% of all three…

Students' solutions of enumerative combinatorial problems may be assessed along two main dimensions: the correctness of the solution and the method of enumeration. This study looks at the second dimension with reference to the Cartesian product of two sets, and at the 'odometer' combinatorial strategy defined by English (1991). Since we are not…

Mathematical learning is to produce a high competence individual with multiple skills in line with the needs of the 21st century. However, mathematical education is still plagued with problem of mastery of mathematical concepts. In addressing this problem, various initiatives and interventions need to be implemented to ensure that mathematical…

Two-hour long developmental teaching interviews were conducted with each of 14 sixth grade students, ages 11-12. The purposes of the interviews were to investigate how students solved arrangement problems (APs), and how their solutions of these problems differed from their solution of Cartesian product problems (CPPs). The 14 students represented…

There is anecdotal evidence that many elementary teachers integrate mathematics lessons and art activities by having students first make colorful, rich material that is subsequently used in an instructional activity. However, it is unclear whether such activities effectively promote learning and transfer of mathematical concepts. The goal of the…

Textbooks are a standard component of undergraduate mathematics courses, but research shows that students often do not view textbooks as productive resources to support learning. This article seeks to understand the factors affecting how individuals engage in reading a calculus textbook excerpt and what they learn from reading. To better…

The paper presents results of two case studies with undergraduate students majoring in applied mathematics and engineering. The first case study deals with students' preferences for and difficulties with application problems and pure mathematics questions in their courses. The students were majoring in applied mathematics and taking a second-year…

This paper analyses student views on an e-learning intervention that incorporated a content development tool and computer algebra systems, aimed at improving performance and applicability of mathematics knowledge. The study deliberately relied on open source tools, with high usability both online and offline, that can be customized to address the…

Teachers spend a lot of time talking about students: They talk about how students learn, how to best plan lessons for them, and how to understand their written work using different protocols. Instead of hypothesizing about what a student might do on a task or why a student made a certain mistake, why aren't teachers just asking the student?…

The purpose of this study is to investigate the impact of teacher education by examining instructional visions of graduates from a teacher education program, 2 or 3 years post-graduation. An instructional vision is a teacher's idealized image of teaching practice, encompassing aspirations and hopes of what could occur in her classroom. We…