Teacher mathematical noticing is a key component of mathematics teaching expertise and has been a focus of recent professional development efforts. In this paper, I propose and describe explicitly the notion of "productive" mathematical noticing, which surfaces from a case study involving a group of seven mathematics teachers who…

New Zealand and Australian curricula require students to learn about weight/mass for at least six years. However, little research identifies what should be taught. This study reports cognitive interviews with 17 Year 9 students who were asked "how heavy is my rock?" Only one student demonstrated some understanding of how to use analogue…

Forty-seven Aboriginal students in the Kimberley were interviewed in English and Kimberley Kriol to investigate their understanding of "everyday" words used within mathematics classrooms. The results showed that some of the Kindergarten and pre-primary students had difficulty with both the Kriol and English words, indicating they need to…

The purpose of this article is to provide strategies for recognizing meaningful mathematics in common play contexts in early childhood classrooms and to offer suggestions for how teachers might intervene in these moments to help children attend to the mathematical ideas embedded in their play. In particular, the author's focus on the concepts of…

It is not surprising, as research has shown, that fractions are one of the most difficult of the elementary school math topics to teach and learn in ways that are meaningful. The authors reference a work by James Hiebert, "Mathematical, Cognitive, and Instructional Analyses of Decimal Fractions" (1992), that mathematical concepts should…

Textbooks, as well as classroom instruction, tend to present estimation as a stand-alone exercise, ignoring that "the process of estimation depends on the situation itself as well as the estimator." When taught this way, estimation is stripped of its power to help students judge the reasonableness of answers and make sense before,…

Background: This article reports on an analysis of errors that were displayed by students who studied mathematics in Chemical Engineering in derivatives of mostly trigonometric functions. The poor performance of these students triggered this study. The researcher (lecturer) works in a mathematics support programme to enhance students'…

The purpose of this study was to determine the students perception on the use of animation courseware in math and to reveal how the sample courseware learning mathematical concepts to different change students' views. This research is a case study involving three mathematics students at SMAN 2 Bintan. Data were collected by means of…

Find out how to use photographic images to support the conceptual development of proportional thinking. This paper provides insight into a sequenced activity that promotes student engagement and makes links to familiar and unfamiliar contexts.

In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students' intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are able…

The purpose of this study was to determine the effects of dynamic mathematics software on the achievement of pre-service mathematics teachers in the topic of polar coordinates and to solicit their opinions about computer-assisted instruction. The study was conducted for 11 weeks with 33 pre-service teachers in the Department of Mathematics…

We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data…

Research over the past few decades points to ways precalculus and calculus courses can be strengthened to improve student learning in these courses. This research has informed the development of the Algebra and Precalculus Concept Readiness (APCR) and the Calculus Concept Readiness (CCR) assessments. In this article, the authors present three…

Despite few limitations, GeoGebra as a dynamic geometry software stood as a powerful instrument in helping university math majors understand, explore, and gain experiences in visualizing the limits of functions and the ?-d formalism. During the process of visualizing a theorem, the order mattered in the sequence of constituents. Students made use…

Oulipo (Ouvroir de Littérature potentielle, or Workshop on potential literature), an over 50-year old movement that began in France, seeks to apply mathematical constraints to literature and the arts. In this article, I will give a brief survey of this movement and how I have built a learning module based on it for my mathematics for the liberal…