The present study describes preschool read-alouds in terms of the types of texts to which children are exposed. The methods involved analyzing the genre and instructional foci of 426 titles read by 13 teachers throughout an entire academic year. Additionally, associations between teacher characteristics and texts teachers read in their classrooms…

This paper examines the mathematical and teaching practices of the renowned self-taught Chinese mathematician Hua Loo-keng in the movement of popularizing mathematics in the People's Republic of China. In this movement, Hua Loo-keng taught industrial workers and peasants with a low level of education how to use fairly advanced mathematical methods…

Rate of change is an important concept for students to study, and little is known about the ways in which secondary students make sense of rate of change. In this qualitative study I examined how four high school students who have not taken calculus reasoned about changing quantities when interacting with mathematical tasks involving multiple…

This paper provides an interim report of a large empirical evaluation study in progress. An intervention was implemented to evaluate the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on Kindergarten students' mathematical development. Four large schools (two from Sydney and two from Brisbane), 16 teachers and…

The 2009 "Counting On" program has evolved from a series that began in 1999 and which continued to expand and change until the current manifestation. The program has always had a twin learning focus upon both students and teachers. Thus it seeks to improve student mathematical outcomes while building capacity within the teachers by…

This practice guide presents five recommendations intended to help educators improve students' understanding of, and problem-solving success with, fractions. Recommendations progress from proposals for how to build rudimentary understanding of fractions in young children; to ideas for helping older children understand the meaning of fractions and…

In this paper two 10th graders having an accumulated experience on problem-solving ancillary to the concept of area confronted the task to find Pick's formula for a lattice polygon's area. The formula was omitted from the theorem in order for the students to read the theorem as a problem to be solved. Their working is examined and emphasis is…

Recursion is a concept that can be used to describe the phenomena and natural occurrences in many different fields. As many applications utilize computer software to model recursion, recursion is a particularly important concept in the computing discipline. However, it is a difficult concept for many undergraduate students to master. A Recursion…

As young children make sense of mathematics, they begin to see with new eyes. What once was uncertain may now be determined. Objects become countable; fingers become tools; and numbers become more than just names. Educators revel in such developments--which mark significant progress toward more sophisticated understanding of number--and work…

For years, researchers have shown the value of using real-world data to enhance instruction in mathematics, science, and social studies. In an effort to help develop students' higher-order thinking skills in a data-rich learning environment, Green Research for Incorporating Data in the Classroom (GRID[subscript C]), a National Science…

We consider a volume of air trapped over a glycerol column in a eudiometer. We demonstrate that there is an approximately linear relationship between the volume of trapped air and the height of the glycerol column. Simply by moving the eudiometer up and down, we cause the glycerol-column height and trapped-air volume to vary. The plot of volume…

Our focus is on the design of systems (pedagogical, technical, social) that encourage mathematical abstraction, a process we refer to as "designing for abstraction." In this paper, we draw on detailed design experiments from our research on children's understanding about chance and distribution to re-present this work as a case study in designing…

An overview is given of three conceptual lessons that can be incorporated into any first-semester calculus class. These lessons were developed to help promote calculus students' ability to think conceptually, in particular with regard to the role that infinity plays in the subject. A theoretical basis for the value of these lessons is provided,…

Math discussions allow all students to get involved and take ownership of their mathematical knowledge. They allow students to think about what they are doing, reason about why it works, and understand the underlying concept. Teachers will be able to learn so much about their students through the discussions. They will be able to tell when their…

As part of an NCETM project, the author is involved with three local schools investigating how engaging in role play might aid children's mathematical development. The project embraces children ranging from part-time Reception to Y4. In this extract, two Reception-age girls, Rachel and Connie, are playing in their classroom spacecraft, and need a…