Promoting Preservice Elementary Teachers' Awareness of Learning and Teaching Mathematics Conceptually Through KTEM

Hortensia Soto-Johnson, Michele Iiams, Todd Oberg, Barbara Boschmans, & April Hoffmeister

In this article, we describe preservice elementary teachers' reactions to Liping Ma's (1999) book, Knowing and Teaching Elementary Mathematics (KTEM), from five universities. Ma's discussion of solely teaching elementary mathematics procedurally and its consequences awakens the preservice teachers' memories of learning elementary mathematics. Ma's analysis of and solution to the problem ignites strong emotions in the preservice elementary teachers and promotes a desire to teach elementary mathematics conceptually. Through the analysis of writing assignments, we summarize how reading and reflecting on KTEM gives preservice teachers an opportunity to examine their beliefs about teaching and learning elementary mathematics conceptually.

Introducing the Emerging Discipline of Statistics Education

Dani Ben-Zvi & Joan Garfield

Increasing attention has been given over the last decade by the statistics, mathematics and science education communities to the development of statistical literacy and numeracy skills of all citizens and the enhancement of statistics education at all levels. This paper introduces the emerging discipline of statistics education and considers its role in the development of these important skills. The paper begins with information on the growing importance of statistics in today's society, schools and colleges, summarizes unique challenges students face as they learn statistics, and makes a case for the importance of collaboration between mathematicians and statisticians in preparing teachers to teach students how to understand and reason about data. We discuss the differences and interrelations between statistics and mathematics, recognizing that mathematics is the discipline that has traditionally included instruction in statistics. We conclude with an argument that statistics should be viewed as a bridge between mathematics and science and should be taught in both disciplines.

The Effects of a Teacher In-Service on Low-Achieving Grade 7 and 8 Mathematics Students

John A. Ross, YunMei Xu, & John Ford

Previous research (e.g., Woodward & Baxter, 1997) found that Standards-based mathematics teaching provides marginal or no benefits for low achievers, in contrast with positive effects for middle and high ability students. A randomized quasi-experiment in 52 Canadian schools found that low achieving grade 7 and 8 students who received support consisting of placement on a learning continuum, instruction focused on their specific learning needs, and concrete materials to represent mathematical constructs, benefited from teaching that emphasized construction over transmission of knowledge. Treatment students showed small but statistically significant improvements over controls in student achievement, and controversially, in mathematical beliefs, and attitudes. The latter finding raised issues of the appropriate balance between Type I and Type II error in educational research.

High-School Students' Approaches to Solving Algebra Problems that are Posed Symbolically: Results from an Interview Study

Mary Ann Huntley & Jon D. Davis

A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from three problems that were posed in symbolic form. Two problems are TIMSS items (a linear inequality and an equation involving square roots). The other problem involves square roots. We found that the majority of student pairs used symbol manipulation when solving the problems, and while many students seemed to prefer symbolic over graphical and tabular representations in their first attempt at solving the problems, we found that it was common for student pairs to use more than one strategy throughout the course of their solving. Students' use of graphing calculators to solve the problems is discussed.