This report focuses on the processes of change in beliefs and practices experienced by practicing elementary school teachers during a sixteen-session course using two of the modules from the "Developing Mathematical Ideas" (DMI) materials. We identify a collection of six metaphors for knowing, learning, and teaching mathematics to succinctly…

This paper presents a study on thinking and learning processes of mathematics and science in teaching through a foreign language, in Finland. The entity of thinking and content learning processes is, in this study, considered as cognitional development. Teaching through a foreign language is here called Content and Language Integrated Learning or…

Problems in comprehending the language of instruction may contribute to language minority children's difficulties with different educational tasks. In this project the relationship between difficulties in language comprehension and task solutions was explored by studying in depth the concrete interactions and communications in mathematical lessons…

This study explored whether and how teachers' mathematical knowledge for teaching contributes to gains in students' mathematics achievement. The authors used a linear mixed-model methodology in which first and third graders' mathematical achievement gains over a year were nested within teachers, who in turn were nested within schools. They found…

In the past decade, there has been an increased emphasis on the preparation of teachers who can effectively engage students in meaningful mathematics with technology tools. This study presents a closer look at how three prospective teachers interpreted and developed in their role of facilitating students' mathematical problem solving with a…

The National Council of Teachers of Mathematics (NCTM) states that "Communication is an essential part of mathematics and mathematics education" (2000, p. 60). In fact, communication is one of the five process standards emphasized by NCTM. The communication standard highlights the importance of young children communicating their mathematical…

The Animation Tutor[TM] is a curriculum project that uses software to supplement instruction in courses such as intermediate algebra. Its purpose is to ground mathematical reasoning in concrete experiences through the use of interactive animation and the virtual manipulation of objects. This article summarizes how the project has progressed from…

ProbLab is a probability-and-statistics unit developed at the Center for Connected Learning and Computer-Based Modeling, Northwestern University. Students analyze the combinatorial space of the 9-block, a 3-by-3 grid of squares, in which each square can be either green or blue. All 512 possible 9-blocks are constructed and assembled in a "bar…

Japanese Lesson Study is a collaborative approach for teachers to plan, present, observe, and critique classroom lessons. Through the lesson study process, teachers systematically and thoughtfully examine both student learning and their own teaching practices. In addition, the process paves the way for a much broader approach to education…

Today's technology standards (International Society for Technology in Education, 2000) challenge teacher education programs across the nation to address the need to produce computer literate teachers who are confident in their ability to choose and incorporate instructional technology into their classroom teaching. The purpose of this paper is to…

The sport of Ultimate has grown from parking lot fun to international competition in its 35 year existence. As in many sports, the team that scores is subsequently on defense. Thus the probability that a team will score next is dependent on which team has scored most recently. Unlike in many other sports, teams switch ends after each score. Thus…

Within mathematics education, classroom teachers, educational researchers, and instructional designers share the common goals of understanding and improving the teaching and learning of mathematics. Teachers work to help students learn; researchers study how people learn and teach mathematics; and designers develop instructional materials to…

The practice of students going to the boards to work problems has been a tradition in undergraduate education for over two hundred years. A study was conducted to determine what instructional techniques enabled students to better learn fundamental concepts in mathematics. This study identifies board work as a highly effective instructional…

This paper examines various issues surrounding the use of writing in the teaching and learning of mathematics using the voice and experiences of a licensed High School teacher instructing introductory college mathematics as a graduate teaching assistant. In general, we detail the journey taken by this teacher to explore the push for writing by…

More than a decade has passed since Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and Professional Standards for Teaching Mathematics (NCTM 1991) were published, and the question of whether students' learning of mathematics has improved during that time has frequently been asked. Scores on the mathematics assessment of the…