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This article describes and analyzes a program of work in elementary mathematics teacher education at the University of Michigan that has, for a decade, been a site for the development of approaches to preparing beginning K-8 mathematics teachers that are both aimed at practice and centered in content. Among the products of this work are video records, instructional tasks, and assessments, as well as structures for collective work on our courses. These materials and ways of working comprise a collection of resources for both the systematic improvement of the knowledge base for teacher education and the professional development of teacher educators. This practice-based approach to the development of both our courses and their instructors has enabled us to improve professional instruction and to build knowledge that is useful beyond a particular course or the individuals who work in it. We begin by discussing 2 central problems of teacher education that our group has tried to address and then describe the types of materials and ways of working that we have developed. We analyze the features of the professional curriculum produced from this work, relate them to the problems, and consider issues about transferability to contexts beyond our own.

In this article, we describe features of learning goals that enable indexing knowledge for teacher education. Learning goals are the key enabler for building a knowledge base for teacher education; they define what counts as essential knowledge for prospective teachers. We argue that 2 characteristics of learning goals support knowledge-building efforts. First, learning goals should be targeted; they must be sufficiently well specified to suggest interventions for supporting learners in achieving them and to indicate the types of evidence needed to determine if the goals have been achieved. Second, learning goals should be shared; they must be mutually understood and committed to by all participants in the knowledge-building process. By drawing on our experience in our local efforts to develop knowledge for preparing prospective elementary mathematics teachers, we illustrate how targeted and shared learning goals support efforts to build a knowledge base for teacher education. We then propose the use of learning progressions for supporting knowledge-building endeavors across sites.

The article discusses the different ways in which teachers' awareness of the difference between procedural knowledge and conceptual understanding can be heightened. By allowing teachers to work with mathematical ideas, teachers become learners and are thus able to impart learning with understanding.

The author uses the method of problem solving learnt from Cognitively Guided Instruction (CGI) training on students. This instructional program helps in building new mathematical knowledge, adapt strategies and monitor on process of problem solving.

Training is conducted to establish kids who are confident, critical, trying to ask questions and who recognize when something doesn't make sense. Some of the ways in which the second-grade teachers support the mathematics learning of the diverse group of students in their class is explored.

Teaching is an important part of the jobs of statistics professors and graduate students, but most of us receive little training for teaching in general or statistics teaching in particular. We have developed a course for statistics graduate teaching assistants that combines practice in statistics demonstrations and drills, discussion of teaching strategies, and feedback on classroom teaching. The goal is to get our graduate students to be more comfortable with engaging their students in active learning. KEY WORDS: Active learning; Demonstrations; Drills; Graduate training; Statistics education., 1. THE PROBLEM Our students do a lot of teaching during their four or five years in the Ph.D. program, typically first as graders, then teaching assistants, and finally sometimes [...]

'Teachers are the key to academic achievement for students.' This statement is widely accepted, but professional development in early childhood mathematics education faces a number of barriers. What are those [...]

Issues concerning colleges and universities, and especially the mathematics departments within them, are examined, focusing on how mathematics departments must plan to meet the needs of the future. Topics include societal changes that affect universities, the influence of corporate management on college administration, corporate dependency on a highly educated workforce, college accountability for use of public funds, changing demographics, emphasis on undergraduate education, mathematics research agenda, and rewarding college faculty for accomplishment in their area of expertise, be it research, teaching, or curriculum development.

The professional development of teachers of mathematics can be significantly enhanced by involving them in worthwhile and interesting mathematical tasks such as the computation of effective tax rates. Workshops are held where teachers participate in solving mathematical problems and discussing solutions. In this activity, teachers share strategies and assess the validity of various approaches to solving problems. It also allows teachers to make a connection between their personal experiences as problem solvers and their actions and beliefs as mathematics teachers.

Educational Development Center, Incorporated, organized a professional development program for elementary, middle and high school mathematics teachers, with algebraic thinking as the main theme. Integrated learning enabled teachers to assess and analyze the themes that enhance algebraic thinking across all grade levels. Describing patterns, functions and algebraic structures, and generating adequate pedagogy were identified as some of the factors fostering algebraic thinking. Problem activities that helped teachers to evaluate algebraic thinking in detail are described.

Efficient development of mathematical pedagogy necessitates providing adequate support to teachers' learning at all phases of the teaching process, and encouraging them to use new pedagogical tools and practices. Teachers use their knowledge in planning instructional activities, implementing the plans and reflecting on the classroom experiences. Support activities such as workshops, planning periods, lesson modeling, feedback and critical reflection help teachers to practice effective pedagogical methods. Such support activities help to enhance professional development.

I believe portfolios are very worthwhile. In fact, even though they are significantly more work, the benefits far outweigh any final exam, any day. The benefits include self-reflecting, re-examining activities, [...]

The MGMP staff-development project suggests that an instruction-level model for problem-centered curriculum, alternative academic skills, and an intensive coaching can develop a professional mathematics teacher. Time spent by the teacher on learning, and the quality of mentoring available will help the teachers in implementing the curriculum. The professional achievements of two teachers associated with the MGMP project are presented.

The National Council of Teachers of Mathematics (NCTM) plans to improve mathematics education by developing a cordial relationship with students, teachers, and parents. NCTM lays emphasis on the connections between mathematics and the real world, and is working wholeheartedly to provide adequate professional-development opportunities for mathematics teachers. NCTM is working towards providing mathematical problems that do not just revolve around performing simple arithmetic operations. The council is also trying to remove the unfounded fears of parents about fuzzy mathematics.

An in-service program on alternative assessment uses portfolios and open-ended questions to make mathematics classes exciting, both for students and teachers alike. The emphasis on journal writing and projects enables students to communicate mathematically, while providing an opportunity to teachers to revise and redirect their teaching. Analysis of the program's performance reveals five important issues agitating the minds of teachers, namely, loss of predictability in the classroom, content coverage, increased demands on time, and teacher-parent communication.

The newly introduced Interactive Mathematics Program (IMP) for high school students changes the traditional teaching techniques by using calculators and computers for better understanding of the students. The objective of the IMP program is to motivate students to solve problems of mathematics by themselves. The teachers also have to modify their teaching processes according to the IMP curriculum. A long term study to find the results of IMP shows that the students associated with the program have a long time association with mathematics compared to the traditional students.

The National Council of Teacher's of Mathematic's Curriculum and Evaluation Standards for School Mathematics advocates enhanced usage of modern computing technologies in bestowing students with better understanding of mathematical phenomena, thereby aiding their growth in stature as real-world problem-solvers. Empowering teachers with the nuances of modern techniques and upgrading the quality of instructional materials are the initial strides toward effective classroom usage of advanced computing technologies.

The Boston University faculty, in attempting to reform the public schools of Chelsea, MA, realized the need for educating Chelsea's school mathematics teachers about the latest technological developments and their utility in educational instruction.. The Classroom Centered Teacher Development Mathematics Project, devised to provide professional training to teachers, brought about a major change in the teaching-learning process, allowing teachers to break free of the lecture-only method of teaching math. The model will be regularly revised to meet future needs.

Mathematics education in elementary and secondary levels requires programs that will teach students to apply mathematical concepts in their daily activities. This can be possible only if mathematicians also participate in programs that train teachers for this purpose. This should be supplemented with a change in attitude toward class environment and grading of students. The changes cannot be implemented easily, and require much planning and perseverence., In this article, H. Van Engen goes directly to the bottom line and places the responsibility for the problem that exists in elementary mathematics on elementary, secondary, and college teachers. [...]

One of the biggest challenges in teacher preparation programs is fostering teachers' abilities to build relationships with students while simultaneously cultivating students' academic potential. This is specifically vital in the [...]

A key component in improving elementary mathematics instruction is the professional development of mathematics teachers. To produce the necessary highly efficient mathematics teachers, teaching subject specialization must be implemented. With adequate funding and moral support, practicing elementary school teachers may freely choose to become subject teaching specialists who can implement the goals of the current mathematics curriculum.

In recent years many national bodies concerned with American education have recommended integrating topics from probability, statistics, and data analysis into the K-12 mathematics curriculum. A variety of efforts are under way to carry out these recommendations, including the ASA's Quantitative Literacy Project. This report describes another such effort. A statistician and a mathematics educator offered current high school teachers a one-semester course that would give them a background knowledge of statistics to help them implement the recommendations. In designing the course, we unearthed some resources that might be of use to others. In offering the course, we experienced a variety of successes and failures that may be of interest to anyone else considering a similar course. These experiences led us to rethink how we would teach such a course in the future and to consider alternative approaches to teacher (re)training. We describe our experience and provide a list of suggestions we hope might aid in implementing the new curriculum recommendations.

Graduate teaching assistants at Iowa State University develop their teaching skills through an apprenticeship-like process. First-year graduate students start out as laboratory instructors/graders. After the first year, some graduate teaching assistants teach a section of an introductory statistics course. This article describes this apprenticeship-like process and the mentoring and resources provided to graduate teaching assistants. KEY WORDS: Apprenticeship; Mentoring; Teaching assistants., 1. INTRODUCTION The process of training graduate students to be statistics teachers is an informal one in the Department of Statistics at Iowa State University. We do not teach a [...]

Preparing graduate students to teach, first for assignment as teaching assistants but also because some will follow academic careers, is a major concern for mathematics and statistics departments. This article provides background and raises issues to keep in mind when reading the program descriptions in the articles that follow. Changing our understanding of what constitutes effective pedagogy, improving the use of technology, and placing an emphasis on working with data in elementary courses raise the standard that teaching assistants must meet. Many graduate students come from countries with cultures and education systems quite different from those in the United States. Training programs should them selves be models of good pedagogy. KEY WORDS: Effective pedagogy; Teacher training., 1. INTRODUCTION Graduate teaching assistants (TAs) play a major role in the teaching of statistics to undergraduates. Their presence is concentrated in first courses. The 2000 CBMS survey (Lutzer, Maxwell, [...]

Suggestions on how to prepare teachers for mathematics instruction are offered. One of these would be to aid teachers in connecting their undergraduate mathematics courses to the math that they teach their students. Another would be to impart the knowledge of basic mathematical results to teachers during their undergraduate studies. Prospective teachers must also be encouraged to develop ways of thinking that use mathematical concepts and processes.

The National Council for Teachers of Mathematics has come up with two documents on educational standards which aim to provide a common philosophy and framework for schools and teachers. The Curriculum and Evaluation Standards for School Mathematics and the Professional Standards for Teaching Mathematics are teacher-support systems that begin at the lowest level in changing the teachers' attitudes and methodology in teaching math., Getting to know something is an adventure in how to account for a great many things that you encounter in as simple and elegant a way as possible. And there [...]

The American Statistical Association (ASA) developed Guidelines for Assessment and Instructions in Statistics Education (GAISE) to provide guidance to teach statistics effectively as part of the K-12 mathematics curriculum. The GAISE could be used to create a K-12 trajectory of the development of basic ideas and statistical reasoning related to the distribution of variables based on data.

The article describes a yearlong professional development seminar that discussed teachers' perceptions of the Equity Principle and suggested ways in which high school mathematics teachers can work toward equity in their classroom practices.

The author describes a modification of lesson study, known as 'microteaching lesson study' (MLS), and its application in teacher education. The method is a cooperative learning activity that promotes deeper understanding about teaching and learning mathematics among teachers.

A brief description about a course for preservice teachers called Number Systems from an Advanced Viewpoint is presented. It is designed for college students having plans to teach mathematics in middle or high schools.

A school-college collaboration in the design and implementation of preservice fieldwork is described and the importance of carefully preparing for instruction, anticipating student misunderstandings and reflecting on instruction after the lesson is examined. An overview of the required preservice college course is provided and an explanation of unexpected outcomes and college student testimony is presented.

The Center for Improved Engineering and Science Education (CIESE) at Stevens Institute of Technology helps mathematics teachers to integrate and implement engaging and innovative collaborative lessons into their curriculum for illustrating complex mathematics concepts. CIESE has developed online projects that incorporate complex mathematics concepts and link students with their peers around the world.

Suggestions and ideas that enable teachers to take a closer look at students' thinking are discussed. A teacher should periodically reflect on his or her own classroom practices in order to increase attention on students' mathematical thinking

Fisk University officials believe in getting young people turned on early to the idea that math is cool. So each summer they host science summer camps for middle school students [...]

In the spring of 2008, Dr. Maria Fernanda Botelho, a professor at the University of Memphis, was determined to improve the success rate in her elementary calculus course, so she [...]

Issues are presented concerning the influence which the Teaching Improvements through Mathematics Education 2000 project has had on the recruitment and preparation of teachers of mathematics of the future.