Materials

The Contexts for Learning Mathematics series by Catherine Fosnot and colleagues from Mathematics in the City and the Freudenthal Institute uses carefully crafted math situations to foster a deep conceptual understanding of essential mathematical ideas, strategies, and models. Building on the ideals of a math workshop, each unit provides a two-week sequence of investigations, minilessons, games, and other contexts for learning. The series’ 18 classroom-tested units are organized into three age-appropriate packages

• Investigating Number Sense, Addition, and Subtraction (Grades K–3) supports the development of such fundamental topics as place value, compensation and equivalence, addition and subtraction on the open number line, and the efficient use of five- and ten-structures.

• Investigating Multiplication and Division (Grades 3–5) explores with increasing sophistication big ideas in multiplication and division including systematic factoring, the distributive, associative, and commutative properties as well as their use in computation.

• Investigating Fractions, Decimals, and Percents (Grades 4–6) examines fundamental topics such as equivalence of fractions, how to multiply and divide with fractions, proportional reasoning, rates, and the ordering of decimals.

To learn more about Contexts for Learning Mathematics, please visit
http://www.contextsforlearning.com.

A 21st-century approach that provides pre- and inservice teachers with an interactive, video-based, digital context for inquiry into the teaching and learning of mathematics.
Designed for workshop leaders and college instructors, each Resource Package consists of three valuable components:

•A CD-ROM that offers users a multi-media learning environment for professional development on topics ranging from instruction to assessment, and that stimulates action, reflection, and discussion with dynamic video clips, children’s work samples, and interviews with students and teachers

•A Professional Development Overview Manual that provides general advice on teaching in a digital environment

•A Facilitator’s Guide specific to the CD-ROM that includes suggestions for using the video clips; sample dialogue from field-tested sites; facilitation tips; and more.

A three-volume set, Young Mathematicians at Work focuses on young children between the ages of four and eight as they construct a deep understanding of number and the operations(Each volume focuses on a different age group and a different area of number – addition and subtraction, multiplication and division, and rational numbers). Rather than offer unrelated activities, Fosnot and Dolk provide a concerted, unified description of development, with a focus on big ideas, progressive strategies, and emerging models. Drawing from the work of the Dutch mathematician Hans Freudenthal, they define mathematics as “mathematizing”—the activity of structuring, modeling, and interpreting one’s “lived world” mathematically. And they describe teachers who use rich problematic situations to promote inquiry, problem solving, and construction, and children who raise and pursue their own mathematical ideas.

In the fourth volume, Constructing Algebra, Catherine Fosnot and Bill Jacob provide a landscape of learning that helps teachers recognize, support, and celebrate their students’ capacity to structure their worlds algebraically. They identify for teachers the models, contexts, and landmarks that facilitate algebraic thinking in young students.

The arithmetic racks (rekenrek in Dutch) are used as a model in Investigating Number Sense, Addition and Subtraction (Grades K-3). The arithmetic rack is a calculating frame consisting of two rows of ten beads – two sets of five (one red and one white) in each row and provides a powerful model for exploring the composing and decomposing of number.
Arithmetic racks can be purchased through
www.mathrack.com

This collection of essays, edited by Cathy Fosnot and authored by several of the MitC staff and collaborators, synthesizes the research on intervention programs and best practices related to mathematical instructional pedagogy and differentiation to assist teachers, schools, and school districts in improving the manner in which they serve children with challenges in mathematics.
Published by the National Council of Teachers of Mathematics
www.nctm.org