Is there any research that establishes the efficacy of Contexts for Learning Mathematics
Even though Contexts for Learning Mathematics is a new supplemental math series its units have been extensively researched and classroom tested, not to mention documented and filmed.
Contexts for Learning was designed and written by Catherine Twomey Fosnot and her colleagues from Mathematics in the City and the Freudenthal Institute. Catherine Fosnot is Professor of Education at the City College of New York and Director of Mathematics in the City. (The AERA SIG on Constructivism has twice awarded her their "significant contribution" award.) Mathematics in the City, located at City College of New York, is a national inservice provider for mathematics educators, K-8. The development of the center and the professional development materials that accompany this series were funded in part by the National Science Foundation under grants #9911841 and #9550080. The Freudenthal Institute is part of Utrecht University in the Netherlands. Founded in 1971 by the German/Dutch writer, pedagogue and mathematician, Hans Freudenthal (1905-1990), the institute has gained an international reputation for research and curriculum design with its theoretical approach towards the learning and teaching of mathematics known as Realistic Mathematics Education (RME). RME incorporates views on what mathematics is, how students learn mathematics, and how mathematics should be taught.
In addition to the authors listed on the covers of their respective books, this series is very much the result of a collaborative effort of teacher educators, mathematicians, classroom teachers, and researchers who have dedicated long hours to bring this project to fruition. In many respects, it represents a 12-year journey of working in classrooms with many talented teachers, developing and researching sequences of investigations using carefully crafted contexts from children's lives, assessing student achievement, filming and documenting the learning, designing digital professional development materials (also available from Heinemann), and finally the writing of the units in the Contexts for Learning series.
Initial funding for the teacher enhancement project and the related student achievement study came from the National Science Foundation (under grant #9911841) and the Exxon-Mobil Foundation. Funding for the subsequent filming and professional development materials also was provided by the National Science Foundation under grant #9550080. Many of the investigations in the units were initially developed and researched under those grants.
In 2002 a large study funded by the National Science Foundation was completed comparing student achievement results in Mathematics in the City classrooms with matched controls. Results showed:
Developed and fieldtested in New York City classrooms, the units in this series have had proven success with a broad range of students with diverse backgrounds and needs. To review this study, including methodology, data, and findings visit www.mitccny.org and select "research".
- a significant increase in student achievement,
- higher level computation strategies representing a deeper understanding of number and operation, and
- a willingness of students in Mathematics in the City classrooms to attempt to solve more problems.
Have any studies been done comparing Contexts for Learning Mathematics to other K-6 supplemental math programs?
An independent study by the Washington State Office of Superintendent of Public Instruction recently evaluated 28 elementary supplemental math programs. This study establishes that Contexts for Learning Mathematics is the best K-6 supplemental math program for teaching strategy development. In addition, this series is also recognized as one of the best supplemental math programs for meeting the diverse needs of today's contemporary classroom. Download a concise slide presentation on related findings or to access the full report go to http://www.k12.wa.us/CurriculumInstruct/Mathematics/default.aspx.
How do you think of your materials with respect to other reform curricula in the US that treat proportional reasoning—do you see them as similar or an alternative in some way?
One of the main differences between US curricula and the RME approach in Holland (and our materials) is the way that topic is treated. In the traditional US curricula, proportional reasoning is usually introduced in grade 6 or 7 as a special topic. In the Netherlands, the ratio table is the prevalent model for multiplication and division (rather than the array, which is more typical of US materials). Thus proportional reasoning is emphasized at the start, as soon as multiplicative thinking is being developed. In our materials we begin multiplicative work with the open number line and grouping of repeated groups. Then we develop the ratio table and use it as a model for multiplication (See our curriculum unit, The Big Dinner). Next we introduce the array in the unit, Muffles Truffles. This array model is extended to division in the Teachers' Lounge and to 3-D arrays in The Box Factory. All three models are used subsequently in minilessons as we work on computation. When we begin work on fractions, equivalence is emphasized in Best Buys, Ratios and Rates, the double number is used as a model for addition and subtraction of fractions emphasizing proportional reasoning, and arrays and ratio tables are used with multiplication and division (see Parks and Playgrounds). Proportional reasoning is at the heart of our work with the ratio table and the double open number line. You will also find many minilessons using these models to develop proportional reasoning in our Resource Guide, Minilessons for Operations with Fractions.