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Meg Meyer

August 2009

“Mathematics for all” is a goal that has not been realized, despite the attention and efforts of many mathematics educators.

The 2008 Trends in International Mathematics and Science Study (TIMSS) showed that mathematics learning opportunities for students in the U.S. are often shallow, compared to many other countries. The curriculum, particularly with the middle grades, is repetitive and lacks depth. And too often assessments do not align with district frameworks and classroom curriculum materials. That means students are either tested on mathematical content they have not had the opportunity to learn, or they are tested on only a small part of what they have learned.

The development of richer, more challenging mathematics classroom environments and learning opportunities requires simultaneous renewal of curriculum, instruction, and assessment.

The Show-Me Center Project (1997-2007) promoted the dissemination and implementation of four comprehensive NSF-funded middle school mathematics curriculum programs and related professional development for teachers: Connected Mathematics, Mathematics in Context, MathScape, and MathThematics. Lessons learned from the Show-Me Project are document ted in the book, A Decade of Middle School Mathematics Curriculum Implementation (Information Age Publishing, 2008).

Mathematics In Context
Mathematics  in Context (MiC) was developed and later revised at the Wisconsin Center for Education Research under the leadership of Thomas Romberg in collaboration with a group of curriculum designers at the Freudenthal Institute (FI) in the Netherlands.  MiC embodies the theory of Realistic Mathematics Education (RME) proposed by Hans Freudenthal.  Instead of seeing mathematics as subject matter that has to be transmitted, RME stresses the idea of mathematics as a human activity, arising from the reality of students. Education should give students the "guided" opportunity to "re-invent" mathematics by doing it.

Conventional middle grades mathematics curricula have generally portrayed learning sequences in terms of related abstract representations to develop procedures and algorithms. In contrast, MiC instructional sequences are conceived as “learning lines” in which starting points elicit informal, often concrete, representations. These concrete representations help students make sense of important mathematical abstractions.

The Show-Me Project
Show-Me Project Director for MiC and WCER assistant scientist Margaret (Meg) Meyer says the project supported change in teachers' practice by targeting curricular change.  The project's goals included:

• Supporting the awareness, examination, and implementation of comprehensive standards-based middle school mathematics curricula;
• Designing, developing, and supporting professional development opportunities for middle grade teachers and administrators;
• Providing communication networks for middle school teachers and their district teams who implement new curricular and instructional techniques designed to advance student understanding and achievement in mathematics; and
• Providing information and professional development to mathematics educators and mathematicians in higher education who prepare future generations of middle grades mathematics teachers.

Changes in Teaching
Since the publication of the 1989 NCTM Standards and the publication of the standards-based curricula, it has been clear that teachers are being asked to teach different mathematics (than they learned) in different ways (than they were taught) and this demands significant professional development.

For example, when using MiC, teachers encounter a tension between (a) teaching for student recall of common algorithms and (b) teaching for student understanding through guided reinvention using mathematical models (including for example percent bars and ratio tables). The teacher supports students’ guided reinvention with these models through the use of questions, examples, and counterexamples that clarify how the models could be used.

As a result, MiC emphasizes that teachers’ professional development experiences should address:

a. the function of problem contexts
b. the rationale for various mathematical models and tools
c. the sequencing of activities to promote progressive formalization of the mathematics, and
d. a multi-dimensional approach to assessing student understanding.

Challenges Remain
Despite the success of these reform mathematics curricula, and of the Show-Me Project, challenges remain, Meyer says. These challenges face mathematics teachers, district leaders, teacher educators, and future mathematics curriculum developers over the next decade.

Challenge 1: Students in many parts of the country have not had the opportunity to learn mathematics using quality standards-based mathematics curricula.

Challenge 2: The four NSF-funded curricula were developed in response to the 1989 NCTM Standards. At that time, few states and fewer districts had a mathematics curriculum framework. The landscape has changed drastically since; most states and districts have their own standards or frameworks. Expectations for students vary widely by state and district. Students meeting proficiency standards in one state can be considered below proficient in another. What happens then?

Challenge 3: Curriculum publishing is a business, and publishers must keep an eye on the bottom line. If a curriculum does not sell, the publisher will not continue to support it. Curriculum developers and publishers need to continue cooperating to ensure the educational and commercial viability of the curriculum materials.

Challenge 4: Over the course of the 10 years of the Show-Me Project, the four sets of curriculum materials evolved in response to several outside forces. One effect of the standards movement has been to push the first-year algebra course down into the middle school. At issue is agreement about what constitutes a first-year algebra course.

Another new challenge was the 2006 publication of the National Council of Teachers of Mathematics (NCTM) Focal Points. The Focal Points identify the curricular content focus of specific grades. If these recommendations are followed, there will be problems with Show-Me Project curricula. That’s because they focus on well-articulated learning trajectories of content to be developed over several grades. The formalization of concepts is not always the first goal at a particular grade level in which the content is taught.

Next Steps
Meyer says future curricula development will continue to be influenced by the research-based efforts of the authors of the Show Me Project family of materials.

The lessons learned from this project cut across the four curriculum programs and share commonalities with standards-based curriculum reform at any level, Meyer says. She believes that documenting these lessons learned will be one of the legacies of the Show-Me Project.