**Archived Information**

Kindergarten Through Sixth Grade Mathematics Focusing

on Problem Solving and Concept Development

Developed and tested by the Mid-continent Regional Education Laboratory (McREL) |

The primary goal of the

Among the basic principles that guided developers were the following:

- Mathematics is a unified body of knowledge and should be organized and taught as such.
- Mathematics, as a body of knowledge, requires certain ways of thinking and cannot be done by the exclusive use of memory.
- Children learn through interrelated experiences and by reacting to problem situations.
- Mathematics is best learned when the applications presented are appropriate to students' levels of understanding and to their natural interests.

One of the manifestations of these convictions in the construction of the *CSMP* curriculum is the spiral approach. The content is completely sequenced in spiral form so that a student is brought into contact with each area of content continuously throughout the program. This approach consciously precludes atomizing the content and mastering each bit before continuing to the next. Students work through repeated exposures to the content, building interlocking experiences of increasing sophistication.

The content is learned in an atmosphere of constant connections with applications, from simple story situations to challenging applications to nontrivial simulations of real world problems. The emphasis at all times is on a two-level approach to learning: understanding and learningłunderstanding the content itself and its applications, and equally important, developing the techniques and processes of learning the content. It is the latter form of knowledge that gives power to apply the former.

To this end, the content is presented as an extension of experiences children have encountered in their development, both at the real-life and fantasy levels. Using a "pedagogy of situations," students are led through sequences of problem-solving experiences presented in game-like and story settings. Powerful non-verbal "languages," such as strings, arrows, and the Papy Minicomputer, allow students immediate access to the mathematical ideas and methods necessary not only for solving these problems, but also for continually expanding their understanding of the mathematical concepts themselves.

Tools and manipulatives such as the calculator, various geometry tools, random devices, various kinds of blocks, counters, and tiles are used extensively throughout the curriculum to pose problems, explore concepts, develop skills, and define new ideas.

This program addresses the needs faced by mathematic teachers as discussed in reports by many national groups, including the National Council of Teachers of Mathematics, the National Science Board, and the National Assessment of Educational Progress. These reports consistently stress several things:

- Problem solving should be the focus of school mathematics.
- The study of mathematics should emphasize developing higher order thinking skills (reasoning, analyzing, estimating, inferring, and others), understanding of concepts, communicating about mathematics, making mathematical connections, and applying mathematics.
- Basic skills in mathematics should be defined to include more than computational facility.
- School mathematics should provide for an integrated study with increased emphasis on content such as geometry, measurement, patterns, relations, numeration, probability, statistics, logic, algorithmic thinking, and applications.
- Mathematics programs should take advantage of technology such as calculators and computers.

At each grade level, a 5-year research and classroom-based development, evaluation, and revision cycle was followed, on a staggered basis. As the program was developed, piloted, and revised, both content and pedagogy were modified to reflect classroom experiences.

**Year 1.** Instructional materials were planned and taught by *CSMP* staff to heterogeneous public and parochial school classes. This experience led to a Local Pilot Test version of the materials.

**Year 2.** The Local Pilot Test materials were used by about 10 regular classroom teachers in St. Louis area schools. *CSMP* staff observed the classes and revised the materials, producing an Extended Pilot Trial version.

**Years 3 and 4.** The Extended Pilot Trial version was used for 2 years in a national network of cooperating schools. Extensive evaluation data, including comparisons of *CSMP* and non-*CSMP* classes, were collected.

**Year 5.** Revisions based on Local and Extended Pilot Test data resulted in the versions of materials that were then readied for publication.

An extensive evaluation dealing with many aspects of *CSMP* usage was conducted. This work led to the publication of many formal evaluation reports (about 60 volumes). Copies of evaluation reports and summaries of evaluation data are available.

Three primary claims can be made for *CSMP*:

*CSMP*improves students' ability to use the mathematics they have learned in new problem-solving situations involving estimation, mental arithmetic, representations of numbers, number patterns and relationships, word problems and producing multiple answers, prediction, and algebraic thinking.*CSMP*students show a higher level of enthusiasm and interest in math than do comparable students in more traditional programs.*CSMP*students perform in traditional computation skills as well as comparable non-*CSMP*students.

In the past several years, McREL has conducted further development activities to update, enhance, and extend *CSMP* to its current *CSMP/21* edition. In doing this work, the developers surveyed all *CSMP* sites and worked closely with teachers in Colorado sites to address classroom needs for mathematics curricula. Close attention was given to ensuring that the program aligned with both national and state standards for school mathematics.

The program is to be taught by the regular classroom teacher in a regular classroom. No other personnel or facilities are required. Depending on the grade level of implementation, between 6 and 30 hours of training are recommended.

Materials consist of both nonconsumable items, which last about 5 years, and consumable items that may need to be replaced each year. There are no special equipment costs.

To implement this program effectively, a school or district should appoint a *CSMP* coordinator (normally the district mathematics supervisor) and agree on an implementation plan that provides for the training of teachers, the evaluation of the program, technical assistance, and support services.

Costs associated with implementing this program vary, depending on the components of the program being used.

McREL-CSMP

2550 S. Parker Road, Suite 500

Aurora, CO 80014-1678

Phone: (303) 743-5520

Fax: (303) 337-3005

e-mail: cheidema@mcrel.org

Internet: http://www.mcrel.org

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