The National Council of Teachers of Mathematics (NCTM) has released Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence, a new report that urges math teachers (K-8) to focus on three big mathematics ideas at each grade level.
In contrast to providing a list of very specific items (standards, learning expectations) grouped under general goals, this report suggests a refocus on a small number of significant mathematical "targets" for each grade level, offering a "way of thinking about what is important in school mathematics." Throughout, there remains the need for clear emphasis on the Process Standards-communication, reasoning, representation, connections, and, particularly, problem solving.
NCTM's additional hope is that the report will encourage teachers to engage in an "ongoing, far-reaching, significant discussion with the potential to guide the thinking of the profession in the development...development of new models for defining curriculum, organizing instruction, developing materials, and creating meaningful assessments that can help students learn critical mathematical skills, processes, and ways of thinking and can measure and communicate what students know about the mathematics that we expect them to learn."
What qualifies a concept or topic to be a curriculum focal point, you ask? According to the NCTm report, a focal point has to pass "three rigorous tests:
All of the focal points and their descriptions can be downloaded FREE from NCTM's web site, but it might be helpful here to list the focal points for the middle school grades. Clicking on the links will provide an expanded description of each focal point for that grade level.
- Is it mathematically important, both for further study in mathematics and for use in applications in and outside of school?
- Does it 'fit' with what is known about learning mathematics?
- Does it connect logically with the mathematics in earlier and later grade levels?"
Grade 6 Focal Points:
Grade 7 Focal Points:
- Number and Operations: Developing an understanding of and fluency with multiplication and division of fractions and decimals
- Number and Operations: Connecting ratio and rate to multiplication and division
- Algebra: Writing, interpreting, and using mathematical expressions and equations
Grade 8 Focal Points:
- Number and Operations and Algebra and Geometry: Developing an understanding of and applying proportionality, including similarity
- Measurement and Geometry and Algebra: Developing an understanding of and using formulas to determine surface areas and volumes of three-dimensional shapes
- Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations
The next steps...First, math teachers need to engage in continued discussions of the focal points relevant to your grade levels. Second, math teachers need to realize that this is not a retreat to basic computational skills. And third, NCTM needs to produce focal points for grades 9-12 mathematics.
- Algebra: Analyzing and representing linear functions and solving linear equations and systems of linear equations
- Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle
- Data Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets