(Center for Comprehensive School Reform and Improvement, Issue Brief, March, 2006.)

By Craig D. Jerald

Assistance providers, education leaders, and policy makers also will need to provide schools with strategies for dealing with knowledge deficits that are identified. Fortunately, another study conducted by two of the same researchers revealed that a teacher's math knowledge can be boosted by good professional development. "Our results show that teachers can learn math for elementary school teaching in the context of a single professional development program."(7) However, the training that benefited teachers most kept the math front-and-center, focusing on mathematical analysis and communication rather than general teaching strategies that might work for any subject.

Finally, assistance providers will need to help elementary schools directly confront deeply held, longstanding beliefs about what kinds of things younger students need in their teachers. That will not be easy. Many educators and even experts believe that focusing on the math skills of elementary grade teachers would be profoundly misguided. Indeed, in the striking conclusion to an article in last fall's American Educator magazine, Ball and her colleagues report that they have been heavily criticized for even conducting this kind of research in the first place. Critics have accused them of somehow cheapening the teaching profession:

[The] negative responses we have received from some other education professionals are noteworthy. Testing teachers, studying teaching or teacher learning [...], using standardized student achievement measures-each of these draws sharp criticism from some quarters. [...] [Some critics] claim that we are "deskilling" or "deprofessionalizing" teachers by "testing" them.(8)

In response, the researchers argue that if empirical evidence shows something to be important for teaching and learning, researchers have an obligation to try to understand it, even if the findings run counterintuitive to our traditional beliefs about what makes a good teacher.

But let's go one step further. If that research shows that something can benefit student learning, we should expect school leaders and assistance providers to address it as they seek to improve schools. The challenge should not be to figure out how to improve math achievement despite low math knowledge and skills among teachers. The challenge should be to find ways to talk about and deal with that problem in ways that do not unduly antagonize or offend teachers. A

fter all, NCLB places a strong emphasis on mathematics for some very good reasons. Students who fall behind educationally seldom catch up later on, and this is especially true in math, a "cumulative" subject area that builds new knowledge upon foundational skills mastered previously. A weak math foundation can have profoundly negative consequences for young people later in life, including the following:

• Many American teenagers struggle with algebra when they reach high school, and researchers have found that failing ninth-grade algebra is a strong predictor of dropping out.(9)
• Multiple large-scale federal studies have revealed taking and passing high school math courses beyond algebra II has a strong impact on whether students complete college, regardless of family background.(10)
• Whether they graduate from college or not, young people with low math skills now struggle to find decent jobs in an economy where skill demands have increased dramatically during the last 20 years-even in so-called "blue collar" jobs that require little or no post-secondary education.(11)

As Don Davis, the director of an apprenticeship program for union electricians in California told the Los Angeles Times in January, "If you want to work in the real world, if you want to wire buildings and plumb buildings, that's when it requires algebra."(12)

Therefore, even aside from the legal obligation to meet accountability standards for math in federal and state law, educators have a strong moral obligation to the grown-ups children will someday become to ensure that students gain a strong foundation of math skills in the elementary grades.

In Sum ...

Some might argue that the problem isn't elementary teachers' mathematical knowledge but their ability to teach math in new ways. That, of course, is also an important issue-one that is being addressed through everything from classroom materials and curricula to staff development and in-house math coaches. Many teachers are benefiting from such efforts. But the ability to use new curricula and techniques-from first grade forward-requires adequate knowledge of the subject matter itself. If anything, the current push to "teach for understanding" requires teachers to have a deeper understanding of the elementary math curriculum themselves.

Far from being radical, that sentiment reflects a growing consensus in the field. Last summer, the American Mathematical Society published a paper by a group of math educators and researchers trying to move beyond the current "math wars" by determining how much common ground they share and what the realm of consensus is. The paper concludes:

Teaching mathematics effectively depends on a solid understanding of the material. Teachers must be able to do the mathematics they are teaching, but that is not sufficient knowledge for teaching. Effective teaching requires an understanding of the underlying meaning and justifications for the ideas and procedures to be taught and the ability to make connections among topics. Fluency, accuracy, and precision in the use of mathematical terms and symbolic notation are also crucial. [...] Well-designed instructional materials, such as textbooks, teachers' manuals, and software, may provide significant mathematical support, but they cannot substitute for highly qualified, knowledgeable teachers.(13)

Finally, of course, no one would suggest that elementary school students also don't need caring classroom environments.(14) But the evidence is now clear. Children need math as well as nurturing. Why can't we give them both?

References

1. NCLB permitted states to establish additional, alternative ways for middle and high school teachers to demonstrate subject-matter knowledge-called the "high objective uniform state standard of evaluation (HOUSSE) provision" in policy circles-for example, through relevant experience and professional development. Most states have taken advantage of that flexibility.
2. Hill, H. C., Rowan, B., & Ball, D. L. (2005, Summer). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406. Retrieved March 6, 2006, from http://www-personal.umich.edu/~dball/Publications/SelecteJournalArticles/HillRowanBallAERJSummer05.pdf
3. Hill, H. C., Rowan, B., & Ball, D. L. (2005, Summer). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 388. Retrieved March 6, 2006, from http://www-personal.umich.edu/~dball/Publications/SelecteJournalArticles/HillRowanBallAERJSummer05.pdf
4. Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah, NJ: Erlbaum. Interested readers might want to consult a short review of Ma's book that does an excellent job summarizing her findings: Askey, R. (1999, Fall). Knowing and teaching elementary mathematics. American Educator, 23(4), 1-8. Retrieved March 6, 2006, from http://www.aft.org/pubs-reports/american_educator/fall99/amed1.pdf
5. Ball, D. L., Hill, H. C., & Bass, H. (2005, Fall). Knowing mathematics for teaching. American Educator, 29(3), 44. Retrieved March 6, 2006, from http://www.aft.org/pubs-reports/american_educator/issues/fall2005/BallF05.pdf
6. The sample items can be downloaded from http://sitemaker.umich.edu/lmt/files/LMT_sample_items.pdf
7. Hill, H. C., & Ball, D. L. (2004, November). Learning mathematics for teaching: Results from California's Mathematics Professional Development Institutes. Journal for Research in Mathematics Education, 35(5), 330-351.
8. Ball, D. L., Hill, H. C., & Bass, H. (2005, Fall). Knowing mathematics for teaching. American Educator, 29(3), 47. http://www.aft.org/pubs-reports/american_educator/issues/fall2005/index.htm
9. Balfanz, R. & Legters, N. E. (2004). Locating the dropout crisis. In Orfield, G. (Ed.), Dropouts in America: Confronting the graduation rate crisis (pp. 57-84). Cambridge, MA: Harvard Education Press. The authors note "Failing ninth-grade algebra is the reason many students are left back in ninth grade, which in turn is the greatest risk factor for dropping out" (p. 73).
10. Adelman, C. (1999). Answers in the tool box: Academic intensity, attendance patterns, and bachelor's degree attainment. Washington DC: U.S. Department of Education, Office of Educational Research and Improvement.
11. The American Diploma Project. (2004). Ready or not: Creating a high school diploma that counts. Washington DC: Achieve Inc. Retrieved March 6, 2006, from http://www.achieve.org/dstore.nsf/Lookup/ADPreport/$file/ADPreport.pdf
12. Helfand, D. (2006, January 30). A formula for failure in L.A. schools. Los Angeles Times. Retrieved March 6, 2006, from http://www.latimes.com/news/education/la-me-dropout30jan30,0,3211437.story
13. Ball, D. L., Ferrini-Mundy, J., Kilpatrick, J., Milgram, R. J., Schmid, W., & Schaar, R. (2005, October). Reaching for common ground in K-12 mathematics education. Notices of the American Mathematical Society, 52(9), 4. Retrieved March 6, 2006, from http://www.maa.org/common-ground/cg-report2005.pdf
14. And some of those attributes are even necessary for teaching math. Ball and other researchers have found that one of the most important strategies numerate teachers use is "error analysis and correction," which involves helping students diagnose why they get the wrong answers to math problems. Teachers need to be able to establish a great deal of trust to correct the math errors of young children, either in a group setting or one-on-one, in ways that respect their feelings and do not turn them off to learning math.

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    • PART I
    • PART II

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