Now that I’ve finished a week’s worth of AMSTI training in math, I find this article concerning the state of mathematics eduction in the United States. The two (AMSTI and the article) aren’t going in opposite directions, I’m happy to say, but they’re not exactly going in the same direction either. The article (and the paper that it references) states that children need a deeper understanding of foundational material: number sense, fractions, decimals, and mastery (memorization) of basic addition and multiplication facts as well as their related subtraction and division facts. Amen.

AMSTI places a great deal of importance on investigations that help students to develop an understanding of the aforementioned concepts, but I didn’t take away a feeling that there was a great deal of importance placed on the memorization of facts.

As is my wont, I’ll just try to do both. I’m leaning, though, in the direction of the report’s findings.

Here are some excerpts from the report’s (*The Final Report of the National Mathematics Advisory Panel*) executive summary:

*— Although our students encounter difficulties with many aspects of mathematics, many observers of educational policy see Algebra as a central concern. The sharp falloff in mathematics achievement in the U.S. begins as students reach late middle school, where, for more and more students, algebra course work begins. Questions naturally arise about how students can be best prepared for entry into Algebra.*

*— A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided.*

*By the term focused, the Panel means that curriculum must include (and engage with adequate depth) the most important topics underlying success in school algebra. By the term coherent, the Panel means that the curriculum is marked by effective, logical progressions from earlier, less sophisticated topics into later, more sophisticated ones. Improvements like those suggested in this report promise immediate positive results with minimal additional cost.*

*By the term proficiency, the Panel means that students should understand key concepts, achieve automaticity as appropriate (e.g., with addition and related subtraction facts), develop flexible, accurate, and automatic execution of the standard algorithms, and use these competencies to solve
problems.*

*— A major goal for K–8 mathematics education should be proficiency with fractions (including decimals, percent, and negative fractions), for such proficiency is foundational for algebra and, at the present time, seems to be severely underdeveloped. Proficiency with whole numbers is a necessary
precursor for the study of fractions, as are aspects of measurement and geometry. These three areas—whole numbers, fractions, and particular aspects of geometry and measurement—are the Critical Foundations of Algebra.*

*— Computational proficiency with whole number operations is dependent on sufficient and appropriate practice to develop automatic recall of addition and related subtraction facts, and of multiplication and related division facts. It also requires fluency with the standard algorithms for addition, subtraction, multiplication, and division. Additionally it requires a solid understanding of core concepts, such as the commutative, distributive, and associative properties.*

Finally, there’s this little gem:

*— Research on the relationship between teachers’ mathematical knowledge and students’ achievement confirms the importance of teachers’ content knowledge. It is self-evident that teachers cannot teach what they do not know.*

Actually, that’s not really a “finally” statement. There are 120 pages of information. Just a little summer reading…maybe I’ll just skim it and use the saved time to prepare math lessons!

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July 9, 2008 at 10:00 am

sagegrammyMathematical investigations are great but they are generally only the threshold, the introduction to a concept. In the end, we have to be able to make calculations and communicate results. Students need to learn and practice computation and be able to communicate results, as well as understand concepts. The “math wars” are as ridiculous as the

“whole language” versus “phonics” debate. There is no “versus”.

Liping Ma was on the National Mathematics Panel. I think her book, “Knowing and Teaching Elementary Mathematics” is very helpful.

July 9, 2008 at 1:29 pm

tgelsI agree with you wholeheartedly. I’ve only taught for a couple of years, and in that time I’ve been surprised at how little “middle ground” I’ve observed between investigations and “traditional” work. The program we’ve adopted (AMSTI) does have an emphasis on communicating results, but not as much so on computations. In all fairness, though, the program doesn’t claim to be a stand-alone way to teach mathematics. I’m looking forward to working it out this year.

Thanks for the tip about “Knowing and Teaching.” I’m going to try to get my hands on a copy.