Fewer is More, too

My son, Jake Dockterman (he likes it when I use his name; it raises his Google hit count), is a bit of a stickler when it comes to the use of the words “fewer” and “less”. He’s not alone, as a web search of “fewer vs less” will reveal. You see “fewer” refers to how many, and “less” refers to how much. If you can count it -- marbles, tortilla chips, brothers and sisters, or Manny Ramirez home runs -- you use the word fewer. If you can’t count it -- applesauce, happiness, sand, and milk -- you use the word less. You don’t say “I’m fewer happy” when something upsets your birthday. And you don’t say “I have less siblings than my friend.” At least, you shouldn’t say you have less siblings. One last note: the signs above the express line at the grocery store should read “10 items or fewer.”

I’m a big believer in the less is more philosophy, and I enthusiastically embrace the sentiments of the NCTM Curriculum Focal Points and the final report of the National Math Panel. Both documents advocate focusing instruction on the essential content, the core ideas that students need for success in math, Algebra in particular. A report from the National Research Council last year recommended a similar emphasis on big ideas in science. Taking Science to School offers a very accessible review of the research on science teaching and learning and recommends: “The next generation of standards and curricula at both the national and state levels should be structured to identify a few core ideas in a discipline and elaborate how those ideas can be cumulatively developed over grades K-8.” The trend (hopefully) in both math and science is a welcome targeting of the curriculum on what really matters.

So, are these reports calling for less or for fewer? The distinction is important. Fewer topics means dropping some of the content that’s crowding the curriculum. Maybe we don’t need to cover probability or tessellation or the orbits of the planets. Covering the lengthy lists of state content standards provides little time for depth of learning. Cutting the list in half doubles instructional time for each learning objective. Fewer instructional goals could mean more time for truly learning those that remain.

On the other hand, devoting less time to some of the items found in state curriculum guides could also lead to more time for other, more critical, items. The big ideas certainly merit more focus than the supporting skills or concepts. Maybe the issue is one of emphasis. Not all content objectives are equal. The NCTM Curriculum Focal Points document makes this case very clearly. NCTM recommends “areas to emphasize” rather than to slash. Focus on the core ideas and use the other objectives to support those crucial concepts.

From my perspective, I think we need both less and fewer. The list of learning objectives in some states has simply become too long and too atomized. The pressure to cover each standard has turned them into a checklist of disconnected items. It’s time for some judicious winnowing of the curriculum. We need fewer standards to give teachers tangible evidence that they have the freedom (maybe mandate is a better word) to focus on what matters. Even so, we still need a re-emphasis in the curriculum. We must identify the core ideas that merit more time and show how the remaining objectives can support them. Less time on some content can lead to more understanding overall. And fewer topics in the list can help make that re-emphasis possible. Less is more, and fewer is more too.

National Math Panel

The final report of the National Math Panel is finally out, and I have to admit that, overall, I really like it. I completely agree with their conclusion that the tension between conceptual understanding and procedural fluency is a false battle. It isn't the standard algorithm OR flexibility in solving problems. Conceptual understanding, fluency, and problem-solving all work together. Quick recall of basic math facts is very important, but it isn't everything. The opposing sides in the Reading Wars eventually accepted a truce; kids need to know how to decode, and they should love and understand what they read. Let's hope the antagonists in the Math Wars have reached a similar accord.
One area noted in the report should readily be embraced by everyone. Effort and attitude matter. They summarize the research of Carol Dweck (see one of my previous blogs) about shifting the learner's attitude from one focused on innate ability to one that recognizes growth through effort. It's critical for students and teachers to acknowledge incremental improvement and the effort it takes to achieve it. I wouldn't be surprised to find a relationship between these attitudes and math anxiety. The panel recognizes the reality of math anxiety and recommends more research to uncover its source. Indeed, the report makes many recommendations for further research. We need it.

The panel's report did, though, leave me wanting in a couple of areas. While the report talks about the importance of problem solving, it never describes what "problem solving" means or how it should be developed. Maybe the research isn't robust enough to illuminate clear directions. I would also have liked more clarity about why the panel members singled out particular areas in measurement and geometry for instructional focus. I don't disagree with the importance of the selected areas of content, but I would welcome more elaboration about how they fit into an algebra trajectory.

Hopefully, NCTM's Curriculum Focal Points and this report of the National Math Panel provide enough guidance for states to review and revise their curriculum standards in math. The list of learning objectives on state curriculum frameworks tend to be long and without emphasis on what's really important. The objectives get treated as separate, isolated teaching and learning events. Fitting them all into a school year inevitably leads to shallow coverage trumping real mastery. Let's concentrate on what's important and make sure kids really get it before moving on. Now, if only we can get the testing establishment to reflect this focus, but that's the topic of another blog.