Explorations In Math

Believe it or not

Published on March 29 2012

This week’s guest post is from Ginger Warfield.  Ginger has been a passionate mathematics leader for over 30 years.  She has served on Explorations in Math’s Advisory council for the past 3 years, is a Principal Lecturer Emerita in the Department of Mathematics at the University of Washington and was the former Chair of the Education Committee of the American Women of Mathematics (AWM) and a longtime Education Editor of its Newsletters.  The blog post below is her education column for AWM’s upcoming Newsletter.  If you would like to write a guest post, please contact Dave Gardner.

In the current state of the world, it can be far too easy to focus on the troubles and dangers that beset K-12 education and be drained of energy by that bleak viewing. It was therefore a particular pleasure to me when at a recent conference of WaToToM (Washington Teachers of Teachers of Mathematics) a presentation on the Common Core State Standards (CCSS) permitted me not one but two patches of optimism. In a general effort to spread the sunshine, I decided to present them here.

The first had to do with the Standards themselves. I have been so pleased and excited about the Standards of Mathematical Practice and the way that the CCSS keep them in the foreground, that I missed another key feature. For decades now the phrase “Mile wide, inch deep curriculum” has been so firm a mantra of everyone involved in mathematics education that I have wondered how many household parrots might by now be able to repeat it. It has seemed to me, though, that any efforts to deal with it have simply produced a shuffling of the elements rather than any narrowing or deepening. The writers of the CCSS addressed this problem by standing it on its head: instead of starting by looking at everything a kindergartner should be able to take in and working their way upward, they started at the top and chose a small number of advanced concepts that any educated citizen should have the opportunity to learn. They then worked their way backwards down the levels and produced what they called mathematical progressions that led to these concepts. With those progressions established, they put in some benchmarks for when students need to arrive at specific levels along the route. In doing so, they made strenuous efforts to avoid requiring any topics, even attractive ones, that are not needed for one of the progressions. The goal — plan — hope is that keeping the requirements focused and non-bulky will leave some room for optional topics that teachers choose to teach. In any case, it will provide a structure such that teachers should be able to find out readily which concepts their students should already have available to use and which they are going to need in the next year or two. All of which has at least the potential to keep the curriculum flowing down a narrower, deeper channel. Encouraging.

For the second patch of optimism I need to drop back and throw in a little local history. Back in the 90′s almost all states, my home state of Washington included, produced State Standards. Washington then went farther and was among the relatively few that produced assessments to go with its Standards. The writers of the resulting WASL (Washington Assessment of Student Learning) took note of the absolutely central role of understanding and communicating the ideas behind the (also necessary) mathematical procedures, worked incredibly hard, and produced a test such that if a teacher successfully taught to the test he or she would indeed be teaching what the Standards intended. Unfortunately, the onslaught of No Child Left Behind loaded the WASL with stakes it was not designed to bear, and after a decade or so it wound up essentially eliminated. I was thoroughly disheartened until a conversation with a high school teacher of whom I think a world, in which she said “Yes, but all the teachers I know are teaching very differently and way better as a result of trying to prepare our students for the WASL. We’ve learned a lot!”

Now two large consortia are hard at work producing assessments to correspond to the common Core State Standards. The WaToToM presentation that I mentioned above included some emerging details about the one that Washington is heavily involved in, Smarter Balanced Assessment. Again I was already familiar with a number of key points, such as their determination to de-emphasize summative testing whose results provide information that fails to benefit either students or teachers, and offer formative and interim assessments designed to give teachers information that they can use to improve the learning of the students they have. They also plan to provide a variety of formats of assessments, including some open-ended one or two day projects that will give students an opportunity to demonstrate a very different set of abilities from those required for timed multiple choice or short answer tests (which will also be used, but in moderation.) Smarter Balanced has a long way to go, but what struck me as I listened was that if they succeed in following the path they have laid out for themselves, then they, too, will have created an assessment such that teachers who “teach to the test” will be giving their students exactly what they need, and learning a lot as they do so.

These are harrowing times, and not even my Pollyanna side can maintain that The Solution has been achieved. But despair has very few virtues, and correspondingly I feel enormous gratitude for the incredible efforts the writers of the CCSS and the folks at the Smarter Balanced consortium have put in and are still putting in. I plan to hang fiercely onto the hope they are proffering!

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