Case for brain based thinking and "whole math" From: DNS BNA Date sent: Thu, 15 Jan 1998 09:27:27 EST To: education-consumers@tricon.net, slim@olympus.net (E. David Thielk) Subject: A Teacher Wanting Comments on His Ideas About Teaching Math Organization: AOL (http://www.aol.com) I've sent Mr. Thielk my comments, and offered to post to this list so he can get more. If you'd like to comment, include his e-mail address in the to: field as I will not forward comments sent only to education-consumers. Dave Shearon, Nashville, TN Subj: Brain based learning and math-long Date: 98-01-13 18:55:49 EST From: slim@olympus.net (E. David Thielk) Sender: CESNEWS@BROWNVM.BROWN.EDU (Coalition of Essential Schools News) Reply-to: slim@olympus.net To: CESNEWS@BROWNVM.BROWN.EDU (Multiple recipients of list CESNEWS) I am writing a series of newsletter articles on brain based learning for a local newsletter. This is the fourth in the series. I am interested in any feedback or response to some of the ideas posted. If you are interested, please reply. If not, just delete. The Forest, Trees, or the Ecosystem? Gretchen and I pride ourselves on individualizing as much as we can. We try to focus on individual student needs, assessing students as individuals, and giving help and push where we feel it will create the most learning. What we have found is that our teaching and assessment have merged, and are often indistinguishable from one another. This is particularly true when we are working with students on math and writing skills. Generally this approach works well, but occasionally we have students who frustrate us because we find ourselves spending a great deal of time with someone who could do a great deal more to help themselves. I have such a student in on of my math sessions. His modus operandi is to work intensely and frantically on math until he comes to a problem in which he can't see a clear path from beginning to end. He has looked at the sample problems in the book, but for some reason, the problem he is facing is slightly different than the sample problem (oh, no . . . . it requires some actual thinking). The other day, he was struggling with a problem which, if following the sample problem given in the textbook, required dividing by zero. He had learned some time ago that you can never divide by zero, thus, he sensed a roadblock. The problem, however, could easily be solved by drawing a quick sketch and "seeing" a solution. Even more effectively, the problem could have been solved by simply pushing back from the table, putting down the pencil, and starting a short internal dialogue about the nature of the problem and what the equation actually implied about the numbers. Unfortunately, many students have not learned to appreciate this approach to problem solving in math. When I asked this particular student to put down his pencil, and proceeded to discuss the problem with him, he quickly "saw" the solution. When we were done, I was a bit amused by his question, "But can you find the answer this way? I mean, can you just draw a picture and find the answer by looking at the graph? Won't you get a different answer if you go through the math?" I am not sure what he meant by "going through the math", but I do know that stepping back to look at the trees for a moment is as important in math as it is in art or literature. Neurobiologists are discovering that the active brain, in a natural setting, processes parts and wholes simultaneously, and taking time for a view of the trees is one way to allow part and whole processing to occur simultaneously. They have also discovered that learning involves both focused attention and peripheral perception. For the math student above, his math potential is very high. What he has missed is the practice of engaging in "whole math" process at the same time he has been asked to mechanically manipulate equations. He has become an expert at blocking out the peripheral perception. He can describe the bark of the tree in great detail, but he is looking so closely, he fails to recognize a woodpecker hole when he encounters a small opening the bark. Whole math, like whole language, means learning to place numerical patterns in perspective, to view them and practice them in a contextual setting. It means to develop skills in relationship to each other and real world applications. It means learning to see the trees, and the forest and to understand the relationship between them. And of course, understanding the relationship between trees and forests means understanding the ecosystem. Perhaps it is time for teachers of mathematics to start the equivalent of the whole language/phonics controversy enjoyed by teachers of language arts. For mathematics teachers to implement what the neurobiologists are telling us would mean a shift in the way we deliver math content. Perhaps the word "delivery" would no longer be appropriate. Essentially it would mean that students should experience mathematical equations in context to real phenomenon. And more importantly, the patterns that occur in nature and are readily observable by anyone should be used as a basis for the manipulation of the mathematical symbols. One way to promote this approach is for teachers of mathematics to look at the inquiry model of learning used by some science teachers. In the inquiry model, the student usually starts with an experience. The experience could be something as simple as watching a toy car move along the floor or observing symmetry in flowers. Of course it could be far more complex, and ultimately should challenge the student to think, compare, predict, analyze, etc. This grounding experience sets the stage for the conceptual development to come later and experiences are all the better if they shake some intuitive foundations the learner may have about the natural world or in this case mathematical patterns. But alas, this is a near impossible task. Our math curriculum is designed entirely on the basis that we must do math this year to prepare students for next year's math concepts. And of course, next year's math program is designed to prepare students for the math that comes the year after that. There is no time to stop and observe the roses (let alone the forests) along the way unless we collectively agree to cover less. Further, to look at the forest means changing the picture of what a math student is actually doing when they are learning math. It means that math curriculum must be fully integrated at the very least with history, social and natural science. Our district defines mathematics as 'the science and language of patterns." I wonder how many of us reflect on this definition each day as we work with students. Helping students see the forests along with the trees will mean restructuring our math programs, and of all the disciplines, math probably has the most barriers to change. We must ask ourselves, Why we are teaching mathematics? Whose needs are we trying to meet? Must we design our curriculum around college and college professor's expectations, next year's teacher's expectations, moving students to achieving calculus, student transcripts? All of these are valid inputs in the process, but also are somewhat peripheral to the more essential goal of giving students the ability to use mathematics to explore and understand patterns. How many of our students truly see math as the science and language of patterns? Perhaps the first step is to truly incorporate the simple definition - the science and language of patterns - into our classrooms and our own view of mathematics. -- David Thielk 611 Rose Street Port Townsend, WA 98368 Community Connections Port Townend High School 1500 Van Ness Port Townend, WA 98368 mailto:slim@olympus.net http://www.olympus.net/personal/slim EDUCATION CONSUMERS CLEARINGHOUSE