5 thoughts on “Madison United for Academic Excellence, 12-December-2006 Presentation”

1. Thank you so much Larry, for making the effort to record these meeting. At the last minute I found myself unable to attend and it’s so good to be able to follow what was said.
   The reform math books are not, in fact, math books, and the classes which use them, not math classes. That is not to say that the skills they attempt to teach in those classes are not useful, but it is not math.
   Consider a typical problem. While buying gas, you go into the Kwik-Trip store to buy a soda. Soda is available in sizes A, B, and C, for prices a, b, and c. Which one would you buy? This is not a math problem. It is real life values and decision-making problem in which simple math calculations may play a role in the decision-making. (The answer is clear, right? You shouldn’t buy the soda at all, but should go to the grocery store next door and buy a bag of organic apples packaged in a compostable cellulose bag and drink water from a bottle you filled at home.) So the student looks at this problem and screams aughhh! There isn’t a right answer. It is frustrating, especially when the teacher is trying to pretend it is a MATH problem. If it was a math problem, it would have a correct answer. That answer might be there is no solution, or the answer might be one number, or a function, but there would be an answer. This is an open-ended investigation with math as only one aspect. Johnny raises his hand and says he would buy the small one because the big one would get warm before he could finish it. Susie says she would buy the small because it’s piggish to drink huge glasses of liquid. Ahmed says he would buy the large because he’s really thirsty and the large is cheapest per ounce. Meg says she would buy medium because even though she’s really thirsty, she has an old car and the large won’t fit in the cupholder. James says Kwik-Trip is an evil capitalist business and he would never even purchase gas there, much less soda. Tom says soda is bad for your teeth, so he’ll drink water from the fountain. Tim will drink water too, because he doesn’t have any money, etc. Teacher says,”You’re all right. See, a math problem has many correct answers.” Well, only Ahmed(rate) and Meg(geometry) have used any math, and the teacher doesn’t draw a distinction between math and non-math thinking about the problem, but 15 minutes of MATH time is gone now. A math problem would be- which combination of sodas should you buy to get X ounces for the least expenditure? Now that has a solution. It is real world math, but it is math.
   These are useful skills to teach. As an adult in the grocery store looking at several jar sizes of jelly which become cheaper per ounce as they increase in size, you have considerations other than price per ounce, like, can you finish the big jar before it spoils, will you tire of the flavor before it is gone, do you have room to keep it in the frig, is it too big and heavy for the kids to handle optimally, do you have a tool to easily reach the bottom of jar w/o getting sticky,… ? I am glad that schools try to find time to teach these skills to children who don’t learn them from their parents, but it is not math. If they want to package it into math class, first they need to do several things: 1)Rename the class ‘design and decision-making with a bit of math.’ Call a spade a spade. 2)If this is to be the only math kids get, the time allocated to math must double at least so that there is time enough to fit in some real math. 3) Clearly distinguish in class between math and non-math thinking to avoid confusion and 4)Offer a pure math option for parents/children who prefer that.
   The educational powers that be have sentenced real math to the dungeon. Children have been victimized and tortured by it for countless years and now it’s getting its punishment, total banishment from the classroom and replacement by an imposter going by the same name. ‘Authentic math'(also known as math that has value) is defined as that which has real world connections to the child. How should people who revel in pure abstract math feel, numb? Their joy in life has been declared to be without value. What would the Shakespeare buffs and poets feel if suddenly those subjects were only allowed to be taught in twisted forms, Shakespeare in 20th century English and only advertising jingle type poems? What if science teachers could only present marketable applications and no basic science except the barest framework necessary to make accessible the applications?
   How about this problem: given a yard with its dimensions and containing various structures, and given prices of various types of fencing, and given no other info how can you build a dog run? This is a good problem to spend some time on. You need to consider a lot of things. Does zoning prevent you from going too close to boundaries, or too high on some side of property? What type of upkeep do different fences require? How tall should a fence be to prevent dog’s escape, and so how big is the dog, and would you ever have a bigger dog or want the property to have value to a bigger dog’s owner when selling? What size/shape is ideal? Is aesthetics most important, or fence life, or perhaps price? Does the dog chew on wood? Will he fit between slats or dig his way out of certain fencing? Where will a run fit on property? Very interesting problem. Even if you aren’t going to be a contractor designing bids or a do-it-yourselfer, you may be a customer considering this as a purchase decision. But this is not a math problem. It is a design and decision-making problem. This belongs in a class titled, ‘shop class’ or ‘business for contractors.’ A math problem is: Given you have a 3 ft. tall dog who likes to jump, and given various fencing types with aesthetic rankings, longevity, costs per ft and also their maintainance costs per year per ft. and wanting the largest rectangular run possible, with sides 3:1 ratio and a total cost cap of no more than $X, including maintainance, over a 20-year span, and given a description of property, and restriction of 6 ft setback from property line and at least 20 ft from house, what is cost to install the most aesthetic fencing that lies within these parameters? This is a story problem, but it is math.
   I know that social structures have changed over the years and many children these days don’t have the ability to even pretend to be attentive in a difficult pure math class, much less to actually be engaged. It is not possible for schools to change this single-handedly. So they need to adapt their classes so that students are engaged and learning some things that will promote life success. However,….. not all children squirm in their seat, turn off, fight, and so on. My kids and many others want a real math class. They also want real Shakespeare and real poetry and real science. They don’t want these things casually dispensed with as ‘valueless.’ In a district this size it ought to be possible to maintain these classes with not much cost. These are the classes which are appropriate for my kids and many other kids as well.
   The schools are overstepping their bounds in making big decisions on behalf of my children and without my input about what has value in life. There needs to be more of a public conversation about these things, and some real consensus before schools just turn themselves completely upside down. For example, is it really a foregone conclusion that working amicably in groups all day has great value, but that individual achievement has none? Oops, I’m veering into a different facet of what things are objectionable in math education these days. Another day for that.

2. You referenced what is and is not math. I am interested in your definition of “math”.

3. Well, if I am going to be boxed into a concise definition, I have to mull it over for awhile to be sure I get it right.
   But I could say a few things related to that thought to grease the old brain cogs and get thinking about it.
   In a chemistry class, one uses a lot of math. When balancing equations, working with molecular weights, looking at diameters of atoms. All the time you are using math. But if I took a chemistry book and covered up the title, you wouldn’t flip through it and mistake it for a math book. It is clearly a chemistry book. Most of the math you use is learned in advance and then turned to chemistry apps. It is similar in other sciences. You don’t think an astronomy book is a math book, or any other science book(possible exception- physics.)
   At the university, math and engineering are separate depts. and no one is confused about which dept. they should be in. It is possible for an engineering prof. to work on a project with a math prof, but they do have relatively clear domain boundaries. Engineering students use a lot of math in their classes, but much of that math is learned in required math classes.
   The point is, should math be taught as a stand alone course, or can students only appreciate it in some multidisciplinary real world context?
   One problem I see with this multidisciplinary approach is that it is difficult to focus hard on the basic math principles of the unit you are in and become well grounded in them when so much attention is turned to the design aspect of the problems. You don’t really see the general principles as they apply to many contexts as you do with a book that gives you lots of varied problems on a topic. You can’t make your way through very many of these projects in the allotted time. You have to learn about the design aspects and the math aspects simultaneously which is mightily confusing to some students. They may well walk away from a unit not knowing what are the important ideas they were supposed to learn in it. In fact, it is possible in many of these vaguely defined projects (seemingly deliberately so) to make one’s way through them while doing minimal math if one is so inclined, and especially in the group setting which is often used where one can lean on strong partners.
   A second problem is that this confuscating appropriation of the word ‘math’ has been very confusing to parents. They are told that students are still learning the same math, but in a different way in their MATH class. That is not, strictly speaking, the right way to phrase things. Words matter. The class may be a very interesting class, but parents should be told that the education establishment has decided that math classes are not needed and are in fact harmful to a student’s love of learning, and that these classes have been replaced by PROJECT/DESIGN classes which will teach them math concepts indirectly. Many parents may love this, think- it’s a great idea and why didn’t they think of this when I was still in school. And maybe some of them not. But at least we’ll be clear on what is going on. The debate needs a framework that allows people to understand and to speak clearly.
   As usual, much depends on the teacher. A teacher who likes to teach math may focus more on the math, minimize the other stuff, supplement, etc. so that you are still learning math. But one shouldn’t need to work around curricula that way. Kids who really like math appreciate a good textbook as well and are very frustrated by these constructivist texts which so often take all the beauty out of math.

4. If you are the Brian I think you are, then I have a question which I can now ask openly since the topic was brought out at the meeting.
   Since the district allows some middle schools to use the McDougal-Littell classic algebra book, there must be a way Cherokee can get that book instead of the ‘Discovering Algebra’ we are presently stuck with. Who makes the decision? Would parent petition with many signatures make a difference? Please, I wouldn’t want to see this turn into a debacle like Seattle airport. The intent is not for another school to lose their text, but for us to get to use it as well.
   Thanks for any help you can offer here.

5. Yes, this is the Brian you think it is. If you want to chat about specific schools or programs, that would be better accomplished by calling me at my office. I would be happy to talk to you about this. I am here on my personal time trying to learn more about the diverse needs of the district.

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