Talk:Communicating in the Language of Mathematics
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Comment 7/3/2008: Writing to Learn Mathematics (Christina Dixon EDT 630)
Writing to learn in mathematics really grabbed my attention because of my recent training with the AMSTI (Alabama Math and Science Initiative) two weeks ago. During this training there was an extreme amount of focus in keeping Math and Science Journals. Before this year, the amount of time my students and I took writing about what we learned in the subject of Math or Science was very minimal. I failed to realize the importance of written communication. I agree that it indeed allows a person to internalize and restate things they hear. I learned that we remember about 10 percent of what we hear, 20 percent of what we see and hear, 50 percent of what we do, and 75 percent of what we write and discuss. This is not stated verbatim, but the gist is writing produces powerful results when it comes to really understanding and grasping concepts. As I wrote in my own math journal during the AMSTI training, my eyes began to open and I really allowed myself to think deeper. I believe writing across the curriculum supports all best practice theories and fail to understand why teachers are not taking advantage of the benefits it provides. Our students deserve to receive maximum knowledge in all subject areas and a simple journal or free write is a gift none of them should go without. This school year I plan to start out giving each of my students the freedom of written communication in Science, Math, and every other subject. I will no longer silence their voice in subjects like Math and Science, but will give them control of their learning by allowing them to have powerful discussions daily!
Comment about communicating with one's self. Dick Ricketts. 5/25/08
Here is an example of carrying on a mental conversation with myself about a math problem.
- Alan has $48. Ben has $41. Carrie has $25. How much money must Alan and Ben give Carrie so they all have the same amount?
- “Ok, the idea is that all three have the same number. Wonder if this is a ‘convenient’ problem where the numbers come out even. Probably so, since there’s no 1/3 penny coin. Hmm; the numbers are not simple enough so that I can just take some from each and give to Carrie. (Will Carrie set them on fire if they don’t share—back to work.) Guess it’d be easier to find out how much each would have of a total than try to find each share separately. Here goes: 48+41=89. That was easy. 89+25; have to go by steps. 89+5=94; check; yes, that’s correct—need to be careful when the ‘odometer’ turns over. 94+10=104. 104+10=114. Wonder why I didn’t go 89 +10+10+5; be easier to do it that way next time. Anyway, 114/3. That ‘4’ might be awkward. Well, 11/3 is…let’s see…9…silly; 9 is what I’m dividing by 3…so 3. The remainder is 2. Grab the 4 to make a 24; that’s 8. Wonder why 24/3 is easier than 11/3; just one step I guess. 3 before 8, so 38 is the answer.
- Check: Alan loses (48-38) $10. Ben loses (41-38) $3. Carrie has 25=10+3=$38. So the answer is $38. Guess I disregarded the $s because they weren’t relevant. Ok; am I done? Look it over one more time to make sure….what’s this! What is asked for? Oh, no! Ahem…Ben must give $10 and…oops! Alan must give $10.00 (guess I better show that the pennies are relevant) and Ben must give $3.00. In that way, all have $38.00. Look over one more time…yes, I have the feeling of certainty. Narrow escape from a wrong answer. “Less haste, more speed…not in my nature…how about ‘Run like a bunny but look over the total scene with the eyes of an eagle’?
- Time thought through: About 15 seconds. I saw the numbers; moved them on the tapestry of my mind (white numbers on a sky-blue background), and talked to myself…three modes of processing. Note: When I thought I was done, it didn’t feel right inside. That’s why I want back and checked what could be wrong. At the bridge table, I have impulses to make a certain call (bid, double, pass) or play a certain card. I sometimes think ‘How could that be right?” However, the impulse is almost always right (unless I let my sense of humor get out of hand). Conclusion: I process a lot of stuff out of consciousness, including math. By the way, in chess I often can predict what my opponent will move next. However, I’m a terrible poker player; I think the money gets in the way.
Comment March 20, 2008
The discipline of mathematics is far larger than any one person can master. Thus, mathematicians tend to be somewhat narrow specialists. One can be a great math researcher and a terrible math teacher, or vice versa. One can be a world class math historian. Such a person may or may not be a good math researcher or a good math teacher. All this having been said, what can one expect from an elementary school teacher who is responsible for teaching a number of different disciplines and manage 25 or more young children at the same time?
Comment March 5, 2008
I think that some of the terms in the paper need to be more carefully defined. For example, can an elementary school teacher who has only studied math up through a course on math for elementary teachers meet the qualifications to be a mathematician or to be a math educator?
My personal opinion is "yes." The teacher needs to be a mathematician at the level of the math she or he has studied. The teacher needs to be skilled in both general pedagogy and in math pedagogy.
Most elementary school teachers can gain the "math and teaching smarts" to meet these requirements. But, this takes time and effort that extends over a period of years.
Comment March 5, 2008
You should say more about the social aspects of learning math. What can teachers do to help make math more of an enjoyable human social endeavor?
Comment by David Moursund 3/4/08
Thinking about learning to communicate in math has led me to think about learning to communicate in other disciplines. This, in turn, has led me to think about the advantages that a child gains by growing up in an environment in which there is both the "general" type of communication and also the discipline-specific communication that is lead by adults who have a reasonably high level of expertise and interest in specific disciplines.
There is a lot to be said for the expression, "The way the twig is bent, …." In my opinion, children who grow up in an environment of enthusiastic success/expertise in one or more disciplines are gaining an advantage over those who do not.
One of the important ideas in the article is that of students learning to communicate well enough with the various sources of information and aids to learning so that they can assume more responsibility for their own education. I am particularly interested in hearing from teachers and others who are successful in helping this to occur.
