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Teaching developmental math

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Teaching developmental math

There is a growing need to learn math for those who have had a bad experience with math in the past, or who have been away from math for a long time. I am interested in improved techniques for teaching math to this group of people.

Members: 30
Latest Activity: Mar 23, 2011

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I have a suggestion to contributors to the group: make more use of the "Start a Discussion" link. I think that will keep the content more organised, than using comments to the main page of the group. (Colin McAllister)

Discussion Forum

Math phobia

Started by subhashree panigrahi. Last reply by Linda Fahlberg-Stojanovska Nov 22, 2010. 14 Replies

Do community colleges deliver?

Started by Danny Clarke Oct 30, 2010. 0 Replies

Teaching Duct Tape Math

Started by Colin McAllister. Last reply by Colin McAllister Oct 9, 2010. 12 Replies

Comment Wall

Comment by Michael Friedberg on August 9, 2009 at 2:37pm
I wish to comment straightly on Danny Clarke`s principle " to start with a problem ". The "industrial age assembly line " system also begins with a problem: " Ann has three apples, and Peter has four apples. How much apples they have together ?"/ The decimal system we also begin with some story like " in order to count trees in the forest we write every ten trees as unit"... and so on. Towards little children we can not behave different.
And so we proceed logically , every new notion is illustrated or introduced by situational story. The tradition of best special math classes and schools is full of mathematical folklore. So where is the problem? The problem occurs when the pupil or teacher want to attack the problem that doesn`t correspond to pupil`s basic knowledge, and is situated beyond the zone of his/her close development. What`s the aim? To get the feeling of success, even imaginary - we know such social groups - the political correctness doesn`t permit me to say more. And the teacher try to make impossible things - to involve a man without real knowledge - in the process of solution. Maybe we solve by this some social problem, and it worth efforts. Is my guess right ?
Comment by Bradford Hansen-Smith on August 9, 2009 at 7:49pm
What I hear are attempts to think anew within confines of what is already in place in the social mind of how we define mathematics and education . It is based on a curriculum that is fragmented and strewn with isolated pieces of information. We can change the tools, the look of delivery and the environment, but if there is not a change in the foundational approach to what is useful curriculum information for progressive development of individuals and the planet, things will not improve.

We are stuck in a parts-to-whole approach to education, thus we construct things with parts, to only get bigger parts. There are endless parts, we will never reach the inclusive and comprehensive Whole. The only way to get to the Whole is to start from the Whole, observe and think about what you observe. I am suggesting we think about turning 180 degrees from what we are doing and think about a Whole-to-parts approach and what that might mean.

Our mathematics is based on drawing images and symbols and assigning values by way of relationships, proportions, ratios etc. Math language is not unlike other languages, it proves itself by its own internal logic. Maybe we should try teaching it like we first learn a language, experiential immersion.

Math is based on drawing symbols, a virtual world has been created that looks similar to the real world, but not really because so much is dropped out in formalizing the generalizations we think are important for students to know.

We draw circles. No, it is only a picture, not a circle. There has been no serious exploration of the nature of the circle because we are stuck with thinking the image is the circle. Until the last few hundred years the circle image was a symbol for the sun, the universe, the Whole, of God, of everything. Now it is the symbol of nothing zero, no value. The Sphere is the only form that demonstrates Wholeness, undifferentiated Unity. No other shape or form does. When we do refer to the sphere we truncated it, cut it apart to get at the parts, called polyhedra, polygons and so ons, destroying the Whole. If you compress the sphere to a flat plane you get a circle disk,a triunity; circle on top, circle on bottom and a circle ring that connects the two. Nothing has been added or taken away. It is still unity, still Whole, everything there, it is simply compressed forming three circle in unity. By folding the circle all that spherical information is being decompressed. We do not fold circle so we have no idea of the amount of information that is generated or the reconfigurations through multiple joining of circles. This might sound very abstract, but a circle in your hands is dynamic, you can feel it, it is experiential and it is Whole. The circle is the curriculum, all that information is there, in one place, everything in the context of everything else. Not at all how we have defined the current curriculum and how we go about teaching kids what we think they should know. Yet in the first fold of the circle there are over one hundred mathematical functions to be identified, discovered for those that do not know math language and can be talked about in common terms. Everything is inherent in the circle/sphere because it is simply the reconfiguring of the spherical Whole.

After twenty years of folding circles with kids and adults in and out of school situations I am have observed students discovering through their own explortion a lot of mathematical functions they did not know was math at all. It works and we do not know it because we do not fold circles. We do not observe the information that is there to even know what to do with it, because we have been taught to draw circles.
There is no more natural and effective way to approach learning than Whole-to-parts. If you think about how babies learn, they take in everything of there environment and begin to see specific relationships and interactions that are of most interest for their needs. What they see is everything in the context of everything else and they explore the interrelationships and connections that are already there and the learn for themselves what they need to know, with of course considered guidance from parents. It is the arrogance of the teacher that thinks they are teaching their students. Students will learn when given sufficient amounts of principled information that makes sense to them because they have made there own sense about it through there own experience. Most of what is given in bits and pieces is not principled because it has been separated from the context, removed from the Whole.

My challenge to any math teacher is to spend some time folding circles and then tell me Whole-to-parts approach is not a more effective way of learning mathematics. With out going further into it you can check out my website to learn more about this approach. It is unfortunately not being discussed any place else because we do not fold circles with any serious consideration.
I would hope that we would be folding circles at least as as much as we draw pictures of them from the primary grade level on up. Folding circles would facilitate a major change that would go a long way in helping to sort out math education confusion, and educational quagmire we are caught in.
Comment by J Edward Ladenburger on August 9, 2009 at 8:51pm
Bradford, I will check your website and fold some circles :)

I am also a generalist and with formal training in physics have always looked to those few fundamental principles from which the "parts" can be deduced.
Comment by Colin McAllister on August 10, 2009 at 9:25am
Danny, Congratulations on your new group "Teaching developmental math". I have a suggestion to contributors to the group: make more use of the "Start a Discussion" link. I think that will keep the content more organised, than using comments to the main page of the group.
Comment by Michael Friedberg on August 10, 2009 at 11:59am
To my impression and concern - the student must climb up the ladder of independence. If the teacher makes by himself all the investigation work and presents to pupil only a final technological process - that is the assembly - line school. Sometimes also this kind of work gives something to pupil -at least the will to ask "Why do we make so?"
So, presenting a new/old developmental school - we must answer the central question: Do we make the student our partner in the stage of investigation? How much time we have for this. And, maybe, on this way we must abandon the idea of regular control works and matriculation exams.
Comment by Danny Clarke on September 8, 2009 at 2:34am
The semester is now 2 weeks old where I teach at Truckee Meadows Community College. As always, the applications or "word problems" give the most trouble. I start each session with an application that requires skills that will be learned during the remainder of the session. At the end of the session I come back to the application and ask the class to help me solve it now that they have been exposed to the necessary skills.

The difficult part for them is usually translating the application into expressions and equations. I wonder if anyone has ideas about how to make the transition from ordinary language to math expressions?
Comment by MariaD on September 8, 2009 at 6:26am
On the subject of word problems - I usually invite students to create word problems from scratch. This makes them pick situations they actually understand, and can resolve through the general logic. Then they create a story that goes with a particular equation. It is actually neat for the group to see all sorts of wild stories people create about the same equation.
Comment by Danny Clarke on September 8, 2009 at 8:00am
That's a cool idea, Maria. Does it help with translating from words to math expressions?
Comment by MariaD on September 8, 2009 at 8:07am
When students create word description themselves, as opposed to being given the description, they are unlikely to create a story they don't understand. So yeah, it helps them translate into other representations, including formulas. Another thing that I remembered: roleplay/model the story with objects! It really helps.
Comment by Guillermo Bautista on December 16, 2009 at 6:06am
Hi everyone. Sorry to barge in. It seems that our beliefs regarding teaching mathematics is somewhat parallel. That is the reason why I joined this group. I am interested in mathematics learning and teaching and at the same time interested in integrating technology in teaching mathematics.

I am not an educator by background, so I hope to learn a lot here.

I have created a blog here, it's new but it's growing fast. Please have a look: Mathematics and Multimedia

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