By Larry Marsh, Kansas City Star Midwest Voices columnist 2009
In theory the "new math" conceptual approach is much better than the traditional "memorize and drill" approach to learning mathematics.
A key problem is ensuring that the teacher really understands the conceptual approach and has the necessary teaching skills and demeanor to transfer those skills to his/her students. This aspect is critical and often insurmountable.
Math is very interesting. If you square a number greater than one, it gets bigger. But if you square a number between zero and one, it gets smaller. That's very interesting, and it turns out to be a critical fact in the stability of dynamic systems.
It's like many substances contract as they get colder, but when water turns to ice it expands. The Egyptians made good use of this fact when they split off the blocks to build the pyramids.
Two important keys to success in education are attitude and priority.
You start with attitude. Both teacher and student must be convinced that math is interesting and fun (and, perhaps, ultimately useful, as well).
Do teacher and student believe in what they are doing or are they just following orders? If students understand the conceptual purpose of the math, they can solve problems that the memorizers will never be able to solve.
Priority may be even more important. What is important in life and what is not. I chose to ignore entertainment and sports (yes, even at Notre Dame) in order to focus on economics, math and statistical methods.
When I do math, I am doing surgery on my best friend, or crossing a field full of land mines. I am very careful.
What many people do not realize is that they are fully capable of programming themselves. The subconscious mind is nothing more than the accumulation of thoughts that we have drilled into our minds on a day-to-day basis.
When I was a clerk at a battalion headquarters at Fort Knox, a new second lieutenant joined the office. He had just gotten married. Every day he had something bad to say about his new wife. "She burned the toast." Within a year he was divorced. No surprise.
Students taking my required stats class can either say to themselves "Statistics is boring" or they can say "The prof is a bit of a nut job, but this stuff is interesting."
If mother, father, teacher and child all have the right attitude and priorities, then the "new math" conceptual approach can be far superior. They've got to believe in what they're doing and really want to do it. If not, it can be a complete disaster.
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Also see:
Google Books changes everything in student teacher education
Spend some of that $650 million for educational video games
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applying your insights
Larry,
I think you would do us a great service by applying your mathematical insight and economic perspectives to our city manager's proposed budget...see Yael's recent posts. I look forward to your comments.
What do you think?
Tom Ryan
The Crossroads
Kansas City, MO
Reply to Tom Ryan's "applying your insights."
Tom:
Thanks for your vote of confidence.
I wish I had Yael's knowledge and experience. I am sure his insights are way better than anything I could come up with.
i thought that sounded like an article!
Good thoughts. What should one make of the teachers and college professors so adamantly against the "New-new Math", or, as they like to call it: "fuzzy math", though?
http://www.csun.edu/~vcmth00m/longdivision.pdf
http://www.aft.org/pubs-reports/american_educator/fall99/wu.pdf
- Grant
Reply to Grant_Martin's question about "fuzzy math."
Fuzzy mathematics is actually a special branch of mathematics.
Instead of things being true or false (zero or one), they can be somewhere between true and false (somewhere between zero and one).
In a sense fuzzy mathematics is an alternative approach to some aspects of statistical methods.
It is easy to show that mathematics is a special case of statistics.
Two points on a graph constitute two equations and two unknowns (slope and intercept).
Solving two equations for two unknowns is just mathematics.
But what happens when you have three points on a graph that don't line up?
Fitting a straight line to those three points cannot be done perfectly. There will be some error.
Since you only need two points, but you have three points, you have one extra point, or, one "degree of freedom."
In other words, mathematics is when you have zero degrees of freedom.
In statistics you can have one or more degree of freedom. Zero degrees of freedom in statistics is a perfect fit. The error equals zero in that case.
Fuzzy math is a branch of mathematics that tries to deal with degrees of freedom in a different way than traditional statistics.
not that fuzzy math
Got it- but I think they refer to "Whole Math" or "Conceptual Math" as "Fuzzy Math" in reference to the math that some politicians have used...
Bottom line to me are four concerns:
- if teachers don't teach a blended form (traditional plus whole) then it could shortchange kids
- if, as it is asserted, kids who take "whole math" have a problem with college math and/or algebra in college and have to take remedial classes (according to the Michigan State study in the comment below), then it would seem to be problematic to only do "whole math". Specifically, it is asserted that kids don't learn long division, carrying in multiplication, factorals, and division of fractions.
- Third- I would think that if elementary kids were taught "whole math", that it should also continue in the middle and high schools. Wouldn't switching to traditional math in 9th grade be problematic?
- Lastly, if parents grew up with Traditional math- how do they tutor kids that have no idea how to add or subtract the traditional way?
- Grant