MathFoundations5: Arithmetic and maths education

[koozdra]

I agree with you completely about calculators. When you do the math manually on paper, you gain a familiarity with numbers that is lost when using a calculator.

[sftw009]

Very good vid! You are absolutely right.

[Kurtlane]

While elaborate "real life scenarios" with a touchy-feely aspect are a waste of time, word problems with loads of math in them are not.

I have found that many students who do just fine with pure math get stuck when faced with traditional word problems: calculating speed and distance, weight and density, water pouring form / into tubs, etc. Which then resilts in bad grades and not understanding basic physics and chemistry, biology, you name it.

[lefthandovRA]

@Kurtlane i was thinking about this point i guess what he means is that real life scenarios are a waste of time for mathmatics...remember his goal here is to teach mathmatics..giving real life scenarios gets u into the trouble of students linking mathmatics with objects in life...i guess using real life scenarios is the job of the physics teacher and the chemistry teacher

[Kurtlane]

@lefthandovRA, no, I disagree. Calculating speed and distance, weight and density, water pouring form / into tubs, etc. is the job of math class. Very few school graduates will become pure mathematicians, while these skills will be used by almost everyone.

Physics and chemistry teachers have their hands full with more advanced stuff, for which traditional word problems form a foundation.. There is hardly any REAL physics or chemistry left in schools anyway.

[Kurtlane]

It's so disdastrous that the typical question I ask form both high school and first year college students is:

15 / x = 5. How much is x?

You should see how many of them cannot solve it.

[Kurtlane]

Being a tutor of, among others, high school kids, I don't know a single school where logarithms, trigonometry or combinatorics are taught. Never mind derivatives and integrals.

A few most basic things about Euclidian geometry are also taught.

Logs, trig, combinatorics are in school books, but no teacher ever gets to them. At least that's how it is here in Orange County, California.

[QuantumMaths]

My statistics course is terrible. This is because we use a computer program to compute everything for us. Everybody knows at a very thin level what all of the terminology is, but it is so bad that we have never actually computed anything (not even the average of a set of data!) My precalculus course two years ago was along the lines of "do a single example and then download a calculator program after you've done it by hand once". I've always thought it was despicable.

[steve9340]

Like your stuff a lot. Watched few of the trig series and now I've begun this foundations series. But I teach math in the US seconday schools (14 - 18 year olds) and I disagree greatly with what you are saying about calculators and discovery learning.

[njwildberger]

I am not sure I have said much about discovery learning, at last not directly.

But I am interested in why you disagree with my antipathy towards calculators.

[steve9340]

For example: This term I was teaching two classes of "third year algebra) for students who had not done well in the second year, and who were not ready for periodic functions in a standard "pre-calculus" course. I did a lot of work with the median-median line, collecting data, using data and the various forms of the equation of a line, and using all that to make predictions from the data set. I didn't always want them to have to find the med-med line by hand, or even plot the data.

[steve9340]

I think it was on balance a huge success. Next term we''ll maybe be studying transformations of basic functions, and most graphing by hand is tedious. The key is that they learn what to expect from the basic transformations y = a*f(x + c) + b etc. Graphing by hand is too slow. They need to work their intuition. In sum, I am not saying always use calculators or never. I'm saying use them in a controlled environment with a purpose.

[otherchaz]

The history of mathematics is a history of humans striving to solve an increasing number of increasingly difficult problems. It represents the cumulative work of generations of mathematical problem-solvers throughout world history. We abdicate our responsibility to our children when we leave them to rediscover and recapitulate that entire history on their own, without proper guidance. We lie to our children when we claim to teach them mathematics, but instead teach them reliance on machines.

[CPLains]

Yes. And machines does not necessarily mean calculators and computers, but can mean a way of teaching that leads students to depend overly on formulae and step by step rules without really understanding what they are doing.