Technological tools are for augmenting, not supplanting.

One reason for my “tech resistance” is because of supplies–we haven’t had enough functional calculators to go around the school most of the year. (I recently got a set through Donor’s Choose.)

A larger reason is that my students are drastically below level, so I’ve been teaching basic addition and subtraction with my algebra. I want students to practice those skills at every opportunity and calculators make it too easy to not learn those skills. (Perhaps one reason why they haven’t mastered second grade math skills when by the time they’ve entered high school?)

It’s not so much that I don’t want to use the technology. I’m just not sure how to allow parts of a tool and not the entirety of it. At what level do you bring in what tools? At what level do you expect students to be able to do something without the tools?

Don’t feel guilty — graphing calculators are hard to integrate at earlier levels, and really only come into their own once the students are far enough to do actual graphing.

However, with the right software, you may still find the calculators useful as a miniature computer lab. If they’re TIs, shop around their education site for something useful.

Just be sure to emphasize that the graphing calculator cannot be a substitute for knowing the mathematics. Something simple to try once they start graphing lines is to give a function that lands outside the standard window, and ask them to figure out what’s going on.

We seem to have more discussion regarding elementary calculator use. Everyday Mathematics, the curriculum our Elementary schools use, recommends calculators. However, the calculator that they use is a TI-15. Here is a link to it: http://education.ti.com/educationportal/sites/US/productDetail/us_ti15_explorer.html

The issue we are seeing is with adding, subtracting fractions and common denominators. When these kids then get to algebra and are required to manipulate algebraic fractions to evaluate and solve, they have real trouble. It might suggest that the TI-15 and it’s “fraction button” contribute to very poor skill development.

For those of you unfamiliar with current calculators, there are fraction buttons on them and they spit out answers in fraction form. So one enters 1/2 + 3/4 and it produces 5/4 or 1 and 1/4. So students in early elementary school can “skip” skills that are necessary to be successful with algebra.

So my question is…are we making robots that can push the right buttons or are we making people that can solve problems? It almost feels like we are indirectly creating an intelligence class system. A class for people that push buttons and a class for people that can think freely? Maybe that is already here…maybe not.

I have given tests where a graphing calculator was required for the entire test. I have given tests with no calculator allowed. I have given tests where the first page has no calculator allowed and the rest of the test requires a calculator.

I have given these tests all to the same class in the same year.

To be honest, though, if I thought the faculty was using calculators as a crutch, I’d be comfortable omitting calculators from the elementary level and only phasing them in at the middle school level.

The most obvious instance is in a “thinking problem” where numbers are not involved. A lower level example might be: why is subtracting a negative number the same as adding the positive version? A higher level example might be: a pendulum can be started by either pushing it from a resting position, or lifting it up to a height and letting go. Which one is best represented by a sine curve, which by a cosine, and why?

An example the AP test uses is analyzing graphs with no numbers attached; they’ll have a picture of the derivative of a function and ask the student to reconstruct the original. It’s purely pictorial, meaning the student has to really understand the meaning of a derivative.

In some cases the calculator is dumb the student has to compensate. For example, the graph of a logarithm often gets fouled up on graphing calculators, because it approaches a vertical asymptote and the picture just cuts off.

Your manipulation might be purely symbolic; while there’s software that handles symbolic manipulation (and also the TI-92, not allowed on the AP test) it only works if you know which way you want to go with the problem. You may be just trying to “simplify” in which case it’s like a puzzle, so human intervention is required.

You may be wanting an *exact* answer, like knowing the answer isn’t just around 1.299 but sqrt(3) * 3 / 4. Perhaps eventually the sqrt(3) cancels, but the calculator won’t be smart enough and it gets some strange approximation like 0.754745 rather than the true answer of 3/4. (Calculators have more issues with rounding problems than you might realize — computer scientists go through all sorts of convolutions in complex calculations to keep errors from cropping up.)

Finally, when the AP test has problems that absolutely require a graphing calculator, usually they are asking for higher level understanding, so it’s sort of a hybrid problem. They’re really not asking the student to integrate between 0 and 18 (because for the particular equation they picked there may be no method other than approximating) but they want the student to understand when the proper moment is to integrate from 0 to 18.

I will try to get up another example on my blog later.

This is MY problem with these calculators. Why ARE graphing calculators so expensive?