# Monthly Archives: September 2011

## The Demise of Graphing Calculators?

Here’s an interesting question posed on a graphing calculator discussion group:

At Hypothetical High School, all students have laptop computers 24/7, and fast and open Internet access both at school and at home. Students will already have free access to Geogebra, Excel, Microsoft Maths, Wolfram Alpha, and heavens knows what else.  If more Maths power is needed, it can be bought relatively cheaply….

For such a school, is there any justification in asking parents to pay an extra AUS \$190 for a graphics calculator?

Just so I don’t confuse anyone, remember that I am a firm believer in the power of technology for enhancing the relevance and power of mathematics teaching.  I have seen students explore and discover amazing mathematics because they had the instant feedback abilities of mathematics software (handheld and computer-based) that answered their “what if” questions whenever they occurred whether or not an official teacher was present.  It levels the “playing field” for all students of mathematics and grants them access to understandable answers that sometimes result from intervening mathematics beyond the current reach of the explorers.  It is one more tool that can be used to lure the curious into the beautiful worlds of mathematics and patterns.

But if all students and teachers have access to calculation/graphing/manipulation tools that are far faster than any handheld calculator, how can we possibly justify charging (or asking) families to pay even more?  The only argument posted in the discussion group in response concerns high stakes testing.  Real or not, that strikes me as an anemic response for many reasons.

• We already ask families (or all tax-payers via school-funded testing) to shell out huge sums for annual testing.
• Testing already occupies a disproportionately (and dis-appropriately?) large amount of the focus of many schools.
• If math and science “explorers” already have laptops, won’t requiring them to learn the specific workings of handhelds just take up more classroom time that should be spent on content?
• Are we really so wedded to testing that we are willing to spend extra time, money, and other resources to keep it in place?

As much as my students and I have grown from the presence of graphing calculators in their hands over my years as a math teacher, is it time to say goodbye to my old friend, the handheld calculator?

I first encountered this problem about a decade ago when I attended one of the first USACAS conferences sponsored by MEECAS in the Chicago area.  I’ve gotten lots of mileage from it with my own students and in professional circles.

For a standard form quadratic, $y=a*x^2+b*x+c$, you probably know how the values of a and c change the graph of the parabola, but what does b do?  Be specific and prove your claim.

## Elementary Multiplication

One of my daughters is now in 2nd grade and I’ve always been interested in keeping her curiosity piqued–whether in math or any other discipline. I never want to push her to memorize anything or accelerate her learning beyond what she’s ready to engage.  But she has always enjoyed games and has been intensely interested in art.  Following are some ideas I’ve been playing with my daughter during our recent conversations.  Perhaps some of parents out there can benefit from my ideas or others can give me some additional leads on other good ideas

I always play number games with my daughter.  A few years ago I asked her how many apples (or dolls, or crackers, or whatever was in front of her at the time) she would have if she had 2 and I gave her 2 more.  There were many variation on this theme.  Eventually the numbers grew larger and then I asked her how many I would need to give her if she had 2 apples now and would have 5 after my donation.  It was my attempt at introducing subtraction without needing to name a new concept.  From my end, this has worked well.  My daughter likes playing with numbers and I keep pushing the window of what she can handle.  I make it clear that she can always ask for hints and that I’m never disappointed if she can’t handle a question I give her so long as she tries.  It’s a delicate balancing act, reading my daughter’s readiness and trying not to overburden her.  When I misjudge, her blank face tells me to go in another direction.