Four Wasted Years



Four years of high school spent with calculators in their hands,  four years of letting a machine do work their brains should have been doing has left kids unprepared for college.  Four years where the only thing that mattered to administrators was getting an A on a progress report did nothing for education.

The math teachers at Packemin have been pushed to use graphing calculators with all our students, particularly the lowest level ones.  Teachers have been told, over and over, to teach the kids how to solve equations using the calculator.  They have been threatened with "U" ratings for not using this device.  An ISS teacher told me that her former school forbid her from teaching simultaneous equations without a calculator.  Kids have gotten so calculator dependent that even simple operations like 12/1 are not being done by hand anymore.  A really sad part of all of this is that the calculators are not easy to use.  The time spent learning to do certain operations on the Casio or TI 84 could be better spent learning to do the work by hand.

I am not anti-calculator by a long shot, but when I see bright kids fall apart because they forgot basic arithmetic, I want to cry.  We've thrown away a generation.  How many more can we afford to lose?

I Feel Good

I just spent 30 minutes with my Casio and I got it!!!!! It is not that hard. In fact, it is easier than the TI 83. I feel accomplished. I am as good or better than any teenie bopper who grew up with technology! (I still doubt its value in the classroom and I still think it should not replace real working knowledge of math.)

Push Button Generation

On Monday, the Casio man came to town. He spent a period enthralling us with the wonders of the Casio 9570GA Plus calculator. These things are amazing. They do everything except wipe your rear end. Passing math should be a snap. All you have to do is push a few buttons and abracadabra, the answer appears on the screen.

Well, it is not as easy as all that. We were shown how to solve an equation and all six math teachers in the room ended up with six different answers, none of which were correct.

Now, I am proud to say that I am not against the use of a calculator in the math class. By eliminating some of the tedium of arithmetic, more complex, thinking problems can be tackled. There are problems that cannot be solved by hand and the calculator is a necessary tool. (We came across many such problems in calculus.) The calculator should be used to enhance learning, not replace it.

I have a feeling that this calculator will not be difficult to use once I am used to it. I remember my frustrations when I began on the TI-83 but once I learned to use the menu, I became a pro. I am certain I can do the same on this. What I am not so certain of is that my students will be able to become a pro. There are just too many buttons to press and too many steps to go through before the answer can be found. I know that the kids will eventually get this, but by then we have wasted valuable class time teaching them button pushing skills and their math skills will still be lacking.

I might be old fashioned but I have a problem having kids using a matrix on the calculator to solve systems of equations when they have no idea as to what a matrix is or does. They are pushing buttons with no understanding. I taught the same thing in a college class but it was only after we had done several by hand and understood how they worked and what they could be used for did we use the calculator and the computer. And, finding zeros using Newton's method is absurd. The kids should at least have a little understanding of what is going on before they hit the buttons. True, my calculus classes are better students, but I never go over the root button without first explaining iterations to them.

Many of students are graduating high school and attending the local community college. They place out of remedial math by scoring a 75 or better on the Math A or Integrated Math regents. Lots of them can do this. I'm guilty of teaching a whole class of students how to pass the exam without really knowing anything. I'm guilty of sending these button pushers on to failure in college. I'm guilty of doing what my supervisors wanted me to do without thinking about what was best for my students. (I really tried to teach them the math. Some actually learned a good part of it. They all passed the regents and most got over a 75. Most of them did not learn any more than how to pass an exam.)

My department is complaining about the Casio, complaining because they have to learn to use a new calculator. It's sad. They waste so much energy on nonsense. Instead they should be arguing about how the calculator should be used and what the kids should be taught to do on it.

One more comment on this topic, but you will have to read it here.

A New Graphing Calculator

I can use any of the Texas Instruments graphing calculators expertly. I went to tons of training and then was able to pick up extra stuff on my own.

I've been looking at this Casio for an hour. Even when I figure something out, I have a hard time remembering how I did it.

I have a headache!

You've Come A Long Way Baby

We graphed a third degree polynomial equation today. We used minimum and maximum points. We used concavity and inflection points. When we finished, we compared our results to the results on the graphing calculator. The kids were amazed at how accurate our picture was. The teacher who entered the room as my class was ending was impressed.

I told the class to remember when graphing straight lines was a challenge. One boy took the picture above. They've come a long way, baby!

Economics

A long, long time ago, when graphing calculators were first introduced to the mathematics curriculum, math teachers did not know how to use them. These calculators have long menus, hundred page manuals and and most teachers felt overwhelemed by them.

Texas Instruments was only one of the companies to introduce a graphing calculator. Theirs was not the cheapest, not the easiest to use, and it did not do the most, but it took the schools by storm. The reason for this was simple--economics. TI was the only company willing to supply the schools with the much needed technical support. They not only came to the schools to do workshops, they provided off site instruction and gave away many calculators and overheads for the schools use. The sad thing is, most teachers can still only do the very basics on those calculators.

I just found out my school will be getting Casios. I wonder who is going to teach us how to use them? Most of the teachers I know will not be able to read the manual and figure it out. The manuals are just too complicated. Will they be used to add, subtract, multiply and divide or will they really be used as they are intended to be used?

Calculators

Kids don't learn arithmetic anymore. Adults are forgetting everything they ever knew about it because calculators will do the computations for them. Fractions, signed numbers, decimals, etc, etc, etc can all be done on these little machines. After all, most of us use a remote to change the station when we are watching television and we certainly use a washer-dryer to launder our clothes instead of beating them with a rock on a river bank, so why not replace our brains with little machines that can be purchased for less than $20?

I don't have a problem with calculators if they are used to enhance learning, not replace it. Kids need to understand how operations with signed numbers work before they just start pressing buttons to hopefully arrive at a correct answer. They need to understand what happens when they find a percent of a number, know whether the answer should come out larger or smaller than the original number. They should know that multiplying by pi will give a number slightly larger than three times the original number. Too many times I have seen kids come up with totally insane answers and write them down because that is what the calculator gave them.

I do believe that arithmetic shouldn't hold anyone back. Not mastering fractions should not be equated with the inability to solve an equation. After years of trying, kids should be able to move ahead with a calculator if that is the only way, and I do mean the only way.

Calculators do have a place in higher mathematics. By freeing the individual from tedious calculations, more difficult conceptual problems can be studied. But, even in the higher level classes we are doing our students a big disservice by allowing a calculator on every exam. For example, kids no longer know trigonometric relations of quandrantal angles or of the special angles, and some of the beauty of math is being left behind. We used to teach them to find sin 15 by using sin(A - B) formula. Now, they just want to get the answer from their calculators.

The AP calculus exam is divided into four parts. Parts II and III allow calculator use. Parts I and IV do not. The calculator parts are the most difficult parts because of the concepts that are being tested. In my class, to prepare for this exam, I give both calculator and non calculator exams. At first, the kids whine about not being able to use the calculator. THEY HATE DOING ARITHMETIC! THEY DO NOT REMEMBER SIMPLE TRIG RATIOS! They soon find that the arithmetic they are being forced to do is the easiest part of the exam. I find that I have to show them silly calculation tricks to make the arithmetic easier, things that they should have learned (and are more than capable of learning) a long time ago.

So, what is the answer to all this? I don't want to do away with calculators. I just think calculators need to be used sensibly. Teaching must include calculator and non calculator questions. Exams must sometimes be calculator exams and other times be calculator free exams.

Mathematics is more than arithmetic, but, an understanding of arithmetic is vital to being successful with it. Technology must be used, but, it must not be used to the exclusion of everything else.