More Than A Step Behind



A group of low-level freshman heard me talking about calculator use being forbidden in the college classes I teach.  He heard this as he was handing his ID card in to get a calculator for the days lesson.  I heard him say, "Mr., why do you make us use calculators when we won't be able to use them in college?"  The boy was clearly disturbed about the caliber of education he was receiving.

I left before I heard the teachers answer so I don't know how he justified calculator use to this student but I do know the AP of the department is demanding that all classes use a calculator daily.  Education and college readiness is not a step behind statistics, it is the being on the first step of the staircase  leading to the top of the Empire State Building behind.

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?

Calculators Need To Learn Their Place



It is not their fault.  They enter high school and the teacher puts a calculator in their hands.

Don't know the multiplication tables?  No problem.  Use the calculator.
Can't work with fractions?  No problem.  The calculator has a fraction button.
Can't solve an equation?  No problem.  The Casio will do it for you.  And for the cheap price available, the school has one for everyone to borrow.
Can't work with complex numbers?No problem, the TI 83 has a mode that will work with all the imaginary numbers you want.

Attend a college that does not permit calculators?

BIG PROBLEM!!!!!!!

Kids are going through school taught to do everything on a calculator.  Passing exams is all that matters and using a calculator correctly will certainly get them through the exams with good grades.  These same kids are now sitting in a college class where calculators are not permitted.  The school has standards and believes everyone should have basic arithmetic skills.  The school believes their diploma should mean something.  Too bad high schools don't have the same values.

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 Girl Can Dream

Surprise, surprise, we had a meaningful departmental meeting today. A guy came in to teach us how to use the new Casio calculator and not only did he know what he was doing, he was interesting. Most of us were actually upset when the meeting ended. Maybe the upcoming staff development days will be just as good. Maybe dreams really do come true.

Upcoming post--The Push Button Generation.

I just have to decide whether I want to post it here or on the other blog. (Don't look now, I haven't written it yet.)

By the way, I have a strange feeling that there are people trying to get into that blog under assumed names so I have decided to keep it open to only those of you that already have access. It really isn't that interesting anyways.

Calculator Dilemma

Technology is important. In fact, it is vital to the twenty first century. In spite of this, every day I grow more and more opposed to calculator use in the classroom.

My MB31 class spent the day proving that a quadrilateral is a trapezoid by showing, with coordinate geometry, that two sides were parallel and two sides were not parallel. The concept of the trapezoid did not give them any trouble, nor did the slope formula. We hit a wall when we got 4/8 for one slope and 8/16 for the other and these kids (not all of them, thankfully)did not recognize that the fractions were the same.

My MB31 kids all passed the Math A regents, most passed it the first time around. The majority of them are juniors. They are nice kids. They are kids that, for the most part do what they are told. Their basic skills are so lacking that I fear for their future success in the next two terms of Math B. How are these kids going to work with imaginary numbers when they can't even comprehend real ones? How will they simplify expressions involving trigonometric identities and fractions when they have no clue as to how to simplify numeric ones or even have no clue as to what a fraction means? More important, what am I teaching them when I get them to reproduce what I show them and they have no real understanding of what they have been taught? How will they go on to college and succeed when their foundations are so weak? I know there are people out there that do not agree with me on calculators. These people are not dealing with the kids of today and would find it incomprehensible that their rudimentary knowledge is so weak. A building will not stand unless the foundation is strong. Calculators are useless without this foundation.

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.