HS Math and calculators...

Discussion in 'Secondary Education' started by GTB4GT, Sep 1, 2012.

  1. GTB4GT

    GTB4GT Cohort

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    I am in my 2nd year teaching math and have this question/concern. A significant portion of time each day (not taken from teaching time) is spent helping kids "troubleshoot" incorrect answers. It seems there are a great deal of errors invovling calculator use. each brand is slightly different and requires different keystrokes/input.I am unfamiliar with many of them and 90% of what we do I can calculate in my head anyway so I rarely use one.

    When I ask the kids about the operating instructions, they give me a blank look. They lean on these things but don't bother to understand how they work.It's frustrating for the student and for myself.

    Do you consider teaching the use of calculator as part of your standards or curriculum? BYW, I graduated HS in '76 so no one had a calculator at my school. I only acquired one in engineering school (a $100 TI that had the same capacity as a $2 calculator today.) If you do, how do you master the variety of different ones? Thanks for any input.
     
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  3. Aliceacc

    Aliceacc Multitudinous

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    I'm with you: I graduated HS in '76 as well. I had been teaching 3 years before I owned my first caclulataor.

    We, as a school, have decided to use the TI30XA calculator in class. Well, that's not totally true. Our freshmen do not use a calculator at all. And our sophs only use the TI30XA once we hit the trig chapter, after Christmas. (Our seniors use one of the Graphing calculators, I forget which one.)

    I spend 2 days in Geometry teaching them how to use the calculator. I made up a list of the functions I use for my SAT classes, so I use that same sheet in Geometry. I introduce phrases like "arc sin" even though we haven't started trig yet.

    The kids ARE allowed to use other non-graphing calculators, but I tell them that for the $12 or so they'll spend in Walmart or Target or the school bookstore, it's so much easier to just have the calculator that I have up on the screen. It's very rare that I have a kid who has another calculator for more than a day or two.
     
  4. giraffe326

    giraffe326 Virtuoso

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    I graduated HS in 2001. We were REQUIRED to purchase a TI-83 or TI-83 Plus.
     
  5. Shanoo

    Shanoo Habitué

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    We have class sets of graphing calculators for our students' use. They aren't allowed to take them home, so there is that, but it does cut down on the confusion you're experiencing.
     
  6. a2z

    a2z Virtuoso

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    We use TI 83 and 84. They are very complex. Sometimes it seems more work to use the calculator than to actually do the math!!! It seems as if one is pressing random keystrokes to make something happen. Calculator use could be a week long set of lessons! The istructions can seem cryptic to some.
     
  7. teach42

    teach42 Comrade

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    Do your students know how to do the math by hand? If not, then I wouldn't even let them touch a calculator until they did. I find a lot of students don't know how to use a calculator because they don't understand the concepts and how to do it by hand. Take a simple order of operations problem. They will all calculate it wrong if they don't know where they need to add the parentheses or to even add them. The only time I would allow them to use it is when they need to do calculations more efficiently after already understanding the concepts. Only then would I teach them how to do it on a calculator.
     
  8. Mathemagician

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    I believe we should be teaching the kids useful skills. I frequently give them assignments using calculators and WolframAlpha. Learning this technology is non-negotiable. They will have access to it in the real-world, and very little (if any) applied math is done by hand. Yes we do some calculations by hand to see the ideas, but calculators eliminate so much of the brute force work and allow me to ask the kids much more challenging and much more realistic questions. We have TI-84s for alg 1, geo, alg 2, and pre-calc, TI-89s for calc 1 and 2, and TI inspires for whoever wants to use them (haven't figured out how to use that just yet though!)
     
  9. teach42

    teach42 Comrade

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    How is it useful if they are mindlessly punching numbers into a calculator without understanding the concepts? Even a monkey could do that. If they don't thoroughly understand the concepts, they won't know whether the output on their calculator is correct or makes sense or not. I guess my experience has just been different. I'm used to teaching kids who are so accustomed to using calculators, sometimes incorrectly, that they can't even do the basic math or know whether their answers make sense. They'll even punch in things like a # times 0.
     
  10. MikeTeachesMath

    MikeTeachesMath Devotee

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    There's a huge difference between using the calculator as a learning tool, and using it as a learning crutch.
     
  11. Mathemagician

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    I'm not saying to teach arithmetic with it. I don't teach arithmetic.

    Use it to find roots. Use it to solve equations. Use it to find regression equations.

    We don't teach the traditional square root algorithm any more because it has little value thanks to the calculator. Same for regression analysis. A monkey could not do that. Use the calculator for the arithmetic and then spend more time focusing on what the information means. Perhaps we are teaching far different courses, but for HS math, I think there are FAR more lessons I do with calculators than without. In my student teaching alg 2, we only gave 1 test with no calculators.
     
  12. GTB4GT

    GTB4GT Cohort

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    thanks for the responses. Some of my students are so dependent on a calculator that they will reach for one if I ask them "what is 5 x 3?".

    In thinking through the responses, it would make sense to adapt a system wide policy. Something that would prohibit calculators until __th grade. at that point, require the use of one type and then teach the proper use of it. then move on. I want to teach the principles of math and math concepts, not teach someone how to punch numbers into a machine to get an answer that is technically corect but that is otherwise meaningless to the student.
     
    Last edited: Sep 1, 2012
  13. KateL

    KateL Habitué

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    Have you actually met your new students yet? I'm teaching algebra 1 this year, and I am absolutely teaching arithmetic. Some of my students are so confused by negative numbers and by fractions. We don't start using calculators until precalc because the students need to understand the basic operations first.
     
  14. Mathemagician

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    No, but I don't have alg 1. If I did, we might do some negative number and fraction stuff. I have alg 2 and geometry. As my old univ. supervisor has stated, if they don't have the arithmetic down yet, why make that the thing that prohibits them from learning other stuff? Another year of it isn't going to change anything. Give them the technology and let them learn something. If they can't do arithmetic, they can't do anything else really so it doesn't make sense to hold them back from doing other things because they can't add in their head.
     
  15. Aliceacc

    Aliceacc Multitudinous

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    Amen.

    I've seen far too many students over the years who believe that anything the calculator tells them is the truth.

    Give them a polynomial function, and ask them to find its roots, or its relative extrema. The kid who types in an exponent of 5 instead of 4 will swear that his answer is right, even though it makes no sense. The ends will go in different directions, when the even exponent should tell him that they need to go the same way. He'll name all 5 roots, even though he should know that a 4th degree equation only has 4.

    The reason so many experienced teachers hold off on calculator use is because we want the kids to understand what they're doing. Once they know DesCarte's rule and its implications, once they can make the connection between degree or leading coefficient and a graph, THEN they can use that graphing calculator or Wolfram Alpha to make their lives easier.

    Technology should SUPPLEMENT the learning, not replace it.
     
  16. Mathemagician

    Mathemagician Groupie

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    DesCartes Rule is generally useless in today's society given technology. I will teach it since it is mentioned in the curriculum, but teach them the Fundamental Theorem of Algebra---that's the key to not making the error you described, but Descartes Rule in my opinion really has no place in modern mathematics curricula.

    In any event, when taught DesCartes rule many kids can look at the sign changes and talk about classification of the roots, but being able to use something and being able to understand something are different. I think it most cases it becomes just extra material for them to forget once they leave the class.
     
  17. Aliceacc

    Aliceacc Multitudinous

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    Not when I teach it.

    It's in the curriculum because someone who has taught the course, and the one that comes after it, can see its use.
     
  18. Mathemagician

    Mathemagician Groupie

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    Maybe, but have you tested your kids on it 2 years after the fact? I doubt they remember it as well as you think.

    I am sure my kids will be able to use the Fund. Theorem of Alg (and MAYBE remember rational zero theorem) and use their graphing calculators or other technology to find roots though.
     
  19. Aliceacc

    Aliceacc Multitudinous

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    Sep 1, 2012

    :lol:
     
  20. Math

    Math Cohort

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    Is this something that you can ask your Department Chair if something like this can be implemented?
     
  21. teach42

    teach42 Comrade

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    You're kidding right? Maybe this explains a lot about why I always get a bunch of students without any basic knowledge of math or whatever prerequisite info they need for the course. I don't know how they can do algebra 1 let alone algebra 2 without knowing the basics. I had several students last year in my algebra 2 course who couldn't even compute the square root of a number among other things and it was impossible to teach them any algebra 2. Everything I wrote on the board was like Greek to them. Math builds on itself so if you don't have the basics down, how could you possibly understand the more advanced material?

    I tutored the physics students as well and pretty much all of them were mindlessly punching in numbers to solve equations that they did not understand. They didn't understand the math or the physics of it.

    You must have genius students or something because the majority of students I taught struggle to understand anything I teach without knowing the prerequisite information that they should've learned before they stepped foot into my class. What makes you think in 2 years, your students will remember all this Wolfram stuff that you taught them? I can live without knowing that.
     
  22. Mathemagician

    Mathemagician Groupie

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    You're misconstruing what I'm saying completely. If your algebra 2 kids can't add two negative numbers, are you saying you are willing to devote an entire period reteaching this (which will likely not stick for students if it didn't stick the first 3 times it was taught)? You can throw another layer of mud on for them, meanwhile I'll give them another way around it.

    To clarify: definitely teach it conceptually the first time it is introduced, but if students come in lacking pre-requisities, you can't re-teach everything.
     
  23. Mathemagician

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    Another thing for many of you no-calculator people to remember is to work with the students you have, not the students you wish you had. Students CAN solve systems of equations even if they can't solve equations with fractions. Students CAN solve quadratic equations if they can't factor. It would be nice if they could all do the basics, but when they can't, give them a way to still succeed.
     
  24. KateL

    KateL Habitué

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    And what's the point in solving systems of equations if you don't even understand fractions? A solid understanding of fractions will get the students farther than solving systems of equations. Also, if the students lack the ability/background for fractions, they probably won't understand systems anyway.
     
  25. teach42

    teach42 Comrade

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    Ditto to the above. What is the point in learning how to solve equations if they don't understand basic math like fractions. If they did, it would be a lot easier to understand how to solve equations. You mind as well just teach them how to mindlessly follow a bunch of procedures without understanding why they're doing any of the steps. According to you, all it matters is the output and what it means right?

    I don't think any of the people who responded here are no calculators people. We just realize it's a tool to supplement learning, not replace it. I can't imagine a scientist or statistician being able to analyze and interpret data without knowing and understanding how it is generated in the first place and the process involved.

    <edited to remove personal info>
     
  26. Aliceacc

    Aliceacc Multitudinous

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    FYI: Mathemagician is starting his first year as a teacher this week. So he can't be the reason that kids come in not knowing their basics; he has yet to teach any of them.

    Anyway, here is my point: I'm not nearly as interested in the answers as I am in teaching my kids the process that gets them to those answers. Sure, the graphing calculator will give my freshmen the answer to a system of equations in no time at all.

    But I don't really need the answers. I can do the math myself. The answers are NOT really the point. What I'm going for is that they understand the relationships involved, and that they can use those relationships to find the answers. That's the huge step that's missing in letting them use calculators too early.

    Until they hit the Trig chapter sophomore year (we took it out of the Algebra I course for just this reason. Plus, it's based on similar triangles, which they don't see until Geometry), they simply do not need a calculator. The numbers in an Algebra I class aren't so ugly that a calculator is necessary.

    Once they hit Trig, we let them use a scientific calculator up until Senior year-- for most of them, that's either Precalc or Calc. We want them to learn the graphing calculator at that point, so they're better prepared to use it in college. And by then, they've also been taught all those basic relationships that we find so very important.

    Anytime I proctor the SAT, I know which kids are in trouble. It's the ones who reach for that calculator the minute I say "OK, good luck and begin." They're the ones who have been so conditioned in letting the calculator do the work that they've forgotten to think. I've taught many entire SAT prep classes without taking my calculator out, and have arrived at the correct answers before my calculator-clutching students. It's because I understand the underlying relationships.

    I don't view what I do as "magic"... push the button and Abracadabra, an answer appears! I teach relationships. I teach my kids the "how" and the "why" and not just the "what."

    Getting back to the original question: OP, can you speak to administration about deciding on one scientific calculator you'll use as a school calculator? As I mentioned, the one our kids use as sophs and juniors is the TI30XA. It does the basics, it's available everywhere. I saw it yesterday (at either Staples or Target, I forget which one) for $9.99. It's the only one we sell in our school bookstore, though our prices can't compete with the national chains-- I think we charge something like $12, so it's still very reasonable. http://www.amazon.com/Texas-Instrum...=1346586811&sr=8-1&keywords=ti30xa+calculator

    It's so much easier to teach them how to use the calculator's functions when, for example, you can put it up on the projector and show them that "sin ^ (-1)" is written in yellow above the "sin" key, and as a result needs the yellow "2nd" function key. If everyone has that same calculator in front of them, they're not missing your next step while they hunt for something close to what's on your calculator.
     
  27. Mathemagician

    Mathemagician Groupie

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    Actually it's the opposite. Take finding 3x3 determinants. That becomes mindlessly following a bunch of procedures, whereas if you do it with a calculator you can focus on uses and meaning. The point is that there is a curriculum to follow. If they come without a mastery of the basic skills, you can't just turn your class into BSI for those kids because that's totally irresponsible.
     
  28. KateL

    KateL Habitué

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    No, we differentiate.
     
  29. Mathemagician

    Mathemagician Groupie

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    That's exactly what the calculator can do...differentiate so that all kids can achieve success with what the objectives are supposed to be. It's a much easier way to differentiate than to have some kids adding fractions while other kids are solving systems.
     
  30. KateL

    KateL Habitué

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    You're really not getting what everyone here is trying to explain to you. When you allow students who don't have good number sense to use calculators, the calculator becomes a crutch. Those students stop thinking and just start punching in numbers. I have students who are still wrestling with the idea that when you multiply two negative numbers you get a positive number, but when you add two negative numbers you get a negative number. If I allowed them to use a calculator for all negative number problems, yes they'd get the right answer most of the time, but they would have no idea why the answer was right or how to know if it was wrong. Number sense has to come first.
     
  31. GTB4GT

    GTB4GT Cohort

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    excellent points. Which leads me to my next question re: the students who are using the calculator as a crutch. Is it possible to teach them number sense as sophomores/jrs. in HS?

    It seems that this is an elementary subject and if a students hasn't mastered it by this point in their career -are they capable of ever doing so? Bear in mind these kids are in alg.1,2 and geometry and are mixed in with students who are proficient or advanced so you can't take large blocks of time reteaching these types of skills.
     
  32. Mathemagician

    Mathemagician Groupie

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    I understand perfectly Kate. GTB4GT explains perfectly what YOU aren't understanding.

    Exactly right. Thank you for having a practical perspective. In addition, many of these students who don't have the number sense are resistant to learning the same thing (i.e. adding and subtracting) because "that's easy" or "we already know that" even when they don't really have good mental math.
     
  33. KateL

    KateL Habitué

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    Oh, I understand. But you have been hired to teach all of the students, not just the ones who understand math like you do. Will your students be allowed to use calculators on the state tests? Mine won't. And even if they could, they probably still wouldn't do well if they couldn't evaluate their answers for correctness. I have to develop that number sense if they are going to succeed in math at all.
     
  34. Mathemagician

    Mathemagician Groupie

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    Yep, HSPA (and the SAT) allows and recommends calculators. And you stole my line. I AM teaching ALL students. You are the one saying: here you guys learn systems, while you guys over here just do more fractions. I am saying: let's all learn systems (since that is what will be tested, and what you will all need to know!!), but some of us may need a calculator to help us along the way...and that's okay! Of course we check our work by plugging back in, see if our solution makes sense, and explain what the solution means (i.e. point of intersection or break-even point or whatever it is in the problem) so it is NOT just punching numbers into a machine.

    What you seem to be saying is that students can't possibly understand or do anything in math if they can't do arithmetic, and I firmly disagree.
     
  35. Galois

    Galois Companion

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    I don't mind students using calculators (SAT allows). However, in California, two very important exams: CAHSEE (need to pass to graduate HS) and the ever important CST exams do not allow calculators. So, students have to master math concepts without the aid of calculators.
     
  36. teach42

    teach42 Comrade

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    I don't see what your point is with #1. What makes you think I gear my class to the lowest students? My class is extremely challenging and any of my students can tell you that. I do what Alice does and focus on the how and why and getting them to think critically. I don't allow them to rely on their calculator as a crutch or as the first thing they reach for. This is what is systematically wrong with education in the U.S. today.
     
  37. KateL

    KateL Habitué

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    Yup. I hope that Math comes back to this thread in November or so and updates us on how his class is doing. I hope that I'm wrong, but I don't think that I am.
     
  38. Mathemagician

    Mathemagician Groupie

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    I student taught, and my students did very well, but thank you. How about responding to the argument instead of slinging mud? I teach conceptually and use calculators to avoid repeating tedious calculations. This leads to more time devoted to ideas and complex problems. I understand if you'd rather skill and drill the kids until they hate math even more than they already do.

    As teachers, we have to get kids to be able to do the problems they are given. Rather than just give them one way as you suggest, support their learning with technology! Traditional learning may work for some students, but some students need to have other ways towards success. I'm sorry you see no hope for these students.
     
  39. KateL

    KateL Habitué

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    Wow. And you wonder why you have the reputation that you do on these forums. I'm done.
     
  40. Mathemagician

    Mathemagician Groupie

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    Where did I wonder? I'm sorry you are so easily offended by a different approach that sees success for all. Let's call it what it is: your done because you don't really have an argument here.
     
  41. Mathemagician

    Mathemagician Groupie

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    Met my students this week. Seems like a great group.
     

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