24 Responses to “Math: how hard can it be?”

1. jove Says:
   May 30th, 2008 at 7:46 pm

   I think you are right. One of the attractions of the living math thing is that it deepens those concepts with some historical context and some attempt to fascinate kids with the wonder of how all that works. But you are absolutely right that folks shouldn’t get their knickers in a twist about it.

2. Rebecca Says:
   May 30th, 2008 at 8:20 pm

   You have such a nice knack for making things sound so simple and easy, Theresa. I do think that repetition is so important with math. When I teach my kids how to do something like multiply two digit numbers, they might not really understand until they have done it a dozen or two times. Then, if it is not practiced often, it seems a function is so easily forgotten. So, I guess I do see what you are saying about the actual list of things being pretty simple and short (especially given the time frame of years in which to learn it) but I can’t help but think those few things must be practiced over and over again in order to gain competency. Just my humble opinion.

3. Shannon Says:
   May 30th, 2008 at 8:37 pm

   When I was in my high school trig class, I hated it…and I struggled. I can remember clearly the teacher saying to my mother, “Well, Mrs. R, your daughter will never be a mathematician.” That was my last year of math.

   When I went to college, I retook Algebra I and II. Then, I went on to Calc I, II, and III. I was a biochemistry major. (Not a mathematician, but pretty darn close.) I can remember my Calc I teacher saying, “Calculus is not hard, but a third of you will fail because ‘your algebra s*cks.’”

   I think most people need to practice. I think most need to practice for both speed and consistency. I think it is great to supplement that with living books to make concepts tangible. But, I am a firm believer in “If you don’t use it, you lose it.”

   Now, my sister, who math comes so easily to, does not need to practice at all. She just gets it and she always did. However, I see her as the exception and not the rule.

4. Maryan Says:
   May 30th, 2008 at 9:02 pm

   I do think it IS just that simple… but for some reason people get mental blocks against MATH!! So I do feel a little pressure to make it FUN! So there’s no MENTAL BLOCKS!! And I too tutored and subbed math students and know that many kids missed the basics.

5. Rhonda Says:
   May 30th, 2008 at 9:34 pm

   My oldest daughter’s weakness is Math. I found that in ps she did not learn the basics because she was hurried along. We have been reviewing some of the basics over a period of time and “wouldn’t ya know it” she is getting it. I did not have to drill her over and over and over again just to make sure that she passed the state standardized tests, I did not have to pound it in her head and tell her that she would fail for the year if she didn’t know it, and I did not have to rush her along so that she was prepared for the next year b/c some textbook SAID that she HAD to be. She learned what she had to learn at her own pace and in her own way. So my child, who was once so afraid of Math and frowned every time the word was mentioned in our household, is holding up her head and facing it head on. Is she still weak in Math, well of course she is and probably always will be. She has those “basic concepts” though and that means she has the world in the palm of her hand. Thanks for this blog Theresa. I needed it!

6. taffyisme Says:
   May 31st, 2008 at 2:23 am

   I guess you could think it’s that simple. I happen to like math and I like teaching it.

   I think of math as a language. It is the language of numbers, of patterns and how things fit together. Knowing all those concepts that you listed is important, but it is a pretty useless exercise unless you know how to apply it.

   Here’s an analogy to describe what I mean. Say that you are trying to learn a second language, spanish for instance. You bone up on your vocabulary, you practice your verb conjugations, you read as many spanish things as you can, you learn about the culture. But you never speak it. The only time you’ve ever used it is to answer the questions in your spanish textbook. Now, immerse yourself in a spanish city where you know no one and the only language that anyone can speak is spanish. Can you get by? Probably, but not without a LOT of mental anguish!

   Math is the same way. you can learn all of these concepts that you listed, answer questions in the textbook, be able to perform all the algorithms easily in isolation. But, unless you can use it, it’s not going to help you much. That’s why I spend a LOT of time on using math in real life. Want to double the recipe? Do the math. Want to change the size of a knit/crochet project? Check the math. Want to build a dog house? Check the math and the geometry. (My brother, who worked in construction for a number of years, often lamented the fact that he didn’t pay more attention in math.)

   I don’t think one needs the expensive texts and I don’t think that the drill and kill approach is very helpful. Knowing your basic facts does make it easier to understand the more abstract concepts in higher math though. But it is as simple as spending 5 minutes a day on flashcard review until mastery is achieved.

   But, sorry Theresa, I do think that it’s important to spend time daily in math - just as it is important in any language study, if one is to become proficient at it.

7. Angela, MotherCrone Says:
   May 31st, 2008 at 6:45 am

   From middle school level on, Math and foreign language are the ONLY subjects that I believe need daily practice because they are inherently different by nature. We speak and read and explore naturally. We enjoy shows like Discovery and History channel, so those subjects can be part of our daily life with ease. Rarely do we do algebra or even triple digit multiplication as a regular part of our day, or conjugate Latin verbs. I look at the big pic, and if it only takes 30 minutes a day, why not just do it?

8. lapazfarm Says:
   May 31st, 2008 at 6:50 am

   Hmmm…I am seeing some interesting assumptions coming from these comments.
   I actually like math, for one. I didn’t enjoy teaching it at public school, but that’s only because of the way I had to do it.
   I don’t think I said that you shouldn’t apply the math you are learning. I actually think that’s very important.
   I also didn’t say you shouldn’t do some repetition for mastery nor did I say you shouldn’t do math daily.
   (Though, to be honest, I don’t think you need to do it daily.)
   I’m just saying it’s a lot simpler than we make it out to be sometimes. That there is more than plenty enough time to learn it, and that we can relax a bit about it if we wanted to. Spend a whole year on fractions if you want, and it wouldn’t set you back for life. Or, conversely, spend a week on it and if you’ve got the concepts, move on.
   Oh, and I was writing specifically about elementary and middle school math. Not high school math. That’s an entirely different “subject.”

9. Chelita Says:
   May 31st, 2008 at 10:39 am

   I loved this blog post! When in high school I didn’t know beyond long division. Fractions freaked me out, everything else made me almost pass out! I didn’t have help at home. And the teachers sat at the overhead writing and mumbling. Then she would say “everyone got it, good”.

   I remember just feeling like NO I don’t get it! But to say that in a room full of peers was so scary. What will they think?

   And then the tests were multiple choice anyway.

   So how were they teaching?

   They were not teaching. The teachers did the work and hoped we would just get it. We would just soak it up.

   It took my wonderful husband to show me with diapers when we had our first child that fractions were not scary. That they made sense. I have since improved WAY beyond long division and went on to obtain my GED.

   With my kids at home and the time to learn and see that math makes sense they have no fear of math. And I have never had to teach. Just make a comment or two when asked or explain why.

   Kids have to know WHY! And in school where they are supposed to learn why they can’t ask why. It holds up the flow of the class. And I have a sneaky big brother idea that the schools make themselves appear needed by making it look hard. You know…don’t try this at home…

10. taffyisme Says:
    May 31st, 2008 at 11:01 am

    Well, I’m glad that I came back to read any new comments because now I understand what you are saying a bit better. We are actually very close to the same page on this! To answer your questions more specifically then…

    Do we really need to spend a large chunk of time and effort five days a week to teach our children less than 2 concepts per year?
    5 days a week teaching the concepts, yes. Not necessarily from the text book and not necessarily as a sit-down “school” subject. But reviewing the concepts? Yes.

    Do we really need to drill and kill until our children get queasy and break out in hives just from hearing the dreaded word “math”?
    If our kids are getting queasy and breaking down at the mere mention of math then we need to change our approach and teach in a way that our children can understand it! And make it less boring! Math isn’t that hard and can actually be fun!

    Do we really need 75 dollar math texts (plus teacher’s guide, test banks, extra practice and guided review), or scripted lessons, or video tutors, or online “homework help” for less than two concepts per year?
    Definitely not! I recently switched back to a more inexpensive program because it did a much better job of teaching math.

    Anyway, that’s my two cents. Spend freely wherever you wish

11. lapazfarm Says:
    May 31st, 2008 at 11:20 am

    Yeah, Taffy. I thought we probably were pretty close also.
    The thing is, as homeschoolers we have our kids one-on-one all day. Teaching is so much more efficient that way that I think it can be done with much less time and effort than in a classroom of 30 kids of varying abilities.
    I know in my classroom I had kids who just wanted to “get on with it, already” because they totally grasped the concept after the first example, but I was stuck having to help kids who were 3 grade levels or more behind because they somehow missed it the first time around.

12. Kathy Says:
    May 31st, 2008 at 4:58 pm

    Being a complete math doofus (how to spell it?), your simple explanation greatly relieves my unresolved math issues. This has really changed the way I think about math in our home education.

    Thank you, thank you, thank you!

13. Kelly Says:
    May 31st, 2008 at 8:46 pm

    You are basically right, but as a math teacher, I think that the most important thing you can teach in math is to look for the patterns. First the patterns in our number system (there are doozies - fantastically interesting), then the fact that you can pretty much draw or build any math problem ever. I found my passion for algebra teaching a few years ago because of those patterns - and the thrill was passing them on to the kids. I constantly hear, “Why don’t other math teachers do this?” Look for the patterns, they are everywhere….

    BTW - the only major omission I saw on your list was for angles in geometry (measurements, and relationships) - very important for vectors, and building.

14. Kelly Says:
    May 31st, 2008 at 8:48 pm

    One more comment…. I’m hoping you’re lumping integers in with basic integers, but don’t forget the graphing (not bar graphing, line graphing - especially linear equations)very important in algebra.

15. lapazfarm Says:
    May 31st, 2008 at 8:59 pm

    You are right, Kelly. I knew I would leave out a few things when I made up that list off the top of my head. Angles of course. And yes, integers can be lumped with the rest of numeration.
    When I listed graphing I meant coordinate graphing, not bar graphs and stuff. Now that you mention bar graphs, I think statistics should have a category of it’s own. I was kind of lumping it in with probability, but I think stats is a better category.
    (I’ll go back and make edits to add those things)
    I think that your point about patterns is valid. And I am thinking that freeing oneself up from the textbook grind will enable more time to be spent on looking at the bigger picture, like patterns and applications.

16. Rachel Says:
    June 1st, 2008 at 9:10 am

    It seems like Math is a problem because we spend more time on repetition when we’ve never gotten it to begin with. I took an Algebra class for college last semester and I wasn’t interested in it at all. As a result, I didn’t actually learn the concepts. I got enough knowledge to pass the tests, got a B in the class, and then the material leaked right back out of my head. I think most grade school students do the same thing: learn enough to get through the test (or just the day’s paper), then it leaks back out again. If you could actually stimulate the interest in the concepts, then the 15 concepts in 9 years would be easy. But how can you?

17. lapazfarm Says:
    June 1st, 2008 at 9:34 am

    Excellent point Rachel.
    I think that we often resort to repetition in hopes that after enough reps it will eventually “sink in.” What was it that Einstein said about the definition of insanity- repeating something over and over and expecting a different result, or something to that effect?
    The truth is, repetition only works to solidify learning if the basic concept is already grasped. You cannot learn NEW concepts through repetition.
    So, the trick is to find new ways to present material in order to help the child learn the concepts in the first place.
    I’m thinking living math books, hands-on, problem solving, and real-world application are the ways to go with that.
    Then, once the concept is grasped, a little repetition to solidify the learning can be a good thing.

18. KC Says:
    June 2nd, 2008 at 8:34 am

    You might actually enjoy reading Lockhart’s Lament (it’s a long read, but really enjoyable): http://www.maa.org/devlin/LockhartsLament.pdf

    It’s the first time in I could really understand the concept that math is more art than science. Math done right is supposed to simplify things and not complicate them. Common math education practices have totally missed the point about what math is all about.

    Hope you enjoy it.

    KC

19. KC Says:
    June 2nd, 2008 at 8:56 am

    For those who really struggle with math, it could be due to having a condition called dyscalculia:
    http://en.wikipedia.org/wiki/Dyscalculia.

    I think I suffer from it a mild case of it, as I can’t hold numbers in my head very well (though I can do math as long as I have pen and paper). I can visualize words and concepts very well without having to see them, but the embarrassing truth is that I don’t have a very good ability to manipulate numbers in my head. I do fine on paper, but I really falter when I have to make change, calculate tip, or figure out percetanges off when something is on sale (basically the times you probably don’t have pen and paper on hand).

    The thing is that I can see the numbers, sort of, but it’s like they are there but not there. As if they are out of focus. Consequently, processing time for math in my head is quite slow, and sometimes it’s just too tiresome to focus on the numbers.

    Still, I didn’t let that deficiency keep me from having a getting a degree in science and having a lot of math classes. And I had a 12 year career in the biosciences, so I can’t complain too much.

20. KC Says:
    June 2nd, 2008 at 9:47 am

    I just wanted to add to the post above. You can listen to a BBC audio clip about dyscalculia and hear from a British physicist, Dr. Emma J. King, who also suffers from it. She is my new hero. She didn’t let her problem keep her from getting a Ph.D. in Cosmology (the quantitative/mathematical study of the universe). She can’t add 4 + 3 without using her fingers. (I can at least do that, I have more trouble with double digit (or more) addition/subtraction and percentages.

    Here is a link to a BBC website that contains a 30 minute audio clip about dyscalculia and also has Dr. King speaking on it too. (Scroll down to Programme 3 and you can find a little audio icon to click on). I don’t know if there’s a written transcript on the site, but I will try to find one.
    http://www.bbc.co.uk/radio4/science/am_i_normal.shtml

    Dyscalculia is the math equivalent of dyslexia.

    HTH someone whose child is struggling with maths. It could be simple math anxiety or it could be dyscalculia.

21. lapazfarm Says:
    June 2nd, 2008 at 10:16 am

    Thanks, KC, for all the great info!

22. KC Says:
    June 2nd, 2008 at 11:09 am

    You’re welcome. I feel strongly enough about it that I decided to post about it on my blog. I want to help others who struggle with arithmetic difficulties too.

23. KathyJo Says:
    June 3rd, 2008 at 12:15 pm

    Interesting discussion. I think, in large part, those expensive math programs are the problem, not the solution. That and the fact that so many parents are math-phobic themselves, so there’s the fear of “missing” something by skipping some of the problems or even an entire lesson.

    We like to focus on understanding rather than just learning math by rote. Obviously, knowing one’s math facts make higher mathematics easier. However, one CAN do calculus even if one is occasionally counting on one’s fingers. But without understanding, even algebra can be out of reach.

    My second son (7) grasps concepts very easily, but he forgets just as easily without practice and review. He’s the type of kid who would probably have understood math even if we used a by rote program. My oldest son (11), OTOH, does not care for math. He’s worked in his math books often a year “behind” because he wasn’t ready to understand the concepts any sooner. I think he would have been flattened by a by rote program. However, he understands math well, even though he can’t seem to find the love.

    I think sometimes people act as if math is a talent that one either has or doesn’t have. But like you, I think there are simply some basic skills that need to be mastered and understood in the early years. When I used to tutor, it was often obvious that the person didn’t need me because he didn’t understand higher level math, but because he didn’t understand the basics.

24. Nature Mama Says:
    June 8th, 2008 at 5:36 pm

    That is so true! Really it isn’t all that much and I know I’m perfectly capable of teaching all of the above without all of that fancy stuff available out there, but you know what… I bought it all when we started 5 years ago *grin* Really dumb when I look back and we have abandoned all the fancy math books now for the simple under $10 ones you can pick up at the grocery store and just incorporate daily items as hands on manipulatives I wonder though if someone has said to me when we started to buy the cheap books and use stuff at home instead of buying a ton of stuff if I would have listened *grin*

    Love the photos of your moths that you guys have found, especially the Luna moth! So neat.

    Nature Mama

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