Math Fact Practice ≠ Fluency

Discussion in 'Debate & Marathon Threads Archive' started by TeacherShelly, Mar 9, 2014.

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  1. TeacherShelly

    TeacherShelly Aficionado

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    I had the wonderful experience of meeting Jo Boaler of the Stanford "How to Learn Math" course and mathematics professor at Stanford. She made a comment, math fact fluency does not come from practice, it comes from understanding.

    I asked her what she'd say in a parent conference when a parent says practice is important for at least two things: music and math. She said you don't need to understand how a piano works to play it.

    She said memorizing facts is not as useful as having number sense.

    Now I'm {almost} excited to have conferences.

    :)
     
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  3. TamiJ

    TamiJ Virtuoso

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    I am so jealous that you met her! I loved that course. It changed how I look at math and a lot of what I am doing in math. Lucky you!
     
  4. EdEd

    EdEd Aficionado

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    That's interesting and thought-provoking, but I think misleading. I do think "understanding" is important to fluency, but practice leads to understanding.

    I'd also say that the idea that a child with an understanding of number sense and addition, but with no memorized facts, will not achieve high levels of computation fluency in the area of addition.

    Did she offer any specific responses to these kinds of thoughts? Certainly open to being challenged and corrected :)
     
  5. ready2learn

    ready2learn Comrade

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    This is what I was thinking. I might be misunderstanding this, but it sounds like one of those things that is nice to say but in practice, you need fact practice to have fluency. Of course, that does not mean forget about understanding.

    Thanks for bringing this up. Made me think.
     
  6. TeacherShelly

    TeacherShelly Aficionado

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    She said that memorization (done by practicing) does not lead to understanding; but if the practice uses mental math, taking apart and rebuilding numbers, that will build fluency because you will be able to do it faster.
     
  7. Missy

    Missy Aficionado

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    Did she suggest any resources on how to teach this?
     
  8. ajr

    ajr Rookie

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    I don't know my times tables and frequently forget addition. You are completely correct - I have very low computation fluency.

    There is an interesting cart/horse problem here, because fluency in computation only matters insofar as the curriculum demands it; fluency matters because teachers grade on it. Any curriculum beyond expects this set of knowledge that isn't in-of-itself useful as a shortcut.

    In terms of Actually Doing Math (tm), it doesn't seem to affect anything. I don't have problems doing data analysis at work, nor do I have problems in my classes (I'm a math major).

    The question I've had for a long time is how much does memorizing facts assist understanding in a practical sense; you have to start somewhere. If you don't start with ANY knowledge, what bits do you have to get someone to understand to progress to higher tiers of understanding? How big of a role does age play - i.e., do we teach facts because the people we're teaching not have the mental development to support the abstractions we want them to have?

    The type of "practice" matters when you're discussing nearly any subject, and it seems to be no different in math. In training for a marathon there's the concept of "empty miles" - you run, but you don't improve because your strategy for running is poor. You run some negative combination of too fast, too slow, too far, too near, too long, too briefly.

    In math, you can memorize the times tables up to 20*20, know a thousand formulas, and memorize a hundred theorems and still not understand anything. Doing hours of this kind of work blindly - which is what people do since that's how it's graded - doesn't help understanding, whereas one carefully crafted example that a person reflects on for ten or twenty minutes can catapult that person well past understanding. I can tell a lot more about what a person knows in math by asking them questions verbally, rather than having them solve equations. This problem is brutal when trying to tutor people who are going into college. They have years of the wrong type of practice.

    Asking someone to solve a problem allows them to lie to me - they produce the right answer, but I don't care about the answer. I want to know how they think. They can get the wrong answer and still know what they're doing, and can get the right answer consistently and have no idea what's going on.

    I think it's easier to assess some of these questions teaching adult learners, because some have a more fully formed ability to deal with abstraction and you can carry on with the understanding and ignore rote practice until the subject has been sufficiently motivated.
     
  9. TeacherShelly

    TeacherShelly Aficionado

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    Missy, yes she has a book called "What's Math Got to Do With It?" which tells how to teach number sense. She is a strong advocate of Number Talks, too and recommends a book called Number Talks by Sherry Parrish. I really want to get the book, but it's, of course, expensive (~$50).

    SHe also uses dot cards which cluster a number of dots in different patterns. The students discuss how they saw the number. They are not supposed to count, but visualize the number. The idea is to make numbers more visual and to teach flexible thinking - that there are multiple ways to see the same thing.

    HTH!
     
  10. gr3teacher

    gr3teacher Phenom

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    Fact fluency is incredibly important. It may not be more important than number sense, but fourth grade math will be a miserable experience to any kiddo that isn't comfortable with their facts.
     
  11. Pashtun

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    I tell the parents in a letter before the year begins. "if you want to set your child up for a successful 4th grade year, have them memorize their mult. facts"
     
  12. gr3teacher

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    I do something similar... it's tough because all my kids skip 3rd grade math and start right with 4th grade math... and parents don't really seem to believe that the kids need to know their multiplication facts... and then the second unit of the year is fractions (with finding equivalent fractions, reducing fractions, LCM, GCF, adding/subtracting with unlike denominators...) and the kids that don't know their facts are miserable and I'm ripping my hair out.
     
  13. mathmagic

    mathmagic Enthusiast

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    Think of it connected to reading: to be a good reader, you have to be able to read the words, but then also understand them. That takes those foundational skills, but also strategies to comprehend. Naturally, the ability to comprehend is vital, but those foundational skills are needed as well.

    In math, sure, I could go through and have great number sense, but if I'm trying to do a / learn 3-digit times 2-digit multiplication problem, I'll be spending far too much mental energy on multiplying single digits that I won't be able to attend as much to the learning of that new concept.

    Needs to be a true mix. If I had my own classroom, kids would be using Xtramath once a day for the fluency, but we'd also be doing number talks several times a week. Both are vital.
     
  14. DrivingPigeon

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    I've always heard that once students have an understand of number sense and operations, they are ready for memorization of facts.
     
  15. a2z

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    While I haven't heard this said, I have observed in students that lag with memorization of facts addition or multiplication that once the number sense comes to that of a typical 2nd or 3rd grader the memorization of facts and the understanding of how they are related seem to come together. This makes fact recall easier. For those that lag with fact fluency, I find that consistent practice with a chart is the way to solidify accuracy of recall. But even then, those with weak number sense or poor memories, tend to not develop the same fluency as those with number sense and fluency.

    You can really see the lack of number sense when you start to work with fractions or factoring. It is painful and near impossible for kids even when they have a chart to work with.
     
  16. a2z

    a2z Maven

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    You can pound out notes on a piano without knowing how it works, but all of the best pianists know how the instrument works because it allows them to understand the subtly of how to play the instrument to its ultimate capacity.

    You can memorize math facts until you can spit them out in a spit second and struggle with fractions and factoring and multiplication of large and small numbers because you lack number sense.

    Most need both to be truly proficient. Of course, there is always the exception to every rule.
     
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