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Math Help

Suppose a football team faces a third down and 5 yards to go situation.

Suppose that the team REALLY needs to make a first down (and that they always punt on 4th down no matter what).

Suppose their coaches love statistics. In deciding whether to execute a running play or passing play they look back at their own data to find that:

(1) On average when they choose to pass the football, they gain 7 yards per play.

(2) On average when they choose to run the football, they gain 3 yards per play.

If they are to be solely statistically driven does it follow that they should select to throw the football?

Of course that answer is no! But here’s my point for today, or better yet a question.

Suppose you have a child that reads very well and generally excels in the language aspects of learning. This child however has an extremely difficult time doing math. Since she is “worse” (DO take note of the scare quotes all of you Ricardians out there) at math does it follow that as good parents we ought to convince her to spend more time working on math?

Suppose you answer, as I would based on my football example, that you should NOT necessarily do this. Is there a difference between football and childrens’ education that suggests otherwise?

6 Responses to “Math Help”

  1. sherlock says:

    Always punting on 4th down and loving statistics seems to be a bit of a contradiction. 😉

    Sorry I have nothing to add to the real meaning of the post.

  2. Harry says:

    Wintercow gives us a puzzle.

    In children’s education there are at least two coaches — the parent and the teacher. Also, here I assume we are talking about arithmetic , but maybe Wintercow has more advanced math in mind.

    Like the statistically-driven football coach, the elementary school teacher may be driven by pedagogical theory — not necessarily the latest — it may go back to Dewey.

    So, I am going to fudge and ask,”Work harder on what?” If it means doing more exercise sheets with two pairs of six bees equals how many bees, and the kid counts the bees, then that may be time wasted, even if that is what professional educators say is the best way to learn the times tables.

    Division is a different matter. In “science time” you could divide one (dead) bee in half with a sharp scalpel and teach dissection technique and insect anatomy at the same time.

    Returning to the football analogy, if it is third and five to go, Krugman would recommend the Hail Mary stimulus pass, which never worked.

  3. sherlock says:

    The “safer” method is to just always punt on 4th down. The coach would receive no real criticism from the media/public as that is the way it has typically always been done. The coach can pass the blame on to his players or “relying on his defense”. A smarter coach realizes that on third down you really have two opportunites to obtain a 1st down and that you can use both downs to achieve the necessary yardage (maybe two running plays?). However, making the decision to go for it on 4th down (when it does increase your chances of winning the game) puts the coach’s neck on the line. If the 4th down fails, all the blame is put on the coach for making that decision. So even a smarter coach who realizes that it isn’t the best option to have one standard to go by in all situations may still make the decison to not go for it because he doesn’t want the blame.

    Replace “coach” with “teacher” and you have yourself an analogy. A teacher may not want to try something new or develop methods based off an individual’s skill and ability, even if does have a better chance of succeding. They don’t want their head on the line so they “stick to the book” and hand the kid her mulitplcation tables.

  4. drobviousso says:

    Well, lets see. In the football example, the average gain is useless. What you want to use to decide is your historical % of gaining 5 yards on 3rd or 4th and 5 in “competitive football” (usually defined as first and third quarters with the score within 14 points and outside the red zone). Then, you pick randomly from a mixed bag weighted by the two historical percentages.

    This, of course, assumes that the defense you are going up against is equally as good at stopping the run as they are at stopping the pass, and that all run plays are created the same and that all pass plays are created the same. You should probably add in play-action passes, screen passes, and draws. If you want to add in fake punts, you’ll need to get rid of all that 3rd down data and use exclusively 4th down data, which will probably reduce your sample size down to useless. Weather has been shown to increase variance but not favor one type of play, so you can ignore that, but you should probably include home field (dis)advantage for your stadium.

    This all assumes you are working to maximize a successful play metric, and not a net expected points added metric or net expected win added metric, in which case this is a trick question. You just look up the proper mixed strategy for your down, distance, LoS, time, and score differential and pick based on *that* mixed strategy, no matter what the game situation is.

    Now, how do we apply that to child rearing? I would say the corollary is to get Selfish Reasons to Have More Kids and ask your child if they want help with homework, or if they want you to read a book to them, or do they want to go collect bugs with you.

    All of that is the long way to answer the question ” Is there a difference between football and childrens’ education that suggests otherwise?” Yes, we have better data on football, football isn’t a zero sum game, and you don’t need to account for the football’s agency.

  5. Harry says:

    Attempts with irony aside, one’s kid’s education is not a game, and is not confined to what they learn in school.

    From the day one realizes he or she is a child, on through the moment one is a parent and until your child grows up, one has an immensely complicated problem with child rearing. You read books, you get advice from parents, you try to apply what happened to you, since that was perfect, or you do the opposite, which might be logical.

    If you participated in The Right Stuff, a dating service that facilitates Ivy League graduates to meet and, er, breed, then from day one you buy educational toys for the nursery and get your kid doing word problems before he can walk, or, if the other side of the brain is working, writing musical scores, just like Mozart.

    Or, if you are a little less Type A, and have not gotten bred to a high performance herd sire, you might be the Chinese Mother from Hell, which may very well result in your children living

    Or, if you are a Hells Angel, you have a few children, get thrown in jail, and let the mothers or the state worry about your kids. If they are lucky, they might get adopted by a good family.

    Then there are the rest of us, who do the best we can as often as we are willing and able.

    So one’s daughter is strong in verbal skills, but finds other things difficult, in particular, math. Conventional wisdom (like the stat football coach) tells us girls are normally right-sided brain people, more verbal, than left-sided boys given to logic — or is it the other way around?

    So this idea becomes embedded in our thinking, and may prejudice how we handle the situation.

    Who knows? Not I. Do I push my kid, or do I let things happen? How do I know what I did made a difference? The difference?

    TUW is, if anything epistemology Center. And that does not mean we don’t know anything.

  6. chuck martel says:

    Comparing a single football predicament with the on-going development of a child is hardly valid from the outset. However, everyone has different talents and individuals who excel at a certain activity not only possess talents in that line, if they are successful they are usually enthusiastic about it as well. Budding musicians don’t need to be forced to practice their scales. Potential NHL stars show up at the rink no matter what. That being said, it’s important to stress to the young that there are things that they may not particularly enjoy doing and that they probably will never become exceptionally adept at. Nevertheless, they must be encouraged as much as possible to acquire at least a rudimentary skill in things that are a part of normal life. Practical applications of mathematics, for instance, are necessary and should be mastered by everyone. The ability to express coherent thoughts “on paper” is also important. It’s very satisfying for a person that knows they’re not a math expert to be able to solve a practical math problem, more satisfying than it might be for a person with a natural talent for working with numbers.

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