Math findings & a big fallacy

A blue-ribbon presidential panel charged with figuring out what has gone wrong with math education in this country. Here is a summary of the findings. They include this observation:

Children badly need both automatic recall of math facts and understanding of big concepts, in effect declawing both sides in the decades-long “math wars.”

This points to a fallacy that seems everywhere in education and elsewhere: the FALSE DICHOTOMY. How would anyone think there needs to be a CHOICE between EITHER knowing material OR understanding it? To be educated about any subject you need BOTH! You also need to be able to apply it yourself.

(Note that the whole range of what education must be is fulfilled in the paradigm of classical education: grammar [knowing]; logic [understanding]; rhetoric [personal application].)

What are some other false dichotomies? (I’ll get you started: faith & works; orthodoxy & mission. . . .)

About Gene Veith

Professor of Literature at Patrick Henry College, the Director of the Cranach Institute at Concordia Theological Seminary, a columnist for World Magazine and TableTalk, and the author of 18 books on different facets of Christianity & Culture.

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  • Joe

    I would normally be lumped into the automatic recall camp but I never for a minute believed that this was exclusive of understanding the big concepts. Automatic recall is the building block that make the big concepts understandable. I have no problem with teaching big concepts, but in my experience the problem was with schools eschewing recall all together.

    Anyway – false dichotomy: faith & science.

  • Joe

    I would normally be lumped into the automatic recall camp but I never for a minute believed that this was exclusive of understanding the big concepts. Automatic recall is the building block that make the big concepts understandable. I have no problem with teaching big concepts, but in my experience the problem was with schools eschewing recall all together.

    Anyway – false dichotomy: faith & science.

  • http://www.hempelstudios.com Sarah in Maryland

    I’m now 30 years old and still don’t know my times tables because I was part of this “math wars.” Throughout school, I took plenty of advanced math courses and did well because we used calculators, but don’t ask my what 8×6 is, because I don’t know.

  • http://www.hempelstudios.com Sarah in Maryland

    I’m now 30 years old and still don’t know my times tables because I was part of this “math wars.” Throughout school, I took plenty of advanced math courses and did well because we used calculators, but don’t ask my what 8×6 is, because I don’t know.

  • http://www.hempelstudios.com Sarah in Maryland

    We’re having a bit of this at our church, actually. Not with math, of course, but with scripture. I like to approach scripture from many different angles, one of which being memory verses. Many people at church feel like this doesn’t help understanding. For me, it helps to fill my mind with the Word of God. As I learn more, I can make connections with the verses I’ve memorized.

    Can the false dichotomy be: memory and understanding?

  • http://www.hempelstudios.com Sarah in Maryland

    We’re having a bit of this at our church, actually. Not with math, of course, but with scripture. I like to approach scripture from many different angles, one of which being memory verses. Many people at church feel like this doesn’t help understanding. For me, it helps to fill my mind with the Word of God. As I learn more, I can make connections with the verses I’ve memorized.

    Can the false dichotomy be: memory and understanding?

  • Joe

    We do memorization with the kids in our Sunday school program starting in pre-k. We add a few verses each year, then the 10 commandments and meanings, then the articles of the creed. By the time they get to confirmation class they are discussing pretty deep theology. This is possible because of the foundation they have built through the years.

  • Joe

    We do memorization with the kids in our Sunday school program starting in pre-k. We add a few verses each year, then the 10 commandments and meanings, then the articles of the creed. By the time they get to confirmation class they are discussing pretty deep theology. This is possible because of the foundation they have built through the years.

  • David Thompson

    Sarah (#4)
    You are exactly right about the same war being fought in the church. Many Lutheran churches now require little or no memory work; the emphasis being on “understanding”. But how can there be understanding without first having knowledge? Three years ago I was at a confirmation service at a conservative Lutheran church where the traditional questioning of the confirmands (in which they the Catechism and Bible verses from memory) was replaced with a short essay in which the confirmands explained “What my Christian faith means to me.” The congregation was impressed because it was so personal (or “authentic” as we say today). The problem was that there was very little content in any of their essays. There was next to nothing that would distinguish them from their liberal Lutheran, evangelical, Catholic, or Methodist counterparts down the road. At the same time, confirmation class should be the time not only when knowledge is learned, but, as Veith says, understanding and personal application is learned as well. It’s not a matter of EITHER…OR, but BOTH…AND.

  • David Thompson

    Sarah (#4)
    You are exactly right about the same war being fought in the church. Many Lutheran churches now require little or no memory work; the emphasis being on “understanding”. But how can there be understanding without first having knowledge? Three years ago I was at a confirmation service at a conservative Lutheran church where the traditional questioning of the confirmands (in which they the Catechism and Bible verses from memory) was replaced with a short essay in which the confirmands explained “What my Christian faith means to me.” The congregation was impressed because it was so personal (or “authentic” as we say today). The problem was that there was very little content in any of their essays. There was next to nothing that would distinguish them from their liberal Lutheran, evangelical, Catholic, or Methodist counterparts down the road. At the same time, confirmation class should be the time not only when knowledge is learned, but, as Veith says, understanding and personal application is learned as well. It’s not a matter of EITHER…OR, but BOTH…AND.

  • Steven

    Another great false dichotomy that I have been questioned about extensively by seemingly intelligent non-Christian friends (I work in classical school and yet I am highly involved with a group of educators that represent traditional, progressive, and parochial education): belief in absolute truth and a desire to teach children to think critically.

  • Steven

    Another great false dichotomy that I have been questioned about extensively by seemingly intelligent non-Christian friends (I work in classical school and yet I am highly involved with a group of educators that represent traditional, progressive, and parochial education): belief in absolute truth and a desire to teach children to think critically.

  • http://www.bikebubba.blogspot.com Bike Bubba

    What Joe said. I was a TA for undergrad math, senior level electrical engineering courses, and grad level EE courses, while in college. One thing I noticed was that no matter what class I was in, arithmetic errors were about a third of the red marks I put on an assignment or test. And yes, those arithmetic errors did prevent a lot of people from understanding the underlying concepts.

    In the same way, I find as a working engineer that a lot of people cannot figure out if their answer makes sense without a computer or calculator. Not a good situation…

  • http://www.bikebubba.blogspot.com Bike Bubba

    What Joe said. I was a TA for undergrad math, senior level electrical engineering courses, and grad level EE courses, while in college. One thing I noticed was that no matter what class I was in, arithmetic errors were about a third of the red marks I put on an assignment or test. And yes, those arithmetic errors did prevent a lot of people from understanding the underlying concepts.

    In the same way, I find as a working engineer that a lot of people cannot figure out if their answer makes sense without a computer or calculator. Not a good situation…

  • Jenna

    False dichotomy: the use of written prayers, especially collects, or prayer offices, and genuine devotion to God.

    What I mean is, the effect of the way of prayer modeled in American Evangelicalism is such that those who pray the Offices and/or the great old collects, or memorized prayers from Scripture (like St. Paul’s great prayers in Ephesians) are suspect. Spontaneous, extemperaneous prayer, especially when in front of a group, is evidence of a heart that overflows with love for Christ. “Formula” prayer – well, you’re somone who only has a “head” faith, not a “heart” faith.

    As if prayers that begin, Dear Lord, I just want to thank you for… *aren’t* formulaic…!

  • Jenna

    False dichotomy: the use of written prayers, especially collects, or prayer offices, and genuine devotion to God.

    What I mean is, the effect of the way of prayer modeled in American Evangelicalism is such that those who pray the Offices and/or the great old collects, or memorized prayers from Scripture (like St. Paul’s great prayers in Ephesians) are suspect. Spontaneous, extemperaneous prayer, especially when in front of a group, is evidence of a heart that overflows with love for Christ. “Formula” prayer – well, you’re somone who only has a “head” faith, not a “heart” faith.

    As if prayers that begin, Dear Lord, I just want to thank you for… *aren’t* formulaic…!

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  • http://www.blogger.com/profile/17639370291865261582 Cindy

    False dichotomies? In theology, this is almost too easy. After all, Lutheran theology hinges on embracing the paradoxical.

    Law and gospel
    Saint and sinner
    Justice and mercy
    Bread and body
    Wine and blood

  • http://www.blogger.com/profile/17639370291865261582 Cindy

    False dichotomies? In theology, this is almost too easy. After all, Lutheran theology hinges on embracing the paradoxical.

    Law and gospel
    Saint and sinner
    Justice and mercy
    Bread and body
    Wine and blood

  • saddlemaker

    As a craftsman, may I offer: art and function. Our culture has worked hard at separating the two, even placing them in tension with one another.

  • saddlemaker

    As a craftsman, may I offer: art and function. Our culture has worked hard at separating the two, even placing them in tension with one another.

  • Booklover

    Ooooooh, Jenna and Cindy, excellent!!

    Other false dichotomies–
    liturgy and true heart worship
    baptism and commission
    ancient worship music and relevance
    heart and doctrine

  • Booklover

    Ooooooh, Jenna and Cindy, excellent!!

    Other false dichotomies–
    liturgy and true heart worship
    baptism and commission
    ancient worship music and relevance
    heart and doctrine

  • http://www.cyberbrethren.com/ Rev. Paul T. McCain

    You are exactly right about the same war being fought in the church. Many Lutheran churches now require little or no memory work; the emphasis being on “understanding”. But how can there be understanding without first having knowledge?


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