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The Well Trained Mind: Thoughts from Chapter 6

This is a series of posts I am writing about The Well Trained Mind, by Susan Wise Bauer and Jessie Wise. Although the WTM has a decidedly homeschooling bent, it is an excellent reference book for any parent who is interested in taking an active role in their child’s education.

Over the next few weeks I am reading the WTM again for the second time, and blogging about my thoughts chapter by chapter. I want to be conscientious about not violating any copyrights, so I will not be including quotes from the book on my blog. I will however, be referencing specific page numbers from the third edition. I invite you to read along with me, and chime in your own thoughts in the comment section below.

Chapter 6

General Thoughts: I believe in teaching math from a Constructivist perspective.  I found a lot of the authors’ recommendations to fall in with this philosophy of teaching math quite nicely.  This was really interesting to me, because that seems to be in contrast to the WTM general theories about the Grammar stage, in which it is sometimes encouraged to teach memorization before understanding.  The authors seem to be of a different opinion when it comes to math.

I also found it interesting that the Horizons math program was not mentioned.  Our own family did not have a very good experience with Horizons: http://teachingmybabytoread.blog.com/2011/05/01/horizons-math/   Horizons does not seem to follow the Constructivist model at all, and was not a very good choice for our family.  Interestingly, many parents on the Well Trained Mind Message board swear by Horizons, which makes me wonder if they have read the WTM.

Page 88: I agree with the bottom section of the page when the authors are recommending manipulatives, but disagree with the top portion when they say that it is okay for higher-order math thinking skills to come later.  As a Constructivist, I believe they should be taught concurrently.

Page 89: The toothpick example was really mixed up to me.  On the one hand, it could be considered the perfect example of Constructivist teaching because they are starting adding from the left instead of the right.  On the other hand they use the word “carry” and the teacher is directing the student in which strategy to use.  This would be anti-Constructivist.

Page 93: Saxon Math is published by Houghton Mifflin which also published Math Expressions.  That’s the textbook our local school district uses.


  1. Jean says:

    Wait, did you say that your school uses Math Expressions, or Saxon? I think you mean ME but it’s not entirely clear. 🙂

    “that seems to be in contrast to the WTM general theories about the Grammar stage, in which it is sometimes encouraged to teach memorization before understanding. The authors seem to be of a different opinion when it comes to math.”

    I think it’s question of what is practical. What does a grammar-stage child need to learn and/or memorize in math before getting to 5th grade? The math facts, pretty much. The goal is to have arithmetic down *cold* so that the child is free to focus on moving upward, instead of always having to stop and figure out what 5×3 is, or whatever. The math facts are concrete–you can demonstrate them with beans, over and over (and over) if necessary. At the same time, once the child understands what multiplication is and has worked the facts out concretely a few times, she can also work on memorizing them, so she doesn’t have to think about what 9×7 is–she just snaps out 63 without working it out again.

    If you wanted to, I suppose you could have the child memorize some of the axioms of mathematics or the commutative property of addition or something. But the math facts by themselves are enough work for most kids, I expect.

    By contrast, there’s quite a lot about grammar (or history, or science) that is fairly abstract. Either way, you’re memorizing and using that superpower. The rule is not for the child to memorize things he does not understand; it’s for him to memorize the most important or convenient things in a given field, which he should understand if he can, but if not understanding will come later as he continues to learn and mature.

    • jenbrdsly says:

      Our school district uses Houghton Mifflin’s Math Expressions, which is the same publishing house as Saxon. I haven’t seen a Saxon book, but from the website it looks very similar to Math Expressions.

      In the public schools, there are some (older) teachers out there who would advocate memorizing math facts before you had a strong conceptual understanding of what the facts really mean. I do not believe that is reflective of what current teacher training is advocating, or what is recommended in the WTM. I would agree that kids need to have their math facts down cold by the end of fourth grade, but only after they had developed that knowledge through exploration, critical thinking, games and just a pinch of drill and kill.

  2. Claire H. says:

    Saxon Math is very “old-school” in terms of it being a lot of memorizing of algorithms and “drill-and-kill”. It’s a solid program but very different from a conceptual program like Singapore.

    I think the authors of TWTM recognize that different children do best with different types of math programs. That’s why there is such a variety of ones mentioned in the chapter- “old school” ones like Saxon & Abeka, Asian-based programs like Singapore and Right Start, and Math-U-See, which is unique in that each level focuses on one particular skill and nothing else (addition in 1st, subtraction in 2nd, multiplication in 3rd, etc.)

    Interestingly, Cathy Duffy in her 100 Top Picks for Homeschool Curriculum book recommends Horizons but not Abeka. She criticizes Abeka for being weak conceptually. I have no personal experience with Abeka so I cannot comment on whether or not this is true.

    • Jean says:

      We’ve used Saxon, which does seem to fit my kid’s brain very well. She gets concepts easily, but needed a lot of practice in order to memorize anything.

      Our favorite way to drill is by jumping on a trampoline and yelling the facts out.

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