Tuesday, April 30, 2013

Knowing and Teaching Elementary Mathematics....

I've been reading/researching Knowing and Teaching Elementary Math by Liping Ma.  Ma conducted a study that compared mathematical understanding among U.S. and Chinese elementary school teachers as it relates to classroom teaching practices.  But don't misunderstand, the book is not a comparative study of American and Chinese teachers of mathematics.  

Ma interviewed elementary mathematics teachers from various elementary schools ranging from very high to very low quality.  She presented four standard topics in elementary mathematics:

1) subtraction with regrouping
2) multidigit multiplication
3) division by fractions
4) perimeter and area of a closed figure

The results were fascinating in that the Chinese teachers displayed more "conceptual understanding" of the math topics.  Where as the American teachers had a more "procedural understanding".  Ma suggests the Chinese teachers were more coherent in their knowledge and the American teachers were more fragmented.  The American teachers knew the set of rules for solving the problem, but in addition, the Chinese teachers also knew why the sequence of steps in the computation made sense.  On page 108, Ma writes, "During their interview, the Chinese teachers often cited an old saying to introduce further discussion of an algorithm: Know how, and also know why."

I know I'm a product of my American education.  I'm definitely more procedural when it comes to math.  I have memorized the steps to solve the equation, but please don't ask me why.  Lately, this has been getting in the way of our homeschool.  I desperately want our kids to have a conceptual understanding, hence all the math research I've been doing. 

Recently, I've become more and more intrigued by RightStart Mathematics.  I started Level B a while back with Ruben.  He actually likes it and really seems to get math.   I'm contemplating switching Riley next fall.  At this point, she's not real keen on the idea, but she has expressed a desire to really "get math".  

Either way, I recommend checking out Liping Ma's book.  It's been translated into several languages and an anniversary edition was released in 2010.


  1. Hi Melissa,

    I have been looking at Right Start Mathematics as well and trying to decide about that with my Luke who will be K next year. We have always used Math U See. I'm wondering how they compare!


  2. Good Morning Tammy, I would say RS is much more hands on than MUS. RS is more spiral in its approach, but the student still must master the concepts before moving on. MUS is strictly mastery with not as much review. RS offers more games and activities for a multi-sensory approach. MUS is more paper/pencil with regular workbook pages. I think they both do a great job in promoting place value. Both are leveled programs vs. being grade specific. I've received wonderful customer service from both. MUS may be more expensive in the long run with multiple kids because you need to replace consumable workbooks. RS is more teacher intensive. The MUS teaching DVD's are helpful. RS emphasizes visualizing strategies for quantities and learning the facts. I believe RS is based on a combination of Montessori and Japanese ideals. I would recommend the Yahoo Groups for each curricula to get a feel for the program and how other homeschooling moms are using them. There are also comparisons in the group files.

    Hope that helps,