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“Let’s Play Math”

If you are familiar with my blog than you already know that I am passionate about teaching math from a Constructivist perspective.

Teaching math from a Constructivist perspective means enabling children to develop their own meaningful strategies for solving problems, instead of just blindly teaching traditional algorithms. It also means giving children time, space, and materials to explore mathematical concepts and create their own understanding.

Let’s Play Math: How Homeschooling Families Can Learn Math Together, and Enjoy It! (Homeschool Math Manuals) by Denise Gaskins, is a beautiful book that explains the “why” and “how” of teaching math from a Constructivist perspective. It is well researched, well annotated, and includes loads of activities that you can try with kids K-12 at home. While reading the book, I found myself remembering a lot of things I had forgotten from my teacher-training in Constructivist math.

The only weird thing, was that the author never actually uses the word “Constructivist”.

I’m still not exactly sure why that is. But clearly, I’m a former public school teacher bringing my own public school jargon with me. The author, Denise Gakins, approaches the topic from the world of homeschooling. So there you go…

The other comments I have about the book Let’s Play Math are not criticisms, they are only observations.

This is more of me and my public school background chiming in.

There were many instances where the author mentions public schools and textbooks teaching math from a very traditional “drill and kill” sort of way. This is definitely not trueand true, depending on the school and district.

Dale Seymour Math Investigations for example, is a solid, Constructivist program used by many public schools. It gets horribly bashed by the homeschooling mother of a certain blog I will not name, which is really unfair. You cannot judge the whole Investigations program by looking at the homework workbook. The real learning in Investigations happens in the classroom, on the floor, with kids playing and exploring math.

My last school, did not use textbooks at all.

Conversely, Saxon Math is a homeschooling program that is the total opposite of Constructivism. Drill, kill, “carry the one” etc. I could just as easily be prejudiced and suspect that many homeschooling moms don’t understand how Constructivist math is being taught in public school classrooms, and that they have a knee-jerk-back-to-basics reaction that leads them to Saxon.

My other comment is about algorithms, and when to teach them. I’m a proponent of not teaching traditional algorithms until fourth or fifth grade, once a child has a multitude of other stratgeties for solving problems.

My experience is that when you teach a child an algorithm too early, they will cling to the algorithm like a life raft, and thinking will stop.

It has been tricky to not let my own public school son learn algorithms until fourth grade math, but I’ve been able to accomplish this through a whole lot of Afterschooling.

I’m not sure if Denise Gaskins would agree with my approach about when to teach algorithms or not. I suspect she would, but I’m not sure. I think it would have been beneficial to slip an entire chapter on algorithms, somewhere in the middle of her book.

Lastly, I have to say that there were so many parts of this book that I highlighted that I really gave my Kindle a workout!

There is a whole section that I’m going to come back to this summer, to keep my kids busy. But was especially useful to me at this moment, were the talking points for helping kids solve problems on their own. Yes, I at one point learned all of talking points, but I really needed the refresher.

My son’s school does Continental Mathematics League, and those problems are really hard. I’m going to print up all of the talking points and post them in our kitchen so that my husband and I will have a list of questions to prompt our son’s thinking. Here are some examples from the book:

  • What do I want?
  • What can I do?
  • Does it make sense?
  • Can you draw a picture?
  • Can you act the problem out?
  • Can you make a chart?
  • Do you see a pattern?
  • Can you try the problem with smaller numbers?
  • Can you work backwards?
  • Can you try something and see if it works?

It doesn’t matter what grade your child is at, those questions are good places to start.

That’s just a teeny, tiny sample of all of insights Let’s Play Math has to offer. I can’t wait until the author publishes Let’s Play Algebra.


  1. Denise says:

    Thank you for the review! I’m glad to hear that my book is helpful even beyond its target audience.

    You are right that I don’t use the term Constructivist because I am writing to an audience that is unfamiliar with many educational theories. My editor marked up all the edujargon he could find and had me replace it with “normal” words. 🙂

    Also, I’m not really sure what the term means, myself, since I see it used in several different, not-quite-compatible ways: as an “ism” (philosophy or belief system?), as a theory about how the mind works (and which applies to any learning situation), as a specific style of teaching (which appears to be what you mean when you use the term), as a pejorative (in the “Math Wars”), etc.

    I’m glad to hear your experience that many public school teachers are getting beyond the American culture of teaching rules and recipes (by which phrase, I’m not sure I mean the same as what you mean by “drill and kill”, since what I am talking about is independent of teaching style). I sure hope that’s true! From talking with local parents and school-age children, however, and from readings like Liping Ma’s book and “The Teaching Gap”, I am not convinced that the widespread use of reform textbooks necessarily signals a true change in the system, any more than the “New Math” books of my childhood did. Cultural systems are very hard to change.

    As for your comment, “My experience is that when you teach a child an algorithm too early, they will cling to the algorithm like a life raft, and thinking will stop.” — I agree completely, and this is one of the points I hope to get across with my blog and books. I plan to write a more nuts-and-bolts book which will talk specifically about algorithms and alternatives, but my game books are higher on the priority list for now…

  2. Cindy says:

    This is a GREAT post. I really resonate with the comments about homeschool and public school perspectives about the math being taught in each location. Some AMAZING things are happening in some public school classrooms. Sometimes homeschoolers (adults) assume that because they were taught a certain way in public schools that math teaching continues to be the same. That’s just not true. As you say–sometimes. But there are many, many classrooms using wonderful constructivist methods and strategies, with little to no recognition of their work. Thanks for such a great review!

    Cindy @ love2learn2day.blogspot.com

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