Bruce and I are now on chapter 27 of Life of Fred Fractions, and nearing the end.
I still really like the book a lot, but I’m less impressed by it as we near the end. I think the author relies too much on traditional algorithms to teacher mathematical concepts. This is completely contrary to my approach to teaching math, which is Constructivist in philosophy. (For more information on Constructivism, please see my post at: http://teachingmybabytoread.blog.com/2011/03/15/subtraction/)
Earlier in the book, it was easy to do a lot of Constructivist activities and explanations side by side with Life of Fred. To compare, order, reduce, add and subtract fractions for example, Bruce experimented with the Right Start Fraction strips in addition to working with the algorithms taught in Life of Fred. So when the book talked about 2/6 being the same as 1/3, Bruce really understood that well, because he could build those fractions himself.
The fraction strips were also helpful for learning about mixed numbers, and the rules about 0/7 = 0 and 7/7 = 1. In all honesty though, Bruce had a really good understanding of fractions before we even started reading Life of Fred, because of all the times he played Reader Rabbit 2nd Grade math. When he was four and five, we also played lots of games with my homemade fraction cards, such as Fraction War, Capture the Fraction, etc.
I had originally taught him how to reduce fractions, using M’nMs and peanut butter. I’ll have to save the explanation for that one for another time!
Fast forward to now, when we are in the higher chapters of Life of Fred and it is now talking about multiplying fractions, and rules about canceling. Now I can really tell that I never taught past fourth grade, or I probably would have had some tricks up my sleeve to teach these concepts from a Constructivist perspective.
In multiplying fractions, “of” meaning the same thing as “times” makes sense. I’ll be able to explain this if I drag out some M’nMs and peanut butter again. But explaining how canceling works, in a hands-on lesson, still eludes me. If anyone has any ideas please let me know! I’m definitely not satisfied with relying on the algorithm alone, which is what is offered in Life of Fred.