# “Exploring the math shelf #2” – Building Blocks of Mathematics

“Exploring the math shelf” is a journey that takes us weekly to our public library to explore their selection of math books. Click here to follow it from the beginning. Whether you are a parent, a teacher, someone supporting a child’s math thinking, I hope you find our books review helpful !

Our weekly trip made us discovered a series of books called “Building Blocks of Mathematics” (by Joseph Midthun and Samuel Hiti).

The series comprises six books

• Numbers
• Subtraction
• Multiplication
• Division
• Fractions

I highly recommend them.

1. The books are amusing, cute, strips books. Once we started with the first one, Rosie, 8,  could not wait to read the next ones.
2. We started with Addition, Subtraction, Multiplication and Division, as Numbers was not available initially, but I do not think it matters. Numbers can be read independently.
3. The book Numbers presents a variety of counting systems, and invites children to create their own. I remember having to create my own Base System as a M.Ed. student, it was quite an instructive process, to say the least ! Rosie started by making random symbols for each numeral she would think of. We started discussing about patterns that usually occurs in counting systems.  Her second attempt was quite close to our decimal system, but in her third attempt, a different logic started to appear. Her reflection is far from being completed, but I can see how the book Numbers could indeed lead to a powerful activity around counting.
4. The book Numbers also goes into place value, presenting how some systems have place value while others do no. I have to say that I had never really thought about it. For instance, the counting symbols used by the Egyptians could be written from left to right, or right to left, each symbol keeping the same value no matter its position. With the Arabic numerals, however, the value of each digit depends on its place in the number (e.g. the 5 in 53 has a value of 5 Tens). Interestingly, it seems to me that the Roman numerals are kind of in-between: V has always a value of 5, but IV and VI have different value, depending on the position of the symbol I (4, when I is placed before V, and 6, when I is placed after V). Place value is a concept so often misunderstood, Numbers provides an opportunity to approach it through another angle that would be helpful even in upper elementary grades.
5. In Numbers, there is even a WHOLE page on Zero, a numeral so often forgotten!!!
6. My hope when I pick a book series, is to find some connections between the math concepts presented in each book (e.g. a link between geometry and fractions, or multiplication and repeated additions, etc). This series exceeded my expectations on that front. The character “+” leads the story in Addition, but is also part of Subtraction aside the character “-” and Multiplication along character “x” . In Division, all characters are present (“+”, “-“, “x” and “÷”) illustrating well the relationship between the four operations.
7. The books contain reassuring words (the character “+”, for instance, saying “It never hurts to slow down when you are doing math”, or “you can always use me to check your work” in the book Multiplication).  I have to say that Rosie is not the most confident person around (the apple doesn’t fall far from the tree), and she found it quite comforting to read that when you are stuck in one operation, you can always go back to another one.
8. The characters “+”, “-“, “x” and “÷” discuss different ways to solve problems, using drawings, number lines, equations, etc. A good review of strategies to discuss with your child.
9. Rosie has not been talking about division at school yet. Still, she was fully engaged in the book “Division”, as the concept is clearly presented, and well connected to the other operations she is more familiar with. I decided not to read the whole book “Fractions”, though. It is well written, but I  want Rosie to keep exploring fractions a little further without going to rapidly into their symbolic representation. I look forward to doing our Time 4 Fractions in the Fall for the third time, I may go back to this book once we are done.
10. Cherry on top: the book Cognitively Guided Instruction (Carpenter et al, 2014) is referred as a resource for educators. If you have been following my blog, you know how highly I recommend this approach of instruction :-)

I could still add to the list,we had so much fun reading them. I hope you do to !

Reference:

• Carpenter, T., Fennema, E., Franke, M., Levi, L. and Empson S. (2014). Children’s Mathematics, Second Edition: Cognitively Guided Instruction. Portsmouth, NH: Heinemann. ISBN-13:978-0325052878.