Children's Mathematics - The Book That Changed My Teaching Forever
My journey to become a Recovering Traditionalist started with the book Children’s Mathematics: Cognitively Guided Instruction
In my first years of teaching I quickly discovered I didn’t know anything about teaching math. I could DO math but I was horrible at teaching it. When I went back to school to get my master’s degree, my supervising professor had me read Children’s Mathematics
I was teaching with the mindset that my students’ didn’t know anything and it was my job to tell them everything they needed to know. But when I watched one of the videos (there are CDs with the book) of a 1st grader solving a division problem, I was amazed. Now she didn’t know how to do formal division like you expect older kids to do, but she did know how to model the situation. My problem was I was expecting students to work at the “formal” level when they really were down at an informal level like she was. She was solving this problem:
Rodney is having some kids over for jelly donuts. 7 donuts can fit on one plate. How many plates will Rodney need for 28 donuts?
What I saw still amazes me every time…she counted out 7 “donuts” represented by blocks, slid them into a pile and said “That’s one plate.” Then she counted out 7 more, “that’s another plate,” counts out another 7 and then she goes back and counts them all to see if she is at 28 yet. She isn’t so she makes another pile of 7, but goes back and recounts each pile to ensure they all have 7, then finally goes back and recounts them all and has 28 donuts accounted for and says “4 plates.”
So why did this amaze me…it’s a kid counting…NO, it’s a kid using what they know to solve a problem. She knows how to count (and count again, and count again) and she used her skill set to solve a problem. The teacher didn’t have to tell her what to do and the teacher didn’t interrupt her to suggest a more efficient strategy. Children’s Mathematics
By the time they begin school, most children have already developed a sophisticated, informal understanding of basic mathematical concepts and problem-solving strategies. Too often, however, the mathematics instruction that we impose upon them in the classroom fails to connect with this informal knowledge.
From the book, I began to realize that I wasn’t letting my students use the knowledge about mathematics that they already had in order to make connections to the mathematics they needed to learn. Children’s Mathematics
Part of this Math Books That Will Change Your Teaching Blog Hop is giving away the book that changed our teaching. So scroll down and enter for your chances to win this wonderful book and be prepared to have it change the way you teach. There is a Second Edition of Children’s Mathematics
Sarah over at Adventures in Guided Math is next in the blog hop line up:
About The Author
This is one of the first books I ever read when I started teaching and you have made me want to read it again! It is a fantastic book and I am super excited that they are releasing a second edition! My math goal for this year is to work on conceptual development of proportional reasoning with my older students.
The book that changed my teaching on proportional reasoning was Teaching Fractions and Ratios for Understanding by Susan Lamon. It’s wonderful.
I have my fingers crossed! Thanks so much for sharing this text and the impact it has. Looking forward to reading it myself.
Smiles,
Sarah
I am always on the lookout for great sources to help with questioning—questioning that inspires deep thinking. (sorry–did not look at your giveaway options before posting a comment). :0)
Thanks for the opportunity to win!
This is such a great book! I read it ages ago, but feel like I should go back and refresh myself on it! Great post!
Jamie aka MissMathDork!
Great book choice! You have peeked my interest. I will have to check this one out.
Greg
Mr Elementary Math Blog
I was so lucky to be an education student at the University of WI when the authors were doing their research and work. It was a very exciting time in math–can’t recommend this book enough!
My supervising professor while getting my Master’s degree at BSU, Dr. Brendefur, was at University of WI as well. I will forever be thankful that he made me read this book and everything else I learned while working with him.
This book changed my teaching so much, unfortunately I didn’t read it until about a year ago. I read it along with the book Math Exchanges and I can’t rave enough about how much my instructional practices have improved. My students are becoming much better problem solvers because of these books. Thanks for choosing such a great book.
Brandi
The Research Based Classroom
I haven’t read Math Exchanges, I’ll have to look into getting that one.
From the post : —-
Rodney is having some kids over for jelly donuts. 7 donuts can fit on one
plate. How many plates will Rodney need for 28 donuts?
What I saw still amazes me every time…she counted out 7 “donuts” represented by
blocks, slid them into a pile and said “That’s one plate.” Then she counted
out 7 more, “that’s another plate,” counts out another 7 and then she goes back
and counts them all to see if she is at 28 yet. She isn’t so she makes another
pile of 7, but goes back and recounts each pile to ensure they all have 7, then
finally goes back and recounts them all and has 28 donuts accounted for and
says “4 plates.”
I was inspired by this to develop it into a long division routine. It worked, a
bit longer than the “standard algorithm”, but 100 times more understandable and
explainable.
So, take 562 divided by 23 as an example.
Then compare 23, 230 and 2300 with 562
The biggest which is still less than 562 is 230
Try another 230, giving 460
Still less than 562
Try another 230, giving 690
Oh dear, bigger now, so two 230’s added so far
We have reached 460, so now add 23 to get 483
Less than 562
Try another 23, giving 506
Still less than 562
Try another 23, giving 529
Still less than 562
Try another 23, giving 552 (four 23’s added so far)
Don’t need to try another, clearly we will go past 562
as only 10 left to get there
result: 562 = two 230’s, four 23’s, and 10 left over
Minimal understanding of place value is needed to put the two bits together and
get two 230’s and four 23’s is 24 x 23 or twentyfour 23’s
This can be laid out in a more formal manner, but that might turn it into
another “standard algorithm”!!!