Tag Archives: Book

Exploring the math shelf #3 – “The Grapes of Math” and other Greg Tang books

“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 !

MathFable

This week, we had fun exploring several math books written by Greg Tang.

  • The books “Math Fables” and “Math Fables Too” present short stories about 1 to 10 animals gathering in a single group first, and then breaking down into two smaller groups.
  • The books “The Grapes of Math”, “Math for All Seasons”  and “Math Potatoes” invite the reader to count items, suggesting strategies to count them other than by Ones (e.g. grouping items in a special way; counting by 5s or 10s, etc).
  • The book “The Best of Times” reviews the multiplication facts from 0 to 10 through short riddles.

Few thoughts about our readings :

  1. As often with the math books we take at the library, we did not read any of the books from the beginning to the end. Rather, we picked a few pages to discuss at night, or when we had  few minutes to spare here and there. These books have a perfect format to do so, and get a daily dose of math.
  2. We spent most of our time with the books “The Grapes of Math” and “Math for All Seasons”, discussing strategies to count. The books give clues leading to one in particular, but we did not read it right away. Rosie came up with her own strategy, and shared it with me first, then, I offered mine, and finally, we reviewed the strategy from the book. It seems a good way to help a child not only build up his/her own mathematical thinking but also make sense of a strategy that may be different from his/hers.
  3. Although the books are mostly focused on thinking, a few “tricks” can be found. I decided to skip the ones connected with concepts that Rosie has not fully explored yet. For instance, my hope is that by providing Rosie with plenty of opportunities to explore multiplying by 10, she will notice on her own the particularity of the products. Therefore, telling her now that she can multiply any number by 10, by just adding a 0 at the end seems going backward in our home journey of making sense of math.

I encourage you to check these books out. And if you like them, there are two more (“Math-Terpieces” and “Math Appeal”) you can explore !

 

 


“1+1=5”, by D. La Rochelle & B. Sexton. It is all about the units !

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Last month, I attended a presentation about units (Cipparone & Bass, 2017). When C. Danielson (“Talking Math with Kids”) mentioned the book “1+1=5”, I quickly wrote the title on a Post’It, knowing that as soon as we were back home,  I would check it out.

I am so glad I did. Such a fun support to make children think about units.

Each page presents a drawing and an equation, such as a unicorn and a goat and “1+1 = 3?”. On the next page, the equation includes the units i.e. 1 unicorn + 1 goat = 3 horns. Indeed, 1 + 1 = 3 :-)

You may have read it in some of my previous posts, I always remind my daughter Rosie, 8, to provide the unit at the end of a word problem, and even invite her to write the units in her equations. This book was just perfect to reinforce my point, and led us to an instructive talk about the importance of the units.

Rosie LOVED that book, and could not stop talking about it for a week, finding new examples on her own. In fact, if you meet a little girl who claims, with a mischiveous grin, that “1+1 = 3”, enjoy: you may have just met Rosie :-)


Reference:

Peter Cipparone & Hyman Bass, 2017. Bringing Out the “Unit” Across Mathematical Domains. Cognitively Guided Instruction. 2017 National Conference, Seattle June 26-28.


Small, 2012 – Reaching out to all children

Here is another book I studied as a graduate student that I found interesting to share.

FullSizeRender-2Small, M. (2012) Good Questions: Great Ways to Differentiate Mathematics Instruction, 2nd Ed., Teachers College Press, NY.

The author suggests 2 different types of math tasks to reach out children with different skills and needs. Makes sense in a classroom, of course, but it makes sense to me at home as I start seeing my son Tom, 4, willing to “do math” with his sister Rosie, 7 (see my previous post here on Doing Math outside, for instance).

Open questions:

The task is “framed in such a way that a variety of responses or approaches are possible” (Blanton, p6). Remember my post on Vygotsky  (here) ?  Well, the goal is to design the task “in the appropriate zone of proximal development for all students” (Blanton, p6), so that every student can be part of the discussion.

Here is an example of what we did recently:

“Go outside and take a picture of a pattern”.

Rosie came back with a pattern found on  a flower, while Tom came back with a  pattern he created with rocks and pine cones. Still, we were able to discuss patterns all together.

Parallel tasks:

It is a set of tasks that children can choose from, that are close enough to be discussed at the same time.

For instance, this afternoon, I asked Tom and Rosie to create a story out of:

  • Choice 1: 10 dinosaurs
  • Choice 2: 3 cars

Again, even if Tom used a number smaller than Rosie to create his story, they still were able to share what they did with each other. Also, Rosie was able to create a math problem, while Tom invented “just” a story involving 3 cars.

Of course, with Tom and Rosie’s difference of age/skills/grade, I may not always be able to provide them with tasks they can explore together, but I really like the idea, and will come back to it regularly.

You may want to  check out the book, too ! It includes hundreds of Open Questions and Parallel Tasks organized by math concepts and grade levels.

 


Math & Children Literature – Part II

A few month ago, I shared “The wonderful world of mathematics: A critically annotated list of children’s books in mathematics” (Thiessen et al., 1998), a helpful ressource to find children books that could be connected to math (here).

Well, there is more !IMG_1500

“Exploring Mathematics though Literature” is another book from the National Council of Teachers of Mathematics (NCTM). It includes a selection of articles previously published by the NCTM, categorized by math topics: Number & Operations, Algebra, Geometry, Measurement, and Date Analysis & Probability. Articles may discuss a book, a math activity connected to the book and strategies children may use, etc. This book is a gem to me: not only it gives me ideas of books to read in connection with math, but also activities to implement. And cherry on the top for me so interested in how children think, it provides student samples. A great source of inspiration for our math journey :-)

Also, Math Solutions, CA, published a series of books connecting fiction/non-fiction books with math lessons for different grade levels. I sure will try some of their recommendations throughout Summer.

If you love connecting books to math as much as I do, you may want to check these books out !

References:

Burns, M & Sheffield, S. (2004). Math And Literature, Grades K-1: Math Solutions, CA.

Burns, M & Sheffield, S. (2004). Math And Literature, Grades 2-3: Math Solutions, CA.

Peterson, J. (2004). Math And Nonfiction, Grades K-2: Math Solutions, CA.

Thiessen, D., Matthias, M., & Smith, J. (1998). The wonderful world of mathematics: A critically annotated list of children’s books in mathematics. Reston, VA: National Council of Teachers of Mathematics.

 


Is your brain thinking about it ?

Here is another book I am reading as a graduate student in math elementary education: “Why don’t students like school”, by D.T. Willingham. I enjoy the cognitive approach the author takes to explain how to better support children’s learning.Willingham

One thing I noted is how your brain has to think about what you try to learn in order to retain it :

“Thus, your memory is not a product of what you want to remember or what you try to remember: it’s a product of what you think about” (p53)

And it is actually quite easy for children (and adults!) to get distracted from  thinking about the concept they intend to learn. Quick example from the book (p64): a math problem involving cell phone minutes in High School may have students think about… the last text they received rather than thinking about… math. And it may be tricky to motivate children with a topic of interest, or add some fun to help them learn without crossing the line of distracting them.

Indeed, I had the perfect example with my child this week.

Rosie came back home one night, and  recognized the symbol “<” in one of my books left on the table. “We just started learning about that symbol at school !” she said. So of course, I asked her to tell me more about it. To which she answered… “I am not quite sure yet, but it is like an alligator. And I love alligators !”

Zoology: 1 – Math: 0

alligator

 

 


Want to do math at night? Try Bedtime Math® !

Another book I have discovered recently: Bedtime Math®, by Laura Overdeck and Illustrated by Jim Paillot. It is series of books, actually, but I just bought the first one for now.

Each page includes a short text about a fun fact (e.g. “exploding food”, “extreme vehicles”, etc) , and  3 levels of word problems (one for the “wee ones”, one for the “Little Kids” and one for the “Big Kids). Click here to see an example of pages displayed on Amazon.

My daughter (1st grade) and I have been doing it at night for a little while, and I must admit, we are having a good time.  My child might get frustrated exploring some of these problems on her own because of the wordings, and the format, rather different than what she does at school. But to discuss and explore informally together, before turning off the lights, it is a neat book. I do like the idea of combining reading and math. The “Wee ones” problems are the ones we usually discuss at night, as most of the time, we would need at least paper, if not manipulatives to explore the “Little Kids” level. That would be more a “Daytime” Math for us. The “Big Kids” Level is most of the time, out of reach for us. These problems cover indeed a wide range of skills !

You may want to give it a try ! If you are interested, check their website here, the books can be bought on Amazon or Barnes & Nobles.

BedtimeMath


Exploring money a little further …

Quick post to complete what I wrote earlier this week (here). Somehow I forgot to include another relevant book about money. Let me address that.

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Indeed, the book “If you made a million” (by D. M. Schwartz and illustrated by S. Kellogg) provides a nice support to extend the discussion my child and I started with Dollars and Cents for Harriet (B and G Maestro). It goes from coins, to bills, to checks, or how $10 could be paid through 1 ten-dollar bill, 2 five-dollar bills or… a 5-inch pile of dimes. It even includes bank accounts and interests, as well as choices you have to make when you have money (e.g. spending, saving, both).

Another great resource to explore money !