Frog and Toad Are Friends

Frog and Toad Are Friends by Arnold Lobel is actually a collection of stories, all of which are a little different. Each story is relatively short and about 12 pages at an easy reading level. Today's entry is going to be focusing on the 3rd story in the book-- A lost button. In the story, Toad loses one of the buttons on his jacket. Frog helps toad find his button, but they realize when looking for his button that there are very many different types of buttons-- small, big, white, black, thick, thin, etc. In the end, Toad finds the button on the floor in his home. He feels bad that he made Frog look around for buttons all day, so he uses all the buttons they collected and sews them all on his jacket.

This book is very good for young children-- Pre-K through 1st grade I would say. Students can be introduced to the ideas of sets and attributes, and since buttons are objects from everyday life, they could actually practice sorting buttons into sets according to various attributes. They could also compare and contrast buttons and create a venn diagram if they sort buttons according to two different attributes (black and 2 holes-- buttons that are black in one group, buttons that are black AND have two holes in the middle, and buttons that have 2 holes but are not black in the third group).

Frog and Toad are two characters that could repeatedly be used in math word problems. I had an experience with a student yesterday who was working online solving word problems and would continually raise her hand to have help reading the words. Every time I went over to help her, the word she needed help with was the name of a place or the names of people. If we use characters from stories that children are familiar with, or places the students go to, they will be much more successful solving word problems. Especially in the early years, if students remember Frog and Toad from the story, they will be able to visualize and comprehend the problem with less difficulty.

Math Appeal

Math Appeal is a collection of "mind-stretching math riddles," which classifies it as a concept book (since it is written to teach mathematics). However, the riddles inside the story are cleverly written and have some of the rich language qualities that make books fun to read. Each riddle takes up two pages-- one with a picture and one with a riddle describing the problem to be solved. The riddles could all be solved by counting, but that is not the purpose of the book. The purpose of the book is to have children think outside of the box and explore various different ways to solve the same problem. I really enjoyed reading a note from the author, Greg Tang, in the beginning of the book. He notes, "I use poems and pictures to encourage clever, creative thinking, and I provide an answer key that teaches four important concepts: thinking out-of-the-box, finding strategic sums, using subtraction to add, and simplifying through patterns and symmetires. I encourage kids to discover different ways of solving each problem and to decide for themselves which approach works best." Another connection that I made in trying to solve some of these riddles is using arrays and multiplication. Students frequently struggle with this in the beginning, but this book presents those ideas in a unique way.

I wouldn't do all of the riddles in this book at one shot, but it would be interesting to do one riddle a day to warm students up and get them REALLY thinking. Encourage kids to find different ways of solving the same problem, and students might find a solution that you didn't even see yourself!

Swimmy

Swimmy, by Leo Lionni, became a favorite book of mine during student teaching. Being in fourth grade, I didn't get the opportunity to use many picture books, but this book was used in the beginning of the year to promote teamwork and creative problem-solving within the class.

For those who are unfamiliar with the book, Swimmy is a little black fish who lives in a school of red fish. One day, a tuna fish comes and eats all of the fish in his school, except Swimmy. Swimmy continues on to explore the ocean and meets various sea animals when he finally stumbles upon a school of little fish, just like himself. He joins this school and encourages them to travel out and see more things in the ocean. The other fish are convinced that they cannot do this because they will get eaten by a bigger fish. Swimmy teaches them how to swim together in a group, shaped like a big fish, so that when they venture out all the big sea creatures think that it is a big fish and not just a school of small fish. Swimmy is successful and the school of fish venture out to explore the ocean.

This book also provides a great opportunity to create word problems. Although it never specifically mentions numbers, variables could be assigned to stand for the "unknown" numbers to create word problems. For example, in the beginning of the book all of the fish in Swimmy's school are eaten except for Swimmy. So, an appropriate word problem could be:

There are 900 fish in Swimmy's school. A giant tuna fish comes along and eats all of the fish except for Swimmy. How many fish did the tuna fish eat?

Students would then have to solve 900-1= 899. If algebraic thinking was going to be explored, then you could model for students how to set up and solve an equation like 900 - x = 1. (Where x= the number of fish eaten by the tuna.)

For younger grades, students could each make their own fish to become a "school" of fish as a class. The teacher's fish could act as Swimmy and problems could be created accordingly.

Some extension activities I found online are mainly creating similar illustrations to ones found in the story and literacy activities, but they can be found on these sites if you're interested: http://www.kinderart.com/across/swimmy.shtml

I'm finally starting to see all of the possibilities out there for incorporating literature and creative activities into mathematics. If students were able to visualize and really visualize the problems through literature, mathematics would come alive and be much more enjoyable for them. As a teacher, I want all of my students to love mathematics as much as I do!

Knots on a Counting Rope

I have been choosing books from numerous lists I have gotten off of the internet to start my studies, but as with anything you find on the internet, it's not always trustworthy. Today's book, Knots on a Counting Rope by Bill Martin, is an example of one of those books that I read the book and looked at what was said online about the book and thought, "Huh?" An important part of learning though is not only finding good examples but finding examples that aren't the greatest. Who knows, maybe I'm missing something and someone else who's mind works differently than mine will comment and prove me wrong.

This book is a story about a boy and his grandfather. The boy has grown up on what looks like an Indian reservation and continually asks his grandfather to tell him the story of when he was born and various stories of his life. The grandfather tells him the stories and every time he tells a story he adds a knot on the counting rope (to count how many times he has told the story).

While I was reading this book, I was waiting for that "aha!" moment where the connection to mathematics clicked with me, but I finished the book and never got an "aha!" moment. You could stretch some things out of it, but I think there are so many other books that are out there that could provide stronger connections to mathematical concepts.

On the bright side, if you're looking for a book to teach dialogue or family traditions and relationships, I'd encourage you to read this book!

Concept vs. Story books

I think before I continue I have to distinguish between concept books and storybooks. They are two very different tools-- but they each have their place in teaching children mathematical concepts. Concept books are books that are written with the intent being to teach a mathematical concept such as counting, shapes, graphing, etc. Storybooks on the other hand are books that do exactly what they say-- tell a story. Quality storybooks lend themselves to repeated readings and engage students through adventures, meeting new friends, etc. In speaking with Mary Napoli, a professor at Penn State Harrisburg, she has noted to me that, "there is certainly value in using literature-based mathematics books such as those mentioned above since they typically present abstract concepts through story; however, it is important that teachers find books that promote pleasure and joy and not simply because it teaches a mathematical concept or lesson." Therefore for the purpose of this project, I am going to include both concept books and storybooks in order to establish a database of both types of books and their uses in the classroom.