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.

Fish Eyes

At first glance, the book Fish Eyes by Lois Ehlert appeared to me as a counting book. The slogan "A book you can count on" underneath the title was somewhat deceiving because the book provides so many more opportunities than just counting. There are a lot of counting books out there and I'm looking for literature which can be used to explore a wide variety of mathematics topics-- not just counting. This book provides opportunities for a variety of mathematics concepts and also promotes imaginative thinking. It opens up with a few pages describing the narrator wishing he/she was a fish and what he/she would do if he/she were a fish.

This book provides a great jumping point for patterns in addition at an elementary level. The pages have a number of fish on them and then in the corner it says something like, "4 striped fish plus me makes 5". Not only does this provide a good transition to the next page, which would have 5 fish on it, but in reading you can just say "4 striped fish plus me makes..." and have the students respond. It is important for students to make connections in mathematics and if students are able to connect that any number plus one is really just like counting up one, they will never struggle with those types of addition problems.

The artwork in this book also allows study for geometry. Ehlert does all of her illustrations in bold, solid colors. The fish are all a little different and have various shapes inside of them. Some fish look similar to others, so these could also be used for classifying and categorizing different objects. Additionally, the book could be used for a study on symmetry and determining which fish are symmetrical and which fish are not. It would be neat to have students make their own fish out of construction paper using different cut out shapes and then explore what fish are symmetrical and which ones are not.

A little motivation to think outside the box and incorporate different books to make mathematics more meaningful:

"I learned math by memorizing facts, doing worksheets, and through direct instruction by the teachers. I never saw any need or understood why I did what I did."

-Matt, pre-service teacher

Eight Animals Bake a Cake

The title of the book, Eight Animals Bake a Cake, by Susan Middleton Elya, immediately enticed me when I saw it in the library this afternoon. I figured that since the title had a number in it, it had to do with math (most likely counting). While I was partially true and you can count the different animals and the ingredients that they bring to bake a cake, the book has many other curricular connections.

There are 30 Spanish words in the book, and each one is presented in context with English words to allow the reader to determine the meaning of the Spanish word. Thus, this book is especially useful for English Language Learners (ELLs). Although math is the same in every country, ELLs may struggle learning the English words for numbers and this book helps with that. Word problems would most likely prove to be challenging for ELLs simply because they have to try to comprehend what the question is asking. This book is a good starting point to creating word problems which use both Spanish and English words, which would not only make the ELL(s) feel included, but also increase comprehension.

The book also shows the characters solving a problem in a unique manner. Although the problem is not in a mathematical context, the concept of problem-solving could be discussed with the class and problems could be created using the 8 different animals (or animales, in Spanish). In a creative way, students could pretend to be the different animals to learn the Spanish and English words and create their own word problems-- incorporating the Spanish/English words from the book. In the front of the book is a glossary and pronunciation guide to help readers with meaning and proper pronunciation.

I found this book muy interesante! (Very interesting!) The book has won numerous awards. For more information, visit the web-site at http://www.susanelya.com/files/l_8animals_cake.htm.

Caps For Sale

Caps For Sale by Esphyr Slobodkina is a book which offers a lot of both math and literacy activities. It is also humorous, which makes it more appealing to children of all ages. The story is about a peddler who is trying to sell caps to make money so he can eat lunch. When no one wants to buy his caps, he sits down under a tree and decides to take a nap (with the caps still on his head). Later, when he wakes up, he realizes that all of his caps have been stolen by monkeys in the tree. The monkeys refuse to give the peddler his hats back, so the peddler throws his own hat on the ground in frustration. When the monkeys see this, they decide to do the same! The peddler then collects all of his hats back and continues on his way.

This book provides math connections mainly for the primary grades K-3. For very young children, they can practice identifying colors and counting the numbers of caps in each color and in all. This could also lead to a study in adding up parts of the whole. (Example: 4 gray caps + 4 brown caps + 4 blue caps + 4 red caps=16 caps total) A problem like this could be a good jumping point for problem solving activities where students are able to get creative. What if the peddler sold 2 gray caps, 0 brown caps, 1 blue cap, and 4 red caps? How many caps does he have left? Depending on the students in the class, the students could even act out problems by having one student be the peddler and everyone else in the class coming to purchase hats. If students are able to see a real-life dramatization of what the problem is asking, they will build visualization skills to help them on other problems.

Another connection this book makes is money. Each cap in the book is 50 cents, so this provides a whole host of curricular connections. Students could use coins to show different ways to make 50 cents. Or, they could pretend to buy a particular number of hats and have to determine how much 2, 3, 4, or more hats would cost all together. (Repeated addition serves as a good introduction to multiplication!)

Visit the Slobodkina Foundation at http://www.slobodkina.com/Childrens%20Library_Caps%20for%20Sale.htm for more information about the book as well as free downloadable activity pages.

"My experiences learning math content were never positive ones. I remember drills and tons of worksheets. If I had learned with a story as the content, it would have been much better."

-Allie, pre-service teacher

Introduction

Hi! My name is Kara Geiger and I am a senior Elementary Education and Special Education major at Elizabethtown College. I am currently pursuing an independent study in mathematics by examining various ways to differentiate mathematics instruction-- specifically in word problem-solving strategies.

Last semester, I completed my student-teaching experience at Bainbridge Elementary School, in Elizabethtown Area School District (Elizabethtown, PA). I spent half of my semester in 4th grade and the second half in Learning Support for 3rd-5th grade. Both of these experiences were priceless for me, providing me with many learning experiences that simply can't be learned inside a college classroom. During my time there however, I encountered many students that struggled significantly with mathematics word problem solving. It was very challenging for them to solve these problems for numerous reasons, and I have decided to devote my time looking at the struggles these students have and various ways teachers can help them overcome them.

I have been fortunate enough to be given the opportunity to continue working with the students from my student teaching experience in an after-school math tutoring program. Hopefully, I will be able to test out some of strategies from my research to see first-hand if they can help children succeed. Growing up, mathematics was always my favorite subject. I love working with numbers to try and solve problems. I am still intrigued by the mathematics problems faced in everyday life, and want students to be able to solve these problems successfully-- and enjoy doing so.

In my preliminary research, I have found many sources supporting the use of literature in mathematics. When I thought about this, it makes complete sense. Not only is it good practice to connect subjects across the curriculum, but the major problem that I have encountered in working with children solving word problems is that they don't comprehend what the problem is asking. If problems are presented in a story form, students have picture clues to aid with comprehension. They also are more prone to incorporate all of their strategies they use in reading comprehension to understand the problem. It makes sense!

As a pre-service teacher however, I am just beginning to explore the use of literature in mathematics. Therefore, I have decided to keep a blog and post after each book I read to reflect upon and share the possible uses in the field of mathematics. Hopefully, throughout the course of the next few months, I will establish a good basis of various books across a wide range of topics in mathematics!