Using Children's Literature to Teach Problem Solving in Math

Addressing the Standards for Mathematical Practice in K–5

Jeanne White

• Verlag: Routledge
• Jahr: 2016
• ISBN:
  9781315527512
• Auflage: 2
• Thema: Bildung
• Thema: Mathematik unterrichten

Learn how children's literature can help K–5 students see the real-life applications of mathematical concepts. This user-friendly book shows how to use stories to engage students in building critical reasoning, abstract thinking, and communication skills, all while helping students understand the relevance of math in their everyday lives. Each chapter is dedicated to one of the eight Standards for Mathematical Practice, and offers examples of children's literature that can be used to help students develop that practice.

You'll find out how to:

• 
  
  

• Encourage students to persevere in solving mathematical problems and use multiple approaches to find the answer;

• 
  
  

• Help students reason abstractly with the aid of concrete objects and visuals;

• 
  
  

• Guide students in constructing arguments to explain their reasoning and engage in critical discussion with their peers;

• 
  
  

• Teach students to recognize mathematical patterns and use them to solve problems efficiently;

• 
  
  

• And more!

The book offers activities for beginners as well as for more advanced problem solvers. Each chapter also provides guidance for ELLs and students with special needs, so no matter your classroom environment, you'll be able to use these strategies to make math class more dynamic, engaging, and fun.

1
Make Sense and Persevere

SMP 1—Make Sense of Problems and Persevere in Solving Them

How many minutes would a student have to work on a word problem in order for you to determine the student has persisted in solving the problem? Do students know what is meant by perseverance? How can students persist if they do not understand the context of the problem? Making sense of a problem begins with the ability to understand the words, symbols, numbers and figures in the problem. English Language Learners may not be familiar with regional dialect and outdated terms; early readers may be overwhelmed by a long paragraph; inexperienced problem solvers may not know how to interpret symbols and figures which accompany a problem.

What Does This Standard Mean for Grades K–2 Problem Solvers?

Students who are successful at SMP 1 read the problem more than once in order to make sense of the information provided. They are able to explain the problem to a peer in their own words. They can analyze what is given, what is not given and the goal of the problem. They can draw a picture or use objects to represent the situation in the problem. They can make several attempts to find the answer, considering the strategies of other problem solvers. They continually ask themselves if their strategy and their answer make sense.

In order to fully apply SMP 1 when approaching a word problem, students in Kindergarten through second grade should be able to take ownership of their procedures by using the following I Can statements:

♦ I can explain the meaning of the problem in my own words.

♦ I can analyze what is given, what is not given and the goal of the problem.

♦ I can use a picture or concrete objects to understand and solve the problem.

♦ I can understand the strategies of others.

♦ I can ask myself, does this make sense?

Seven Blind Mice by Ed Young

The book Seven Blind Mice (1992) represents a version of the folktale The Blind Man and the Elephant and follows seven blind mice who attempt to figure out the nature of a strange Something at the pond near their home. They must rely on their sense of touch to make sense of the object. Each mouse travels alone to the pond and feels a different part of the object, resulting in disagreements over the identity of the object. The last mouse to go to the pond, White Mouse, first listens to the ideas of the other mice concerning the identity of the object. She attempts a different strategy and runs across the strange Something from end to end, making sense of the various parts of the object mentioned by the other mice to reveal it is an elephant. You can use this book to illustrate SMP 1 by providing a concrete example of how to make sense of a problem and then persist at finding its solution as well as incorporate how to decompose the number 7.

Operations and Algebraic Thinking K.OA

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation.

As you read the book, engage students in a discussion by asking the following questions based on the I Can statements:

♦ What was the problem in the book and why was it a problem for them? Explain the meaning of the problem. (One day the mice found a strange Something at the pond and they were afraid because they didn’t know what it was; they didn’t know if the strange Something would drink all of the water at their pond or not let them get to the water.)

♦ What information could the mice use to solve their problem since they are blind? Analyze what is given, what is not given and the goal. (They could touch the strange Something but they couldn’t see it; they could only use the information from their sense of touch to try to identify the object.)

♦ What were some of the ways the mice tried to solve their problem? Use a picture or concrete objects to understand and solve the problem. (They went one at a time to the pond to find the object; they each touched the object and then told the other mice what they thought it was; each mouse wanted to experience it for him/herself in order to figure out what it was.)

♦ What did White Mouse do differently than the other mice? Ask yourself, does this make sense? (She wasn’t sure if the answers of the other mice made sense so she wanted to go to the pond too; she decided to touch every part of the object instead of just one part and see if she could agree with one of the answers.)

♦ How did she use what she learned from the other mice? Understand the strategies of others. (White Mouse listened to the ideas of the other mice before she went to the pond to find the object; she used descriptions given by the other mice to help form her answer.)

For a second reading of the book, model how to use the I Can statements to solve a word problem related to the story:

There were 7 blind mice who found a strange Something by their pond then ran back home. One of the mice, Red Mouse, went back to the pond the next day to touch the strange Something. While he was at the pond, how many mice were still at home?

Use a think-aloud method to begin modeling the I Can statements:

“First, I have to think, can I explain the meaning of the problem in my own words? There are 7 mice. One mouse is at the pond. How many mice are still at home? Next, I have to analyze what is given, what is not given and my goal. I am given the total number of mice at the beginning of the problem, which is 7. I am given the number of mice that went to the pond, which is 1. I am not given the number of mice that are still home, which is my goal. I can use 7 counters to understand and solve the problem by acting it out. I will use 7 counters as the mice at home. I will move 1 of the counters to an oval, which will be the pond. Now I can count the mice that are still at home. There are 6 mice still at home.” (See Figure 1.1.)

Figure 1.1

Once the students have observed and listened to your think-aloud strategy, they can become more involved in applying the next I Can statement. Draw a picture based on your concrete model and ask the students if your picture represents the problem and if your answer makes sense while further modeling:

“I’m not finished yet because I have to look back at my answer and ask myself, does this answer make sense? Well, if I started out with 7 mice and 1 mouse was taken away from the group, there would be 6 mice left because 6 is 1 less than 7. So my answer does make sense. Does anyone have another way, or strategy, to solve the problem?”

Students can share their ideas for solving the problem with a peer using objects, pictures, words and symbols based on their readiness levels and experiences. Ask students to share their work with the class and see if others came up with the same answer but used a different strategy. If students are able, they should explain their strategy and you can restate their explanation in order to model the last I Can statement:

“Janet, let me see if I understand your strategy for solving the mouse problem. You drew 7 mice then you crossed 1 out because you said that would be the mouse at the pond. Then you counted the mice that were not crossed out and you also got 6 for your answer. Okay, I understand your strategy for solving the problem. Thank you, Janet.”

It is important to do similar problems with students so they can generalize the procedures for making sense of a problem and trying different ways to solve it. Show the students a problem using a different number but a similar context:

There were 8 little rabbits who found a carrot patch but the farmer chased them back to their home. One of the rabbits, Brown Rabbit, went back to the patch to dig out a carrot. While he was at the carrot patch, how many rabbits were still at home?

Help the students think about how they should approach this problem by asking some questions:

♦ How is this problem similar to the problem about the 7 blind mice? (There ...