Making Thinking Visible

Making Thinking Visible
Making Thinking Visible

Arts Integration

Arts Integration
Arts Integration

Once Upon a Time...Slaying Dragons & Story Problems

Fairy tales are more than true; not because they tell us that dragons exist, but because they tell us that dragons can be beaten.
                                                                           -Neil Gaiman, Coraline

I fought dragons nightly. At our kitchen table. I mentally donned my chain mail armor, strapped my trusty sword and scabbard to my side and prepared to do battle with the math textbook. There were different kinds of dragons on those long nights. There was the fraction dragon and the long division dragon, but the most terrifying of all was the story problem dragon. Despite my mental armor and weaponry, I was usually reduced to damsel-in-distress status because I dissolved into tears within ten minutes. 

Story problems still cause anxiety to ripple through me. I think most teachers feel that way. I know many students do, too. And if the problems are multi-step, I'd rather give up the fight and toast marshmallows in the dragon's fiery breath. With chocolate and graham crackers.

But then, I had an epiphany.  I was teaching fraction story problems when the reading teacher inside my head said, "You haven't taught the text structure."  I went home that night and began to plan for the next day.

When reading teachers teach about different types of text, they use mentor texts. Mentor texts are books, essays, poems, etc. in which the author has used structures, features, and traits that support the the teacher's lesson focus. In short, a mentor text is any text that models the reading or writing strategy that is being taught. I began to think about story problems as mentor texts. My students needed to learn how to read the text structures of story problems, and then they needed to learn how to write that same text structure. I believed that doing so would also improve their ability to tackle any story problem.

I wrote a collection of mentor texts for story problems. I currently work with fifth graders, so the problems I used are focused on fifth grade standards. I divided my students into small discussion groups of 3 or 4 and gave each group 3 mentor texts (story problems). While they read the texts, I asked them to use a thinking routine called See-Think-Wonder.  We had used this in other subjects before this lesson, so it was a well-known learning routine. 

My students began to read the story problems, and they jotted down their noticings. This is the "see" part of the routine. Here are some of their responses: 

  • I see numbers.
  • I notice that there are characters (people) in the problem.
  • I notice it says "altogether."
  • I notice it says "more."
  • I notice it uses clue words.
  • I see fractions. 
  • I see a beginning, middle and end.
  • I see that every one ends with a question mark. 
Then, they read them again and discussed what they thought about what they observed. 
I think we have to add in this one.
I think that the ending of a problem always asks a question.
I think that the first sentence is like a lead.
I notice that all 3 problems have three sentences.
 One of the things I began to notice in my students' responses is that some were focused on the mathematical thinking: "I think we have to add in this one." and "I see fractions."  Others were noticing how the texts were written. The distinction between the two types of thinking are important, because I believe they indicate differences in understanding. 

The last part of thinking routine is "wonder." What do your observations and thoughts make you wonder? I saw a big range of understanding in my students' questions, too. 
I wonder what the answer is.
I wonder if all story problems have 3 sentences.
I wonder if story problems are like mini stories.
After my kids had the opportunity to examine the mentor texts within their groups, they reported out to the whole group, and I charted their responses. Then I explained that while all of their observations were important, I wanted to focus on some specific ones. I highlighted all of their responses that had to do with how the story problems were constructed.

Out of their observations, we decided that story problems are a lot like stories. They have 3 parts: A beginning, a middle, and an end. Each one of those parts has a specific purpose for the reader/mathematician. My kids noticed that the beginning is written to introduce the mathematical situation. For example: Ayesha and Ben each started a dog walking business. 

The middle part of the story problem presents the mathematical information and tells even more about the situation. For example: Ayesha charged $5.00 per customer per day and was able to walk 6 dogs every day for one week, while Ben charged $6 per customer per day and walked 4 dogs every day for one week. 

They also noticed that the mathematical question was almost always asked at the end of the story problem. For example: Who made more money by the end of the week? 

After looking closely at how story problems are organized, we used what we discovered about them to discuss other problems that have different structure. Knowing the structure of a basic story problem helped us tackle harder ones. My students worked with a partner to write their own story problems. We analyzed these together. Finally, I returned their fraction story problems, and they tried again. Let's just say that dragons were slayed!

It's important for students to read and write like mathematicians. Recently, there have been many articles and books written about using reader's workshop structures in the math class. That's all well and good. However, it's not just about the workshop's about the type of thinking that a student does while reading and writing. Guess what? They need to do that type of thinking when they read and write in math! There should be a skill transfer, and if there isn't, then teachers need to facilitate those lessons. 

If you like what you read here, you might want to take a look at the materials I used for those lessons. You can find them by clicking on the picture.

In addition, I'm a featured author on Rachel Lynette's Minds in Bloom blog this week! There's more reading and writing like a mathematician goodness over there. Click HERE to read about ways to help your students write better math responses. 

I've teamed up with other teacher authors for Teacher Talk, a monthly blog link up filled with teaching ideas and goodies. Consider visiting them below!