Update from the 2e Center for Research and Professional Development

2e Center News

July, 2017

About this Column

The 2e Center is located on the campus of Bridges Academy in Studio City, California. In this column, we share what’s happening at our center and report research findings, teaching ideas, and parenting suggestions we have found to be successful in helping 2e kids thrive.
— SB

By Susan Baum

The 2e Center works with Bridges Academy to develop strength-based, talent-focused strategies that are not only beneficial to 2e students but effective for all students. These strategies can be easily implemented in any classroom.

In our continuing series on strength-based, talent-focused strategies, we concentrate on ways to engage students using their creative thinking abilities. For some 2e students, especially within the ADHD population, creative thinking is a talent area. These learners are great at coming up with original ideas. Inventions, robotics, creative writing, cartooning, and improvisation are a few examples of opportunities where many of these kids excel.

These same students can also be creative in how they avoid tasks — for instance, easily inventing 50 reasons why they didn’t do their homework. It’s important to harness their divergent thinking ability to help them cope with academic deficits. In this column and several upcoming columns, we will focus on using creative thinking within the core content areas to both engage learners and help them to build an understanding of concepts and principles.

The column for this issue focuses on using creative strategies in mathematics — a problematic area for some 2e students. Math can be anxiety-producing for some students, especially when they have met with failure early on due to issues with poor working memory and slow processing speed. These deficits can interfere with students’ ability to memorize math facts and can make it difficult for them to participate successfully in activities requiring mental math. Furthermore, learners with poor reading comprehension skills have trouble understanding word problems in math, especially when the problems do not reflect their own experiences or reality. Failure in math over time can result in students believing they are math failures.

Rachel McAnallen is an educator whose expertise is teaching all students how to fall in love with math. She has been highly successful in working with learners who struggle with math, and she firmly believes that math should be a creative experience in which students generate their own problems. Students’ focus, in her opinion, is better placed on the conceptual understandings — the “know why” of mathematics — rather than on procedural knowledge — the “know how” of arithmetic. As our guest columnist in this issue, Rachel presents a lesson designed to engage students in mathematical thinking by teaching them how to write their own story problems and how to develop many, varied, and unusual questions to accompany the story.

SB

 

Wonderful Word Problems! Teaching Kids to Write Their Own Story

By Rachel McAnallen

Word problems — a phrase that dredges up memories of nightmarish train schedules and evokes groans in even the most well-adjusted of adults. Although they represent an important application of mathematics, word or story problems can be a source of boredom, confusion, or even anxiety for many learners. A major reason for learners’ frustration is that the problems do not make sense to children, given that they are neither written through a child’s eyes nor within a child’s reality. Furthermore, students don’t understand how the questions at the end of the problem are generated. For many of our more concrete 2e learners, word problems written in textbooks seldom represent any situation that they have experienced. Thus, solving the problem becomes a mechanical (procedural) task rather than a problem-solving (conceptual) one.

Perhaps the best way to give students a solid understanding of word problems is to teach them how to make up a story from their own reality. This exercise lets students bring their own creativity and experiences to the lesson. Through the multi-step process of formulating their own story, students first learn how to generate questions related to their story and then learn how to answer these questions. More importantly, they begin to develop a conceptual understanding of where these problems occur in their own lives and how the questions relate to the story.

A Lesson on Story-problem Writing

Following is a description of a lesson on teaching students to write their own story problems. It takes three days to complete, along with homework assignments.

Day 1

Goal: For students to define and explore how reality provides a basis for storytelling

Activities:

  1. Explore with your students what one’s own reality means (e.g., what is real in your life, which may not be real in someone else’s).
  2. Provide students with facts about your own reality. Here’s information that I share with students: I have a house and a mortgage payment. I have pets. I have to eat so I buy food. I play video games. I use my computer and smart phone every day. I have to catch an airplane once a week. I have to pack a suitcase with loads of math materials.
  3. Give students five minutes to write down ten items from their reality. Have them share their information, noting what is unique about their reality and what is similar to others’. Note the kinds of items that students share. Once I learned that a student collected spiders; another told me about her horses. Trust begins to grow in the classroom as students share their personal realities.
  4. Now the creativity begins! Share a story that you have developed about your own reality. You may want to project it. Here’s an example of a story I shared:

Because Rachel loves pets, she has three dogs and two cats. One dog is an older Labrador retriever named Bud, and another is a high-energy golden doodle named Murphy. Because Murphy is so high-energy, Rachel had to get a dog for Murphy, which means she had to get a dog for her dog. The third dog is an Australian Shepherd named Finnegan. He’s a herding dog and must always have a job to do, so his job is to herd Murphy. The two dogs are such a joy to watch, with Murphy always out running Finegan, and Finnegan always trying to get Murphy back in line. Bud, in the meantime, just lies down and watches the antics of the two younger dogs. Most of the time, the dogs eat the same food. 

  1. Have the students use the information they generated in their own reality list to create their own story — real or fantasy.

Homework: Have the students revise and edit their own story. They can add more information and even illustrate it.

Day 2

Goal: For students to learn how to ask questions, including how to formulate a question, what kinds of questions there are, how to make a question interesting, and how to ask quantitative questions

Activities:

  1. Start the lesson by asking the students: Who asks the most questions in class? They probably will say “the teacher.”
  2. Respond by saying, “That’s right. But today you will be the ones who are asking the questions, and I will be answering them. Let’s see how good you are at asking questions. Everyone needs to ask me a question. As long as the question is not too personal, I will answer it as honestly as I can.”
  3. Write the questions on the board.
  4. Discuss the type of questions asked by looking at types of answers required. Three common types of answers required are:
    • Yes/no answers to questions such as, “Do you have a favorite color?”
    • One-word answers to questions such as, “What is your favorite color?”
    • Explanation answers to inquiry questions such as “Why did you become a teacher?” 
  5. Ask the students to identify the types of questions they asked. A quick show of hands will let you know if they understand the different kinds of questions.
  6. Return to your story, reread it with the class, and ask students what questions they have about it. Answers to questions must be found in the information already contained in the story.
  7. Write the students’ questions on the board and ask them to think about the kinds of questions they generated. Challenge them to try to ask all three types of questions. Here are some examples of student questions that my story generated:
    • Does Rachel like pets?
    • What is the name of the golden doodle?
    • Do you think Rachel would contribute to the Humane Society? Why or why not?
  8. Ask students to write at least three questions about their own story and to write the answers on another sheet of paper.
  9. Have the students pair off and share their stories. At this time, they can challenge their partner to answer the questions and to name the kind of response that the question called for.
  10. Enter math! Revise your story and add numbers. This helps students build meaning as they discover all possible situations that can be quantified in any story problem. Here is my reality story with numbers:

Rachel loves pets so she has three dogs and two cats. One is a Labrador Retriever named Bud, who is 12 years old; and another is a four-year-old high-energy golden doodle named Murphy. Because Murphy is so high-energy, Rachel had to get a dog for her. The third dog is an Australian Shepherd named Finnegan. Most of the time, the dogs eat the same food, which costs about $45 a week for all three of them. Last February, Murphy had to go to the dog doctor to get a shot for kennel cough and the bill was $75. Bud has arthritis and his medicine costs about $35 a month. He has been on this medicine since he turned 8 years old.

  1. Have the children pair up and generate math questions from your revised story. The following are examples of the questions students generated from my dog story after I provided these prompts: Think about questions where you might have to add, subtract, multiply, or divide to get the answer. Can you think of one that might take multiple steps to solve?
    • How many years has Bud been taking his arthritis medicine?
    • How much did Rachel spend on her dogs the month that Murphy got kennel cough?
    • What is the average cost of dog food per day, per dog?

    In order to differentiate the prompts, you might suggest that students think of one question that a first-grader can answer, another that their classmates can answer, and one difficult enough to challenge the teacher.

Homework: Ask students to get ready for the upcoming “Problem Solving Convocation” by doing the following:

  • Put numbers in their story.
  • Generate at least three questions and answer them.
  • Record the questions on another piece of paper.

Day 3

Goal: To provide an authentic opportunity for students share their stories

Activities:
Divide the class into groups of three.

  1. Ask students to challenge other members of their group to solve their problems.
  2. Provide time for the groups to complete the problems and discuss the answers.
  3. Finally, have students discuss with their teammates what they liked about each other’s problems and how they could have been even better.
  4. Debrief with the whole class about the experience.

Optional Closing Project: Have students create a math-story-problem blog in which they can publish their own problems as well as invite others to contribute problems. Suggest that they might hold a contest for stores that are the funniest, most creative, most complex, etc. It’s all up to them.

Samples of Students’ Original Stories 

Here are two examples of fifth-grade students’ creative response to the lessons. The first resulted from a recurring dream this student had — very much a part of his own reality. The second, is about a real experience in this young girl’s family.

Mr. Bubblehead

“Don’t take me, please!” I screamed from my bedroom. I had been lying in my bed sleeping.

“I am the old green scum,” said Mr. Bubblehead. He had two mouths. His head had triple the amount of eyes as he had noses, and half as many noses as he had mouths.

Then, with a bright light, the ship came down. I noticed that I was inside the silver ship with millions of red and green buttons in a pattern, red, green, red, green, etc. Then I saw this big screen showing Neptune, the god of evil. All of a sudden, Mr. Bubblehead grabbed me, put me into a chair, and tied me there. I looked around and noticed that the ship was made of 1,578 panels with 30 screws in each panel. Again he said in his annoying voice, “I am the old green scum.” 

I was beginning to think that was all he could say, and I wondered why he was saying this. Maybe it meant that he was scum. It sure looked like he was. He also acted like it. Then I felt hands grabbing me and shaking me. My eyes opened. Noticing that I was in my room, I yelled, “Whoopee, it was just a dream — I mean nightmare.”

Questions:

  • How many eyes does Mr. Bubblehead have?
  • How many noses does Mr. Bubblehead have?
  • How many screws hold all the panels of the ship together?
  • If there were 4,700 buttons, what color would the pattern end with?

Next is the second example, from a fifth-grade student. This story problem reminds other kids of their own realities — living with a younger sibling.

The Pest

My brother, Lucas Walter Dunn, is a little devil. He is always talking back to my mom but never gets into trouble for it. A lot of people think his blue eyes are so adorable, and his blonde hair is so perfect. Well, if you were his sister you wouldn’t think of him that way. He always picks on me, about ten times a day. He thinks he has a better way of doing just about anything.

I have to share a room with him. He is always leaving his dirty underwear on the floor mixed in with his clean and dirty clothes. But I just tell him, “If you want to be a pig, then go on and be a pig. One day you are going to be married, and you will have to give up being a little slob.”

My mom continues to buy him new underwear all the time. She bought him 50 new pairs just two weeks ago. I think he left about 23 pairs on the floor, so Mom ran out and bought him 10 more. Today I found five more pairs added to the mess on the floor. He never picks anything up. The pile just keeps getting bigger.

If you ever meet my brother don’t be fooled by his so-called cuteness.

Questions:

  • How many pairs of underwear are on the floor in my room now?
  • How many times does my brother pick on me in four weeks?
  • If my brother has 410 strands of hair on his head, and I pull out 40 of them, how many would he have left in his head?

Conclusion

This lesson has so many possibilities for all students, not just those who are 2e. The open-ended nature of creating story problems allows students to respond at their developmental level. Those students enchanted by the story-telling aspect will create problems more original than those found in a textbook. Those who loved making their stories quantitative will find the question-generation aspect of the experience to be their outlet for creative thinking. You will be surprised how they integrate complex and sophisticated math applications into their stories.

 

Known simply as Ms. Math to children across the country, Rachel McAnallen has devoted her life to sharing the joy and beauty of mathematics with learners of all ages.  A professional educator for over 59 years, she travels the globe teaching her subject at every grade level.

In addition to her experience in the classroom, Rachel has served as a department chair, a school board member, and a high school administrator. She claims the latter position is responsible for the majority of her grey hairs.  She has a passion for teaching, golf, and mathematical modular origami, though not always in that order.  A life-long learner, Rachel approaches the world around her with a boundless curiosity and a playful sense of humor that is reflected in her teaching style. She believes that mathematics is a language to be spoken, a music to be heard, an art to be seen, and a dance to be performed. Rachel loves to dance. 

Return to top