Abstract
This study explored prospective elementary teachers’ perspectives on real-life connections in the case of story problems. A series of tasks were designed to uncover the participants’ collective perceptions of real-life connections by speculating on participants’ emerging beliefs about real-life connections and how their beliefs were reflected in the story problems they posed or evaluated. Findings revealed the following ideas: (a) there were overly positive beliefs with insufficient specifics; (b) participants perceived utility and reality as critical components of real-life connections; and (c) there were vast discrepancies between their beliefs and the way they posed or evaluated story problems for real-life connections. These results will generate further discussions about the issues and challenges teacher education programs face, while providing suggestions for future research.
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Appendix: Post-questionnaire
Appendix: Post-questionnaire
Real-life-connected math stories evaluation
<Part I > Please evaluate the following math stories. For each math story,
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(1) Please indicate the quality of real-life connection on a scale of 1–5, with 5 representing the highest quality.
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(2) Explain the strengths of the math story in terms of the real-life connection.
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(3) Explain the shortcomings of the math story in terms of the real-life connection.
<Sample story problems used for evaluation>
Example 1 . Grade: 2
You are invited to a birthday party at Classic Bowling lanes. The party begins at 12 pm [noon] and ends at 2 pm. But you have a soccer game that starts at 2 pm. The bowling alley is a half hour away from your soccer field. What time will you need to leave the party to make it to your soccer game on time?
Example 2 . Grade: 3
I have four equal sides with four equal angles, what shape am I?
Example 3 . Grade: 3
Each lunch table in our cafeteria holds a maximum of 22 students. If there are 102 students eating at lunch today, how many lunch tables will we need?
Example 4 . Grade: 3
John and his Mom and Dad went to the apple orchard. Each member of the family has a basket, that’s 3 baskets to fill with apples. The family each put 6 delicious looking apples in their baskets. They had 3 baskets with 6 apples in each, how many apples did the family have all together?
Example 5 . Grade: 3
Tom and Tim were having some friends over to watch a movie. They wanted to order pizza for everyone but they weren’t sure how much to get. Jet’s Pizza was offering specials on Supremes, cheese and pepperonis, and Hawaiians. Small pizzas have 5 pieces, mediums have 7 pieces, and larges have 10 pieces. So, Tom and Tim asked their friends which kind and how many pieces of pizza they would like. Max and Sam each wanted 2 slices of Supreme and 3 slices of Hawaiian. Sally wanted 3 slices of cheese and pepperoni. Greg wanted 2 slices of cheese and pepperoni and 1 slice of Hawaiian. Wally ordered 2 slices of Hawaiian, 1 slice of cheese and pepperoni, and 1 slice of Supreme. Finally, Tom and Tim decided what they would eat. Tom and Tim each wanted 4 slices of Hawaiian, but Tom also wanted 1 slice of cheese and pepperoni. But, just as Tom went to call Jet’s, Sally decided to change her order. She now wanted to change one of her slices of cheese and pepperoni to a slice of Supreme. Which kinds and sizes of pizzas should Tom and Tim order so that everyone will get what they ordered?
Example 6 . Grade: 4
Use the clues to find the numbers
1,000 s | 100 s | 10 s | 1 s |
|---|---|---|---|
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|
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|
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1. Write 5 in the tens place.
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2. Find ½ of 24. Subtract 4. Write the result in the hundreds place.
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3. Add 7 to the digit in the tens place. Divide by 2. Write the result in the thousands place.
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4. In the ones place, write an even number greater than 2 that has not been used yet.
Example 7 . Grade: 3
Mr. and Mrs. Smith have five sons, each born 2 years apart. From the data below, figure out the birth order of the sons and their ages.
Edward is older than Michael and Ian.
Michael is 4 years older than Larry.
Yves was born when Edward was eight.
Ian is now 6 years old.
Example 8 . Grade: 4
“All 20 of my students have been working very hard all week during math. I think they deserve a break for a little snack. I’m going to bake cookies for them tonight.” Said Mrs. Lynn to her husband, Mr. Lynn.
“That’s a good idea. If you make the cookies smaller than normal, each student would be able to get more cookies!” said Mr. Lynn.
“I think that is a great idea, I know my students will love that too.” Said Mrs. Lynn.
“Wow, it sure smells good in here tonight.” Said Mr. Lynn.
“That’s what 80 little cookies smell like. Yummy isn’t it?!” asked Mrs. Lynn.
How many little cookies does each student receive from Mrs. Lynn?
Example 9 . Grades: 5
Your parents are planning on taking you and your siblings on a family trip to see your grandparents who live in Tampa, Florida. Dad wants to know how many times he will have to stop for gas if he travels at 60 miles per hour and his car gets 30 miles to one gallon of gas. The gas tank holds 20 gallons of gas and you are going to be driving 1,800 miles.
Example 10 . Grade:8
You have a collection of sports cards with exactly four types of cards (soccer, baseball, basketball, and Nascar). The soccer and basketball cards make up 60 % of the collection, and the basketball and baseball make up 20 % of the collection. If the 18 baseball cards in the collection represent 5 % of the total number of cards, how many of the cards are Nascar?
<Part II>
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1. Do you think real-life-connected math stories are more appropriate for specific concepts (e.g., time, money)? If so, why?
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2. Can you create a math story that is not connected with a real-life context? If so, please provide an example.
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Lee, JE. Prospective elementary teachers’ perceptions of real-life connections reflected in posing and evaluating story problems. J Math Teacher Educ 15, 429–452 (2012). https://doi.org/10.1007/s10857-012-9220-5
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DOI: https://doi.org/10.1007/s10857-012-9220-5