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# Common Error Patterns in Pre-service Teachers Attempts at Writing Fraction Word Problems - PowerPoint PPT Presentation

Common Error Patterns in Pre-service Teachers’ Attempts at Writing Fraction Word Problems. Cheryl J. McAllister Southeast Missouri State University Cheryl Beaver Western Oregon University Mathfest 2009, Portland, OR.

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### Common Error Patterns in Pre-service Teachers’ Attempts at Writing Fraction Word Problems

Cheryl J. McAllister

Southeast Missouri State University

Cheryl Beaver

Western Oregon University

Mathfest 2009, Portland, OR

• Premise: Teachers need a deep conceptual understanding of the mathematics they will teach.

• Question: How proficient are pre-service teachers with procedural and conceptual understanding of fractions?

• Do identifiable error patterns occur when students attempt to write story problems for fraction operations?

• How can instruction be improved to increase students conceptual understanding?

• For each of the following fraction problems the mathematics they will teach.

• Solve the problem showing your steps.

• Write a word problem that would be solved by doing the problem you just completed. Be sure you use correct grammar and punctuation.

• Samples collected from Preservice teachers at Western Oregon University and Southeast Missouri State.

• Independently analyzed samples and developed a list of common errors.

• Incorrectly written word problems did not seem to be correlated to computational errors.

• Errors were identified as general or related to a specific operations.

The question call for a whole number response. University and Southeast Missouri State.

• In writing the story problem, the writer asks a question that calls for a whole number response.

• Jill has 2/3 lb of jelly beans. Her mother gives her another 4/5 lb of jelly beans. How many jelly beans does Jill have altogether? (for 2/3 + 4/5)

• Most often an error for addition problems, but occurred in problems for all operations.

Ambiguous wholes in problem (similar to previous) University and Southeast Missouri State.

• Instead of writing a problem for a/b, the problem is written for a/b x N, where N is an unknown natural number.

• Jake ate 2/3 of his animal crackers, while Dani ate 4/5 of his. How many crackers in all did they eat? (2/3 + 4/5)

Ambiguous units or wholes University and Southeast Missouri State.

• If Mary has 4/5 piece of ribbon and adds 2/3 to it to make a bow, how much ribbon is there for the bow?

(2/3 + 4/5)

Logic errors University and Southeast Missouri State.

• Jack has 1⅔ of his garden planted with various types of flowers that he bought at Pete’s Flowers. He has 2⅜ of a garden left to plant with flowers. What is the product of his entire garden after he finishes planting all of his flowers in the garden? (1⅔ ∙ 2⅜ )

• Eight out of 9 people at a movie had 6/7 of a bag of popcorn left at intermission. What would the fraction number be to represent all the remaining popcorn for all the people in the movie? (8/9 ∙ 6/7)

Subtraction specific error University and Southeast Missouri State.

• Instead of writing a word problem for a-b, the student writes a problem for a-(axb).

• Sam has 2/3 of a lb of jelly beans. He gave 2/9 of his share of jelly beans away. How many pounds of jelly beans did he have left?(2/3 – 2/9)

• This error occurred in over 22% of the subtraction problems written by the students in the study.

Multiplication specific errors University and Southeast Missouri State.

• Instead of writing a problem for a x b, wrote a problem for a + b

• On Monday, Bill ate 3/4 of a pizza. On Tuesday he ate 8/9 of a pizza of the same size. How much pizza did he eat in those 2 days? (3/4 x 8/9)

• Instead of writing a problem for a x b, wrote a problem for a + (a x b)

• Eliza has 6/7 of \$100 saved up. She found a job and increased her savings by 8/9. How much money does Eliza have? (6/7 ∙8/9)

Division specific errors University and Southeast Missouri State.

• Inappropriate use of sharing concept of division (partitive division).

• You have 1/4 of a cake. You want to divide it into 7/9 of a group. How many in each group? (1/4 ÷ 7/9)

• Instead of writing a problem for a/b ÷ c/d, student wrote a problem for a/b ÷ c.

• You have ¼ of a cake and 7 out of 9 people want cake. How much does each person get?(1/4 ÷ 7/9)

Mixed numeral specific error University and Southeast Missouri State.

• Instead of using the mixed numeral A b/c, the student writes a word problem using A ∙ b/c.

• If I had 1 whole pie and you had 2 whole pies, how much would we have if you gave me 2/3 of yours and I gave you 3/5 of mine? (1 2/3 ∙ 2 3/5)

Overarching issues University and Southeast Missouri State.

• In a set of samples gathered from 73 students, about 50% either wrote no division word problem or wrote “What do you get when you divide a by b?”

• Students don’t understand the difference between how many and how much.

• There are common interpretations of language different from mathematical meaning.

• Students don’t think logically about what their word problems are trying to say.

How can we change things? University and Southeast Missouri State.

• Focus on units and wholes.

• Emphasize conceptual understanding of fractional models.

• Actively teach language skills related to mathematical ideas.

• Combine the use of manipulative models with student attempts to write a story problem.