# Common Math Errors

## Bar Diagramming to Solve Word Problems: Great Strategy to Teach in Guided Math Groups

Randy Charles wrote a must read monograph on word problems. In this article he talks about the two main ways that teachers teach words problems: 1) key word approach 2) Polya’s problem solving phases. He reiterates that research says don’t use the keyword approach! He also makes a good point about Polya’s phases as being a framework, not a step by step guide to solving problems. He goes on to talk about how bar diagramming is a visual approach that provides many possibilities for students to approach word problems. He then gives several examples. READ THE ARTICLE IT COULD CHANGE THE WAY YOU THINK ABOUT WORD PROBLEMS! Let me know what you think!

Happy Mathing,

Dr. Nicki

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## Solving Word Problems Part 1: Work it out In Guided Math Groups

Word Problems are one of the biggest challenges for students in math. In 1977, Australian educator Anne Newman discussed five steps that students need to work through in order to solve a word problem successfully–

(1) reading the problem / READING

(2) comprehending what was read /COMPREHENSION

(3) transforming the words into a mathematical strategy/TRANSFORMATION

(4) applying a mathematical procedure/PROCESS SKILLS

(5) writing the answer/ ENCODING

Her research showed that over 50% of errors that children make occur in the first three steps– before they even begin to solve the problem!

WOW!

She suggested a 5 step protocol for word problem solving error analysis. She would ask the following questions:

1. *Please read the question to me. If you don’t know a word, leave it out.*

2. *Tell me what the question is asking you to do.*

3. *Tell me how you are going to find the answer.*

4. *Show me what to do to get the answer. “Talk aloud” as you do it, so that I can understand how you are thinking.*

5. *Now, write down your answer to the question*.

The five questions link to the 5 processes (noted alongside them). Whereever the student has a break down, this is where the teaching point begins. Now, if asked to rework the problem and the student gets it right and can self correct, Newman labels this as a careless error. All other errors are teaching points. Try this out on your students and let me know what happens.

Reference:

Reference 1 (Be sure to watch the video)

Happy Mathing,

Dr. Nicki

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## Math Bugs and Slips: Talking with Students about Common Errors

*Watching for the Tricky Parts*

Math can be tricky. Students make common errors, referred to as “math bugs” in the research literature (Ginsburg, 1987). One of the things that we can do is have a focused discussion each week about the tricky parts of problems that students make. These have to do more with conceptual understanding and procedural fluency. “Slips” (Ginsburg, 1987) are the silly mistakes that students make that can easily be corrected.

As a guided math strategy, the teacher actually has an in depth discussion about the tricky parts of whatever the students are currently studying. Let’s take a look at a Math Bug vignette done during a guided math group:

**Mrs. Kay**: Okay, everybody, today we are going to talk about Measurement Math Bugs. Our 4^{th} grade standard says that you all will know how to make conversions within the Standard Unit of Measurement. This means that you will be able to convert inches, feet and yards. So let’s look at a typical problem and the common bugs that pop up when solving this problem.

* Problem: Susie is going to make a dress. She bought 2 ft. 5 inches of material. She has to pay for the material by the inch. How much of the material does she have in inches?*

*Math Bug Answer 1: 10 inches*

*Math Bug Answer 2: 7 inches*

**Mrs. Kay**: Who can tell me what the error is in Math Bug 1?

**Tom:** They multiplied the 2 by the 5.

**Mrs. Kay**: Who agrees? Thumbs up if you agree, thumbs down if you don’t and sideways if you’re not sure. [Most students agree and a few aren’t sure.] Ok, yes they multiplied here. What is the math bug in example 2?

**Maria:** They added, but you’re not supposed to add. You’re supposed to first change the 2 ft to inches. Then add that to the five inches and that gives you the total in inches.

**Mrs. Kay**: Who agrees? Thumbs up if you agree, thumbs down if you don’t and sideways if you’re not sure. [Everyone agrees] Ok, so if we were to write the steps for doing conversion problems, what would we write. Let’s chart it and then you write the steps in your own words in your math journal.

*(Mrs. Kay Charts it and the students note it in their journals).*

Ginsburg, H. P. (1987). How to assess number facts, calculation, and understanding. In D. D. Hammill (Ed.), Assessing the abilities and instructional needs of students (pp. 483503). Austin, TX: PROED.

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