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### Teach math extended-response writing skills

october 25, 2010

Take stock of what students have learned and what they need more exposure to. One area of weakness may still be your students’ explanation of their math problem solving. Additional instruction on how to write a strong math extended response is a great topic for any time of year! Here are two strategies to try:

## Frame a “good” response

Provide an organized skeleton of what the response should sound like. The skeleton includes words/phrases that reference the key information that should be in a good response. For example, a math frame might include the phrases: in the problem… key information… to solve… the answer…

As students write out their math explanations, they are to use each of the frame components (in order). They will connect their ideas using the frame phrases. This produces a thorough and developed response.

For every aspect you want addressed within their responses, be sure to include that aspect as a frame component. For example, if the question asks students to also identify the operation used to solve the problem, then your frame may include: in the problem… key information… to solve… the operation… the answer….

Note that there are not capitals at the start of each transition phrase. These are not sentence starters; it simply requires students to use these words and phrases to link their ideas. However, these transition links could be used at the beginning of a sentence, in the middle, or at the end of a sentence. There could also be several sentences in between two transition links.

One easy way to develop a frame is to solicit the help of your colleagues. Write responses to sample math problems and study each other’s written responses. Pull out words/phrases that are evidence of a well-written answer. Ideally you want to work as a team or department to develop a consistent frame that meets the needs of your state’s math extended-response questions. Being consistent helps the students as they move among grade levels, too.

Framing is a great strategy. . .temporarily. Eventually students need to be weaned away from you always providing the framework for a strong and meaty response. Over time, move from “I” (the teacher) always providing the frame to “We” (the teacher and students) creating a frame to “You” (the students) internalizing frame elements and applying them independently within their written explanations.

## Make the questions invisible

Invisible Questions require students to write responses that are so thorough that the reader can guess the original question/problem. First, separate the question/problem from where students are to write out their responses. (Write the problems on the overhead, and have students write their solutions/responses on separate paper in their notebooks.) When it’s time to go over students’ written responses, turn off the overhead. Removing the question makes it “invisible.”

Now ask students to share their responses aloud. When they reveal a partial response that makes little sense (e.g., “I added it, moved it, and that’s how I got it” or “Because it gets added”), then you are ready to talk. The students themselves will probably giggle at their own ridiculous responses. They may even request you reveal the original prompt so they can read the original question in order to clarify what they meant. Emphatically refuse. They need to understand that their written explanations need to be stronger, more complete.

### Reveal the new short-response procedures:

1. Part of the original question must be embedded in the response. (NOTE: This is addressed in the frame. For example, the transition link “in the problem” is part of the original question/problem.)

2. All pronouns are defined. There is no use of “it” in the response (e.g., “I added it, I moved it, and that’s how I got it.”) The reader doesn’t know what “it” is. A quotient? A product? A variable? The students need to use their math vocabulary; they need to sound like mathematicians.

3. The response is revealed in complete thoughts/complete sentences. It makes sense and can stand alone without any reference to the question. In fact it’s such a complete response, the reader could guess the original problem/question.

To really emphasize the value of these three principles, consider assessing each in-class extended response question to be worth 6 points (or more). Students can earn:

- 1 pt. for embedding the question within the response.
- 1 pt. for avoiding pronouns (e.g., it, they, them, etc.)
- 1 pt. for writing in complete sentences that make sense all by themselves.
- 3+pts. for a mathematically correct/accurate answer.

This scoring approach honors that it’s not just about having the math correct. Students must be able to communicate their reasoning in writing.

## Develop a consistent approach

Whether you utilize either of these two strategies, or develop another, being consistent is essential. As the students progress from grade level to grade level, they should hear consistent information. As a staff, agree on a uniform approach for writing strong math explanations. Identify common elements and expectations so students aren’t confused.