## The Evolution of Writing in a Math Classroom

#### by Jawad Brown

The Standards insist that instruction in reading, writing, speaking, listening, and language be a shared responsibility within the school. (Common Core State Standards Initiative. (2010). Introduction, English Language Arts Standards.)

This push for writing has made me re-examine my curriculum and see where I can utilize more writing to deepen the mathematical understanding of my students. When I started writing in my class, the focus was on students answering open response questions. Here is an example of an open response question from MCAS (Massachusetts’ state assessment):

Transitioning to the Common Core, specifically the mathematical practices, over the past four years has led me down a road toward more meaningful writing in the math classroom. Below I have outlined my path toward writing starting with a process coined QDAWG, to portfolios, and to where I am now using a model called RAFT. All of these have pros and cons, which I have listed, but the trajectory has been toward creating writing experiences within my classroom that deepen and reveal student understanding more fully and completely. The evolution from writing to effectively responding to state assessment questions to writing as a vehicle for students to learn mathematics is a Common Core shift that has pushed and improved my practice.

### QDAWG

This is an example of QDAWG that I used for students to answer open response questions. I used this strategy to address the immediate challenges that students had with open-response questions. This was a way for students to formulate strong repsonses, through a process that was sticky enough to remember for the MCAS. **Q** is for restating the Question in your own words. **D** is for Devise a plan. **A** is for Act out your plan. **W** is for writing your answer in a complete sentence and **G** is for Gotta double check.

##### Pros:

- Students could answer questions and show math work at the same time.
- Students could use this for all open response questions.
- Students worked through this process quickly and effectively.

##### Cons:

- Students are not deeply thinking about the content that is being asked.
- Students are not required to fully express their answers through writing, which made it difficult to determine their level of understanding.

### Portfolios

These are three examples of portfolios that students would complete in my class. On the front students had to read and annotate the problem that was being asked. Once that was completed students were asked to show all math work on one side then explain their math on the other. On the back of the portfolio students were asked to show their answers with an illustration (graph or diagram). The back also includes the rubric for each part of the portfolio. Students would get portfolios on Fridays and come to class with them on Mondays, where one student would be called to explain their work to the class. Examples of student work are below:

##### Pros:

- Students can show math in three different ways.
- Students learn that the use of illustrations can help with their written explanation of answers.

##### Cons:

- The entire process is time consuming.
- If students’ answers are wrong and they present , they will be explaining how to answer questions the wrong way.

### RAFT

In both cases above the writing in my class was more about answering the questions that are being asked. This year I am trying to have students answer the given questions AND explain their thinking. In order to get better explanations and push students to use writing as a place for students to work out and show their understanding I adopted the RAFT model. The RAFT strategy pushes students to write with purpose. RAFT stands for Role, Audience, Format, and Theme. This model situates the students as a writer with a role and a particular audience and gets students thinking about what format and approach they should take in their writing.

This is an example where students are using RAFT to answer a word problem. Students were asked to answer the same question from two points of view. For this example students were told that their audience would be two different types of people. The first was an 8-year-old child and the second person was a mathematics professor. This created a writing situation where students needed to explain their answers in ways that both audiences can understand.

##### Pros:

- Students have to use mathematical vocabulary.
- Students have to fully understand content to explain it for two different audiences.

##### Cons:

- Students need more time to write purposefully.
- Students have to be able to fully master the content before answering.

### Reflecting on My Evolution

These approaches did a couple of things: they gave students an opportunity to show mathematical comprehension in a diversity of ways through writing, and each allows mathematical understanding to go beyond computation. The first, QDAWG strategy, was a result of focusing on open-response questions that led to an understanding of content, but did not significantly deepen their understanding or serve as a way of expressing their understanding. When I created the portfolio, I wanted students to more fully express understanding by requiring answers to be written, illustrated and calculated. This allowed for deeper writing, because the presence of other representations provided a great base of understanding from which students could explain or write about the problem they were solving. Lastly, RAFT gave students a way to look at the same content from someone else’s perspective by writing to different audiences. RAFT assignments really showed how deeply students understand content. Writing became the means for expressing and exploring mathematical ideas.

Each approach has its pros and cons, and I have started to assign each approach depending on the standard being addressed or on what the strategy accomplishes. The writing process in my math class is still growing and evolving. I am not sure exactly what writing will look like next year in my math class, but I do know that it’s an essential part of my curriculum and that these approaches to writing are pushing student understanding forward.

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I enjoyed observing your personal reflection and how you knew where you wanted your students to be in terms of writing in the classroom. I think your ideas help other teachers such as myself understand that there is a way to put real-world examples into math. I have always been a firm believer that students will learn math language and its equations. However, I believe they need to see how math relates to familiar scenarios that they can envision, which in turn will help them relate to the information in real-life situations and on a personal level. I particularly like how you had them explain in simplistic terms to an eight-year-old and a professional mathematician in terms that were appropriate for them. I find as students start to analyze what they learn, a couple of things for the students. It allows them to break the information down into a comprehensible way in which they can turn around and converse about it to their peers, parents and other teachers. By allowing students to do this in itself will allow them to apply what they have learned in math to other things in life. That is our goal as teachers. Everything we learn is intertwined. Without one learned thing, another is not as functional. Secondly, explaining it in terms that a professional mathematical would be willing to listen and explore will allow a student to build on the vocabulary that is used in math. Expanding the use and the understanding of more complex ideas will allow them to apply what they learn now to things they learn in the future. I almost think I would want to add one other step to what you have started. I would like to have my students explain through writing, to both an eight-year-old and a professional mathematician, how they could use or relate the information in a real life situation. As they do this, they will begin to conceptualize how math is a part of our everyday encounters and can pull from this insight at other times. Nicely done. I plan on using this idea and adding mine, in order to build on how my students react to this application of math and writing. Thank you.