I do these more for myself than anyone else, but here, I am quoting the most useful parts of this ASCD book (click links to read online for free). Basically, I'm editing out the boring. You're welcome.

I'm also just doing a couple of chapters at a time because it's kind of dry and I never know how much time I will have to read. So consider it a series if you like.

I'm also just doing a couple of chapters at a time because it's kind of dry and I never know how much time I will have to read. So consider it a series if you like.

Joan M. Kenney

So the question becomes: If students have been taught the material and haven't learned or retained it, what can we as professionals do to change the scenario?

Writing [in this way] slows down and focuses my thinking; I am able to hear each word in my head and see it on paper. It is like a

*mindful meditation*during which I shut out the rest of the world and am totally engaged in the process.Another benefit of writing is that it allow the page to become a holding place for our thoughts until we can build upon them. We can revisit our written thoughts as often as needed and thus revise our thinking

*.*Although I start with an overall plan when I write, I do not know where the ideas and words will take me until the process of writing drags them out of me- much as many artists do not know where a picture is going until the paint touches the canvas.Mathematics is beginning to be viewed less as a series of arithmetic calculations than as "the science of order, patterns, structure, and logical relationships" (Devlin, 2000).

*Writing to Learn*(1989), it is important that all students be involved in the mathematics classroom. Twenty-five students cannot all speak at the same

time, but they can all write at the same time, and writing encourages them to become engaged in their learning.

Written explanations in mathematics are about

*what*is being done and why*it*works. The type of thinking involved in justifying a strategy or explaining an answer is quite different from that needed to merely solve an equation.*The process of writing about a mathematics problems will itself often lead to a solution*.Once students have done some initial writing about a problem, they can share their strategies in small groups. In attempting to solve the problem, the students will have additional opportunities for writing.

If students begin the problem on their own, they are starting from their own mathematical way of thinking. Bringing their written solutions to the small group helps students investigate mathematics more deeply.

**Students need to untangle what is in their own minds first, get it on paper, and then share their thinking with others.***(Love this statement with all my heart!)*This ensures that there will be a range of responses to each question.

To quote Stigler and Hiebert (1999):

When this type of learning experience is used, the range of individual differences will be revealed. Individual differences are beneficial for the class because they produce a wide range of ideas and solution methods that provide the material for students' discussion and reflection. The variety of alternative methods allows students to compare them and construct connections among them. It is believed that all students benefit from the variety of ideas generated by their peers. (p. 94)

In order for mathematics writing to be effective, the following guidelines must be observed:

- The problem must be appropriate for the students who are going to be writing about it.
- The students must know how to use blocks, diagrams, pictures, or grids to work out their solutions before writing about them.
- The students must have confidence in their ability to respond to the problem as individuals. They must think of themselves as successful mathematics learners.
- The students must feel comfortable sharing their answers without fear of being ridiculed. This means that the teacher and other students have to accept all responses as worthy of discussion.
- The problem must be discussed with the whole class, and all strategies must be reported.

In other words, teachers should use writing to engage students in mathematics thinking at the outset of a lesson and continue asking them to put their thinking in writing throughout the lesson to refine their thinking.

As the NCTM (2000) notes,

...Allowing students to grapple with their ideas and develop their own informal means of expressing them can be an effective way to foster engagement and ownership. (p. 63)

By recording their thinking about mathematics problems, students help explain the solutions- and the process of

*arriving*at a solutions helps to

*develop*the solution. Writing clarifies what it is the problems are asking. In order to justify their solutions, student writers are forced to think through, and find the meaning in, their responses.

Student writing helps teachers determine the type of learning that is occurring, informs them as to whether or not the students understand the lesson objectives, and reveals the level of understanding behind the students' algorithmic computations.

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