It is difficult to learn something new and challenging without ever putting it into words. This is just as true when learning math as it is when learning anything else. Thus, it is a good idea to make time for students to discuss their ideas with their classmates in pairs, groups, and as a whole class. It is also helpful to give students many opportunities to write about math.
In this post, I'll focus on expository writing, where students summarize and present key ideas. Typically, this will happen at the end of a unit, and will take the form of a report or poster. In this sort of assignment, the personal style and the self-centered focus of a personal learning journal is usually inappropriate. Moreover, while spelling and well-crafted sentences do matter, not everything the students learn from their English teachers applies to the writing of a math report. And the formal, ultra-concise style of mathematical proofs is also inappropriate. Some other guidelines are needed.
I first came across this idea many years ago when Carlos Cabana sent me the result of a discussion he conducted with his students and colleagues at "Railside High". They were shown examples of technical writing (such as users’ manuals), and asked to identify some of the key features of those documents. Here is the list they came up with:
* Diagrams with labels
* Numbers to separate text and show order of steps
* Text with mathematical vocabulary
* Telling and showing what you mean
* Titles and headings
* Showing common errors
* Use of boldface, capitals, italics, etc.
* Tables and charts
* No naked numbers (i.e., all numbers include units or labels - e.g., 7 squares in each line x 3 lines = 21 square units)
In preparation for writing this post, I asked professional technical writers for any ideas they would add to the list. Here are some of their suggestions:
* Start by deciding what you're going to say
* Open with a summary, which may include ideas you are tempted to use as the conclusion.
* Organize the rest hierarchically, with parallel subtitles
* If appropriate, link to basic references such as a glossary
* Remember that the piece has a topic. It is not about its author.
* Be concise: avoid repetition, superfluous details, off-topic digressions, and self-evident information
* Keep sentences short
* Use plain language: short, common words
* Use terms consistently
* Use examples
I also asked Carlos to comment on that original list. He explained that in addition to the importance of clarity in communication, the purpose of these guidelines is to strengthen the writer's understanding, particularly in the case of multiple representations, a key ingredient in his (and my) pedagogy. Color-coding, arrows, "thought balloon" annotations, diagrams, etc. are largely about highlighting the connections between the representations. See for example this assignment (based on lessons in Algebra: Themes, Tools, Concepts), and check out the student work Carlos sent me (Glenda | Mariela.) These are examples from middle school students and English language learners, so you should adjust your expectations if you're thinking of high school kids. Younger students will typically need more help in understanding how to use the tools of technical writing.
Carlos adds that learning about technical writing in math class pays off in the humanities and science. Some of those skills (use of colors, annotations, etc.) are useful in helping students read, make sense of what they are reading, and mine a text for evidence. All the skills are also helpful in writing detailed lab reports in science.
Thanks to Carlos Cabana, the Railside teachers, Louise McFarlane, and Cate deHeer.