Tuesday, July 27, 2010

Transparent Algebra: Writing

It won’t come as a surprise that I value writing. A lot. For me, writing helps me think about whatever I’m thinking about. It makes me clarify what I understand and don’t understand, and what I believe. One of the main reasons I blog is to help me think about stuff.

I also value writing in the classroom, whether that’s a Language Arts classroom, an Art classroom, or, yes, a Math classroom. I want my students to reflect on their own learning process, to think more about whatever they are thinking about, and to be able to communicate that to others both verbally and in writing. My struggle is how to do that well in a Math classroom.

It’s a struggle for me primarily for three reasons. First, the old excuse of time. I’ve complained previously (see my comment here, the one from me that starts “@David Cox - You're going . . .” - I can't link directly to it) about not having as much time as I’d like in my Algebra class, and providing time for writing is one more thing to try to squeeze in.

The second issue is overcoming expectations. Students (and their parents, and my administrators) have an expectation of what a math classroom looks like. I’m pushing the envelope on those expectations in quite a few ways, and writing will be one more way. While I’m willing to have those conversations, there’s also the practical matter of not pushing too far, too fast, or I might lose some folks along the way.

The third, and perhaps most important issue, is that I’m not sure how to do it well. When I’m writing primarily for myself, like on this blog, I know what to do. But when I’m having students write in the service of mathematics learning, then I feel like I need to reach a higher standard of purpose and meaningfulness. I don’t want to have them write just because I find writing valuable, I want them to write because it is valuable for them.

So, given all those caveats (yeah, okay, excuses), here are my fledgling ideas for how I’m going to use writing in my classroom. Please chime in not only with suggestions about my ideas below, but additional suggestions of how I could use writing in my Algebra classroom. This first year back I anticipate not being able to do as much writing as I eventually hope to, but the great thing about this blog is that it will still be here a year from now when I try to improve what I did this year.

  • About Me
    The first writing assignment the students will do is an About Me piece. In fact, I’m actually giving this to the students before the school year even starts. I already called all the parents to make sure they had broadband access at home and I asked for an email address when I talked with them. I then emailed them some preliminary information about the class (more on parent communication in a future post). Next week I’m going to follow-up that email with a second email, that will have a little more information for the parents, but is primarily information that I’m asking them to pass along to their student. (Once the school year starts we’ll have Google Apps for Education, and therefore students will have an email address I’ll use but, for now, I’m going through their parents.) One part of that is giving them the About Me assignment.

    They do not have to work on this before school starts, it will be an assignment the first week, but I highly recommend that they do for two reasons. First, that’s one less piece of homework they’ll have to do that first crazy week back. And second, it will allow me to know a little bit about them before that first week of school. Here’s the prompt as well as my own About Me piece, as I want to – as often as is practical – complete any writing assignments I assign to my students. This will also give them a chance to know a little bit about me before the first week of school.

  • Reflection
    One of my stated goals for this course is for students to be metacognitive, to think about their own learning and use that self-knowledge to become better learners. So a yet-to-be-determined number of times a semester I’m going to ask them to reflect on their learning. I’m not sure of all of those prompts yet, I’d like to strike a balance between giving them something pretty specific to focus on (like Dean’s suggestion in the comments here), and leaving it general so they can write about what they feel is important.

    I’ve tentatively scheduled the first reflective piece to be at the end of the first week of school. I’m going to ask them to reflect back on the first week, to share any questions or concerns they have about the structure and expectations of our class, and to set a couple of goals for the semester (one related to our class, one related to another class, or an activity or sport, or something outside of school). Then periodically throughout the semester/year, I’ll ask them to reflect on their learning, what’s working for them, what’s a challenge, and anything else they’d like to share. I’d love any suggestions for prompts you’d like to share in the comments.

  • Conferring
    I really like the idea of conferring, where teachers meet with students to talk about their writing. I’m going to try something similar about the first of October, when I’ll ask my students to write something. It might be along the lines of the reflection mentioned above, or it might be about a mathematical topic, I’m not sure yet. In either event I’ll ask them to submit it and then schedule a time to come in and meet with me so that we can talk about it. The timing (first of October) is designed so that this happens once we're well into the school year, but before our scheduled Parent/Teacher Conferences.

  • Parent/Teacher Conferences
    We have two nights scheduled for parent/teacher conferences in the middle of October. This is designed as a time for parents to have 5-7 minute conversations with teachers. While I like the spirit of this, I don’t particularly like the format, as I don’t think it’s particularly timely or useful. If a student is struggling in my class, I don’t want to wait until mid-October and conferences to talk about it. I also don’t think 5-7 minutes is necessarily optimal, and I’ve always been a fan of having the student present at any conference that talks about the student. While I can think of a few rare occasions when it would be helpful to meet without the student present, the vast majority of the time I think they should be there.

    I’m going to suggest to the parents in my class that they bring their student with them. I’m also going to ask my students to write something for parent/teacher conferences a few days ahead of time. This will be along the lines of the reflection/conferring ideas, but directed toward this parent/teacher/hopefully-student conversation about how Algebra is going for them. I’ll then ask them to share it not only with me, but also with their parents before conferences. That piece of writing will then provide the focus for our conference, and should provide some student voice even if the parents choose not to bring the student.

  • Writing about Mathematics
    I’ll be asking my students to write about mathematics on a fairly regular basis. They’ll have writing questions occasionally as an opener, sometimes as part of their assessments, and fairly frequently as part of our in-class activities. Again, I would love any suggestions you have in terms of prompts that would help elicit their thinking about mathematical ideas.
There are other things I’ve considered but have decided not to do, at least initially. Most notably are scribe posts, an idea I first learned of from Darren Kuropatwa, and an idea I really like. At the moment, I don’t feel like I have time to do them well, or that they would add enough value for my students. I know I could do them, but I feel like I would be doing them just so that I could say that I’m doing scribe posts. Given all the other new (and perhaps unusual) things I’m asking my student to do, I’ve decided to hold off for now on scribe posts.

That's what I've got so far. I’d love your thoughts on any of the above ideas, including suggestions for prompts, as well as any additional suggestions for me to mull over and perhaps implement sometime this year (or next).


  1. Karl,

    I don't teach math, but I was in a book club reading Content Area Writing by Steven Zemelmann, Harvey Daniels, and Nancy Steineke. It was a great resource overall, but it also contained the best example of writing in math I think I've ever seen.

    They suggested having students do a double entry journal for math problems, where their math (numbers, equations, pictures) are on one side, and their thought process was on the other. I've always thought of double entry journals in reading as a written think aloud; this is a written think aloud for math.

    It sounds like you're doing some amazing things with this course. What a great opportunity for you and your students.

  2. Ben Bleckley - Too funny, that book is currently sitting on my dresser, waiting to be read. I'll look for that example. Thanks.

  3. Karl,

    I commend you for embedding writing into the Algebra classroom. Writing is a critical skill and it helps all of us think at deeper levels. A resource I recommend to teachers I work with is the Write to Know series. It is inexpensive - $9.95/book I think and has writing prompts already developed. They have one specifically for Algebra -
    and for other content areas as well.

    Another resourse is the Write Now video prompts. These were developed by our local PBS station -- they have a variety of content areas. http://kellyscurriculumcorner.blogspot.com/2009/08/write-now-video-prompts.html

    Also Discovery Education has a large number of writing prompts ready for teachers. However, teachers can also create their own prompts.

    Happy Writing!

  4. Most of my writing assignments are shorter. A type of "focused free write". I give them 5 to 7 minutes to write about a specific topic. Examples include: compare/contrast the two different methods we saw for solving the last problem (used after students share their work), explain how the graph relates to the table relates to the equation, write everything you know about solving a quadratic.

    Sometimes I collect what they've written, not for a grade, but for me to see their thought process/level of understanding. Sometimes I then share the summarized results with the class the next day. Other times I have them share their thoughts in their small groups, then have each group share a summary to the whole class. Other times it is just for themselves.

    I don't think I did enough of this last year. Thank you for reminding me!

  5. To learn to write is to learn to think, Robert Frost said.

    I love the idea of having students write/reflect on their learning in math (or any other subject (though we ought to think about other ways of doing the same, especially when dealing with students from non-literary traditions, or oral cultures.) My math teacher at my previous school had a "Math is Real" writing program, which met moderate success. the lesson learned was that the writing had to be authentic. See Angela Maiers comments on authentic writing referenced here http://bit.ly/c6IaaG

  6. Kelly Pauling - Thanks for the links. Have you used the Algebra Write to Know book? I'm just wondering what level it's written for. Sometimes books says "Algebra" but they're really about algebraic thinking in younger grades. Which is great, but not necessarily what I'm looking for.

  7. Jackie Ballarini - Thanks for sharing that. Have you thought of throwing all those prompts into a document (or wiki) and posting them somewhere? Hint.

  8. BOC - Robert Frost? What does he know about writing? :-)

    Yeah, that's what I'm struggling with. How to make writing about math "real" as opposed to "schooly."

  9. Karl,

    The Algebra book is part of a High Set. They have an elementary and middle school sets. I am not a math teacher, but the content looked appropriate for high school, especially when compared to the the others.

  10. I appreciate the cross-curricular message you're communicating to your students and also the value you're placing on writing, particularly meta-cognitive pieces. That is how you teach students to understand the why which you expressed a personal struggle with as you're asking them to stop doing and think about what they're doing, an exercise we don't practice enough as we try to "cover" the content. I love the emphasis you're placing on knowing them too. Before class has even started, you are creating a culture that values each individual. Having said that, stop making the rest of us look bad. :)

  11. Great topic!

    I really enjoyed what Bill Lombard aka Mr. L had to say about it in his book http://www.tttpress.com/store/books_language.html.

    I agree that it is difficult to make writing in mathematics not seem contrived. Thankfully, I have a wonderful humanities team teacher who has helped me to understand and implement what I want to impart. Truly it is trying to bring out the inner math geek in each of my students.

    Sometimes I ask my students to reflect upon what they are struggling with or put it into context of a scenario of helping someone else.

    I enjoyed working through Alice in Wonderland with my students and talking about all of the mathematical ideas and concepts Carroll placed throughout the text. Since the movie was so fresh in their minds it was easy to grab their interest with it.

    I also enjoy the Exeter Problems (http://exeter.edu/academics/84_9408.aspx) and the Drexel Problem of the Week (http://mathforum.org/pow/productinfo.html). These are more open ended questions that have challenged all of my students to propose ideas to one another.

    My final suggestions are the Fermi Problems (http://en.wikipedia.org/wiki/Fermi_problem) and the Lateral Thinking Puzzle Books (search Amazon). While these may not directly be tied into the curriculum, they are challenging and cause a lot of critical thinking and fun. Even Kakuro is a ton of fun with some critical thinking and reinforcement of middle school math.

    After reading your blog for so many years, I don't believe your intention is to just get them writing about the joys of the quadratic equation but to have them enjoying the thinking and reasoning. I am with you on that, and I look forward to hearing more.

    www.brokenairplane.com (Ed Blog)

  12. I was intrigued by your post about writing in math class. It seems so elemental, yet so few of us do it. Although the ideas of personal learning reflection are a wonderful idea to get students writing (B. Russek had some great reflection ideas - http://wac.colostate.edu/journal/vol9/russek.pdf), I think that also being able to communicate math with words is important for comprehension and cognitive development. What if students were paired and had to write to one another about math...a pen pal of sorts. Maybe from one class to another? But the ability to communicate algebraic relationships into words, and then putting those words on paper (or electronically) could have a huge impact. Groups of students could have wikis or blogs to communicate about math with one another if you wanted to save a tree or two. The possibilities are endless.

  13. Thanks for posting your plans and rationale for your algebra class. I've struggled in the past with getting kids to write in math, but as I'm starting in a new school in the fall, I'm going to make the attempt again. I like some of the other comments here as well -- things like double-entry journals, etc. I have a book sitting in my new classroom on writing in math -- too bad it's not here with me as I grab a final few days of camping before going back to work...

    I plan to beg, borrow, and steal ideas wherever I find them, and one of those is the course syllabus you posted earlier this summer. I really liked the section you had on expectations, and I'd like to adapt what you've done to the middle school math classes I'll be teaching in the fall. If you don't mind...