You Want Me To Do What In My Math Class?

 

Personal photo taken in my classroom, 2018.

 

Several years ago, in an effort to increase engagement in my classroom, I set about getting my students out of their seats and talking to each other about the mathematics that they were doing. I thought that if I could just get them talking to each other about the lesson, they would have opportunities to engage with the mathematics in new and different ways. As you can see in the photo above, students are engaged with the work, and with each other. Much of the work I did on my classroom that first year was based on Peter Liljedahl's work on Thinking Classrooms. It was good work, and very successful in the classroom. 

Fast forward to the 2020-2021 school year. Some of my students are participating in virtual school, while others are coming to school on a rotating, color-coded schedule. Students rotate between green and gold days, only meeting with half of their class, maintaining a six foot distance, and always masked.  Obviously, this set-up makes it difficult to work in groups, or to have meaningful conversations about the mathematics. Who (besides the math teacher) wants to yell across a room about math?  

This begs the question, "How do we keep our students talking about the mathematics?"

If I am being completely honest, I have worried that some of the students' mathematical conversations during this unique time in education are not quite what they should be. I imagine (fearfully) that some are like an old comedy routine.  

 

But I digress. The issue of keeping the students talking about mathematics is actually a nuanced question. Do I want them to be able to regurgitate the procedure for solving a problem, or do I want them to be able to explain to me that they actually understand what is going on in the mathematics? As I was reading chapter three of the text by Turner & Hicks (2017), I came across this statement: "If we want our students to produce a blog post, we need to engage them in the practices bloggers use. Our work here, then, is to shift from declarative to procedural knowledge" (p. 51). This sounded like what I wanted. I wanted the students to be able to do the next-level thinking that used to come out of collaborative work.

When I got to chapter seven, Turner & Hicks (2017) quoted a previous work where they declared,         

Setting a minimum number of slides, images, transitions, links, or other digital elements in  student projects does little to improve digital literacy. In much the same way that some of the most reductive writing pedagogy has created patterns (five paragraphs of five sentences each, for example), we now see similar trends happening with slide shows, websites, digital stories, and other types of digital writing projects. Rather than focusing on content - and developing an appropriate message - the assignments focus on the most basic elements of form: the things that can be counted. (pp. 128-129)

This is what I am looking for. Turner & Hicks (2017) are describing students writing a blog to learn to create digital arguments (pp. 51-54), but the outcomes are the same that I am looking for in mathematics classes. I want them to understand the why behind the procedure. 

It was about this time in the reading process that I gave myself a minute to think things over. "Wait. Am I actually thinking about having my math classes write a blog? Is that measurable? Is it pedagogically sound practice? Shouldn't they be doing the math instead of writing about it? I mean, when they were doing it before, at least they were engaged with each other, pulling good ideas from not-so-good ideas, and synthesizing their work collaboratively." I ended my self-help talk with a decision to keep reading the text and to do research on writing in math classes. 

According to Baxter (2002,  as cited in Bixby, 2018) "Regarding direct benefits to students, research has shown that math writing tasks help students gain a better understanding of the mathematical concepts" (p. 143).  when I had my students collaborating on assignments, it was to bring out the higher order thinking. Perhaps writing would have the same effect. Bixby (2018) states, 

[It] also presents an opportunity for the student to go back and examine his or her mathematical thinking - a metacognitive activity. Without the writing, the student would find remembering how she was thinking to be difficult, which would make revisiting that thinking difficult. (p. 144)

This is absolutely what I want for my students. Maybe a blog is the way to go? Students can articulate mathematical issues to a broad readership. The act of formatting the blog, and keeping it current will take the students in new and different directions as they search for resources to embed, and media with which to work.   

In the National Council of Teachers of Mathematics (NCTM) Standards for Mathematical Practice (n.d.), standard three states,                                   

            

Mathematically proficient students understand and use stated assumptions, definitions, and  previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They justify their conclusions, communicate them to others, and respond to the arguments of others. (pp. 6-7)

Turner & Hicks (2017) claim similarly, "We must have students use clear reasoning and effective evidence to support their claims" (p. 58). 

It seems that through the text and associated readings, as well as standards that are in use daily in my classroom, I have convinced myself that the desired outcomes of students writing a blog are the same as those of collaborative work in mathematics class. Each is a way to communicate about the mathematics with others. Each format follows a logical progression through the work. And each requires deep thought to be able to articulate your ideas clearly to others.

  

 References

Bixby, M. (2018). Effective and efficient use of math writing tasks. Mathematics Teacher. Retrieved September 20, 2020, from https://www.nctm.org/Publications/Mathematics-Teacher/2018/Vol112/Issue2/Effective-and-Efficient-Use-of-Math-Writing-Tasks/

   Green and gold student attendance days. (2020, September 14). Mountain Brook High School. Retrieved, September 22, 2020 from https://www.mtnbrook.k12.al.us/site/default.aspx?PageType=3&DomainID=13&ModuleInstanceID=6880&ViewID=6446EE88-D30C-497E-9316-3F8874B3E108&RenderLoc=0&FlexDataID=30819&PageID=19

 Liljedahl, P. (2015). Building thinking classrooms: Conditions for problem solving. Retrieved from:                 http://peterliljedahl.com/wp-content/uploads/Building-Thinking-Classrooms-Feb-14-20151.pdf

         Maths Guide. (2018, May 14). 7 times 13 is 28 [video]. Youtube. 

                    https://youtu.be/oN2_NarcM8c

   National Council of Teachers of Mathematics. (2010). Common core state standards for mathematics.

            https://www.nctm.org/ccssm/ 

   Turner, K.H., & Hicks, T. (2017). Argument in the real world: Teaching adolescents to read and write                 digital texts. Heinemann.