My Mathematical Mind Shift

Today's post is brought to you by Andrea Reichenberger.

I have always hated math.  Yep.  I said it.  I hated it with a passion. The difference is that now, I understand why.  When I was a student, there was never any discussion about math or the thinking behind it. There was never any modeling.  (Unless you count watching the teacher do 20-30 math problems on the chalkboard, but we know THAT isn't modeling.)  There was one way to do math and if I didn't understand it, my teacher, with pity in his eyes, simply shook his head at me and moved on to the next unit.  That same teacher also spent way too much class time teaching us how to figure out bowling scores. I still wonder WHERE that was in the curriculum. I hated it as (at that time) I had never bowled, so I had no connection, no prior knowledge and I was already failing his class. Strikes, spares, and adding numbers from one or two frames in the future wasn't exactly engaging or motivating to me. What I realize now is that my teacher didn't have a foundational understanding of the critical elements of instruction.

As I reflect on this past year, I know the math coach, whom I share an office with, is smiling.  We've learned a lot from our conversations and our professional development planning.  We quickly discovered that those discussions about math are never actually “just about math.”  They are about instructional practices in general and necessary in every discipline.  We now know that what is good for literacy instruction is good for math instruction.  Most of our students who struggle with math are also struggling readers—and we have the data to prove it.  As a result, the message needs to be delivered—loudly, clearly, and quickly: if you read, write, speak, and listen in your discipline (which we certainly hope you do) then you are using literacy to deliver your content.  Yes, even in math.  There is a “Mathematical Practices” poster hanging in our office that serves as a daily reminder.

Make sense of problems and persevere in solving them.

My favorite word here is “persevere” as it reminds me of conversations we have about reading stamina and endurance as well as about how we are working to shift our instruction to ensure that the students are doing the majority of the thinking and talking in the classroom. Problem solving is necessary in every discipline and providing a variety of scaffolds is the key.

Reason abstractly and quantitatively.

In my mind, this is the same as CCSS reading standard one. Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Construct viable arguments and critique the reasoning of others.

This is a beautiful combination of some of my favorite literacy standards.  Write arguments to support claims…using valid reasoning and relevant and sufficient evidence (W.1). Initiate and participate effectively in a range of collaborative discussions…building on others' ideas and expressing their own clearly and persuasively. Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented (SL. 1).

Model with mathematics.

Modeling with (insert any discipline here) is also a necessary instructional practice.  I think about how we should model a think aloud as we attack complex text, use background knowledge to make meaning, a well as the strategies we use to attack vocabulary.  We need to model our thinking as the expert in the subject area in which we teach.

Use appropriate tools strategically.

I could take a lot of liberties with this one.   How does one narrow down the tools of literacy? But I believe we can easily make the comparison to the language standards in which students are required to demonstrate a command of the conventions of standard English including grammar, spelling, punctuation, etc., or the use of reference materials (L.1,2,4) as well at assessing the credibility of print and media sources (W.8).

Attend to precision.

Developing and strengthening writing as needed by planning, revising, editing, rewriting...(W.5).Enough said.

Look for and make use of structure.

In my mind, this connects to text structure. Students who are aware of different text structures, signals, and key words have better comprehension. In Effective Teaching Strategies that Accommodate Diverse Learners, Kame’enui and Carnine state, “In textbooks and other expository texts, organizational features and structures help students understand, learn from, and remember what they read.  Research has shown that understanding how text is organized helps readers construct meaning” (1998).

Look for and express regularity in repeated reasoning.

One of the most important tools of literacy in any discourse is academic language. Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening (L.6). That is just as important in math as it is in every other subject area.

Those of us who know what good instruction looks like in the classroom and spend a lot of time with the standards—not to mention a lot of time collaborating with fellow coaches, can easily make these connections.  It’s been an entire year of “Aha Moments” for us as we work together to help our teachers help themselves improve their instruction for the benefit of our students’ learning.  If I could take my high school math class again with a teacher who blended best practices with their content, I probably would have been more successful.  I also don’t think I would have had to learn how to figure out bowling scores since the bowling alley now does it for me!