How We Teach is the Message

Math Specialist as Learner

matrix

Leading Teachers to Impact Student Learning, Part 3: Math Specialist as Learner

This blog post is the third in a series based on a talk I have given at NCSM 2016, AMTNJ 2016, AAMT 2017, and the T3 International Conference 2017 about growing teacher leaders and the many roles that mathematics specialists play in this work. In this post, we explore the idea of Mathematics Specialist as Learner and discuss some of the ways we might reimagine leveraging technologies we are currently integrating into our practice. Refer back to Part 1 and Part 2 for previous information. See Part 4 of this blog post to continue the story.


Another important role that we play as math specialists in the pursuit of increasing student learning is that of Learner ourselves.

Learner

Coyle again from The Talent Code:

“A coach’s true skill consists not in some universally applicable wisdom that he can communicate to all, but rather in the supple ability to locate the sweet spot on the edge of each individual student’s ability, and to send the right signals to help the student reach toward the right goal, over and over” (p. 178).

Coach's true skill

Replace “student” with “teacher” and this description describes our work in helping teachers move through the landscapes of learning.

“A coach’s true skill consists not in some universally applicable wisdom that he can communicate to all, but rather in the supple ability to locate the sweet spot on the edge of each individual teacher’s ability, and to send the right signals to help the teacher reach toward the right goal, over and over” (edited, p. 178).

Coach's true skill with edits

Coyle contends that to provide this kind of targeted guidance and support, coaches have to have a “vast grid of task-specific knowledge,” what he calls the matrix.

matrix

This underlying matrix is critical for our success as math specialists—it is the skill set and knowledge and resource bank that allows us to not only identify where our teachers are in the landscape of learning for a particular element of teaching, but also allows us to know what comes next in the landscape—what are the next possible steps—and what moves, challenges, or experiences might help this teacher grow there. The more well-developed our matrix is, the more we can help our teachers grow. We grow our matrix in much the same way that teachers grow their practice—by doing the hard work of deep, deliberate practice as learners ourselves.

Let’s dig in for a few minutes here and look at an example of this sort of learning through deep practice.

First, let’s go back to Mamaw (big Clara) for a minute. A few years ago, Mamaw was 92 years old when she came to my husband with this question: “Josh, do you know what I would buy if I had one million dollars?”

Mamaw 1 million

Think about that for a minute… What WOULD a 92-year-old woman buy with one million dollars?? My husband gave a few hopeful guesses: “A fishing boat? A family house on the coast?”

No, her answer was: “A cell phone.”

So, after addressing some misconceptions that Mamaw had about the cost and upkeep of cell phones, Mamaw got a cell phone. She was thrilled to find out that they cost far less than one million dollars!

Speaking of cell phones, here’s a pie chart that roughly approximates how I currently use my cell phone.

Cell phone use

I use it to make phone calls, but I text even more often than that. I use it to look up information on the internet and to participate in social media. I’m also not too proud to say that I use my cell phone as a glorified flashlight and a watch/clock. And a camera—I perhaps overuse it as a camera with two little toddlers at home who are always getting into mischief!

Now, here’s a graph that shows how Mamaw uses her cell phone…

Mamaw cell phone use

100% phone calls.

And, really, this graph is only true for the times when she has her cell phone turned on. Mamaw turns her cell phone off when she’s not calling someone—we’re still working on clearing up some of the nuances about how cell phones work and accrue charges.

So, here’s something I want you to ponder… Is this (Mamaw using her cell phone 100% of the time for phone cells)…is this a misuse of a cell phone?

No, certainly not.

But maybe it’s an underuse of this technology.

Which brings us to another big idea that I’ve been learning about throughout my professional journey:

Leveraged technology is more effective than integrated technology.

Leveraged technology

Mamaw has integrated her cell phone into her life, but she isn’t really leveraging it. This occurs in our mathematics classrooms, too. I’d like to postulate here that using a calculator only to calculate is like using a cell phone only to make calls. It’s not a misuse of that technology, but it is, perhaps, an underuse.

Here’s my journey as a learner in this very domain.

In my first years of teaching, my calculator use in instruction looked like this: about half the time we used calculators to calculate and the other half of the time we used calculators to graph.

My early calculator use

This was (literally) all I knew how to do on these devices. I had integrated these devices into my daily instruction, but I definitely wasn’t leveraging them.

I was not misusing this technology, but I was definitely underusing it…and I didn’t know it. I didn’t know what I didn’t know.

Over the months and years since then, formal and informal math specialists helped grow my practice—other teachers, conference presenters, workshop leaders, math coaches, online leaders, etc..

One of the first new things I learned: a fellow educator introduced me to some of the statistical capabilities of our handheld graphing calculators. I didn’t yet know how to do scatterplots, regression, and analysis, but my colleagues helped me grow there.

Quadratic Regression

Months later, I didn’t yet know how to create box plots, histograms, and other data representations on our handheld calculators—my colleagues helped me grow there.

Box plot and histogram

Years later, I didn’t yet know how easy it is to collect data live with probeware and motion detectors that plug directly into our handheld calculators—my colleagues helped me grow there.

Data collection

Years later, I didn’t yet know how built-in applications and other functionality of the handheld calculators could be used for students to explore mathematics, including through dynamic geometry constructions—my colleagues helped me grow there.

Transformations 84     Parallelograms in Circle

Years later, I still didn’t yet know that our handheld graphing calculators had built-in programming functionality that could be used to introduce all students (and all teachers!) to the basics of coding and computer science. I didn’t yet know that we could write simple (and robust!) programs that perform mathematical computations and that we could also connect external devices (like the TI-Innovator) to the calculators that allowed us to program lights, sounds, and other inputs and outputs from our calculators—but my colleagues helped me grow there, too.

Slope Program

Side note: TI just released the TI-Innovator Rover—I’m so excited to continue my learning journey about leveraging technology by exploring how the Rover can drive conceptual curiosity for our students in math, science, and CS.

While my calculator use in my early years of instruction looked like this:

My early calculator use

it has grown over time, learning, deep practice, and through leadership from my colleagues to now look more like this:

My later calculator use

I don’t know that this is the ideal—it’s just reflective of where I am right now along this learning journey. However, I think it does represent a much more leveraged view of using this technology to advance student learning in all areas of mathematics—not just in computing and graphing.

Considering these two charts over time helps me see my growth in practice.

Leveraged tech early and late use

I didn’t know what I didn’t know when I was first starting out—but I’m so thankful that other math educators and leaders in my zone of influence knew what came next in my learning progression and helped me to grow there.

Remember that leveraged technology is more effective than integrated technology. We are certainly not misusing technology when we integrate it into our classrooms, but we might be underusing it.

How might we help teachers in our care grow in similar ways? How might we leverage technologies we are currently integrating?

HMW leverage technologies

How might we reimagine the breadth of impact and usefulness of powerful technologies that we already have in our classrooms? What does it take for us to learn more in these realms so that we can help our teachers grow there, too? This is the essential work we do as learners growing through deep practice.

How does perseverance play a role in the work of mathematics specialists? Read on to Part 4 in the Leading Teachers to Impact Student Learning blog series to explore this topic further.

 

References

Coyle, D. (2009). The talent code: Greatness isn’t born. It’s grown. Here’s how. New York, NY: Bantam.

Michelle Rinehart

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