Mathematics Teaching and Learning Target

Last weekend, my kids and I made bows and arrows out of PVC pipe and dowels. We found some plans online and made a quick trip to the hardware store. After an hour or so of construction, we were ready to shoot.

Most of the first shots didn't make it too far. My youngest son Aaron struggled to get the arrow on the string. When he finally was ready to pull the string back and aim, the arrow fell off the string. Even after the first few releases, the arrow was only making a short flight to a few feet from where we stood. He eventually got it, and we started to see how far we could shoot the arrows. After about 10 minutes, everyone was done and we headed inside for lunch. ​

The bow hasn't been out since, and I think I know why. "We should make a target," Aaron said. I agreed. This activity would certainly be more fun and more rewarding with a target. And we could instantly tell if we were getting better at shooting.

In his book, Unmistakable Impact, Jim Knight suggests the use of a "Target," a simple, one-page document that clearly states a school's goals for instructional improvement. Most improvement plans fail, Knight suggests, because they are too long, too complex, and too unrelated to instruction. This reminds me of arrows never flying, falling to the ground after a short flight, or soaring over the fence in wild flight.

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In a typical week, a school leader will receive dozens of emails and several catalogues of teaching practices, and over a year will be presented with literally thousands of options for instructional improvement.
​Jim Knight, Unmistakable Impact

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I have found that at times my own work with teachers has lacked focus. There hasn't always been a clear target in view. So I'd like to offer a few questions that I am pondering related to our work. What would a precise Target look like for mathematics teaching and learning? What elements for teachers and students would it include? How might it be comprehensive yet concise?

There have certainly been efforts to identify best practices in teaching. I've started to pull together a few source lists to start with:

1. Setting up Positive Norms in Math Class. Jo Boaler. (PDF)
2. CCSSM Standards for Mathematical Practice
3. SMP Look-fors (ems&tl Project, 2012) (PDF)
4. NCTM Principles to Actions (PDF)
5. Mathematics, the Common Core, and Language: Recommendations for Mathematics Instruction for ELs Aligned with the Common Core. Judit Moschkovich, University of California, Santa Cruz. (PDF)

If you're familiar with these resources, I think you'll agree that they are top notch. Each certainly deserves time and attention on its own. However, focusing on a few key elements from these and finding ways to connect them might make for an all-star target list.

Knight's approach to improving instruction is built around four critical instructional areas: 1) community building, 2) planning content, 3) delivering instruction, and 4) developing and using formative assessments. When everyone involved in the educational community can agree on a concise target, efforts to improve teaching and learning take on new focus. Pulling from my above source lists, I'd like to suggest the following target for teachers (T) and students (S).

Community Building
(T) Develops socially, emotionally, and academically safe environments for mathematics teaching and learning
(T) Works collaboratively with colleagues to plan instruction, solve common challenges, and provide mutual support as they take collective responsibility for student learning
(S) Understand that everyone can learn math to the highest levels
(S) Construct viable arguments and critique the reasoning of others

Content Planning
​(T) Establishes clear mathematics goals to focus learning, situates goals within learning progressions, and uses the goals to guide instructional decisions
(T) Recognizes and supports students to engage with the complexity of language in math classrooms
(S) Understand the mathematical purpose of a lesson and how the activities support their learning
(S) Connect their current work with the mathematics studied previously

Instruction
(T) Implements tasks that promote reasoning and problem solving
(T) Allocates substantial instructional time for students to use, discuss, and make connections among representations
(T) Facilitates meaningful mathematical discourse, poses purposeful questions, builds procedural fluency from conceptual understanding, and supports productive struggle in learning mathematics
(S) Make sense of problems and persevere in solving them 
(S) Ask their own math questions
(S) Choose and apply representations, manipulatives, and other models to solve problems

Assessment for Learning
(T) Elicits and uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning
(T) Provides students with descriptive, accurate, and timely feedback on assessments, including strengths, weaknesses, and next steps for progress toward the learning targets
(S) Know how their personal learning is progressing
(S) Reflect on mistakes and misconceptions to improve their mathematical understanding

Building this list was not easy, but I think that's part of the exercise. It takes effort to look discerningly at teaching and learning. I invite any comments or suggestions you may have, perhaps in response to a few questions:
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1. Are there teacher or student actions that are completely missing that should be added?
2. Is there a way to make individual actions simpler and more precise? There are currently 18 actions on this Target, and I think that's close to the maximum.
3. Is there redundancy in teacher or student actions? If so, let's pare the list down and reduce distraction.