equity through pedagogy - part 5: pedagogical considerations for Teaching mathematics

Welcome back to Flipping the Focus.

Leading up to the Mid-Atlantic Conference for Professional Learning, March 13-15, in Atlantic City, this marks the fifth (and final) post in this series devoted to pedagogical practices and frameworks that educators can leverage in their collaborative efforts to respectfully and equitably honour student voice.

1. Introduction
Envision learning environments where students and their teachers are engaged to interact in profound and meaningful ways--ways that...

MAC PL 2019, March 13-15, Atlantic City

• help students to seeing “...themselves as powerful mathematics [learners]” (Anthony & Walshaw, 2009a); and
  
• grow teachers’ and leaders’ confidence that a better prescription for student success in mathematics is one that’s grounded in occasioning students’ thinking.
  

In this post, the characteristics of The Pedagogical System for Teaching Mathematics (SIM K-12, 2017) are explained and questions are asked to engage you, your colleagues and students in thinking about how this system might better frame the teaching and learning that goes on in your class and school each and every day.

I’d also like to draw your attention to the following: You’ll not only find the framework described in this post as being effective in supporting mathematics teaching and learning, but also as having the potential to influence teaching and learning in other subject areas and aspects of school life.

As you continue with the post, consider framing your thinking against these, sample goals:

• (Teacher Focus) To deepen your understanding of practices that engage students with differences in backgrounds, learning strengths, needs and interests.
• (Leadership Focus) To inform your next best moves to supporting the growth of individual and collective teacher learning and practice.

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"Having explored this framework--alongside many educators, students occasioning thinking, and complexed with other pedagogies--has
​been transformational for my own teaching and student
learning, as well as that of my colleagues."

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2. Background
The Pedagogical System is a framework that provokes us to consider how teaching and learning needs to be...less about telling...less about prescriptive moves and responses. Really, it calls us to shift our mindset about teaching, leading, and learning to one that gives more value to student thinking. This philosophy, grown out of mathematical, educational research, is mirrored through several references and resources. Some suggested reading and resources are included in the references section to this post. 

This stance is one that depends on each and every one of us. Students, teachers and leaders all have a role to play in improving the conditions for student engagement, achievement and well-being.

Consolidated and adapted from the work of Anthony & Walshaw (2009a), System Implementation & Monitoring-K to 12 in Ontario (2017) has produced summary graphics and tools to help inform and guide educators as they inquire towards improving teaching and student learning.

The system (or framework) consists of four, interrelated components. This is so important to recognize and identify: none of the parts work in isolation of the others. These components include the following:

1-Worthwhile Mathematical Tasks
2-Tools & Representations
3-A Non-Threatening Classroom Environment
4-Classroom Discourse

Let’s consider descriptions for each of these components in the form of reflective questions.

• Worthwhile Mathematical Tasks
  • Do the tasks students engage in support how mathematics is viewed; how it can be understood through thinking and reasoning; and how it can be used?
• Tools & Representations
  • How are students making their thinking visible? Are tools being used to organize thinking? Are multiple representations used, and are they connected for building a deepened understanding of mathematical concepts?
• A Non-Threatening Classroom Environment
  • Does the classroom community encourage each of its members to think and reason, communicate ideas, and receive, provide, and take action on feedback?
• Classroom Discourse
  • Do students value mistakes? Does the classroom community look forward to and honor the explanations of all students? What are the characteristics of productive, accountable discourse?​

Already you can get a sense of some criteria that you could use for monitoring inquiries into building communities of learners and a coherent school culture, where students see themselves and others as empowered learners of mathematics.

Let’s take a moment to look more closely at the first component.

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What defines a task as being rich or worthwhile?

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3. Worthwhile Mathematical Tasks
Let's start with considering problem-based teaching in mathematics.

The premise to problem-based teaching in mathematics is that students are able to meaningfully construct their knowledge by engaging in a variety of problem solving strategies. Coincident with developing their understanding, students also build procedural fluency since many of the concepts provide opportunities for students to work with numbers and expressions.

Ultimately, basing one’s approach to teaching and learning, in this way, moves us away from seeing mathematics as being about the right answer and/or getting to an answer TO seeing mathematics as valuable and connected to the real world.

According to Anthony & Walshaw (2009a), some of the characteristics of problems and tasks that are rich (or worthwhile) include the following:

They tend to...

• Have a focus on original thinking;
• Provide opportunities for productive struggle;
• Be designed and presented at an appropriate level
  • E.g., Low-floor for entry and a high ceiling for extending (Boaler, 2016);
• Be open-ended;
• Include contextually-based problems that invite students to make sense of mathematics; and
• Provide opportunities for students to develop procedural fluency in meaningful ways.​

4. Leading Through The Pedagogical System
Previously mentioned, you might have made some connections to criteria that you could use for monitoring inquiries into building communities of learners and a coherent school culture.

Linked to a tab called "Connections" (here), you’ll find a leadership-related tool with a variety of criteria for effective mathematics teaching. All of them are related to The Pedagogical System and are connected through formative assessment--both assessment FOR and AS learning (Anthony & Walshaw, 2009b).

Whether you’re conducting classroom walk-throughs, facilitating collaborative team learning, or observing and providing feedback to lessons, you might find these criteria essential to guiding discussions around effective practice and having discussions with students about their learning.

In your conversations and inquiries, consider how these criteria could allow you to better uncover and understand the hidden skills and talents of the educators in your school and your students.

5. Final Remarks
As you reflect, how are you seeking to co-create conditions that can give life to equity in the teaching and learning you do with students and your colleagues each and every day? 

In closing, I can't help but to think of the conversations that can be inspired when we take collective action to improving student learning. As this blog is a means for readers to network and gradually change the context for how they teach and learn, we all benefit by drawing nearer to the perspectives shared here and shared beyond with our professional learning networks.
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I am more than happy to collaborate with you and make our learning visible, here, in this blog and across Flipping the Focus' social media platforms, as well as your own. If at any time, you have questions or comments, please feel free to reach out to me at Flipping the Focus. 

Sincerely,

Chris Stewart
Education Leader, Flipping the Focus

CONTACT

BOOK CHRIS

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6. References
Anthony, G., & Walshaw, M. (2009a). Characteristics of Effective Teaching of Mathematics: A View from the West. Journal of Mathematics Education, 2(2), 147-164.

Anthony, G. and Walshaw, M. (2009b). Effective Pedagogy in Mathematics. http://www.iaoed.org/downloads/EdPractices_19.pdf

Anthony, G. and Walshaw, M. (2009b). Characteristics of Effective Teaching of Mathematics: A View from the West. http://www.educationforatoz.org/images/_9734_12_Glenda_Anthony.pdf

Boaler, J. (2016). Mathematical Mindsets: Unleashing Students Potential Through Creative Math, Inspiring Messages, and Innovative Teaching. San Francisco, CA: Jossey-Bass & Pfeiffer Imprints.

System Implementation & Monitoring K - 12. (2017, February 23). The Pedagogical System with Reflective Questions. Retrieved from https://sim.thelearningexchange.ca/tag/the-pedagogical-system/
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7. Suggested Reading
EduGAINS. (n.d.). Guides to Effective Instruction. Retrieved from http://www.edugains.ca/newsite/math/guides_effective_instruction.html

EduGAINS. (n.d.). Targeted Implementation and Planning Supports for Mathematics (TIPS4M). Retrieved from http://www.edugains.ca/newsite/math/tips.html

Ontario Ministry of Education. (2018). Focusing on the Fundamentals of Math: A Teacher's Guide. Retrieved from https://math.thelearningexchange.ca/

​Principles to Actions: Ensuring Mathematical Success for All. (2014). Reston, VA: NCTM, National Council of Teachers of Mathematics.