Conceptualizing the Essentials of Math Instruction

The following graphic captures the essence of what matters about teaching and learning mathematics:

Though the concepts here are listed, there is not a hierarchy in terms of priority. The components are interwoven and the approach is cyclical.

Establishing a Mathematically Rich and Safe Environment

Interacting and collaborating during learning;
Emphasizing mathematics as a human endeavour;
Fostering relationships;
Providing an academically safe environment to take risks and make mistakes; and
Sharing power, voice, and choice

Honouring Indigenous Ways of Knowing

“Mathematics and culture come to be seen as integral components of one another.”¹ (Barta et al., 2014, p.4)

Honouring the four directions/teachings of the Medicine Wheel;
Creating care and connectedness – relationship within one’s self, with others, and with the natural world;
Developing multiple pathways to learn and show what you know;
Emphasizing the importance of story and place; and
Sharing power, voice, and choice

Practising Holistic Assessment

Triangulating data: conversations, observations, products;
Honouring the learner (emotional, spiritually, academically and physically); and
Using assessment for, as, and of learning via a variety of strategies.

Responding with Effective Instructional Practices

Creating experiences for students to engage with number relationships;
Sharing power, voice, and choice;
Making sense through dialogue and interactive experiences; and
Teaching responsively (scaffold).

The Math teaching strategies in this Mathematics resource provide teachers with many options to weave ideas using indigenous ways of knowing/learning into their math lessons. (Myrna Turner, Cultural Coordinator, Muskoday First Nation Community School)

Developing Number Sense

“The concept of life in numbers describes a relationship between the action, personality, and animation of numbers with the people using them in a given situation.”¹ (Barta et al., 2014, p.3)

Relationships exist between and within numbers;
Multiple instructional approaches are used to build student understanding of number relationships; and
Comparing, composing and decomposing, estimating, visualizing, and representing are used in connection with each other and are vital for developing number sense

Integrating Relevant Research

Bibliography
Resources to Share

“Over the last 15 years, researchers have shown that learning is not just about accumulating knowledge; it is about the formation of an identity … not a stable construct … but as a set of ideas, beliefs, and behaviours that may be performed in specific domains, such as the learning of mathematics”² (Boaler & Selling, 2017, p. 82).

Indigenous Ways of Knowing Connection to Essentials of Math Instruction

Questions for reflection

How are these concepts interwoven?

How will you simultaneously develop these big ideas into your practice?

¹Barta, J., Eglash, R., & Barkley, C. (2014). Introduction. In J. Barta, R. Eglash & C. Barkley (Eds.), Math is a verb: Activities and lessons from cultures around the world (p 3). Reston, VA: National Council of a Teachers of Mathematics.

²Boaler, J., & Selling, S. (2017). Psychological imprisonment or intellectual freedom? A longitudinal study of contrasting school mathematics approaches and their impact on adults’ lives. Journal for Research in Mathematics Education, 48(1), 78-105.