Language, Values, Ways of Knowing and Connections to Culture: Keys to supporting Aboriginal students in mathematics learning A workshop based on Transforming mathematics education for Mi’kmaw students through Mawikinutimatimk Lisa Lunney Borden DreamCatching 2009 May 3-6, 2009 Winnipeg, Manitoba

Situating the research Doctoral study looking at areas of concern that need to be addressed for Mi’kmaw students in mathematics Through mawikinutimatimk (coming together to learn together) four key areas of concern emerged: – Language – Values – Ways of Knowing – Cultural connections

Meaningful personal connections to mathematics Learning from Language A question of values Ways of learning What’s the word for…? Is there a word for…? Nominalisation and Verbification Using more Mi’kmaw Spatial reasoning Estimation and Fairness Enough is for survival, Number is for play Context and Connectedness Grounded in Necessity and Experience Challenges and Complexities of Ethnomathematics What is Mi’kmaw Mathematics? Show Me Your Math! Hands-On The importance of cultural connections Apprenticeship and Mastery Visual-Spatial Learning

Transforming our approach to Linear Equations Working with a partner, discuss what a typical class might look like for the concept of linear equations. Consider the example here: What kinds of language might teachers emphasize in teaching this concept? What will students need to know to be able to find the equation of this line? What connections might be important? What models might be used? The run The rise Going Over Going up How is the graph changing? How do I get from one point to the next? Where does the line seem to start? Every time I go over 3 I go up 2 to get back on the line. It starts at 4. The slope is the ratio of the rise to the run. The y- intercept is the point where x = 0.

Using models to develop equations Continue the pattern and find a general rule to describe the terms in the pattern: 3, 5, 7, 9, 11,… How can we take an essentially numerical task and make it more concrete? What models could be used to transform this into a hands-on task? How might this help students to discover the general rule?

Building Equations with our hands and our minds Continue the pattern Sequences and series are an important part of the high school curriculum. On this page we see the sequence of numbers known as the triangular numbers. Using the linking cubes at your table build at least the first six terms of this sequence with your table mates. Consider each of the following questions: What is the tenth term in this sequence? The 20 th ? The n th term? Explore adding t 1 + t 2, t 2 + t 3, t 3 + t 4, and so on. What sequence of numbers is generated? What is true for t n + t n+1 ? How can you use your models to show this? What happens if you add t 1 + t 3, t 2 + t 4, and so on. Can you make a general prediction about this sequence as well? How can you use your models to show this sequence? An extension would be to explore the graphs of these various sequences.

A Visual Approach to trig Identities Given that the diagram below is constructed on the unit circle, what can you discover about the various trig ratios? Talk with a partner to investigate this unit circle. What statements can you make about the various trig ratios? Can you give an expression for each side of each triangle in terms of the given angle? What happens when you “think like Pythagorus”?

Creating a radian number line Draw a circle of any size on your paper. Mark the center of the circle and draw in the radius. Cut a piece of paper that is equal to the circumference of the circle. Compare your cut piece to the radius of the circle. How many radii long is the cut piece? Why is this? How might we use this to understand radians? Discuss with a partner.

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