Language, Values, Ways of Knowing and Connections to Culture: Keys to supporting Aboriginal students

in mathematics learningA workshop based on Transforming mathematics education for Mi’kmaw students

through MawikinutimatimkLisa Lunney Borden

DreamCatching 2009May 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 VerbificationUsing 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 EquationsWorking 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?

14

12

10

8

6

4

2

5 10

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 20th? The nth term?Explore adding t1+ t2, t2+ t3, t3+ t4, and so on. What sequence of numbers is generated? What is true for tn+ tn+1? How can you use your models to show this?What happens if you add t1+ t3, t2+ t4, 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 lineDraw 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.

Contact Information

Lisa Lunney BordenEmail: lborden@stfx.ca Website: http://people.stfx.ca/lborden/