In my last blog post we looked at Collectivist versus Individualist value systems and how they impact how and what we teach and asses. I also touched on how to incorporate culture into our math classrooms so that all of our students feel valued. In this post I’m going to explore Indigenous and Western worldviews in more detail as well as provide ways that we can incorporate more of the First Peoples Principles of Learning into our daily math teaching.
There is no ONE Western or Indigenous worldview but the following are some commonalities that are seen in most:
These values are also seen in the First Peoples Principles of Learning (FPPL). Here are the first two principles of learning; see how they connect to the chart above:
- Learning ultimately supports the well-being of the self, the family, the community, the land, the spirits, and the ancestors.
- Learning is holistic, reflexive, reflective, experiential, and relational (focused on connectedness, on reciprocal relationships, and a sense of place).
Again, there is so much to unpack here! I am going to unpack a lot of these ideas over these blogs but what I really want to highlight at this point is that very little of this has to do with content, but rather with HOW we are teaching math and what we are valuing in the teaching and learning of math. I believe that if we really want to improve the achievement gap between Aboriginal learners and non-Aboriginal learners, then we need to be having conversations about these different worldviews and value systems with our colleagues. Regularly.
Starting with “Learning ultimately supports the well-being of the self, the family, the community, the land, the spirits, and the ancestors”
I was listening to this podcast last week (it’s fantastic) and one piece of information really struck me as connected to the different value systems that this principle of learning refers to: for many First Nations, Metis and Inuit students, it is far more motivating and important to do well in school or improve their learning for the sake of their communities. Rather than “this will help you to be successful/make a good living”, instead “this will help you to serve/help your community better”. I’ve never thought about this and until I heard it, it hadn’t occurred to me that when we tell students how school benefits them, we are completely missing the mark with some of our learners as they are not individual focused. I’d also like to add that being numerate is a life skill that helps us make sense of the world around us and ensures that we are making informed decisions.
I’m going to address a few of the parts of these principle next:
Learning is holistic, reflexive, reflective, experiential, and relational (focused on connectedness, on reciprocal relationships, and a sense of place). Notice the overlap between the Collectivist value system, Indigenous worldviews and this (focus on relationships).
Here are some practical ways to incorporate these principles of learning and Indigenous worldviews:
1. Include experiential learning often. This means using manipulatives, visuals, skits, nature, problem-based and project-based learning. Learning by doing can also be a powerful way to engage more learners and reduce behaviour problems. I always feel the need to reiterate here that manipulatives are NOT remedial, nor are they only for struggling learners. Manipulatives are tools that help all students to understand WHY the procedures work as they do or what is actually going with the operations and numbers they are using (this is conceptual understanding). Sometimes, using manipulatives is significantly more difficult/challenging that just using numbers because the concept is more challenging than the procedure (see Teacher Resource Bundle on Education Now for videos and lessons)
An example of a concept that is more challenging to understand conceptually than procedurally using manipulatives:
a.) 0.3 x 0.4 à the procedure is easy as long as you remember the rules but what does this actually mean? There are a lot of interesting things to examine here: firstly, the product (answer) is smaller than either of the factors you multiply…WHY? Take a look at this using base 10 blocks. The large flat is 1 whole, so the sticks are tenths and the small cubes are hundredths:
0.3 x 0.4 means three tenths of (a group of) 4 tenths.
Here is ONE group of 0.4 :
while here is 3 tenths of 0.4 :
The product shrinks because we are NOT taking a full group of any number but rather we are taking less than HALF of a group of 0.4. See our video for more details: https://my.educatingnow.com/courses/97139/lectures/1414027
Although the manipulatives add a challenge, they are important for students to understand what is going on here and why a multiplication shrinks the numbers as this is new for most of them who have internalized a rule that ‘multiplication makes the answer bigger’.
2. Valuing and exploring multiple strategies and interpretations is another way to Indigenize your math classroom. When I first started using math teams and gave students feedback forms to fill out on the process I honestly expected them to complain about having to learn multiple representations as one of the group requirements was to explore all the different ways their group members thought about and solved the given problems. However, not one single student complained about this and in fact it was listed as one of the aspects they enjoyed most and found most helpful in the team approach. They found it useful and interesting to see all of the different ways they could solve the same problem. I found this also helped them to develop growth mindsets because they stopped viewing certain ways as better than others. These different strategies and methods occur when we give students problems and allow them the opportunity to solve them BEFORE teaching formal methods.
a.) At the beginning of exploring larger number multiplication in a grade 4 class this problem was given: “there are 4 rows of 16 carrots in the garden. How many carrots is this?”
Student 1 uses Cuisenaire Rods. She says “4 tens are 40 and 4 sixes are 24 so all together that’s 64 carrots”
Student 2 says “4 groups of 8 is 32 and another 4 groups of 8 makes 4 groups of 16 which is 32+32 = 64”:
Student 3 says, “16 + 16 + 16 + 16 = 64”
So much amazing learning happens when students share out how they are thinking about the math. It benefits the one sharing as much, if not more than, the ones listening and working towards understanding all of the ways. It also sends a message that there are many right ways of doing math and some contexts and numbers are better suited to some strategies than others.