I’m interested in developing student thought processes that extend beyond mathematical content into a broader and deeper analysis of problems. My approach centers on having students find systematic ways to discuss, dissect and make conclusions about not only the mathematical problems but also their personal feelings and relationships to those problems.
Traditionally, mathematics has been taught by learning to solve basic computational math problems first, and then a few application problems at the end. My strategy is to flip that lesson model and give my classroom the application problems first and let them surprise me with the strategies they bring in to solve the problems.
Here’s how I do it:
–First I bring in context related to the lives of the students. For everything that we do in math, there has to be some context for why we do it.
–Next, once they have an intuitive understanding of the context and the problem, I link to that and formalize the expression by weaving in the mathematical standards.
–Throughout the process I act as a learning facilitator, doing less “teaching” and more formalizing the students’ knowledge.
An example of how this works in practice:
When I teach the unit on statistics, it’s never just about statistics—I always wrap a real-world story around the lesson to put it in context. In one case, we looked at obesity rates among teenagers. That topic allowed me to pose questions such as: “What’s the disparity between ethnic groups in urban settings?” “Where do we see that in the statistics?” and then “Why do we bother studying this?”
Once the students have an intuitive understanding of a concept like “the more junk food you eat the more likely you are to experience a health problem,” then I can link to that understanding and bring the context of mathematics to life. I might bring in the idea of looking at a normal population distribution and then ask, “What’s the standard deviation?” This provides a compelling context for understanding what standard deviation actually means.
Approaching problems with the context first is also especially helpful for students who believe they struggle with math. Having an accessible story to grasp intuitively gives all students an equal footing for an entry point into the mathematics.
Students have an innate ability to reason through a problem. Once they get to a stopping point where they don’t know how to do something mathematically, that’s when the teacher can step in as a learning facilitator to show how this would be solved through higher level math or through the next steps what the student has already done.
I think that rather than focusing on “teaching practices” we should also be focused on “learning practices.” I am focused on finding ways that allow students to engage more fully because they are the ones doing the learning.
What I did well…
In sharing this practice, what I did well was provide access for teachers to engage in the practice even if they had high-anxiety about engaging with “math content.” Out of the group, only 1 teacher is a high school math teacher; yet, each of the teachers was able to utilize their own understanding of the learning task to create some answer to each section of the learning task.
What I would do more of, better, or differently…
One thing I would have done differently is to be much more clear about where certain elements of the learning task lay the foundation for later content development within the larger course. For example, how the development of the XY-table leads to graphing could have been enriched by explaining that the graph would have been of a Rational Function. Rational Functions are a topic of study in the larger course, and this task provides an example of what a rational function might look like in context.
In what ways do I still want to learn and grow in this practice…
I want to still grow in my practice by learning how to build classroom structures that let students select their own topics of study. How do I let students utilize their own understanding of context while also developing their use of strong academic vocabulary and writing? If I had to narrow down my desire into a single phrase, I would want to see how this practice is paired with “mathematical/academic writing support.”
About David Rennie
David Rennie is a high school math teaching in the greater Los Angeles area. David’s passion is working with pre-service, new, and nearly new teach...