I have always used financial math as a real-life context to engage my students in learning concepts such as place value, proportional reasoning and exponential growth, so I am thrilled that the new BC math curriculum includes a component of financial literacy throughout the program.
Below, I have listed some of the financial literacy learning outcomes for middle- and high-school grades, and I have linked to posts on my blog with relevant activities and resources. This is a work-in-progress, so be sure to come back to this site ever so often to see what’s been added.
My grade 6 unit on decimals and fractions was always a favourite for me and my students. My students loved it because they finally got to have a class party (is it just my students, or do your students always ask to have a class party?). I loved it because the students did all the work to plan the party and got lots of practice with decimals and fractions while doing it.
In my experience, I have found that teens love (1) their phone and (2) a heated debate. When my grade 8 students were studying linear relationships, I combined those two interests into a activity in which students critically evaluated advertisements for service plans offering free (or discounted) cell phones.
Do teens know the difference between saving up for a major purchase and borrowing for it? Do they know when it makes sense to borrow and when it’s more prudent to save?
I had my grade 8 students explore those questions during a unit on percents. In their favourite homework assignment of all time, I asked students to think of a major purchase they wanted to make before graduation (approximately four years away). Their choices were interesting an varied: concert tickets, iPhones, travel, clothes… Continue reading
Last week, I sat down to mark a quiz on radicals and exponents that I had given my grade 10 class. I knew that students had found the quiz difficult (there were gasps and shrugs from each student at some point during the quiz), but I was still surprised by the results. Problems that required skills that I had demonstrated accurately in class were answered incorrectly, and students made errors that suggested misconceptions. What was most discouraging was that both my students and I knew that their performance on the quiz did not reflect the significant amount of work they had done to prepare.
As I mulled over the results, and contemplated what to do next, two thoughts emerged:
- Students saw questions that looked a bit different from what they had seen in their homework and they panicked. As soon as the sinking feeling of I don’t know how to do this crept in, they weren’t able to employ the skills that they had used successfully several times before.
- Students had learned how to use specific skills to solve certain types of problems, but didn’t know how those skills could be applied together. For example, they knew how to convert a fractional exponent to a radical, and they knew how to rewrite a number with a negative exponent as a fraction with a positive exponent, but they didn’t know how to deal with an exponent that was a negative fraction.
With these two observations, I was reminded of my greatest weakness as a math teacher: as someone who is predisposed to think quantitatively, logically and to make connections between math skills, I often forget that many (possibly even most) students have a different cognitive disposition and need to learn how to think mathematically. In other words, the strategies that have largely contributed to my success in math are strategies that are intuitive to me. Being aware of my (subconscious) intuition, and making my strategies explicit/visible, is essential in helping students to develop those same strategies.
So, rather than asking my students to do corrections on their quiz to see if they can improve their score (which is essentially asking them to do the same thing but expecting a different result), I have attempted to map out what the skills and content look like in my brain (radicals-and-exponents-concept-map). My hope is that by making my thinking more visible, students will be able to articulate and deepen their own thinking in order to enhance their understanding.
Over the weekend, I had the privilege of facilitating a session with IB Primary Years Program (PYP) teachers about inquiry in math class. Because we all work in British Columbia, we share the opportunities (and challenges) of delivering the new BC curriculum within the IB framework. As I prepared the session, the image of a double-headed arrow kept coming to mind.
I have just finished a series of patterns investigations with my math 10 class. In this specific series, students explored the connections between quadratic equations (in both vertex and factored form) in order to connections between the equation and the features of the graph (like the position of the vertex, and intercepts).
These kinds of activities are a regular feature of math in the IB Middle Years Program (MYP) in which students are required to consider a series of specific situations to identify a pattern, describe it as a general rule, verify that their rule works and then justify why it works.
I’ve had a love-hate relationship with this kind of task since I started teaching MYP math almost 10 years ago.
I hate investigations because…
- Students find it difficult to approach novel situations.
- I find it difficult to prepare students for novel situations.
However, I love investigations because…
- Investigating is what mathematicians do. While math students typically spend more time doing tests (i.e. using specific examples to demonstrate that they understand a general rule that someone else discovered), mathematicians are on the frontier of searching for new pattern, generalization and rules. By engaging students in this process (even if they are discovering patterns that are new to them, but well-known to others), they are engaging in the authentic work of mathematics.
- Investigations support inquiry skills. In looking at a variety of specific situations in order to find trends, patterns and generalization, students develop strategies of problem-solving, visualization, hypothesizing and generalizing. These skills support similar processes in other disciplines, like finding trends in a data set, identifying themes in a work of literature or cause-and-effect relationships in history.
- Investigations foster independence. By looking for patterns and general rules, students develop the confidence to use what they know as the basis to discover new things, making them less reliant on the teacher as the source of knowledge.
- Investigations cultivate persistence. Not all problem-solving strategies will work in every situation. The more experience students have investigating patterns, the more comfortable they will be with trying an approach and switching to a different strategy when necessary. Rather than seeing this as a set-back, they will accept it as a normal part of the process.
As you can see, the benefits of investigations outweigh the challenges. Promoting a classroom culture in which students are willing to take a risk on an unfamiliar problem and persist with challenging work requires on-going effort, but I believe the benefits are on-going as well.