This is a response to this opinion from @RobynUrback.
@RobynUrback, I agree with your assertion that our kids deserve better when it comes to their education in mathematics; however, you have misdiagnosed the problem.
You are right to say that kids haven’t changed, but you have not addressed the fact that the world for which we are preparing them has changed (and will continue to change), nor have you addressed the fact that what we know about how students learn has also changed.
You point to the change in the math curriculum as the problem that needs to be fixed, but you have not addressed the problems in its implementation. The math curriculum has changed, but teacher preparation has not. The math curriculum has changed but the metrics that we use to monitor student progress has not. Continue reading
During my grade 10 unit on exponents, right around the time a frustrated student asked, when am I ever going to use this!?, I promised to show my student how exponents can help them make money without doing anything. They were hooked!
This is the magic of compound interest! Money saved (or invested) with compound interest grows exponentially. Likewise, money borrowed with compound interest results in debt that grows exponentially. If this is unfamiliar to you or your students, this primer on compound interest offers a great introduction.
In this open-ended task, students explored compound interest. Specifically, students selected a principal amount for a loan (or investment) and then did a bit of research to find a suitable interest rate. They also selected a reasonable term for the loan (or investment). Students then used the compound interest formula to determine how their debt (or investment) would grow if the interest was compounded annually, monthly, weekly or daily.
Mathematically, this task allowed students to practice calculations with exponents. Students also got to practice communicating mathematical information, and using graphs, equations and tables to convey information.
In terms of financial literacy, students explored the frequency of compounding, which is a small thing (often listed in the finest of fine print the terms of a loan, investment or bank account) that can make a big difference.
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.