I’ve been reading a lot about formative assessment lately and one recurring theme that stands out to me is the importance of wrong answers. From multiple choice questions to class discussions, finding students’ misconceptions, incomplete understandings, over-simplifications and over-generalizations is so much more valuable than seeing how many questions students can answer correctly.
I love spreadsheets! I love spreadsheets so much that my colleagues gave me an “I love spreadsheets” t-shirt. I use spreadsheets for typical spreadsheet tasks, like managing a budget and analyzing data, but I also use spreadsheets for other stuff too, like taking notes for research projects.
I think learning to use spreadsheets should be a standard high school learning outcome. It doesn’t matter to me whether students learn to use spreadsheets in a science class, math class, information technology class or humanities class, as long as they learn to use them. Here’s why I think it’s so important:
- Spreadsheets let you do a lot of computations really quickly. When students use spreadsheets to solve problems, they can focus on other parts of the problem-solving process, like posing interesting questions and selecting appropriate mathematical techniques to solve them. Conrad Wolfram explains this better than I could in this TED Talk. Here’s an example of how I have used spreadsheets to speed-up the computation in order to focus on deeper problem-solving.
- Because spreadsheets allow students to out-source computations, they are a great introduction to programming. When using spreadsheets, students learn to tell a computer what to do. This begins with familiar language, like the mathematical operations, but can become more complex with functions like conditional formatting, relative referencing and pivot tables. Learning how to determine what you want to do with a data set and then learning how to say that in a language the computer will understand is the beginning of programming.
- Finally, spreadsheets have applications across the high school curriculum and in all kinds of work. I know most students are unlikely to use spreadsheets as enthusiastically and as widely as I do, but most will need them at some point and its a good skill for students to have.
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.