Formulas or relationships?

There are lots of ways in which the way that speak affects the way that we think, and I suspect that the way that teachers speak affects the way that students think. At the moment, I’m thinking specifically about the use of the word formula.

Mathematics Physics Mathematical School FormulaThe word formula is used a lot in math and science. Students learn how to use formulas to solve problems, and teachers provide formula sheets so that students can focus on application rather than memorization. These are both great things, but I wonder whether, as teachers, we could achieve more by using the word relationship rather than formula.

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Wrong but not Crazy

pexels-photo-207756.jpegI’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.

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I [heart] spreadsheets

8399214678_8b1ee3f361_bI 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.



Teachers’ Time

I am a teacher who has recently made the move from a school-based job to an office-based job in curriculum development. It’s a big change and there are lots of adjustments but one of the biggest surprises is the time. Although my work days now are shorter than when I worked in a school (eight hours a day instead of nine), I feel like I finally have time: time to think, time to research, time to collaborate and time to reflect.

time-managementAs a classroom teacher my days were highly structured and very busy. I had a limited amount of unscheduled time and a long list of things to accomplish in that time. Prioritizing tasks was pretty straight-forward because most of my to-do list was related to preparing for my classes and I had a timetable that dictated when each of those classes would happen. I learned how to use my time as efficiently as possible, but most of the time I was moving from one urgent task to the next urgent task until I came to a task that could be put off until the next day, signalling that it was okay to go home.

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Kids haven’t changed, but…

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

Compound interest

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!compound_interest_28english29

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.

Financial Literacy in the new BC Curriculum

Piggy Bank and canadian dollars close up shotI 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.

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