NCTM Reflections Part 1

The National Council of Teachers of Mathematics hosted its annual math conference this past week in San Francisco.  Many MVLA teachers had the chance to attend, and below are some highlights from the sessions that we attended.

A Not So Average Talk About Averages

This talk gave visual ways to understand some of the formulas that we use in statistics.  Can you see how the formula from mean comes from the image below?  What other formulas can be seen in a visual way?

Using Financial Applications to Build Algebra 2 Competence and Confidence

One strategy from this session that could apply to many of our classes was to give a formula with values plugged in and have students tell the story. Suppose we are studying the compound interest formula. What would the story be for the image below?

The more that the equation has been simplified, the harder it is to tell the story.  What is the story for the image below?

This reminded me of a presentation that I shared earlier in the year from Kate Nowak titled "Plan a Killer Lesson Today". In this session she presented a strategy with examples of how to invert a lesson. So instead of the traditional I do/You do/We do you can invert the model so it is You do/Y'all do/We do. If we applied this to the sample above we might give students the formula along with our first example to study and reflect on. Then we'd come together to talk through our interpretations and end with explicit instruction from the teacher in order to get students ready for the upcoming assignment. Can you think of formulas from other high school math classes where this would be a powerful strategy?

Math Mistakes and Error Analysis: Diamonds in the Rough

This is the session that I most wanted to attend but was not able to make it to. Highlights from this session showed up on Twitter, with the tweet below completely grabbing my attention.

Solving Equations using a Clothesline / Double-number line? Yes, please! #NCTMannual pic.twitter.com/zd2CIkZ83R

— Kyle Pearce (@MathletePearce) April 14, 2016

The picture above shows a double number line, and the series of pictures shows how it can be used to reason about solving equations. This is another strategy that many lower level Common Core curriculums are using to help students build number sense and solve problems. Some teachers are even hanging up clotheslines and using folded pieces of paper to help students rearrange quantities as they solve problems.


The Rewards and Challenges of Standards Based Grading

Ever wondered what standards based grading is and why some schools are headed towards standards based grading? This session focused on the why and how of their school's journal from traditional to standards based grading.  Below are some of the things that the presenters had to say:

Some course teams have moved towards a somewhat standards based grading approach, or rather a holistic approach to grading.  These teams have a scoring system that is similar to the one from the presenters that is below.

Interested in learning more about the details of standards based grading? Check out the presentation!