Henri Picciotto's

November 2015

Hello, everyone!

I have news: two new Lab Gear books, and two Northern California appearances. There is more info at the end of this issue the newsletter. Click here if you're in a hurry to find out about them.

Hoping to see some of you soon!

## Blog Posts

Here are links to posts on my Math Education Blog that you might find interesting.
If you are so moved, you may comment on the posts, and/or subscribe to the blog.

In a previous post, I argued that effective teaching requires navigating skillfully between the "sage on the stage" and the "guide on the side" roles. I follow up on this here, by discussing a classroom example, and an example from my own struggles with a tough problem. I claim that generic hints (such as "try a simpler problem" or "what do you notice?") are often insufficient, and that we should not shy away from supporting student exploration more assertively.

### Geometric Construction for Middle School

Once again, I argue that geometric construction deserves a more central place in the curriculum. My reasons should appeal to you whether you appreciate the long history of this particular branch of math, or the magnificent problem-solving opportunities it offers, or the role it can play in developing a logical foundation for a transformational approach to high school geometry. The post includes links to a middle school version of my geometric construction unit, and to my other writings on this subject. Click here.

### Pythagoras: Handwritten and Hand-Drawn

Call me old-fashioned: I hand-wrote a blog post! In it, I guide students through a proof of the Pythagorean theorem by suggesting a step-by-step approach on grid paper. In spite of my terrible handwriting, this turned out to be one of my most popular posts ever! Check it out. (And don't worry, I have not turned my back on contemporary tools. Here is an applet that makes the same argument. However, I insist: only show it to students after doing the activity on graph paper, and follow it up by asking for a write-up of the argument!)

### Learning Styles, Teaching Styles

Apparently, research shows that "learning styles", whatever they are, do not provide us with approaches that are especially appropriate to specific students. (If you want to find out more about this, the Wikipedia page on Learning Styles includes several relevant links.) Nevertheless, I still advocate teaching important concepts using multiple modes, including e.g. visual or kinesthetic. Read my post here, and from there click to a follow-up guest post by Michael Goldenberg.

## MathEducationPage.org

New on my Web site.

### Triangle Congruence and Similarity Again

I tweaked my documents on a transformational approach to triangle congruence and similarity, based on feedback I received from Bill McCallum (of Tools for the Common Core Standards.) If you downloaded earlier versions, please delete them and replace them with the current versions.
- Version 1 (more opinionated and footnoted)
- Version 2 (co-authored with Lew Douglas, better section on similarity)
The main change is to the SAS proof, which did not correspond to its illustration.
Relevant blog posts:
- Rethinking Triangle Congruence and Similarity
- Triangle Similarity Update
- Perpendicular Bisector Theorem

## Lab Gear Books

The new Lab Gear books are out! They are largely based on the old Lab Gear books, with the following improvements:
- There is more emphasis on the transition from blocks to symbols
- Activities are correlated to the Common Core (some of the wording is updated accordingly)
- All activities work with the available number of blocks in a student pair set
- They incorporate what I've learned in the past 20 years
There is some overlap on the key concepts, but the two books emphasize different content (basic algebra vs. Algebra 1,) and represent somewhat different pedagogic styles. I recommend getting both so as to have more choices, and more activities. Of course, as always in my books, the math is solid.

Get the books (and the manipulatives) from Didax.

If you're not familiar with the Lab Gear, read about it here.

## Northern California December Events

### Saturday, December 5, 2:00 to 5:00 pm, downtown San Francisco

In-person meeting of the local branch of the Math Twitter Blogosphere. If you used to attend the gatherings of Escape from the Textbook!, you will appreciate the return of grassroots math teacher collaboration meetings to the Bay Area. Anna Weltman will lead a geometry activity, and I will lead a discussion of "reaching the full range." RSVP

### Saturday, December 12, Asilomar

I will be at the California Math Council Northern California meeting. I look forward to attending some talks in the morning. In the afternoon:

1:30 to 3:00 pm:
I will present "A Lab Gear Approach to Operations and Equivalent Expressions". The Common Core and common sense both require an introduction to basic algebraic concepts in middle school. The Lab Gear manipulatives help students transition from numbers to variables, and from the concrete to the abstract. We will work through activities that promote an understanding of operations and their properties, especially the distributive law, combining like terms, and factoring. This is a necessary prerequisite to understanding equivalent expressions, a key concept for grades 6 to 9.

3:30 to 5:00 pm:
I will help Lew Douglas present "Increasing Coherence in High School Math". The traditional 9-12 math curriculum is badly fragmented: Algebra, then Geometry, then more Algebra, and finally a hodgepodge of topics known as Pre-Calculus or Math Analysis. An integrated approach can help, but not if it merely slices up the courses and mixes up the pieces. Whatâ€™s needed is unifying concepts that the various pieces can fit into. We will focus on transformations and system extension as examples of these, and include glimpses of others.

See you soon?