Creating a “Geometric Eye” Using Desmos

Geometric Eye

Several years ago, I came across some videos by the artist Dearing Wang that showed how to create mandalas and other geometric figures using only a compass and straightedge. One of them was a figure he called a “Geometric Eye“. Drawing one by hand took hours. Using the online Desmos math app, you can create one in minutes! Here’s my screencast explaining how:

NCTM Comes to Music City

The National Council of Teachers of Mathematics held a regional conference in Nashville, TN last week. Since I live in Music City, this was too good an opportunity to pass up! I’ve attended several NCTM conferences, both national and regional, and this was by far the best and most technologically savvy one.

To begin, I installed the conference app on my phone, which made planning and organizing my experience a breeze. It synced the sessions I wanted to see with my calendar, so I received reminders and updates for each one. The app also promoted interaction among attendees through its Activity Feed. We could also keep up with what was happening via Twitter using the hashtag #NCTMregionals.

The first session I went to was “Hands On Trigonometry”, by Elizabeth Petty. She led us through a lesson on the unit using paper plates and twizzlers to demonstrate what a radian is. We then folded the paper plates in half to create an x-axis, then thirds to mark the 30 and 60-degree points on the circle. It was an excellent example of using a hands-on activity to reinforce a difficult math concept.

The next session, “Keeping It Real: Authentic Real-World Math Lessons”, was presented by Ginny Stuckey of Mathalicious. Their mission is to develop lessons that use real-world data and situations to spur critical thinking in students. The lesson Ms. Stuckey demonstrated involved how municipal fines can quickly become impossible to pay off for low-income offenders.

Next up was one of the best sessions of the conference, “Using Manipulatives and Investigations to Teach Geometry”, by Christine Mikles. Ms. Mikles uses the CPM Geometry text, which is full of hands-on activities. Here’s an example of using two mirrors and a protractor to learn about central angles in regular polygons:

Polygon with mirrors

The last session I attended on Thursday was “Slices of Calculus”, by Nina Otterson. As a veteran calculus teacher, I was very excited to learn a new way to teach how to calculate the volumes of solids of known cross-sections. Ms. Otterson’s approach makes a lot of sense: she has her students learn what ratio of a square’s area is an equilateral triangle, an isosceles right triangle, and a semicircle. Then, they find the volume of the solid using a square, which is easy, and apply the appropriate ratio. Her students build models of each type of solid. Here’s one I built using equilateral triangles whose base is a pair of intersecting parabolas:

Solid with Triangle cross-sections

Friday’s first session was “The Math Department I’ve Always Wanted: Twitter As My PLC”, by Michael Felton. It was an excellent presentation on how math teachers can use Twitter to ask questions of other teachers, get great ideas for lessons, and get feedback on their own lessons. Michael is part of the “Math Twitter Blogosphere” (#MTBoS on Twitter), where some of the most innovative teaching is being developed today. If a teacher needs some ideas on how to teach practically any math topic in a creative way, he or she can find it at MTBoS.

Next, I went to a session sponsored by CPM (College Prep Mathematics): “CCSS Math Practices? Trust CPM’s 25 Years of Writing Experience”. This company is a nonprofit textbook publisher run by math teachers. Their series of books stresses the importance of hands-on explorations to teach math concepts. I was very impressed with the passion and excitement of the teachers who use these books.

Finally, I went to another session by Michael Felton, “Desmos and Modeling”. I’ve used Desmos‘ online grapher for several years now (I even did a presentation on it at a TAIS conference last year). They have moved far beyond a simple function grapher, though. Their site now includes all kinds of activities that teachers can use in the classroom. The one Michael demonstrated involved matching transformed sinusoidal curves, and it was a lot of fun. Go to https://teacher.desmos.com/ to see all the fantastic lessons they offer. Teachers can also keep track of students’ progress as they work through the activity.

All in all, an excellent conference. It is fascinating to see how social media is transforming teaching, and how much teachers are trying to incorporate active learning into their lessons. I figure a conference is worthwhile if I can take home at least three good ideas/lessons/activities from it. After this one, I have more than dozen to try out with my students!

 

Add a Little Twitter to Your Learning Management System

I’ve been using Twitter more and more the past few months, picking up great ideas from other teachers and bloggers. Now I’m considering applications of it with my students. It would make a nice back-channel communication method for students who would like to comment on something without resorting to email. By creating hashtags for my courses, we can all have running conversations on a variety of topics. To encourage that, I’ve embedded a Twitter feed into my courses’ Moodle pages:

Twitter2

Now they can see the tweets my “fractad” feed is getting, as well as send a quick tweet directly to me.

Here are the steps involved in making your very own Twitter feed you can embed in your Moodle, Haiku, or Blackboard page:

1. Go to your Twitter Home page, and click on the gear icon at the top right.

2. Choose “Settings”.

3. In the menu on the left, choose “Widgets”

4. Click the “Create New” button, and select the various settings for your widget.

5. Click the “Create Widget” button, and copy the html code that will appear. Use this code to embed the widget into your LMS page.

One thing that’s very cool – you can create a Twitter feed for any Twitter user. If your school has an account, you can embed that feed into your page. Or, you might want to embed the feed of a professional organization you follow (NCTM, in my case).

If you’re relatively new to Twitter, and you aren’t sure who or what to follow, here’s a list of people and organizations that I’ve found to be very useful:

Math & Science:

@lostinrecursion (Paul Salomon)                             @rmbyrne (Richard Byrne)

@MT_at_NCTM (NCTM Mathematics Teacher)       @Mathalicious

@fnoschese (Frank Noschese, science)                  @ddmeyer (Dan Meyer, math)

@desmos                                                                   @mrbarlow (science)

Education:

@Socrative                    @Edudemic

@ASCD                        @KindleTeacher (Meg Griswold, English)

@edutopia                    @kindleworld (Andrys Basten – lots of Kindle tips)

@PatBassett (Former NAIS president)

(Chrome users: don’t forget to install the Notifier for Twitter app!)

Update: I just showed my calculus students the feed on their Moodle page, and they were incredibly excited. I’m already getting lots of interaction with them!