For my first post after a very long hiatus…due to a mixture of professional and personal reasons…I want to highlight my favorite math educator, Fawn Nguyen, who I suspect doesn’t sleep. She somehow finds the time to produce the work of two or three of us mortals. She is a full time middle school math teacher, which tends to keep the normal person fairly busy. On top of that, she has created and regularly maintains three excellent websites:
Finding Ways to Nguyen Students Over is Fawn’s blog where you can get the gist of her educational outlook and where her unique personality reveals itself. She manages to be both irreverent and passionate as she shares her day to day adventures as a middle school math teacher in California. One doesn’t have to teach middle school to mine gems from her blog. Her insights and issues resonate with upper elementary as well as high school math teachers.
Visual Patterns Site
Fawn must have been bored over Christmas/New Years vacation last year. On December 27, she posted in her blog her idea for a new site Visual Patterns, created for the “purpose of helping students develop algebraic thinking through visual patterns.” The patterns on the site are created by Fawn, other math teachers, and students. The site is simple. There are tabs on the top: 1 – 20, 21 – 40, …, 101 – 120. Each tab accesses 20 different patterns. There are only 15 patterns on the 101 – 120 tab, with space for 5 more before she adds another tab. There is a tab called Gallery, in which there are 11 patterns created by students. Another tab, called Teachers, is one that I hadn’t looked at yet, thinking that it was the patterns created by teachers. When I checked it out, I found a wonderful resource in which Fawn explains how she assigns patterns to students.
With 115 good patterns to choose from, it is hard to decide which ones to assign. Also, perhaps she has run across the problem that I have when I set loose a classroom of students to figure out one pattern. I find that if students are all working on the same pattern, especially if they are working in groups, some students allow others do the thinking and simply copy the groupthink with no understanding. (On the Math Talks site, discussed below, Fawn does have all students work on the same pattern, but they do it independently for 5 minutes, then share their work with their neighbors, and then the whole class discusses the pattern.)
Fawn developed a system to randomly assign different patterns to students. For independent work that can be given for homework or classwork, click on the Teachers tab to see how Fawn assigns the patterns to her students. She wanted students to be able to choose from 3 patterns and wanted each student to have their own 3 patterns to choose from. To accomplish this, she used the free online Research Randomizer. When you go to this site, a blank form appears. Fawn explained how she filled out the form for 39 students. At the time she posted this, there were 111 patterns. Now there are 115.
In addition, Fawn created a downloadable Word document template form which has room for students to show their work on 2 patterns for each 8.5 x 11 page. On the form, the student fills in their name, date, Pattern #, and the following:
1. Draw the next step
2. Draw a quick sketch of step 27
3. Complete this table (2 columns: Step #, # of ________) Step #s 1 – 5, 10, 27, then a blank
4. Write the equation
Wanting to try out the Random Number generator and the form, I went to the site and followed Fawn’s instructions. Student #1 was assigned 64, 115, 32, Student # 2 was assigned 47,105, 53. I followed Student # 1 and worked through Patterns # 64 and #115 on the template. There was plenty of room for my messy calculations that I did in the margin.
On each Pattern in the Visual Pattern site, the correct value of units for Pattern # 43 is given. This is a good way for students to check their answer after they create an equation on the Student Sheet. It doesn’t give the answer away, since they still have to come up with the value for # 27 in addition to an equation. What I love about the patterns is that there are many ways to envision the same pattern. In fact, I have to admit that I envisioned a pattern incorrectly in my haste to write this post. My Step # 43 did not agree with Fawn’s. I checked it over a few times, and then figured that it had to be a mistake on the site! (Fawn nicely asks people to comment if they find a mistake.)
Here’s the pattern:
I emailed her and included my filled in template. Within a couple of hours I received a reply from her and she very gently explained to me that I had counted the number of squares on my Step 2. I had visualized it as the large 3 x n rectangles on the bottom and the small 2 x 1 rectangles on the top. My mistake was that after the first step, the 3 x n rectangles were overlapped by the 2 x 1 rectangles that were in the “middle” (not on the left end and right end). As a result, I said that there were 15 squares in # 2 when there were really only 14. On Step 3, I had 2 too many squares and my error increased by 1 for each step.
Here’s how I saw it once Fawn set me straight on my error:
Here’s how Fawn saw it:
She showed how she had visualized the pattern, which was totally different from how I had visualized it. This is magic in these patterns. For any given pattern, there are multiple ways that the equation can be created. Her equation was Squares = 4(2n+1) – n – 4.
Here’s how some teachers might want the equation to be simplified.
Once I see this simplified equation, I can go back to the figure and “see” it. But I would never see y = 7x on my own. In my opinion,the pattern just doesn’t visually elicit that equation without some mental somersaults being turned.
I’m not sure how often Fawn gives students the 3 random patterns to choose from. I can envision giving students 3 to choose from each week with the expectation that they hand in a sheet with 1 or 2 patterns filled in by the end of the week.
Math Talks Site
Not wanting to rest on her laurels with only two sites, Fawn recently added a new site early this month, Math Talks, that meshes well with the Patterns Site. If you click on the link, Fawn has clearly outlined how she uses Math Talks in the classroom. Several screen shots from her site are below:
In her Visual Patterns Talks, she reinforces the idea that people see the patterns very differently. That is the beauty of working with patterns. Students can be creative.
Wondering about how the scribing happens, I wrote a comment on Fawn’s Math Talks Site in early November. Here is my comment and her reply:
Yes, Fawn is my hero. She not only is an excellent teacher, but takes the time to share her strategies with the world (or at least those of us interested in math education.) By the way, MTBoS stands for Math Twitter Blogosphere for those of you who haven’t heard of it. I attended the 2nd annual MTBoS Twitter Camp this summer in Philadelphia, where I met Fawn and many other talented, generous math teachers. It was a whirlwind of activity presented by and for math teachers from all over the country…and some from overseas. I plan to attend the 3rd annual MTBoS Twitter Camp next summer, wherever it is held.
I highly recommend subscribing to Fawn’s three sites…as well as the next site she is sure to dream up soon!