Long Time No Blog

Hello there! I haven’t blogged in forever because I’m too busy enjoying my job. That being said, I am leaving my job next year to get my Masters in Special Education. So, my job is open! This is the official job posting:

The Howard Gardner School of Alexandria, Virginia, an intentionally small, educationally progressive, independent secondary school, is seeking outstanding candidates for a full time position teaching Mathematics for the 2017-2018 school year. Using hands-on learning through environmental science and the arts, The Howard Gardner School’s mission is to help bright, creative, non-traditional learners use their unique strengths to thrive academically, intellectually, and emotionally.

Candidates will have the key traits of enthusiasm, adaptability, self-directed initiative, and a strong content area understanding across all mathematic disciplines. We are seeking a faculty member with a strong belief in, and an understanding of the importance of, differentiation in the classroom, team-orientation, a strong background or experience with outdoor education and progressive education, and the desire to work collaboratively across disciplines and curricula to foster a process oriented and nurturing educational environment.

Our week includes three full days of in-classroom education, one day of directed field studies, and one day of internships and service learning. We leave our school building entirely at least twice a year for multiple overnight camping and outdoor learning trips. Our students come from a diversity of backgrounds and have a variety of skills and needs. Portions of our student population deal with ADHD, school anxiety, or learning differences. The faculty is expected to play many roles within the community such as: teacher, mentor, field guide, advisor, parent-liaison, coach, and colleague.

We will begin the visitation and interview process on Monday, May 1st. Interested candidates should submit a resume or curriculum vitae, cover letter, and references to Admin@TheHowardGardnerSchool.org immediately. Compensation is commensurate with experience and education, and competitive with area schools. Please refer questions to the email address above.


More Similar Figures

While I was at NCTM I left my Math 2 classes with this three-dimensional figures task. When I returned, I was greeted with a messy classroom full of ants (marshmallow bag left open : / ) , but also this:


It’s pretty clear that these are mathematical shapes, but I could never get past the fact that Platonic solids, particularly stellated ones, are aesthetically pleasing. But I did some research and came up with a not totally visual task for my students to work on. Since I wasn’t going to be there, everything is extremely spelled out – on a non-sub day I may leave some things more open.

Platonic Solids task

This task first has them construct three out of cardboard. I had printed a bunch of nets, but I guess they couldn’t find them because nobody used them. I kind of like it without the nets better anyway, because that’s a nicer, richer visualization task. Then they were supposed to re-create two of them with toothpicks and marshmallows or with straws. Only a couple actually attempted straws. I made all of the shapes with straws just to try it out, and I’m still struggling with the icosahedron. I’m really excited to try to make a stellated one.

The question I wanted them to answer is why there are only a limited number of Platonic solids. I’ll admit the task only gets them most of the way there, but I think it’s a good start.

The coolest thing about this whole thing is that I gave nets for the stellated shapes to my advisee group, and now I’m seeing kids just folding un-assigned 3D figures. I’d say that’s an engaging task! I definitely want to continue in this vein of highly visual mathematics with rigorous tasks aside from just “see how cool math looks.”

Although it does look pretty cool!

Polynomial Sense

In math 3 we’re talking about polynomials, their degrees, and what it means to have imaginary solutions. We just finished doing a ton of work on adding/subtracting and multiplying/dividing complex numbers. I’m feeling confident that if I gave them a page of “multiply these complex numbers” problems, they would definitely know to distribute the real and imaginary parts. Most would draw the box (honestly, I still always use the box). The difficult part is definitely multiplying individual numbers – they know they have to multiply 2i x 4, just not necessarily what it is. To practice, I adapted this game, but made it about 16 times more complicated. I got four 8-sided dice from the RPG club adviser, in different colors to represent positive imaginary, negative imaginary, positive real, and negative real numbers. We soon realized that it would be extremely difficult for anyone to win the game as it was designed, so we improvised.

dice game

This week I showed them second, third, fourth, and fifth degree polynomials and asked them to describe the pattern.

polnomial pattern

Then I told them something like this had 2 imaginary solutions and asked them how they knew:

degree 4 rereimim

That’s not the actual one, but one that was on the very conceptual handout I gave them next. I’m attaching it in case you’re interested. It involves some writing. Click for pdf: matching polynomial equs

I’m realizing we are way ahead, and I’m not sure how I feel about that. I guess I could decide it’s definitely a good thing, because they’re all doing well on assessments and seem to be grasping concepts. I could also decide it’s a bad thing, that we’re rushing through material and not delving as deeply into it as we could. In any event, I’m taking advantage by re-including some polynomial standards I initially rejected because of perceived time constraints. I’ll be doing polynomial long division next week – let’s see how it goes!

Reading Assignment September 28th

I will admit that at this point in the school year I’m falling behind on my reading. Even so, here are a few interesting things I had time to look at:

First Day of School at the ABS on Islesford
Via Diane Ravitch, this is a close look at a tiny community coming together for the first day of school. This reminded me a little of my school because it’s so small and community-oriented. I love their goals!

Toddlers Know More Math Than You Think, Study Says This is encouraging! Young minds are intuitively able to pick up on patterns and absorb knowledge quickly. Totally worth staying for the last statement!

A Not-So-Simple Majority
Another reason to love This American Life. This story seems simple at first – a group of parents whose students do not attend public school have control over the school board. Left at that, the situation is clearly problematic. The whole story, however, is much more nuanced and it’s less clear what should be done in the community. This is a great examination of race, class, education funding, and education inequality.

Publisher Accidentally Puts Porn Star on Math Textbook
Pretty self-explanatory.

8 Mistakes Parents Make When They Help Kids Apply to College
The first one is key – we ask our students to consult Colleges that Change Lives a good amount of the time. Small schools usually have smaller class sizes, specialties, and a smaller pool of applicants (in general and for financial aid), but applicants are less likely to have heard of them. It’s not true that more well-known colleges will provide a better college experience! The rest of this is mainly about financial stuff, which is extra important nowadays, and spins into:

Congress Didn’t Pay a Lot to Go to College. Today’s Students Shouldn’t Either.
College degrees are becoming simultaneously more essential and less affordable. This is a great reminder that many middle class desires said to be unrealistic were the same conditions that were not just realistic but reality for lawmakers.

OK, I have to go get some yarn – I need to crochet an owl hat for yet another co-worker baby shower.

Summer Reading July 16th

Over the summer the amount of reading I do experiences exponential growth. I’m hoping to do a biweekly roundup of education-related reading that I found thought-provoking or helpful.

Here’s what I’ve been reading in the past 2 weeks!

To Close the Achievement Gap, We Need to Close the Teaching Gap
The Huffington Post has a great piece by Linda Darling-Hammond, a Stanford professor whose work focuses on educational equity and teacher quality. This piece highlights some of the unique challenges facing teachers in the United States. Not only do two-thirds of teachers teach at schools with over 30 percent of their students in poverty, teachers in the US have less time to collaborate and receive productive feedback. Darling-Hammond offers four concrete things schools can do to help teachers become more effective.

Rooting Out Blind Spots in the Language of Group Roles in Complex Instruction-Based Group Work
Cheesemonkey Wonders has an excellent set of roles for assigning group work. I’m excited to try these out in the fall.

When Teachers Romanticize Their Students’ Poverty
The Atlantic has a realistic yet positive reflection about teaching in the Mississippi Delta by April Bo Wang. She contrasts her romanticized expectations with the realities of her students’ situations. “There was nothing beautiful about their poverty,” she writes. “There was no way to glamorize the fact that Ty had no electricity or running water at home, that Jonathan wrestled hogs on the weekend for extra cash, or that Yaya’s relatives fought over custody of her baby to get the extra government check.” This should be required reading for all new teachers.

The War Over the Core, Ctd
Andrew Sullivan has a great summary of teachers’ unions AFT and NEA reacting to what they call the “test and punish” systems of the Common Core, Race to the Top, and No Child Left Behind. Both are critical of Arne Duncan for continuing to support standardized testing, and the NEA has called for his resignation.

Why Poor Schools Can’t Win at Standardized Testing
Also from the Atlantic, Meredith Broussard takes a look at the big data behind textbooks and standardized testing in the Philadelphia school district, one of the nation’s largest. She finds that the standardized tests are in the control of textbook publishers, whose books are not always accessible to students. These textbook companies write and score tests based on the content of their books, books that cost in some cases 3 or 4 times the schools’ budgets. I read this piece as a strong argument against standardized testing, at least in the hands of textbook publishers.

And Finally: “We’re Fine Here, How Are You?” Normal Moments in Art History Where No One is About to Get Murdered
This isn’t necessarily related to math education but it’s great and you should read it – from Mallory Ortberg at the Toast.


Have you watched any of ViHart’s YouTube videos? I had been alerted to them earlier this year and used the angle-a-tron one as part of a sub plan last year. Now that it’s summer and my official duties include nothing, I watched all of them, and I endorse them. I’m particularly inspired by the hexaflexagon concept. Watch:

I’ve made 2 in the last hour. Here’s one in two different states of flexigation:


These are great! I have little to no concept of their alignment with common core but they are now in the back of my mind (and the cushions of my couch).

Also, can I just state that I am thrilled to be entering into the exciting world of math blogging? I am very eager to communicate with the rest of you, especially once the school year starts back up again.