Tag Archives: collaboration

Roots of Unity Final Projects


These are the results created last November for the art/math integration project described here.


By the way, happy pi week everyone!

Pi Week

Pi Week

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Art Integration: Roots of Unity & String Art

I talked with an art teacher this afternoon about ways to integrate art and math into a project. She had some great ideas, plus we came up with more ideas in the course of our discussion, many of which I plan to try for Algebra 2 or Precalculus (both which I teach this year, fall and spring respectively). Geeking out while discussing the intersection of math and art reminded me of this awesome collaboration and its result from a few years ago!

Our first idea (in terms of implementing soon) was some colorful string art crossed with a discussion of the roots of unity, since my students are (today) using and graphing complex numbers for the first time. Math teachers, art teachers, and any interested others, check out this rough draft of the project and let me know any thoughts and advice:

Roots of Unity Project


Colorful "string" art on the 17 th roots of unity

Colorful “string” art on the 17 th roots of unity


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Teamwork: The POE House

This was an assignment I just wrote for a course I’m taking: to describe a day in my classroom from a journalistic third-person perspective. I figured I’d post it here as well. This is a slightly-fictionalized version of what occurred in my Principles of Engineering class on and around March 25th, 2014.

POE House Lighting

POE House Lighting

Upon walking into Nick Yates’s engineering classroom at Patterson High School in east Baltimore, the first thing one notices is students gathered together working on a project at the center of the room. Walking closer, the project reveals itself to be a large structure, roughly eight cubic feet, which the students explain is a model house. Each wall has a different truss design, built out of coffee stirrers that form triangles that fit together into a square wall, two feet on a side. The students are collaborating in teams, each team responsible today for lighting up a wall of the house.

The students are a diverse group. Six countries of origin are represented here in this one room: United States, Nepal, Mexico, Congo, Nigeria, and China. Among students born in the US, the majority are black, but some are white and some are Latino. Boys outnumber the girls in this engineering class, as they do in the engineering field, but the girls tell of after-school mentoring programs and field trips that have helped encourage them to stick with their engineering classes and to pursue a STEM career.

As one boy positions a light emitting diode (LED) on the wall, his partner pulls off electrical tape and hands it to him to secure it in position. Another partner reads off of a circuit diagram in her engineering notebook, where they have designed the electrical circuit, instructing her teammates how to connect the wires in between LEDs. And the fourth team member is using alligator clips to join three solar panels together to make this wall’s lights powered by environmentally sustainable source.

After a while, the team steps back to admire their handiwork. They bring over a lamp to simulate the Sun’s rays hitting the solar panels, and flip the light switch to on. But the LEDs do not light up. They are daunted for just a moment, but soon start troubleshooting the problem to try and fix their electrical system. One student suggests they check all the wire connections, to make sure they are all twisted together properly, and two members of the team immediately start to do that. Another suggests getting a multimeter to check if the solar panels are even generating electricity. As others check every place where two wires meet manually, she goes to get a multimeter from the teacher’s desk. She asks one of her partners to hold the multimeter’s leads to the wires while she operates the device. Each solar panel is reading about 1.83 volts of electricity, but the lights are still not lit. Another team member suggests checking the plan, to make sure the solar panels are wired in series so that their voltages add up. The team consults their notebooks, verifying that their actual work reflects their design; it does. Some of the team is beginning to lose hope, and one suggests calling the teacher over for help. But one student, remembering the time he held an LED to a nine-volt battery too long and the bulb blew out, suggests making sure each LED is working. His teammate asks how they should test the LEDs, perhaps by holding each one to a battery to see if it lights up? He grumbles a little about this, thinking of all the work they had just done to tie the LEDs together with wires into a circuit, only to have to undo it all. But at this point the girl with the multimeter steps in, saying they could use the multimeter to figure out which if any bulb was dead. The team works together and finds they did have a non-working LED. They replace it with a new one, and the lights come on. Success!

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Summer of Learning

(This post was mostly written last Tuesday, so dates referenced will be from then.)

So, last summer for me was a summer of travel. Over 10,000 miles round trip, from sea to shining sea, along roads new and old, long and short.

This year will be a summer of travel for my mind, instead. I have a number of different learning projects I am planning/attempting, from workshops to conferences, from in-person classes to online classes.  Nearly all of which is free!

Here are a few of my plans:

Fab Lab

Yesterday, I attended  a class which introduced me to our local Fab Lab at the Community College of Baltimore County (CCBC). A Fab Lab  (Fabrication Lab) is a community-driven and community-accessible location with computers, machines, and other tools needed for making things. A global network of more than 90 Fab Labs worldwide is run out of MIT. Artists, designers, engineers, inventors, as well as ordinary people with an idea they’d like to make  a physical reality, all use Fab Labs.

The Fab Lab at CCBC is a little over a year old. It has a 3D printer, a CNC router, a CNC mill, a laser cutter/engraver, and a vinyl printer. I made the following key chain using the laser engraver, with the help of the lab’s manager who was teaching me how to use the various machines and associated softwares & tools.

Laser Engraved Key Chain

And a sign for my Computer Integrated Manufacturing (CIM) class, done using the CNC router and featuring a picture of a robotic arm:

CIM Sign, milled from medium density fiberboard using the ShopBot at CCBC’s Fab Lab

Very cool.

VEX Robotics & Automation

Yesterday, today, and tomorrow, I’m in a training at the University of Maryland Baltimore County (UMBC, just around the corner from CCBC and its Fab Lab above), where I’m learning more about VEX robotics and their role in the Project Lead the Way engineering curriculum. Including learning how the pieces fit together, the functionality of the various sensors & other pieces, and how to program the VEX kits in RobotC, a variant on the widely-used C computer programming language.

I had two groups of students (6 students total) who began using and programming with VEX/RobotC this year. I learned some of it with them, but really appreciate this chance to work with the automation kits myself and really learn it much more deeply.

It’s been fun so far! Here’s the testbed full of motors, lights, and sensors where we are learning how everything works and how to program:

VEX Test Bed

Tomorrow we’ll be unleashed onto some actual functioning projects!

Online Class(es)

I’ve begun an online computer science course, Algorithms: Design and Analysis I, via Coursera.

I’m planning this summer to learn a lot more about computer science / programming. I only took one CS course in college (CS101). Yet I’ve been somewhat into programming ever since programming the quadratic formula (and many other math-related programs, plus a few fun/game programs) into my graphing calculator in tenth grade. In college, I also used some simple computer programs to design some original fractals (Java) and search for patterns in continued fractions (PARI/GP). And I had many friends in both high school and college who majored in CS or related fields. Since I’ve been teaching engineering, several of the courses I teach have involved programming components (see, e.g., the VEX Robotics and Automation section immediately above).

So I figured I’d like to learn more about CS & programming. I signed up this spring for Coursera’s CS101 class, which (though I can’t find a source for this statistic) I think more than 100,000 people worldwide also took along with me. It included video lecture segments, mini-quizzes embedded into the videos, automatically-graded programming assignments, and discussion fora where students could help one another (since the professor could not interact with so many of us individually). It was a decent review for me, since it’s been years since I took CS101; I learned a few new things including some specifics of the JavaScript language as well as some things about how computer hardware works. Though it was very easy overall.

Coursera, along with a few other recent innovative websites like it, is being referred to as a MOOC: massive online open classroom (or course). Because its classes are free and accessible worldwide (“open”) and are enrolled in by tens or hundreds of thousands of students at a time (“massive”). Some people are talking about MOOCs as the next big step in the educational revolution; I can attest that the experience is much more like an actual class than just viewing lecture videos. I have yet to really engage the discussion fora for help, but I see study groups forming there, both in-person meetings based on geography, and Skype study groups being set up  based on time zone or language spoken. Many other people ask questions in the fora which are quickly answered by fellow students or volunteer teaching assistants.

If this topic intrigues you, check out the two articles linked above (the words ‘some’ and ‘people’). They are quite interesting and thought-provoking about the future of education!

This summer, I signed up for the Algorithms course, which looks like it will be much more challenging, though also like I will learn a lot from it. First I had to pick a programming language. I feel like a lightweight in several languages, from my experience in Java years ago, to knowing a little C based on my robotics teaching experience, to knowing a little Python based on using it to control a virtual robot and help it navigate a maze in an after-school club I advise. I spent this weekend taking a crash course in Python to catch myself up to speed. After that, so far in the Algorithms course, one week in, I’ve programmed a multiplication algorithm and programmed/analyzed the running time of a merge sort algorithm. I’ve spent dozens of hours on it so far, but am really enjoying it!

Both CS101 and Algorithms are taught by Stanford professors; Coursera partners with faculty from several universities.

On a lighter note, I’ve also signed up for this Udacity course that says it will be looking at/analyzing/explaining some cool physics problems, while also visiting actual historical locations in Europe of the scientists who studied them. I’m thinking it will give me some nice perspective and/or new ideas for teaching the physics-related sections of Principles of Engineering (POE).

Materials Science

Speaking of new ideas for teaching POE, I’ve also signed on to take a week-long materials science course at Howard University in Washington, DC. It is being sponsored by ASM International, a materials science/engineering professional society formerly known as the American Society of Metals. They provide free materials camps for teachers across the country at many different sites (see their website for more info).

I signed up for this because a) it’s free; b) it’s local – I can just catch the MARC train from Baltimore into DC; but mostly c) to learn more about and be able to teach the materials unit of POE better. I feel that the materials engineering unit/lessons in POE are often the dullest sections for my students. All of POE is quite difficult/challenging, with a lot of advanced mathematics and high-level physics concepts. But the other units I am able to better balance out between the difficulty of the concepts and the exciting projects we do. In this unit, students analyze properties of various materials, discuss what causes those properties, discuss how materials are used in manufacturing processes, do various materials-related math word problems, and use a stress analyzer machine to pull apart (stretch it until it breaks, called a tensile test) a piece of metal and then analyze its graph. While students love seeing the metal piece snap in two, I am not able to sustain that interest through the rest of the unit, which I take as a failing on my part. So, I hope to learn more during my week of Materials Mania, as well as to find ways of engaging students better in the topic.

Fullerene Nano Gears, image from Wikipedia

Hooray for the start to my summer of learning!

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Good PD

Like many teachers, I have suffered through some pretty awful professional development (PD) days. Some where we are read to off a PowerPoint slideshow, one of the techniques we are told is not good teaching practice. Others are more interactive (e.g. think-pair-share) but still boring and/or not relevant to actual teachers.

I am a firm believer that PD needs to be much more self-directed to be effective. We, as teachers, are professionals. As such, we can be trusted to work toward our own professional growth.

I get so much out of reading blogs by and tweeting with other math teachers–including lesson ideas, projects, worksheets, innovative techniques, clear explanations, and feedback on my ideas. Mythagon does a great job explaining the value of the math blogging/tweeting community here. The engineering education community is smaller, but I’ve worked to create and find spaces for that collaboration to occur as well, including by creating an online course to share resources with other engineering teachers in Baltimore City, and by starting this very blog.

In an official PD Day setting, where teachers have school but kids don’t, what could a more self-directed PD look like? It could include time to develop and grow a virtual professional learning community (blogs, twitter, as described above). It could include time to collaborate with other teachers in the building or district, self-selecting colleagues in your subject area or outside it, and deciding as a group what topics need to be discussed. It could include a variety of seminars/presentations, each led by teachers, of which you can pick which ones to attend that you need the most development in.

The best PD is that which I can use in the classroom the next day or week or month. Some of the best days of PD for me personally have come from a series of workshops organized specifically for PLTW engineering teachers, through the Community College of Baltimore County and the Time Center. They’ve been offering these trainings for the past several years, and recently received an NSF grant to expand their ongoing-PD model to other schools and states across the country.

Crane, built from FischerTechnik parts and programmed via RoboPro

I attended one of these PD’s a few weeks ago about using and programming with FischerTechniks and RoboPro. We learned advanced programming techniques (variables, subroutines, displays, inputs/outputs, commands & operators, branches and wait fors). We applied some of these techniques to arithmetic operations, and some to operating the crane you see above.

For the second half of the day, we had time to complete a project of our own choosing. I needed some help and practice time with pneumatics, as they were not part of my original training in the Principles of Engineering and Computer Integrated Manufacturing courses but have since been added to the curriculum in both. To use the new curricula, we had to purchase supplemental kits, since our FischerTechnik kits did not come with pneumatic components. So this was still pretty new to me, and I really valued the time I had to explore, learn, and get help from both the professor and a teacher-classmate. We built the simple pneumatic system you see below, which will store compressed air in the tank using a motor and cylinder pump system, then convert the pressurized air to vertical or lateral motion. This has been especially useful, since I’ve been using the instructional resources provided that day, plus my greater understanding of this topic, to teach pneumatics and fluid power to my CIM students this week!

Our pneumatic system

I shall be attending another PD this Friday at CCBC to improve my skills in using Autodesk Inventor, a 3D modeling software.


It’s down to the home stretch for both Mustaches For Kids and #NaBloPoMo!

Please support my moustache & Baltimore students by donating at DonorsChoose via my page. Plus, if you give now, you can use the codeword JOLLY and have your donation matched!

Also please support my partners in Baltimore’s NaBloPoMo by visiting and commenting at their blogs:

Only one day left in November – we’re almost through!

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November in Geometry

Although this is my sixth year teaching, I’ve been struggling with classroom management issues this fall in my last-period Geometry class. So we haven’t been able to do some of the cool projects I talked about last year (click the Geometry tag to see more). And a few topics we haven’t been able to delve into at quite the same level as I could with a more-motivated group of students.

A few details on some topics we’ve worked on during the past month or so:

The lesson on three-dimensional polyhedra went fairly well for the first two parts. Students constructed polyhedra from nets and by building their skeletons out of gumdrops (vertices) and toothpicks (edges). They discovered the relationship between vertices, edges, and faces found by Euler (V+F=E+2). But when I tried to bring the whole class to proving that only five regular polyhedra exist, I lost 80% of the class. I don’t know if it was too many steps, too long for their attention spans, an aversion to the logic of proofs, or the overall class dynamic. I don’t believe the math was too complicated for them (it just has to do with angles in regular polygons, spatial relationships, and our previous topic – tilings of the plane). I provided a sheet for taking guided notes. But much of the class turned that sheet in without having taken any notes.

Some of the more successful lessons have been a few that tied into what my students were learning in their engineering class. In late October – early November, my sophomore Geometry students were building and analyzing truss bridges in their Principles of Engineering course. Several teachers got together to plan lessons in various subjects that tie into the topic of bridges. In October, near the beginning of that unit, I did a lesson on the strength of various shapes. Students tried to use paper to hold the most books at least one inch off the table. They constructed a bridge that could hold the most rolls of pennies, using just one index card. And another bridge of multiple index cards, designed for length.

A couple weeks later, after they had developed designs in the engineering class, I had them analyze some of the geometry of triangles. This connected their bridges to what we were currently talking about in Geometry, with triangle congruence, proof, naming, and the Pythagorean Theorem.

Bridge Geometryhttp://www.scribd.com/embeds/73632593/content?start_page=1&view_mode=list&access_key=key-1xgwxwz3mcqb0iig9brt//

We’ve also learned about isosceles triangles, angle relationships, and circles in the past month.


Reminders: Please support my moustache & Baltimore students by donating, and please support my partners in Baltimore’s NaBloPoMo by visiting and commenting:

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AOE Site Visit

AOE Fall Site Visit today. Combined with our school’s open house this evening in the heavy rains, that made for another >12 hour day. Tomorrow I’m promising myself <9 hours (shooting for a standard 8 hour workday, but promising <9).

Encouraged by some of the feedback from our site visit. We have continued to make progress as an AOE in all four areas (academy development, curriculum/instruction, advisory board, & work-based learning). We’ve put a lot of pieces in place that are helping our students. Still have more work to do in every area, but solid progress has occurred. Some is thanks to me, but much is thanks to our awesome team of teachers, or thanks to our terrific industry partners.

While impressed with that progress, the major piece that is still not in place is the AOE as a small learning community within the larger high school. With common planning time built into the school day for our AOE teachers (by grade). Including a pure academy model where students stay with academy teachers for all subjects and don’t go to other academies except for electives or rare offerings (e.g. AP calculus). Not because other academies’ teachers suck, but because our AOE teachers will collaborate and make connections around engineering, and because our AOE teachers will meet and collaborate around improving education for our shared students. Right now there is lots of cross-academy teaching, which doesn’t fit in with the AOE model.

If this were to fall into place, it would make much of what we are doing for AOE so much easier, and make some things possible that are not currently possible. With the new principal and new leadership team, today was really their first in-depth introduction about the goals of the NAF/AOE model. So here’s hoping that we will have a commitment to work along these lines for next year.

Anyway, I apologize for errors of grammar and sentence fragments and such. I usually proofread for you, but not tonight. Need some sleep now. :^)

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