Things are still busy at the Math Forum. I was given the opportunity to grade student responses for an algebra PoW based on the Math Forum’s rubrics for problem solving and communication. I found it difficult to grade similar responses with fresh outlooks, but the rubric allowed me to look for things that I wouldn’t ordinarily look for. If I were to grade the responses without the rubric, I would have scored the answers based on how deep the student seemed to understand the answer and scale that based on how accurate their answer is. Though, with the Math Forum rubric, the idea is to look for insights into the thought processes of the student. In separating problem solving into accuracy, strategy and interpretation, I can evaluate better how a student approached a problem and where they may have gotten stuck even if they didn’t explain beyond their strategy. As well, the communication criteria allows for students with less mathematical methods of thought to shine… so long as they actually explain what they’re doing or not understanding. It’s this insight that allows us at the Forum to do what we do.

This week also held the May T3 at the ExCITe center. The Math Forum crew invited me along to see a few short talks about technology development and outreach in Philadelphia, as well as off-kilter examinations on intellectual and academic life nationwide. What particularly interested and entertained me there was Kevin Egan who compared higher education to the development of Punk music. In the simile, he juxtaposed modern experimental and customized education with The Talking Heads, Gary Numan and DEVO. Though, I have to wonder why he left out Joy Division!

In other news, Tracey and I are working on getting the Ask Dr. Math twitter going! Keep an eye out for tweets from our numerical hero.

Coming up, I have plans for personal interest posts regarding STE**M** with a bold **M**. Come back sometime next week, and you might just learn something cool.

For one of the Trig & Calc POWs I found that my solution differed greatly from the examples in the teacher packet. Though, that’s the entire goal of my work so far. The problem was to find the area of a pizza cut in an unusual way. There were only a few solutions in the Teacher’s packet, a lot of them used Heron’s Formula where I developed a system of integrals. I don’t think I ever learned Heron’s formula in any high school classes, but I know how to analyze a geometric situation using trigonometric and calculus concepts. The goal, on my end at least, was to see how my solution differed from other students’ solutions.

I feel as if, by working this way, I’ve stumbled upon the guiding principle of the Math Forum POWs. Beyond deepening my understanding of spatial and geometric analysis, comparing my solution with that of many others from various educational backgrounds helps me to better understand how to help someone else solve the same problem. And, I mean more than just being able to suggest a repertoire of various laws or theorems. In understanding how a student solves a problem, I can figure out how they were thinking, and what ideas came to them as they were reading the problem.

From an engineer’s perspective, this problem screams “integrals!”. I know in the previous post I talked about “no one size fits all solutions” but I like to have one tool does all. To me, integrals and derivatives are more valuable than a toolbox of formulas and theorems. I know that I can find acceleration through derivatives or areas and displacement through integrals, so a huge amount of formulas and equations are basically obsolete. Though, to a student who hasn’t had calculus (or won’t ever take it) the formulas and theorems are the only tools they have. By way of comparison, my toolbox hasn’t necessarily been upgraded. Metaphorically speaking, the comparison is unto a machine shop full of lathes, drills and lots of other precision tools versus a similar shop with a C&C machine. In principle one isn’t necessarily better than the other. The one is a massive collection of tools that may not see use in every problem, but is equally effective as a machine designed to “do it all.”

I also noticed, in general, that other students’ solutions were less savvy about precision. Not in that they were imprecise in their answers, but that they didn’t consider where over-precision would over-complicate a solution or was simply unnecessary given the conditions of the problem. In most sciences, it’s satisfactory to be within 10% of an accepted value while in pure mathematics the answers are more black & white. In my brief time solving POWs I’ve found myself at odds with the answers after carefully considering how precise my answer can be assuming that any measurements given to me are fallible measurements. It’s a habit I’ll have to let go of for my time here at the Forum.

Another problem I worked on was about finding a point on a line such that two other points had a difference in distance of one. I knew I could have solved it via algebra and an established equality, but I knew a more “advanced” way to solve it. (Yes, I wanted to show off.) I solved it via linear algebra and matrices. The problem suggests that there may be more than one solution, so that tipped me off to use my knowledge of linear systems. As it turns out, there were only two solutions which were resultant from the algebraic manipulation of a square root. Even still, I solved the problem correctly, even though I had to submit some clutter with extraneous solutions.

So In conclusion, Math is fun and I’m having a great time at the Math Forum!

]]>For now, my supervisor Suzanne has given me a few questions to get me going in the office and on this blog.

**What is the Math Forum?**

The Math Forum is an online community and resource for teachers and students to enrich, discuss and evaluate their mathematics education. “Ask Dr. Math”, “MathTools” and “Problems of the Week” are just some of the services offered. Though it’s really much more than the sum of its parts. At first glance, it’s a math website. A static place where textbook rules are written down and explained. But when looking deeper, The Math Forum is really a team, a service, and an idea. It evolves. The team develops and manages internet resources to create a worldwide connection service between students, teachers and parents that ultimately improves the mathematics education experience for all. The idea is that when the scale at which educators and students communicate increases, the quality of their education increases as well.

**How might a student use the Math Forum?**

What kind of student? Asking me, you’d get the answer of an engineering student. Passively, an engineering student would use The Math Forum as a knowledge bank. In solving engineering problems, it’s not enough to simply take notes in class about problem solving strategies because there are no “one size fits all” strategies. The simplest way to get through engineering school is to have a mental library of physical, mathematical and chemical laws and theorems to use as templates for categorizing and eventually solving a wide variety of problems. The fundamental flaw in this way of thinking, and as well the separator between good engineering students and great ones, is that it ignores the fundamental understanding of these laws.

Mathematics is the language of engineers, but while many engineers speak it, only the best fully use the art of it. The Math Forums online tools are nothing but a boon to engineering students. The problem solving strategies developed, discussed and published through the myriad projects are all focused on developing a deep understanding of mathematical thought. Engineering students rarely see a mathematical proof, yet we are commonly asked to do them. Making mathematical proofs is one of the best ways to learn the hard sciences of engineering, but where does one learn how to do them? The rubrics involved in the PoWs at the Math Forum ask for nothing short of the rigor of a mathematical proof if not the expression of a deeper or insightful understanding. In perfecting this art through the PoWs, Ask Dr. Math and it’s massive archive, an Engineering student can greatly improve their ability to solve engineering problems accurately and with more detail.

I’m honestly surprised that very few of the other MSE students in my class use The Math Forum. There are around forty MSE students in my graduating class, which also represents one of the largest at Drexel thus far. Every student knows each other; it’s a tight community. There is always a large group of MSE students gathered to discuss and develop strategies the night before –and often for full days before– a midterm or a final. I’m sure we would do collectively better if we developed personal strategies with the services offered by The Math Forum during the academic term.

Also lots of KenKen… after my work is done of course!

**How might a teacher use the Math Forum?**

After watching a few of the Ignite lectures, I had a pretty good idea about how to answer this question. A teacher might use the Math Forum like a student. Though instead of studying Mathematics, they’re studying how students learn. Beyond the Ignite lectures, The Math Forum serves as a library of student ideas and behavior rather than a library of mathematics strategies.