## Trying to find math inside everything else

### Slope

At Twitter Math Camp, Karim Kai Ani and I debated for a bit on what slope really means, and how best to teach it. Since slope is the upcoming topic for this week, I thought it would be good to reflect back on our arguments.

Karim argued that slope should always have units, and that removing the units created a contextless concept that made it difficult for students to grasp. I argued that, while that is true and units are useful in many cases, the concept of slope as a unitless ratio is an important concept, digging deep into what it means to be a ratio, so that a line with a slope of 2 could be 2 miles up, 1 mile over, or 2 cm up, 1 cm over, it didn’t matter. The differences are exemplified in two of our lessons: my “Steepest Stairs and Wacky Measurements” (soon to be updated) and his “iCost.”

(c) Mathalicious 2011

I mentioned this debate at dinner last night to my boyfriend, who is a math PhD candidate. He said what we were talking about reminded him of the difference between a rate and a ratio. He said that a ratio was a “quotient of quantities of the same unit” and a rate was a “quotient of quantities of differing units.” Further clarification was that a ratio’s units had to be the same dimension, while a rates did not.

So then, really, the question becomes, is slope a rate or a ratio?

It’s both. Karim argued for rate but that’s really just the algebraic or calculus-based definition of slope. My argument for ratio was a geometric one. Both are important, and are related, which is why they go by the same name.

But I wonder if it would be easier if the concepts had a different word. What if we only used “grade” or “gradient” for the geometric definition, and slope for the algebraic one? Or slope for the geometric, and just rate for the algebraic? The problem is they are so intertwined. For which there is only one person to blame.

Damn you Descartes!

### Math Needs to Be the Spark

At Twitter Math Camp I gave the following talk. The abstract from the program said:

When planning interdisciplinary projects, math teachers need to take the lead in order to create cohesive and authentic projects, and to ensure that the project doesn’t just become psuedocontext for their math goals. Uses two major interdisciplinary projects developed at my school as examples of how to bring all the subjects together, so math isn’t left out in the cold.

Here’s the talk:

After that I opened to questions. The one that I remember was asked by @JamiDanielle: “How can you get other teachers who might not be on board for these types of projects to join in?” And I think this process is actually how. If you go to a teacher with an idea and just dump on them to figure out how to connect it to their class, it’s not going to end well. It’s easier and less work to just not take part. But if you go to them with an idea already half-formed of how they can implement it, it is much easier to build off of that idea and will make teachers more willing to work together.

### The Projects

High Line Field Guide v5 - This is the High Line field guide project mentioned in the video, and first mentioned in this blog post, “The Start of the New Year.”

Intersession Project Requirements – It would be difficult to post everything we did in the Intersession project, but the overview from the video and this packet of requirements for the product should be useful. Anyone interested in more can ask.

I’m back from Twitter Math Camp, which was one of the most amazing experiences I’ve ever had. I’ve never made friends so easily, but I was so exhausted afterwards, because we pretty much spent 96 non-stop hours together (except for sleeping time). When people asked me if I had vacation plans this summer, I mentioned I was going to St. Louis for “a conference” and was told it didn’t count as vacation. But oh, it totally did.

I’m not sure whether I should blog about the conference or the after conference. I’m a terrible note-taker, so I’m sure others will better be able describe what went on, but highlights include spontaneously lesson-planning with Karim of Mathalicious, community-building and website ideas with Sam Shah, Megan‘s totally awesome Interactive Notebooks talk. But honestly some of the best sessions were the My Favorites… sessions, where people just went up for a few minutes and shared something awesome they did. And it was so much awesome. I also loved how, when something great was said, everyone in the room would say “Someone tweet that.”

As for after-conference events, Pi Pizzeria was actually quite good (and so I appreciate a Deep Dish Pizza as being something tasty, but not pizza). The brewery tour was nice, even though is was super-hot and I don’t like beer, but as before, the company was so good. Anyone going to St. Louis (or anywhere close) needs to visit the City Museum, an amazing experience, even if Max Ray did almost lose his wallet from up high. And I was convinced to go see Magic Mike by Julie and Sam, and seeing it with them and the other tweeps (like Marsha) made it hilarious. (Julie taught the whole audience a special dance!)

I think the thing that sums it up the most was our final activity:

I’ll post about my talk and what I shared later. Have a lot of chores to do now.

### Partnership for Global Learning – Final Day

Today was a fairly brief day to wrap up the conference, but it did have a few noteworthy elements.

The Power of Simulation – MUNSA Secretariat
Run by those same students as the Model U.N. Panel, they once again made us marvel at how they were so well spoken and prepared, sometimes more so than some adult presenters. We went through a simulation on the effects of land mines. Silently we walked from the conference room and down the hall to the atrium. Once there, we stopped and lined up horizontally. We were silently brought forward in waves to cross the atrium, but as we did, we had to pick up a card. If the card said we were alive, we crossed. If dead, we had to lie down on the floor. If maimed, we could sit or choose to crawl on to another card. If maimed twice, we had to sit as we were too injured. The imagery of the bodies sprawled across the floor was powerful, the silence was eerie, and the whole event was motivating for all of us to want to do more.

Maya Soetoro-Ng was supposed to be at the conference to speak but couldn’t make it. Instead she sent us a video message/lecture. To me it just underscored two things: video lectures are the lowest of the low in terms of engagement factor, and technical difficulties can make your lose a class and make it hard to get it back.

### Partnership for Global Learning Conference – Day 2

Today was the second, main day of the PGL conference. There was a lot going on, a non-stop day of events. Let me try to break it down.

Curriculum Development for Global CompetenceHeidi Hayes Jacobs
This talk was…agitating. The speaker was sarcastic. She seems to have not adjusted her talk at all for her audience, railing against us for not doing things that we are, in fact, doing at that very conference, such as watching a film about the schools in Finland. She asked the question “Why aren’t students doing TED talks?” when they, in fact, are. It’s what TED Youth Day is all about, and we had a session about it in the ISSN conference. Her pleas for Web 2.0 tools often seemed superficial in their application (Wordle), and she seemed to have a point of view that tech was better just because it was tech. (Later in the day I had a conversation with my co-worker about how an abacus would be a great tool for improving place value numeracy.) The Clearinghouse at Curriculum 21 does seem like a great resource, though.

What’s Global in the Common Core Standards?
A good question that wasn’t really answered. This session seemed to be about how they are answering that question, but not really working on it ourselves or providing an answer.

Light-Speed Technology for the Global ClassroomAlan November
Excellent talk. While perhaps not as mind-blowing as Andreas Schleicher, I felt like Alan really had an idea of the complexity of not just using technology but knowing how to use it. He informed a lot of people of the dangers of things like the Google/Facebook filter bubble and had some lessons on how to really circumvent it. It’s important that our students learn, and thus we learn ourselves first, how to search more specifically. (His example, in trying to find how UK schools teach the American Revolution, was to focus the search only on .uk sites, specifically their version of .edu, which I forget at the moment.) Our students also need to know how to check the veracity of a site (the example of martinlutherking.org was given, but searching for academic .edu sites that link to it reveals its insidiousness). His talk also really had a much more global focus, and how we can find those different perspectives online if we know how to look.

Game Design and Gaming for Students
Great session, I came away with a lot of resources, contacts, and ideas. I think I’ll have a whole future post on gaming in the classroom, so I won’t elucidate too much. But I hadn’t really considered game design as an educational tool. Think about it, though: when you think about game design, you don’t need to just know the rules of a game, you need to know WHY those rules are the way they are. A much deeper understanding.

Teaching about the UN: Model United Nations as a Tool for Global Learning
This session was run by students and they were all really impressive. We ran through a practice MUN session ourselves, I got to ask them about how their school runs it, and I got really excited for the possibilities of our embassies in our school this year.

Tme to collapse now, one day left!

### ISSN Summer Institute – Day 2

Day 2 of the ISSN Summer Institute came to an end, and it was quite a full day. Some good sessions, some poor sessions, and a really amazing keynote speaker.

TEDx -
This session was moderately useful in introducing the ideas of having TEDx talks in our schools. I learned about the TEDx Youth Day, which seemed like a great opportunity, though it being in November seems like it would be hard to get ready for in time. It got me excited for the possibility for hosting one, or even a viewing party, with our schools, though.

Project-Based Learning
This double session was pretty great. We walked right into a project, the presenters stepping into their roles, pushing us into our roles as engineers, that I think got the session off to a great start. The presenters modeled the group roles, the material management, the rubrics, and how to start with the problem and provide the information we need to know only once we’ve determined that we need to know it, and different strengths worked on different things (engineering, budgets,marketing), but all the groups naturally had to work together. An excellent example.

Networking
This session was…not very useful. I found the New York Region session to be more useful in terms of networking.

Then the ISSN Summer Institute officially ended and we transitioned into the larger Partnership for Global Learning conference. We had a lovely dance performance before dinner, but our keynote speaker Andreas Schliecher was amazing. He presented data from the PISA assessment on what really affects student learning, what acts as a predictor of student success more than just grades, the relationship of equity and success. I really liked how lateral accountability is one of e keys of success, because it makes students professional without removing accountability. And all of his claims had data to support it.

Because, as he said, “without data, you are just another person with an opinion.”

### ISSN Summer Institute – Day 1

Day 1 was fairly interesting. We started off with a speech by principal Salome Thomas-El, which was a pretty good motivational tool to get us started. Then our GPS session started. It’s always great to be able to talk to other math teachers, and we had a good discussion on what is definitely the hardest part of the ISSN Outcomes: the Take Action phase. Figuring out what having students take action looks like, and how we can fit it into our classroom when it always seems like this key important phase takes away time from our overpacked curricula is still a work in progress, but progress was made. Finding a way to weave the standards into the action, such as learning about graphical representations of mathematics at that time, seems like one way to go.

Then the Learning Expeditions were finally revealed. We were given a variety of choices of exhibits, museums, and memorials to visit, but we could only choose one, and only 12 people could go on each exhibition at most. My number was chosen towards the end, so I didn’t get my top choices of expedition, but my trip to the Hirshhorn was still fairly enlightening, and doing it as a learning expedition reminded me how having an assignment at a museum can make it much deeper and force people to look at an exhibit closer.

Now we’re talking about kicking off the year with an expedition. We yearn for the day that we can have one as self-guided with our students as these were.

### ISSN Summer Institute

I’m writing from Washington DC now. Well, technically Rockville, MD, since that’s were the hotel and conference is, but we’ll be in DC itself for parts of it, and that’s where the Amtrak dropped me off. I’m at a conference run by the Asia Society along with my principal and four of my co-workers (Mandarin, Special Ed, ELA, and Earth Science). I was willing to go because it was funded, a trip is better than staying home, and I might get something out of it, but now I’m fairly excited for some of the sessions I’ve signed up for after looking through the itinerary. Here’s a breakdown of what I’ll be doing. I’ll try to have write-ups on at least the more interesting sessions, if not all of them.

WED
10:15 – 11:30 – GPS Performance Outcomes and Global Leadership – Math
1:00 – ??? – Learning Expedition (I have no idea what this is, but it should be good.)

THURS
8:30 – 10:10 – TEDx at Your School: Innovate and Integrate
10:20 – 12:50 – Using Project-Based Learning for Unit Development
1:40 – 2:50 – Networking: Learning from Colleagues by Sharing Lessons from the Field – Math
7:00 – 9:00 – Learning with the World: PISA Results and Preparing All Students for a Global Future

FRI
8:30 – 10:15 – Curriculum Development for Global Competence
10:30 – 11:45 – What’s Global in the Common Core Standards?
11:45 – 1:30 – Light-Speed Technology for the Global Classroom
1:45 – 3:00 – Game Design and Gaming for Students
3:15 – 4:30 – Teaching about the UN: Model United Nations as a Tool for Global Learning
5:00 – 6:30 – Partnership for Afterschool Education Reception

SAT
9:45 – 11:15 – The Power of Simulations
11:45 – 1:00 – Teaching the Interconnectedness of Global Understanding