The premise is that the algebra 1-geometry-algebra 2-precal-calculus sequence is broken and doesn't work for him. Interesting bits:
- we teach things in algebra 1 (like rational functions with factorable denominators) to kids in 7th or 8th grade in algebra 1 that weren't part of algebra 1 for most of history.
- He has a book (missed the author) with 'everything that you need to know about trig, algebra, and geometry - it's 119 pages long.
- His challenge - assuming competency with fractions, decimals, etc. - can we do all of that stuff in a 100 hour course? This is a course that covers the essentials of algebra 1, geometry, algebra 2. There's less material included in that than in the three courses currently, but what would there need to be?
Now... we discuss...
Some ideas from the group about things that can be thrown away:
- "most of geometry" - angle theorems, centroids, etc. The idea of proof is important, but does the two-column regime actually communicate that? Do students come out of geometry able to prove things?
- half angle/double angle/trig identities
- vocabulary - associative, commutative, etc.
Our group's "keepers" (partial list - didn't get to completion):
- Right-triangle trig
- Modeling: choosing appropriate algebraic models for data, using graphical and algebraic representations together, applying and interpreting the models
- Understanding equations as relationships: create, manipulate, and solve single equations and systems of equations
Presenter's proposal: a one-year intensive experience in abstract math, with topics left out of this course taught in the subjects in which it's applied (exponential growth in bio, etc.). His big idea is that we've divorced math so much from the applications that it's not effectively transferrable to other courses.
Discussion following that:
- One report of collaboration of science and math teachers just on aligning vocabulary had a big effect on this transferability.
- Can't we just teach multiplication and exponents conceptually, so that it's not a set of rules, but just a consequence of the concept? Presenter reports his district teaching exponents in alg. 1 and alg. 2; you can't tell which kids had it the first time around - it was divorced from use and totally forgotten. They were rules, but when kids understand that it's repeated multiplication, kids don't need the rules, and can actually use them.
- What if we co-taught these bits in other courses? That's a scheduling nightmare, but we could be the resource for kids and teachers.
- Shoving kids through this content is counter-productive: it's painful for all involved, doesn't help kids later, and takes time away from really understanding
- The assessments are part of the problem: what do they assess, and is it what we really value?
- A year of mathematical thinking (content fairly unimportant, context important) is a popular notion here
- Dan Meyer and 101qs.com came up; the issue here is that these are overwhelmingly proportional reasoning problems, so it's not a solution for everything, but it can suck kids in.
- A great point that it doesn't have to be about being 'real world,' but 'interesting' is great too
- Awesome point that we need to be careful not to teach students that math problems are things with unambiguous answers that can be solved in 10 minutes.
- Does mathematical thinking have to only involve doing mathematics? Can it be done by making these, in a hands-on way? If we reinforce mathematical reasoning tacitly, won't that make the pencil and paper stuff easier and more meaningful?
Some slides from a Standards-Based Grading conversation in a different session: http://www.slideshare.net/lpahomov/educon-2013
Now I'm in "Qualitative Formative Assessment: Letting the Learning Environment Dictate the Tools", with Reshan Richards (@reshanrichards).
We start with an odd activity:
Draw a creature that's half-perro, hal-canard that is sitting near an iconic Philly landmark while contemplating the area of a circle. Provide a grammatically correct sentence as a caption. Stand up and stretch.
He's the creator of the Explain Everything app, and he is looking at making assessment a bit more dynamic, including screencasts.
He has some issues with flipped classes, as they're just time-shifted lecture. Yup, that's true! Also, issues with a paradigm that means that you know exactly what page you'll be on 8 months from now - is it student-centered, in that case?
I'm hearing lots of stories of technology purchased and deployed with little support and buy-in. Lecture/demo as a training method for faculty isn't good, just like it doesn't work well for students.
Each table asked a question, shared them via Google Doc, and re-organized based on interest. I'm in this one: "How do we not put the (laptop) cart before the horse? Adding gadgets without motivation/need/understanding/purpose - it doesn’t help. How do we add technology in a way that positively impacts student learning, and doesn’t just look shiny?
There were lots of observations about top-down tech decisions being problematic, and one good story about an increasing training web of folks that help each other, all the way down to the kids. Training and support really takes more effort/money than buying the darn things.
The discussions that I was involved in diverged pretty widely from the topic here, which is too bad, but they were good in their own right.