A new home

In an effort to simplify my life, I have begun the process of moving my various blogs and webpages to a single place.  This blog ca now be found at sswoolley.org/edtech.

Thanks for reading!

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Geometric Thinking; March 7th

It was interesting to go back and reread my blogs.  In my first post, I talked a little bit about how I had not really considered the idea that geometry was about relationships.  Although I never really mentioned this again, I think in almost every subsequent post I talk about something related to geometry: art, technology, algebra, language, etc. In our last class, we also talked about how for most people, geometry was not a positive experience.  One of my classmates said the only thing he remembered were endless months of proofs, and that he hated it.  My own high school used integrated curriculum, so I have no memories of “boy, algebra really sucked,” or “Geometry was lame,” or “Trig was the hardest thing ever.”  I just took a math class (one, two, and three).

What is really getting me is that as far as I understand it, geometry is the branch of mathematics most closely related to something people should enjoy: beauty.  If anything, geometry should be everyone’s favorite class.  That it’s not tells me we’re doing something wrong.  I want to fix that.  At least for my own students.

Geometric Thinking; February 28th

What did you learn?

I thought the resources were totally awesome.  It was amazing how cheap so many of these books were.  I am going to order a bunch of them.  I also really liked the last activity with measuring because it made me think about how arbitrary our measuring systems are.

What questions do you still have?

I don’t have any questions right now… I will be thinking about this during the week and likely come up with some later.

How can it apply to classroom practice?

This is making me think a lot about how valuable it might be to talk with my students about where mathematical terms come from.  Sometimes they’re arbitrary, and sometimes they’re not.  When they’re not, I think knowing why we do things the way we do and what they mean can help them better understand what the math is about.

Geometric Thinking; February 14th

What did you learn?

I got one of my earlier questions answered, which was how to tie algebra and geometry together better.  Unfortunately, the state standards now exclude matrices, so our school, for example, doesn’t teach them any more.  I also didn’t learn matrices in high school.  I learned a little about them in college, but not much.  Every time I learn a little more, I find myself thinking a couple of things:

  • Matrices seem really powerful and amazing
  • why would the people who write the state standards think they were not worth learning?

What questions do you still have?

  • Who writes the state standards?  Why do they make the decisions they do?
  • Are there any good books that cover this?  Was that Modern Geometry book good?

How can it apply to classroom practice?

I am not sure yet, I need to think about this more.

Geometric Thinking; February 7th

What did you learn?

It’s amazing to me how much of this stuff I still remember from high school.  I don’t think I’ve constructed a perpendicular bisector with a compass since about 1990, but I did it so many times back then (and liked geometry so much) that it stuck with me.

Have I mentioned that I love geometry?  Also, constructions make good art.

What questions do you still have?

I feel like too many of my students don’t like math.  It seems like an abnormally large number of people, given that math is so ubiquitous.  I want to know how I can find a way to help my students learn to like math more than they do.

How can it apply to classroom practice?

Maybe I need to start by asking them some questions about their feelings and history with math.

Geometric Thinking; January 24th

What did you learn?

One of the things I’ve been thinking about off and on lately is one of the questions asked in class: “What is technology?”  I’ve also been watching some videos lately about the connections between art and mathematics that are really blossoming in origami lately.  Putting these two things together, I am beginning to be very curious about using more art and science in the classroom as ways of implementing “technology.”

What questions do you still have?

I am wondering if technology might not be defined as anything not typically used in a classroom that can be used to further learning.

How can it apply to classroom practice?

I am not sure yet.  So far I’ve begun by showing two of the most interesting videos to my students.  I’d like to move beyond that and start creating more art- and science-based tasks for my students, but I don’t feel like I know enough yet to do that.  So I need to learn more.

Geometric Thinking; January 31st

What did you learn?

What stuck with me the most was the discussion about language in geometry.  I found myself thinking about all the specialized language that’s also used in algebra (what I’m teaching now), and realized that it’s a bit like learning a foreign language, except that the language learning part is implied and not really explicit.  I think in geometry there is more emphasis on vocabulary, but this is also important in other fields of mathematics.  I also got to thinking that students are likely to encounter other fields with specialized language, but that math might be the first major one.

What questions do you still have?

I want to know if a greater emphasis on language development in earlier math might not help students with their learning later down the road.

How can it apply to classroom practice?

I think I might try to take time out once or twice a week to talk specifically about terms, what they mean, and how they relate, to help students clarify their conceptual understanding.

Geometric Thinking; January 10th

What did you learn?

I had done the app with the quadrilaterals before, but in a different context.  Doing it in a new context, thinking about the situation with different questions, made it an entirely different lesson.  I learned that it can sometimes be a really good thing to use the same materials in different ways, to give students a chance to see that there are many ways to use and approach the same problem/situation/tools.

What questions do you still have?

One thing that struck me right off from the reading was the paragraph on page 25 talking about how some problems are framed toward algebraic thinking and others toward geometric, but that it can be difficult to see how to think the other way in each.  That made me wonder if this was because it’s difficult to write problems in such a way that both kinds of thinking seem an equally good choice, or if something else was behind it.

How can it apply to classroom practice?

Aside from what I mentioned in the first answer, I am also thinking I might try to design some tasks for my students that suggest both algebraic and geometric solutions, to see if students choose to solve them geometrically.  I am teaching algebra and advanced algebra.  I could see my advanced algebra students perhaps using some geometry, as they have already studied it, but I am not sure about the algebra students.  I’d like to give them the opportunity, though.

Math doodles

One of the teachers in my department pointed these videos out to me.  I am not 100% sure at this point what the goal of this blog is, but what I can tell s far is that it’s a series of short videos of someone (Vi Hart) doodling, beginning with some bit of math.  They’re pretty amazing, so if you’ve got a few minutes, check them out.

Geometric Thinking; January 3rd

What did you learn?

There were a couple of things.  From class, I hadn’t really thought about geometry as being about relationships, but that makes some sense to me.  I have often thought a lot about the reasoning that’s taught as part of geometry.  I think that without relationships, it would be difficult to make the connections necessary to reason from one idea to another.

Rereading Never Say Anything… was really, really helpful to me.  I’ve been leading more whole-class discussions, and spend a lot of time talking to students in small-group discussions.  I feel like I’ve been slipping a little in my practice, and so reading again about how to ask good questions has given me some good ideas of what to work on.

What questions do you still have?

Right now one of my biggest questions is about how I can start helping my algebra students get ready for success in geometry, and how I can also help them get excited about the things they’ll get to learn there.

How can it apply to classroom practice?

As I said above, the big thing I can do right now is to make some improvements in how I question my students, and how I respond to their questions as well.

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