Annie at the Math Forum

ATMOPAV, October 27, 2012
Annie Fetter and Val Klein

Some resources we’ll use today:

Growing Worms (PDF)

How Many Berries? (PDF)

K-5 Scenarios

Thanks to so many of you (130!) for coming to my talk.  My apologies to the other 60 or so people who couldn’t get in.  I had a great time, and appreciated your willingness to do some math, share your ideas, and talk with your neighbors about your thinking.

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Exploring (vicariously) interactive applets that let students “notice and wonder”, talk about mathematical situations, and develop conceptual understandings of triangle properties, linear equations, systems of equations, and factoring trinomials.

Session 12, Thursday, October 25th, Meeting Room 17, Convention Center

National Council of Teachers of Mathematics Regional Conference, Connecticut, October 2012

Session 12 Handout (PDF)

For more about the Math Forum, including information from my colleagues Max and Suzanne’s talks, visit our Hartford page at http://mathforum.org/workshops/hartford2012/.  And don’t forget to fill out the survey in the NCTM Hartford App!

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Types of Triangles – Annie Fetter

Link above includes handouts, sketch, and Sketch Explorer version

Key technology strengths:  exploring dynamic models of different triangle types, allowing students to develop intuition about different classes of triangles and what characteristics they do and don’t have.

Runners – NCTM e-Examples from Principles and Standards

Session 12 Runners Prompts (PDF)

Key technology strengths:  developing intuition about distance/rate/time and the concept of slope, without needing to know the formal vocabulary at all, as well as the ability to try things and get it wrong, and get instant feedback without fear of judgement by others.

Galactic Exchange – The Math Forum’s ESCOT Project

Session 12 Galactic Exchange Handouts (PDF)

Key technology strengths: the applet does the recordkeeping for you, and students can explore systems of equations without needing to know that they’re doing that, or even knowing that such a thing exists!

Algebra Tiles – National Library of Virtual Manipulatives

Session 12 Algebra Tiles Handout (PDF)

Key technology strengths: the variables actually vary!

Reminder: Want to be cutting edge?   Complete the survey about this talk in the NCTM Connecticut app!

Many years ago, back in the the mid-90s, I was in Colorado and visited my friend Anne’s school.  I was planning to do a Geometer’s Sketchpad workshop with the teachers after school, teaching them how to author “scripts” (the pre-cursor to Custom Tools in Sketchpad), with a focus on the centers of triangles.  Anne was gracious enough to let me teach her geometry classes for the day in the computer lab, and so the students had the neat experience of learning the same thing their teachers were going to learn after school.  (“You mean our teachers don’t even know how to do this??  Cool!”)

We started by constructing a centroid and creating the script.  The students were familiar with Sketchpad, so things went quickly.  We moved on to the circumcenter, and this is where things got interesting.  I gave the definition and they started constructing.  And I heard this exchange:

Student 1: “Hey, man, what’s wrong with your circumcenter?”

Student 2:  “Nothing’s wrong with it.  I followed the directions!  What’s wrong with yours??”

I wandered over, and I find that Student 1′s circumcenter was inside the triangle, just like the (visually boring) centroid was.  Student 2′s circumcenter was outside the circle.  Opportunity time!  I ran to the front of the room and wrote a question on the board:  “When is the circumcenter inside, outside, or on the triangle?”

Not one minute later, I had 28 high school sophomores looking at me like I had two heads, basically telling me, “That’s a stupid question!  Obviously, when the triangle is acute, it’s inside, when it’s obtuse it’s outside, and when it’s right it’s on the triangle.  Why are you even asking us something so simple??”  I was beside myself with excitement because, traditionally, it’s not at all obvious. This is because most students are just told that fact.  They don’t discover it.  It’s just one more thing that they have to memorize that makes geometry class onerous and quite possibly their least favorite math class.

But these kids figured it out for themselves, independently, saying things to their neighbors like, “Uh, isn’t it just whether the triangle is acute, obtuse, or right?  Or am I missing something?”  Because they had a dynamic tool.  They dragged.  It moved.  They controlled it.  They had constructed the situation, so they knew how the objects were related to each other.  While this power of discovery never comes as a surprise to me, it’s still so cool to see it in action.  These are moments I never forget (obviously, since I’m blogging about it some 16 years later!).

We continued on to do the orthocenter and incenter, making scripts and exploring some properties of each.  This is where the title of this post comes in.  I noticed one boy staring off into space at one point, not doing anything on his computer.  I walked over and said, “What’s up?”

He replied, very seriously, “Let me get this right.  You actually like math.”

I said, “Yea, I do.”

He nodded and then stared off into space for another 20 seconds, before he went back to work at his computer.  It’s like he had never met someone who actually liked math.  His teacher was a great teacher, very committed to math and education, and I’m pretty sure she actually liked math, but maybe he just saw her as someone who was doing her job.  I was just some random person off the street who actually likes math.  Who knows?  I’d like to think that he might have thought differently about math from that moment on!

Session Description: This is your opportunity to join an elite corps of highly trained mathematical mentors. Real students from around the world send the Math Forum their solutions to challenging math problems. Volunteer mentors write back to students, starting a mathematical conversation. Come learn the skills involved in being a math mentor, and the impact you could have on the next generation of mathematical problem-solvers.

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Today we’re going to write some replies to students who submitted answers to the problem Stacking Wood, a problem targeted at middle school students. We’ll start by solving the problem and talking about the mathematics involved and thinking about the sorts of mistakes that kids might make when solving the problem.

Read Stacking Wood

Preparing to Mentor

1. Solve the problem.
2. Talk about the mathematics concepts involved.
3. Think about the sorts of mistakes that students might make.

Let’s Try It!

1. Read Lily’s submission and write a reply together: Lily
2. Read Jacob’s submission and each group writes a reply: Jacob
3. Write a reply to a student or two with your partner: More Student Solutions

Next Steps?

My thanks to those of you who came to my talk and played along with these activities. The links below will get you a copy of the handout and send you directly to the applets themselves.

I would love to get some comments from any of the attendees. Can you name one thing that you took away from the talk that you’re eager to try out or work on?

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Exploring (vicariously) interactive applets that let students “notice and wonder”, talk about mathematical situations, and develop conceptual understandings of triangle properties, linear equations, systems of equations, and factoring trinomials.

Session 610, Friday, April 27th, at the Marriott, Salon D

National Council of Teachers of Mathematics Annual Conference, April 2012

Session 610 Handout

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Types of Triangles – Annie Fetter

Link above includes handouts, sketch, and Sketch Explorer version

Runners – NCTM e-Examples from Principles and Standards

Session 610 Runners Prompts

Galactic Exchange – The Math Forum’s ESCOT Project

Session 610 Galactic Exchange Handout

Algebra Tiles – National Library of Virtual Manipulatives

Session 610 Algebra Tiles Handout

Thanks to everyone who came to the Key Press Ignite Session at NCSM in Philadelphia.  I am really looking forward to hearing your responses to the homework prompt:

How did you become the teacher you are today? Specifically, what motivated you to become that teacher? What experiences helped you to realize, or at least begin, that process?

Couldn’t make it? Not to worry. Watch the video! You can still do the homework.

Just to make you curious, here’s a little teaser in terms of some folks’ responses to the homework prompt:

Suzanne: Motivation? Lectured from Dolciani for three years, then raised two kids and watched them learn. Experiences? Writing about that learning for John Holt’s journal.

Arjan: Motivation? I hated being lectured to. I hated learning like that.

Max: Experiences? It helps that I went to an interesting high school where I saw all sorts of teaching in my classes. And my mom’s a Montessori teacher.

Geri: Motivation? The Saxon ½ Book. It was so boring! Experience? Woodrow Wilson Institutes, especially the collegiality and collaboration.

Erin: Motivation? The students’ bored faces when I did direct instruction, and watching other teachers lecture and realizing that it was dreadful. Experiences? Suzanne walked into my classroom and said, “Try this.”

Your response here – do your homework and leave a comment!

My friend Debbie, the enrichment teacher at a local elementary school, sent me the following pictures, along with this question: “What do you think about the attached? Fourth grade E[veryday] M[ath] ch 6 intro.”

My short answer was, “I think it’s brilliant!” I’ll expound on that more in a follow-up post, but wanted to throw this out there first in case anyone else had thoughts they wanted to share. (Yes, Unit 6 is about division.)

Pennsylvania Educational Technology Expo & Conference, Hershey, PA, February 2012
Debbie Wile, Wallingford Elementary School, Wallingford, PA
Annie Fetter, The Math Forum @ Drexel University, Philadelphia, PA

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Introductions

• Who are Debbie and Annie?

The Path to This Talk

• Annie’s Online Classes, and How It Works
• Christina’s Geometry Class
• Debbie’s Students

What’s Next?

• Literacy Applications
• Peer Editing
• Big Brother is Watching
• Precursor to Open-Ended Responses – Talking is Easier Than Writing
• Other Applications?

Discussion

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Helpful Links

• Geometer’s Sketchpad from Key Curriculum Press – check out the trial version
• Screencast.com, for Jing
• Making Movies Using Jing – Instructions [pdf]
• Constructing Quadrilaterals with Sketchpad Handout [pdf]
• Transformations Handout [pdf]

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Debbie is the enrichment teacher at Wallingford Elementary. She teaches students in grades 1-5.

Annie is an Educational Programs Leader at the Math Forum. Read more on her blog profile page.

Act 48 code: DL061674

Exploring interactive applets that let students “notice and wonder”, talk about mathematical situations, and develop conceptual understandings of triangle properties, linear equations, systems of equations, and factoring trinomials.

ATMOPAV Mathematics & Technology Conference, Fall 2011

Get the session handout [pdf]

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Types of Triangles

Runners

Galactic Exchange

Algebra Tiles

Technology can help students develop concepts such as multiples, fractions, and area through pattern analysis and engaging representations. Learn implementation strategies exploring technology and math.

ATMOPAV Mathematics & Technology Conference, Fall 2011

Annie Fetter and Valerie Klein, The Math Forum @ Drexel

Frog Farming

Pool Investigations

Balloon Booths