Not giving them the answer

The 7th grade math teacher and I co-coach our school's math club after school.  Today, as we were doing math problems together with our scholars, as a group, she paid me one of the nicest complements I have ever received.  She said "You are so good at not giving them the answer and asking them questions so that they can get to the answer on their own."  

What am I learning about collaboration?

I am actually beginning to believe that the difference between being a good math teacher and a great math teacher is more than just meeting frequently to talk about "teacher things."  That stuff is necessary and important, don't get me wrong.  But I am starting to really think that doing math with others is an important and necessary part of being a professional in math education.  

Proving the Pythagorean Theorem

Even though, the math team didn't officially meet this week, but the 7th grade teacher, Molly, and I spent some time proving the Pythagorean Theorem.  She mentioned that she wanted her 7th graders to be able to come up with the Pythagorean Theorem on their own and asked if we could work on some ideas together.  I of course said yes!


She started off by asking me how I had taught it in the past, and I admitted that I had never really given my students the chance to explore the Pythagorean Theorem.  Looking at past lessons, I always told my students what the theorem was, and then we talked about it, but they had never discovered it on their own.  I did mention how one year, I had my students work in pairs on a mini-lab that explored the areas of squares and how they relate to the Pythagorean theorem.  Molly shared her idea that she wanted to use colored squares and have her students outline a right triangle and then compare the areas of the squares.  I shared that during my mini-lab, I had students create a 3x3, 4x4, and 5x5 square on graph paper and then (1) find the area of each square, (2) how are the squares of the sides related to the areas of the squares, (3) find the sum of the areas of the two smaller squares.  How does the sum compare to the area of the larger square, and finally (4) use grid paper to cut out three squares with sides 5, 12, and 13 units.  Form a right triangle with these squares.  Compare the sum of the areas of the two smaller squares with the area of the larger square.


As we talked, we got out some colored squares and graph paper, and began playing around with the Theorem.  We created different sized right triangles and manipulating the squares to see show how the area of the square of the legs would always equal the area of the square of the hypotenuse.  We started off approaching the Pythagorean Theorem as teachers, but very quickly found ourselves talking about the math behind the famous theorem.


After we had explored and talked for almost an hour, I suggested to Molly that we look at the Connected Math: Looking for Pythagoras (http://math.buffalostate.edu/~it/projects/Walczyk.pdf) book for some other possible ideas to teach her students, as well as the NLVM Pythagorean Puzzles (http://nlvm.usu.edu/en/nav/frames_asid_164_g_3_t_3.html?open=instructions&from=category_g_3_t_3.html)


(To be continued...)


What am I learning about collaboration?   
After working with Molly this week I learned that collaborative professional development doesn't have to be something formal... it can happen between two teachers to want to explore something together.  I also learned  that it helps to stop approaching things "as a teacher" sometimes, and to to just play around with the math and see what happens.  It was great getting the chance to work with Molly one on one this week and I am inspired to keep this action research going. 

The Game of Poison

Today during our Math Team meeting, I taught my colleagues how to play the game of Poison.  I had recently taught the members of the Math Club how to play and thought it would be fun...


(To be continued...)


What am I learning about collaboration?
Sometimes something as simple as a Nim game can be a great way to get students and adults to start talking about math.  Who knew?

Making time for Math

The math team met again this evening.  Like last time, I set up an agenda on Google Docs and encouraged the other math teachers to add on to it.  This time, however, I set aside the first half of the meeting to do some math together.  I asked everyone to bring their laptops, so that I could introduce them to the Peg Puzzle ( http://nlvm.usu.edu/en/nav/frames_asid_182_g_3_t_1.html?from=category_g_3_t_1.html)  When we started, I directed everyone to NLVM website and asked them to play around for a bit, and then suggested that we come back together and share what we learned....

(To be continued...)

Setting up Meeting #2

I sent out an email earlier this afternoon, asking our JBA math team when the next availble date to meet that works for everyone is.  Because of PDs and Thanksgiving, I suggested Monday, November 21st or Wednesday the 30th, but opened it up to the group.  Within an hour, the AP, ICT teacher, and 6th grade teacher got back to me!  This was encouraging!

It looks like we may have a Faculty meeting on Monday the 21st, so I asked the AP if we could possibly have that time to meet and I am waiting to hear back from her.  If not, it looks like Wednesday the 30th will be our 2nd meeting.  I have already revised the agenda on Google Docs slightly to reflect this.

What am I learning about collaboration?
The feeling that I get from my colleagues is that they do want to meet and want to collaborate, but that isn't always easy.  We all take our job and responsibilities very seriously and teaching comes first.  I completely agree, and hope that future meetings can tie into what we are teaching.  Again, I want these meetings to be practical and as useful for my colleagues and I as possible.

A Minor Setback

Unfortunately, at the last minute, the math team meeting that we were supposed to have today, didn't happen.  The 6th grade teacher had a personal reason, the ICT teacher had an after school club, and the AP was called into a meeting.  The 7th grade teacher and I debated whether or not to meet "officially" and thought it would be best to reschedule for a date when the whole team could meet.

I was a little disappointed, but I understand that things do come up and that it's important to be flexible.  So far I haven't gotten the vibe from my colleagues that they don't want to be these meetings to happen, so I will be optimistic that this is just a minor temporary setback.

In the meantime, I created the agenda so that when we do meet, our meetings would have a focus.  Nobody else has added to the agenda specifically, but the 6th grade teacher did add a document to our Google Collection.

The good news is that the 6th grade teacher, ICT teacher, and AP said that they were glad that they didn't miss anything, which makes me feel like they want to be a part of these meetings also.  I just don't want our group to slowly happen less frequently as the school year goes by.

What am I learning about collaboration?

It's not easy to get, even a well-meaning group of people, together.  I am a little disappointed, but am still looking at this as only a minor set back.  It has been a crazy week at JBA with grades being due, Benchmark Assessments, and the schedule changing for the new marking period.  I will be sure to send out an email asking for the next best available dates for people so that we can get our math team back on focus.

Our First Meeting

So we just had our first math team meeting.  Originally we planned to meet for an hour, but ended up meeting for an hour and a half after school, in my classroom.  The 6th grade math teacher, assistant principal, and I (and briefly our ICT teacher) were the only ones in attendance.  The 7th grade teacher was unable to make it, and at the last minute the ICT teacher was unable to either.  The three us us decided to meet either way and take notes on our Google Doc so that we could share it with the others.

Our agenda consisted of:

• Discussing Math Portfolios (the principal had asked the AP to talk to us about this)
• Teaching strategies that should be used across all grades so they are ready for Algebra I
• What are our department goals?
• Where are we now?  Where do we want to be?
• Looking at our data?
• How often do we want to meet? 

Together the three of us went though each of these points and discussed our responses.  We had the agenda up on the Smart Board and as we collaborated, we added to the document.  For each of the points, we discussed next steps.  This was important to me because (1) we had an "official" working document from our meeting, and (2) our next steps were practical things that we would bring or do during our next meeting.  (I can attach our "final" agenda in another post.)  

We decided that Wednesdays overall seemed to work best for everyone, and meeting every other week would be a good start for us.  Due to upcoming PDs, we decided to meet the following Wednesday, November 9th.

What am I learning about collaboration?

It feel really good to actually get the chance to meet.  I think our agenda also helped to keep us focused, so that we didn't get off topic.  We had specific goals to accomplish and we were able to speak about all of them.  For our next meeting, in addition to addressing our next steps, I want to actually do some math with my colleagues.  Using the "Teaching Math in the Middle School" article about Teaching Circles, I have decided to use the Frog and Toad problem.  I even found a website that we can all go do.

I am a little worried that we might be trying to do too much during our meetings.  Personally I would rather do less deeply, than try to cover too much, however I want everyone to feel like they are contributing to these meetings, and it's not just me.  I think the Google Doc agendas that everyone can add too will help with that.

Looking forward to our meeting next week!