The Digit Place game

For this week's math team meeting, I decided to start us off by teaching my colleagues how to play the Digit Place game.  I had learned about this game during a PD I had gone to in December and thought it would be a simple and fun way to get us started.  The 6th grade teacher was familer with the game, but the 7th grade teacher, and our ICT teacher were not. 


This elementary school teacher's classroom blog has the instructions on how to play.  After I explained the directions, we got a white board, marker and paper towel, paired up and started playing.  We ended up playing for about 15 minutes or so, and then had a discussion on how we could potentially use this game in our classroom and questions we could ask to encourage our scholar's thinking.  As we were sharing, I wrote down the questions that were coming up with on the board.  Some of the questions we came up with to ask our scholars were: "What do you know so far?" "Are there any digits that you are certain are in the number?  What information helped you?" "Have you eliminated any digits?" "What would be your next guess any why?" and "How could it help you to guess a number that included digits you had already eliminated?"  


What am I learning about collaboration?
One of the reasons that I chose the Digit Place game was because I wanted to keep it simple.  I anticipated that we would play the game for a few minutes, talk about it briefly, and then go on with the rest of our meeting, but that was not the case.  After playing each other, the discussion that we had was awesome.  What started out as a simple game, became a discussion on transforming the tasks that we ask our scholars to do to encourage our scholars to use thinking, reasoning, and problem solving skills.  I was amazed at the enthusiasm that something so simple as a game on digit place, could lead to.  


I think one of the reasons that this worked well was because it was something that the teachers could potentially share with their classes.  One of my complaints of past PDs has been the lack of practically.  There might be some good ideas, but I always liked the PDs where I left with something I could bring back to my students and try tomorrow.  A teacher's time is valuable, and nothing makes me more frustrated than feeling like I just wasted time at a useless PD, so I think one way to make collaboration more meaningful is by keeping things practical.  Who knew that something as simple as the Digit Place game could be so productive?

Accepting the fact that I do not know it all...

I have been following a fellow teacher (and blogger) on http://www.thenerdyteacher.com/ since the beginning of this school year. He often blogs about technology and how he uses it in his ELA classroom, and he usually posts some interesting stuff. Yesterday he posted something on Twitter that caught my attention. He said "Collab for me was accepting the fact that I didn't know it all and I learn and grow with others. #edchat" Being that my action research and this blog is all about what I am learning about collaboration, while using math problems with colleages as a focus, that tweet really got me thinking about why I chose collaboration as the focus of my second action research topic.  

Teaching isn't easy.  Or at least teaching has't always been easy for me.  Don't get me wrong, I have seen growth in myself as a professional since I started, but I take it very personal when I am not successful.  I knew that I enjoyed teaching, but going into my fifth year teaching middle school math, I was feeling the strain that comes from feeling like I have to do it all on my own.  I still believe that it is ultimately up to me whether I am successful or not, but I am learning (and slowly accepting) that I cannot do it alone.

What am I learning about collaboration?

Collaboration doesn't have to be this formal "thing" that you do, but it should be focused around what you are trying to do.  If I want to be a better math teacher, I need to surround myself with those who I believe to be great math teachers.  And it's not enough to mealy surround myself with them... I need to talk to them, question them, and ultimately learn with them.  I don't think any good teacher can do it alone...  and it has taken me almost five years to realize and begin to accept that.

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.