Wednesday, September 26, 2012

Monty Hall Problem

In my Foundations 30 class we started our probability outcome last week.  As a "hook" to the outcome, we spent a day exploring the Monty Hall Problem.  For those of you who grew up watching Let's Make A Deal, you will know who Monty Hall is!  For those of you who don't, simply google Monty Hall Problem.  It is a mathematical paradox that has had many people talking about it.  Most of my students did not know about this show or who Monty Hall is.  I explained to them a bit about the show and we watched a short clip on youtube about the show so they had some background.  I then explained to them the finale of each show - three doors presented to a contestant, 2 of which had goats and one which had a prize - typically a car.  The contestant had to pick one door, Monty Hall then opened one of the other doors where he knew there was a goat, and then asked the contestant if they wanted to stay with their original choice or switch to the other door.  I left it at that and gave the students a few minutes to discuss whether they would stick or switch and why.   As I walked around and listened to the conversations I was impressed at what they were thinking.  Some were saying they would stay because that was their gut feeling and they would regret if it was in their original pick, others said they would stay because you had a 50-50 chance anyways, and a few said they would switch because they would increase their chances.  It was also interesting because the level of engagement was higher than normal and I had a couple of students googling the problem on their phones!   After a few minutes I had some students share their thoughts.  It was interesting as how most felt it was a 50-50 chance and the few who thought the chances would increase were shy to share why since they weren't the majority!   I didn't give anything away, just listened and asked why they felt the way they did.   I then shared how we had done this as a group of teachers last year and that we were also split on our opinions.  We then watched a mythbusters youtube video on this problem.  It explained and showed that a person actually doubles their chances of winning if they switch.  That surprised many of the students.  This was a good hook for probability.

The next day was when I realized how engaged some students were and how great of a hook it was.  I had a student who struggles with math, doesn't have regular attendance and often comes late say to me "you know I hate math but that problem we did yesterday...I couldn't stop thinking about it and I hated that... but I still think I'm right with 50-50 and it bugged me and was all I thought about."  AWESOME!!!!!  When you can get a student who openly hates math to THINK about a math problem, you know you have engaged them!   I only wish I had a bag of magic tricks to do this every day!  Maybe by the time I retire I will have this bag of tricks!  For now I'll take it when I can and be satisfied that I was able to succeed even once for now!  And not that I'll stop looking, as I'm always looking, but I am happy for the feedback that I received!

Wednesday, September 19, 2012

What I Learned From Observing A Colleague

I mentioned in a previous post (here) that one of our PLC goals was to observe and learn from other members of the group.  Yesterday I did my first observation of a colleague.  I even managed to convince the person to let me video tape their lesson.  She agreed as she said she is always telling her students to get comfortable with being uncomfortable, so she thought she should be able to step out of her comfort zone too!  The agreement was that she would view anything I edited first before I showed it to the rest of the group.

I feel it went really well.  My initial plan was to observe her use of popsicle sticks for questioning random students.  I wanted to see how that was working for here.  However, I learned three things during my time in her class.  We both teach the same course and I had just taught the same lesson the previous day.  She began her lesson a little differently from what I did.  She did a word association for two new terms.  I really liked the idea and will consider doing something similar as I move forward.  I liked that the students had some good ideas and were okay with sharing them. That was my first learning experience of the class.

 Second learning experience:  I did get to see how she incorporated the use of popsicle sticks to ask questions and I will likely be starting this with my grade 9's once I find time to go and buy the sticks!!!!   I have a few "blurters" in that group and the same ones are always putting up their hands.  I generally try to stop the "blurting" and typically don't allow a person to answer once they already have until we have been through the entire class, but I think popsicle sticks will assist with controlling this.  I could tell that her students are already used to this process.  When called upon they were ready with an answer.  She was sure to say that they needed to be prepared with an answer, but it was okay to be wrong.  I believe that is very important.  I try to instill that in my students as well.  It is important to be thinking about the question and it is okay to be wrong - that is how we learn!  I liked that when she was doing her word association, the third student she asked said all of their answers had already been used, so instead of letting the student off the hook, she asked the student for a real life example.    There were some great questioning techniques that I had an opportunity to observe.

My third learning experience was quite a surprise to me!  My colleague was working on Venn Diagrams with the group.  This is a relatively new topic for me.  I did have two strategies for working through problems with intersections, but I learned a third strategy from a student!  It is always nice to find multiple strategies to solve problems, and always exciting when you can learn from the students.

I had video taped the entire lesson, and was able to edit a 3 1/2 minute video for our PLC group to watch.  I think the video captures three effective teaching strategies.  1)  Word association - we need to let students develop and explore terminology first, before it is defined mathematically.   2)  Random questioning - this keeps all students engaged.  If a student knows that the teacher will only call on those students who put up their hands or blurt out the answer, it is easy to disengage.   If they don't know whether they'll be called on, it is important to be following along.   3)  When a student doesn't feel they have an answer to contribute, you don't let them off the hook.  You also don't leave them out to dry.  You ask the question another way or try to scaffold the question so they can answer.  This is how they will learn.

I was really happy that I could get all three of these ideas in a short video clip.  We will be watching this at our next PLC meeting so we can reflect on those practices.  Hopefully one day we will all be comfortable enough to share these video clips outside of our PLC groups.  When this colleague and I were discussing this, we talked about how we as teachers, need exemplars.  It is one thing to read about a strategy, or listen to a colleague talk about it, but it is another thing to view a strategy being done effectively.  It is funny how we always talk about needing exemplars for our students so they know what is needed to show deep understanding, yet we don't think about that for ourselves.  We need to start thinking about ourselves.  If we want to improve, what is the best method to move us forward?  I believe part of it is learning from others and that involves observing them.  I look forward to going into another colleague's classroom at some point.  I am hoping they will also be open to my video taping so that everyone can learn from the experience.  I went into this one hoping to learn about one idea, and came away with three ideas.  I'd call that a success!

Tuesday, September 11, 2012


I was introduced to Dan Meyer's 101 questions (click here) last spring and have begun to use them in my classes.  I use them as an introduction to an outcome, or even just an activity during a class.  It is amazing how teenagers (grades 9 - 12) filter their questions in front of their peers.  They don't want to appear "stupid" or "silly".  I have been trying to teach them that we ALL have thoughts and questions when we see something and they are not stupid or silly.  I will ask random students to tell me the first question that came to their mind when they saw the picture.  It can be like pulling teeth!  I'll get "I don't know".  I tell them that they must have a question when they look at the picture and they'll finally say something.  Usually I'll get a couple questions and then the next person will say they had the same question as someone else.  Doubtful...  I do find the grade 9 students are more open than the grade 12 students.  I ask my students if they have younger siblings or relatives and if those youngsters drive them crazy with their "why" or "what is that" questions!  I tell them that I have a 4 and 7 year old and they are ALWAYS asking me "why is that...", "why can't I...", "what is that..." etc.  I get to the point where I tell them that is enough questions!   However, I feel bad about this as I feel we, as adults, stop kids from having thoughts and an imagination.  I tell my high school students that I want them to stop filtering their questions and just ASK the question that is in their head.  By the end of the year last year the students were getting pretty good at this.

And now I've started over.  I have new classes and new students and I feel like I'm pulling teeth again with them!  The first go at this a week ago was not overly successful.  I think I had three questions from the class for a picture.  Tomorrow I will be doing two new pictures.  I decided tonight to ask my 4 and 7 year old what questions they have when they saw the pictures.  They were super excited to help me out when I told them I was going to show them grade 12 math (even though it's not directly grade 12 content)! 

Here is the first picture I showed them (we are starting set theory tomorrow with venn diagrams as a big part of the learning).   The link can be found here
Right away my 7 year old says "we're doing these in math (she's in grade 2) and this is sorting".  I couldn't believe it!  My grade 12's better have a clue!!!! Haha!  She then went on to say she knows why the middle guy is there "because he has a keyboard which is the yellow and he holds his instrument which is the blue"  Unbelievable!  Anyways I asked my kids to ask me questions about this diagram.  Here is what they came up with (even my 4 year old had questions!):
Why is there only one animal in the yellow?
Why different groups?
Why are there different animals?
Why are there three animals?
Why is there one animal in each color?
What is this sorting?

My kids had so much fun with this.  We did two more pictures and they wanted to keep going!  I told them we would do some more another day. Once again I got tired of their questions :(  Why do we do this as parents and teachers?????

Tomorrow I am going to see what my grade 12's come up with and then I'm going to share the questions my kids had with them.  I will remind them that they too, were once full of questions and that those questions are still in them.  I want them to become comfortable asking the questions.  We'll see if they can come up with more questions than my kids did!

Monday, September 10, 2012

Our PLC Group

In our school division we are very fortunate to still have PLC days set aside throughout the year.  I know in some divisions these have been reduced or taken away.  In the past few years I have found these days to be very useful.  Our school has been working on building effective PLC groups.  I am very excited about our group this year.  We have chosen two goals to work on.  One of them comes from Dylan Wiliam and his book Embedded Formative Assessment.  We have all read this book.  Dylan Wiliam is coming to our school for our second PLC day this year!

The first goal is that we are all going to work on improving our formative assessment strategies in our classroom to impact student learning.  We have all read the book and decided to choose one or two new strategies to try.  We decided that it was important to limit ourselves to one or two new things so that we are able to follow through with them.  Once they become routine then we can add in some more.  There were so many great ideas in the book that it was hard to choose only one or two!  

When we had our first meeting, we all shared what we were going to try.  It was neat to see how different strategies stuck out to different members.  The majority of our group either already does or is going to start incorporating entrance slips into their daily routine.  I blogged about these here.   Those of us that already do this feel strongly about how it impacts student learning so most other members decided it would be a good one to try.  A large number of our group also decided that they were going to use tracking student growth (which I blogged about here).  After that, it was interesting to see what others were going to try.  One person is trying to improve their randomness of questioning by using popsicle sticks with students names.  Another is going to try the red/green disks for a quick view of how students are doing during the lesson.  Another teacher is going to have students do self reflection using a rubric of understanding.  I am going to try learning logs to have students self reflect on their learning.  These were all ideas from Dylan Wiliam's book.  There are many more that I would like to try, but I need to focus on small parts at a time!   We will be reflecting on these practices at our monthly meetings.

Our second goal is to improve communication with parents, students, the community and each other.  We will be sending out group emails to parents on a regular basis.  We want them to feel comfortable talking to us.  We want them to know what is going on in our classroom.   We plan on creating some videos that explain our math pathways, assessment policies, etc.  We will share these with the parents and students.  We are also going to step outside our comfort zone and start to learn from each other.  Our goal is to observe at least one other teacher's lesson in the next three months.  This is uncomfortable for some as they are nervous when others are observing.  We are not doing this to be critical.  We want to learn from each other!  Each of us has strengths that should be shared with others.

I am looking forward to improving my teaching and hopefully that will impact student learning.  I believe this PLC group will allow me to do this.

Sunday, September 2, 2012

The Phrase I Dislike the Most

I will have some really good conversations with parents about how their son/daughter is doing in math during the course of a semester.  However, there is one phrase that I hear at least once a semester.... and I REALLY dislike hearing it.   It is when a parents says "I was never good at math either..."   Do people really think that math genes are hereditary?   You don't often hear people tell someone that their child can't read because "I don't know how to read either."   Why do people feel it is acceptable to say that they are bad at math?   I think that by saying that you are poor at math you have now told your child that it is okay that they are struggling with math.  A more positive approach would be to say that "I too struggled with math, but I know it is important to work really hard, ask for help, and not give up as these are important skills to have."  I don't like it when a parents sloughs off their child's struggles because they couldn't do it either.  That is not acceptable!  

I read a really good blog post about a positive way parents can approach math with their children.  You can read it here.   I really like the suggestion to have parents ask their child to tutor them in math.  I think that this would be a fabulous way to get to the deep understanding of an outcome.  If a student can explain the outcome and teach someone else they have a solid understanding of what is going on.

I would like to work on communicating with parents the importance of hard work and persistence.  I understand that some parts are going to be difficult, and everyone does not learn at the same PACE, but it doesn't mean you CAN'T ever learn it!   Let's not allow students an out to learning!