My Thoughts about MTH 629

For anyone that is about to take MTH 629 at Grand Valley State University here are my thoughts about the class.  Click link to see web video

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3 Act story

In my teaching I feel that every lesson has three acts to it.  The first act is to have the students discover the material on their own.  The students are not positive what they are going to solve or encounter in the lesson but they proceed knowing/hoping that it will be come clear as the lesson progresses.  The second act is one where the students get confirmation on their work.  This can come from either peers or from the teacher who is acting as a facilitator of knowledge.  The third act is where the students are asked to enhance their understanding by being able to solve various types of problems and being able to use their knowledge to solve various problems relating to the same concept.

When I first read this I had hope to create a story with three stages.  Since that is not what this required I am still going to add my story to this post and hope you enjoy.

Three little pigs and solving a quadratic.

One day three little pigs were sitting in class, listening to the big bad wolf go on and on about how to solve a quadratic.  The big bad wolf wanted her little piggies to make sure they could represent quadratics in multiple ways and felt that one way was not enough.  The three little piggies were not the greatest students, they would snicker and make fun of the big bad wolf, so when they were asked to solve a quadratic equation, they found out just how mean the big bad wolf could be.

The first little piggy said this is easy, they graphed the quadratic and said there big bad wolf that is how you solve a quadratic.  With dismay the big bad wolf shook her head and blew the little piggy paper away.  This brought tears to the little piggies eyes and she ran to work with the second little piggy.  Once the first piggy got there she explained what the mean ugly big bad wolf had done.  The second little piggy laughed and said she wont do that to me, I solved using a table, showing where the y-values were zero and that would represent the solution to the quadratic.  Once the first little piggy heard this she said that is great, and then showed off her skills of graphing.  

They could hear the big bad wolf and she came near the piggies,, who  felt confident as they described what they had done.  The big bad wolf looked, not as upset as before, but once again shook her head a blew their work all over the place.  Both little piggies started crying a hurried off to the third little piggies house.  When they got to the third little piggy they explained what had happened.  The third little piggy had an idea, when she solved the problem she used factoring and the quadratic equation to solve for the quadratics.  The other piggies then described their two ways of solving and together they thought.  Wow there is more way to solve for a quadratic, this is fantastic.

Once again the footsteps of the big bad wolf shook the ground and as she approached, her face showed a sign  of disappointment as she expected to blow their assignments away yet again.  The three little piggies, a bit scared, showed the big bad wolf what they had done to solve for the quadratic.  The big bad wolf inspected the work, but this time instead of blowing the assignments away the wolf smiled.  She told the little piggies that two heads were better than one and that three are better than two.  This is the same as solving for a quadratic, there is more than one way to find the answer.   

My view on mathematics teaching

I believe that to be a successful mathematics teacher then you need to teach all subjects in the discipline.  I find that many mathematics teachers will become an expert in one area and stick with that area and only be comfortable teaching in that area.  I believe that this is not the right thought process for an educator to make.  I believe that to successfully teach students you need to know where they are coming from and where they are going.  If you have only taught high level math classes then you are not sure about the basics that your students are coming in with, and if you don't know where they are going then you are not sure what needs to be emphasized for future success.

Along with teaching all subjects within the discipline, I feel that having a team teach teaching experience allows you to reflect on what and how you are teaching.  This is my first year teaming and it is an experience that has opened my eyes to what/how students think.  My AP Calculus students advocate for themselves and ask thought provoking questions, teaming students will slide back in their chairs and you as a teacher will have to pull questions out of them.

Final Thought: In my opinion to be a successful mathematics teacher you need to be flexible, driven and open to new ideas.  It is funny because I feel those are the same things we ask from our students.

How I plan

When I sit down to plan for the year, I try and gather all the infromation I can.  I look at standadized tests, ask collegues, consult the book, and use prior experience to prepare my yearly schedule.  Once I establish my yearly schedule I being breaking the lessons.  I am typically a one lesson - one day schedule, but have found through experience that some lesson just can not be taught in one day.  These days I doucument, and will make alternative problems for the students to discuss.

My planning is not very detailed, with the student participation leading discussions.  I have a couple key points that I want students to explore through out the lesson, but how we get there can be very different between each classes. 

When I started planning for AP Calculus this year I did not take the same approach.  I did not have any previous experience to help guide me through, and I recieved no assistance with material, I was a man on an island and had to make sure that my kids could swim.  I used the book heavily to plan these lessons, I still used students questions to guide the lesson but made sure to hit on specific concepts that the book considered important. 

Next year I will play on my experience of both seeing the AP test along with where my students this year struggled.  I feel that planning always needs to be revisitited and revised