Thursday, June 16, 2011

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

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.   

Tuesday, June 14, 2011

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.

Monday, June 6, 2011

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

Tuesday, May 31, 2011


How should students be graded in mathematics:

We use UCSMP, and we follow their percentages they feel should be used for grading.

70% Tests
20% Quizzes
10% Homework

This is a lot of pressure on the students to perform well on the tests.  Which I believe is good, because I feel that students need this to be prepared for when they leave school.  I have also inserted projects as tests to help students that may have difficulty with test anxiety.  The homework is graded on effort, not correctness.  I feel it is important for students to held accountable for their own work.  If they are choosing not to check them homework and to not to it, then in the end it will only affect themselves. 

I think there could be validity in lowering test percentages to 50 or 60% and make it mandatory to do projects or even a paper to cover the additional 10-20%.

Monday, May 23, 2011

Following/Blog Roll David Coffee

Going through Johns list of blogs he follow I found David's.  This one drew my eye because the first post I saw was about the common core.  This is the way of the future and is something that I want to learn more about so I along with my department can be ready once the switch begins. 

Another link/ blog I wanted to follow was wiki.  I tried setting one of these up for my AP Calculus class, but failed miserably.  I am looking for more knowledge on how to successfully set up and use one of these in the classroom.

Project Ideas

Instruction Dialog: Probability.  I want to focus on if I am addressing my objectives and if my presentation of the information is sequential.

Pedagogy: Direct vs. Facilitator, what is the best way to present mathematics to students (especially struggling students who now need to pass Algebra 2) Found a good article see Bibliography

Concept Map: Content Area: Derivatives and Rules to how to take derivatives of different functions and problems leading up to related rates.

What do I do to try and make me a better teacher

I think everyday I try to get a little better at being a good teacher.  I know it is a long road, a never ending one actually, to being a great teacher.  One goal each day is to make sure I ask my students inqury based questions.  Ask the students why, how come, is that important, and how can that be seen in your everyday life, allows me to gain insight on what my students truley need.

Inqury based instruction I feel gives the students a chance to explain what they know, and infact gives me the opportunity to realize what they do not know.  Having the students justify their reasoning allows me to gear my classroom and instruction towards what they are missing.  If I just ask them if they "get it" I am gaining no feedback.

Thursday, May 19, 2011

ANNT Bib 2

1. Shifting from Traditional to Nontraditional Teaching Practices using Multiple Reprsesntations. Rider, Robin. Mathematics Teacher, Vol 100, No. 7. March 2007

Was an example of a teacher that realized he needed to change the way he presented inforamtion to his class.  Like many of us, we will first change by adding in graphs, and tables and showing them how the are important.  We will talk about how to tansition between one another, but what I have noticed about that change is just what the author stated.  You can change instruction, but if you do not change your assessment to model your instruction, then it will be for nothing.  This is what I found very inlightining.  In my classes I am trying to find better ways to teach students Algebra 2 and the use of technology is something I am trying to use more.  After reading this article I believe I have some better ideas on what and how to approach the issue of teaching struggling students high level mathematics.

2. Putting Understanding First.  Wiggins, Grant & McTighe, Jay.  Educational Leadership, Vol 65, No. 8.  May 2008.

This Article talks about how a mathematics classroom should be constructed.  I feel this is a very good article about pedagogy.  I am interested in whether it is more important to direct teach or take the approach of a facilitator.  The article speaks of teaching for meaning and transfer and gives three bullet points for how to construct and teach mathematics.

1. Direct Instruction
2. Facilitation
3. Coaching

Good article of designing a classroom and instituting the skills necessary for students to gain understanding into what the mathematics is really doing.

3. Modifying Our Questions to Assess Students Thinking.  Chappell, Michaele F. Thompson, Denisse R.  Matheamtics Teaching in the Middle School, Vol.4 No.7, April 1999

Starting the article, 7 standard questions are asked to students and through out the article infroamtion is gathered from how the students respond.  They give three diffrent examples of each, and explain the information that can be gathered from asking a student to explain their reasoning.  This part of the activites gave a tremendus amount of feedback and is something I try to employ but focus more on the correct answer.

I think this was a good read, and used good examples to explain/show what we should be looking for as eduactors and how we can use assessments to gain understanding of our students.

4. The Challenges of Implementing Innovation.  Edwards, Barbara S.  Connecting Research to Teaching. Vol. 93, No. 9.  December 2000

I thought this was a great article that describes the challenges of implementing new ideas, concepts or teaching styles to a classroom.  In the article Barbara talks about how even the best ideas are hard to implement, and they never seem to work out the way you want the first time.  With the struggles at the start most attempts are soon faded away and you return back to what has worked before.  I think this was a great article to read as we are constantly in a reform movement in mathematics.  We are being asked to teach at a level that no other mathematics teachers has before in Michigan, four years for all students. 

The article also made a point to say that teachers that are not strong in their discipline will likley fade back to what has worked before faster than those that are stronger.  Being able to understand the mathematics will make it, not easier, but more likley to succeed in implementing your new ideas.  If you are thinking about reforming your teaching then I would suggest this read, and now that in time you will succeed just do not give up before that chance arises.

Tuesday, May 17, 2011

Bill: Where I am Now

Hi everyone,

I am currently completing my fifth year of teaching at Greenville Public Schools.  I graduated from Central Michigan (may 2006) with a secondary education degree in the fields of mathematics, chemistry and physics.  I was hired at Greenville in June 2006, which I was pretty excited about espically since I missed my interview and figured I was heading out of state to find a job (Opps).  During my five years I have taught from algebra to AP Calculus.  The AP Calc course was taught this last year, and I am very proud of this because it is the first time that AP Calc has been taught at Greenville, and I develope the program and I guess survived through the first year of it.  Along with teaching math, I have also taught physics.  This brought up a dilema for me last year as I had the option of taking over the physics program, or stay with math.  Happily I choose to stay with math.

Along with teaching I have been very active coaching at greenville.  I have coached football (Freshman head coach - 5 years), wrestling (Assistant Head Coach - 5 years) and baseball (freshman head coach - 4 years).  This past spring I had to drop baseball so I could focus on completing my masters (Only way I could take this course).  During my coaching time here at Greenville I have been apart of their first ever State Championship (Wrestling 2008) and their first Runner Up in state (Wrestling 2011).

Overall I love what I do here at Greenville.  The kids are great hard working students and the faculty works well together to make it possibly for all students to learn.  Greenville is a place I would like to spend the rest of my days teaching, jsut hope the budget cuts do not make me look elsewhere.

Bill Breen

Annotated Bib 1

Annotated Bibliography
“Tailoring Tasks to Meet Students’ Needs,”  McDuffie, Wohlhunter, Breyfogle, Mathematics Teaching in the Middle School, vol 16, no 9, May 2011.
Four strategies to make curriculum/lessons/instruction fit student needs.  Eg. ELL & Special Education students.
1.  Switch to a familiar context
2.  Supplement foundational gaps
3.  Incorporate overarching goals
4.  Adjust for reading levels
I would recommend this article to others.  It really emphasizes how little changes to how we present material to students can make big differences for their learning and understanding of the content.