Math Video on Constructionist Teaching

The classroom depicted in this video is innovative and certainly a lot different than any math class I have ever taken.  While there is a place for traditional mathematics teaching, having lessons where students are involved and the students can see math in a new way is an integral part of being an effective teacher.  One thing that particularly stuck out to me was the teacher's introduction to algebra within the context of a class that had nothing to do with algebra.  In fact, the students probably won't see algebra for another year or so.  Introducing students to concepts like variables early in their life makes the transition into using the variables a lot easier.  When I was in school when a new concept was brought up out of nowhere it would always be scary and hard to understand; we were caught off guard.  However, when I had previously seen something used - even if I didn't fully understand the concept yet - I felt that twinge of recognition and it gave me the confidence to think I could probably learn this concept pretty easily.  Additionally, seeing the concept in use before learning exactly how to use it gives motivation for learning it.  Knowing that what you are learning has come up earlier gives the impression that this concept is probably important and will be used again, and this is great motivation for students to actually want to learn something.

Interview Summary

What we Asked:

5 Questions for Students:

1. What do you like about other subjects that you don't find in math?
2. Do you think the math you learn will help you in your life and how so?
3. Do you think the grades you get in math reflect your knowledge or understanding?
4. Give reasons math should or shouldn't be learned if a student "knows" they won't use it in their future?
5. Which classes that you are taking currently do you think will be most useful in your life?
   
   
   
   

Battleground Schools

Summary:
Mathematics education is thought of in two different, and often conflicting, ways.  The first is a conservative viewpoint where math is thought to be unchanging, objective and inaccessible to most.  The second is a more progressive viewpoint where math is thought to be dynamic, exploratory, and of importance to everyone.  These two differing opinions generally correlate with the two political poles, and for years there has been unrest between the two regarding how, and why, we educate our children in mathematics.

Interview After-Thoughts

After interviewing three high school students and three high school math teachers I have learned a lot about the practicality of teaching mathematics.  In school we tend to get caught up in the theory of teaching, but this assignment really anchored everything back into reality.  The following is a reflection on a few of the ideas that jumped out at me most from the interviews and how those ideas relate to my idea of how I will teach.

Interview - Notes

These are my own (unedited, unrevised) notes I made on the tapes of the interview with three high school math teachers.  I thought it might give me some context for the reflection I wrote to go along with this assignment.  All three of the teachers' thoughts are jumbled together but I think knowing who said what isn't important for this interview.  The ideas themselves were important - not who said them.

Using Research to Analyze, Inform, and Assess Changes in Instruction

While reading Robinson's article Using Research to Analyze, Inform, and Assess Change in Instruction, I thought about my own impending teaching career and what this article means to me.  The following are two quotes that I have responded to from my own "new teacher" point of view.

“Small peer groups often provide students with an acceptance and a sense of cohesiveness that is invaluable.”

I sometimes overlook the value of peer groups and learning from each other as well as from the teacher.  It is tempting to think that students will automatically look to each other for help if they need it, but I agree with Robinson that it is something that needs to be strived for and actively nurtured in the classroom.  Students need that sense of community in a classroom and in our Principles of Teaching lectures it was mentioned that one of the signs of a “great” teacher is the ability to instill “a sense of shared project” among students.  That is exactly what Robinson seemed to be doing and the change worked.  Students did better both in class and on exams, both strong indicators of her success.

Two Memorable Math Teachers

Throughout my career in school I have had a few really great math teachers.  The following are two of my favourite teachers and what made them so great in my eyes:

Mrs. Flower: My grade 9 math teacher was enthusiastic about her job.  She seemed excited about all of the math we were learning and wasn't afraid to let us know how much she loved math.  At the beginning of the year she gave out her home phone number and encouraged us to call her if we had any problems with the homework.  She congratulated anyone who did well on a test, but if anyone failed they would be moved up to the front of the class.  She claimed that studies how have shown that students who sit at the front of the class do better in school than those who don't.  She seemed to care a lot about us and was always in a good mood.

MicroTeaching

I taught a short, 10 minute lesson on the game Mafia to 3 of my classmates.  I used my first lesson planning technique: BOOPPPS.  Afterwards we got feedback from our peers as to how the lesson went and what could be improved.

My First BOOPPPS Lesson Plan

Mafia Lesson Plan (10 mins)

Bridge: 1 min

-Mafia is a game that can be played with high school students, and can be used for:

• subbing (if you need a time-filler)
• a fun game for students to play if there is extra time in class
• a reward

-Mafia requires no materials, is easy to set up and is flexible in length

Teaching Objectives:

-engage all students in learning the game

-explain all rules in a clear concise manner to avoid confusion

Relational Learning vs. Instrumental Learning

In reading Richard Skemp’s article Relational Understanding and Instrumental Understanding, I was reminded of my own high school experiences. Just as Kemp argues that there are “two effectively different subjects being taught under the same name, mathematics,” there seemed to be two different types of mathematics that my peers and I were learning. While I went to class with the aim of understanding the concept then applying my knowledge to various homework problems, my best friend would go to the same class and take essentially the exact opposite approach: do the homework problems and only if absolutely necessary would bother with learning the concepts.