How to Impress Your Friends by Learning to Pen Twirl!

 

	What?	How long?	Materials?
Bridges	Check this out!  Have you ever been in class and saw someone do this?	30 seconds
Learning Objectives	Each student will be able to perform the most basic pen twirl – The Thumbabout
Teaching Objectives	To include everyone in participating and attempting to twirl their pens or pencils
Pretest	Has anyone ever done this before?  Can anyone perform any type of twirl?	30 seconds
Participating Learning	Give each student a pen or pencil.  Then show them the steps to twirl the pen.  Put pen inbetween thumb on one side and forefinger and middle finger on the other side.  Apply force with the middle finger.  Move forefinger out of the way and allow pen to twirl using your thumb as an axis.	6 minutes	Pen or Pencils.
Post-test	Can anyone demonstrate a Thumbabout?  If not, is there anything that you think you need to practice?  What do you think you need to do differently?	2 minute
Summary and Wrap-up	Great jobs.  Now it’s time to annoy teachers and other students and twirl your pens as much as possible!	1 minute

Classroom Teaching Techniques

After watching Dave Hewitt's lectures in class, I was made aware that there are a lot of different teaching techniques to supplement different learning techniques.  There are visual learners, auditory learners and even tangible learners.  I never thought about using sound to enhance the learning experiences of students.  I think that sound is an uncommon tool to use but it seems to help attract the attention of the students.  Another good technique that I saw Dave Hewitt implement was the guiding instruction rather than lecture.  He made the students attain the answers through logic and reason without actually giving them the information.  This type of learning allows students to, what Skemp calls, understand relationally rather than understand instrumentally.

I think that Dave Hewitt has obtained all these learning techniques not by natural talent, but by reflection.  I think that in order to be a good teacher, reflection is necessary.  Dave Hewitt has a lot of resources to his disposal and that includes the video cameras.  By watching himself a few times, he is able to better himself as a teacher.  Furthermore, watching his student's reactions to his lecture allows him to gauge his effectiveness.

Dave Hewitt has great techniques as a teacher and I think that to be a great teacher, one has to constantly reflect and constantly search for better teaching methods.

Math Teachers: The Good, The Bad and The...

No, not the ugly.  Not the Bad either.  Throughout my high school years, I have had the privilege in mostly surrounding myself with great math teachers as I always took higher level and enriched classes in high school.  Most the math teachers I  have had in high school were teaching math because they loved to.  But also, I think my experience can be attributed to the fact that my fellow classmates were all interested in math as well.

I think that most of my math teachers tried to incorporate games into their lesson plans.  Of course, when I was in high school, I didn't always enjoy the teachers but upon reflection, I think the teachers did a wonderful job bringing out the best mathematician within me.  I liked that a lot of examples were used in class to illustrate key points.  I also think that the different computer applications and fancy calculators really made learning math fun.

I also think that my great math teachers incorporated elements beyond the scope of the curriculum into the classroom.  I think that a lot of students will find it interesting even if the students do not necessarily understand completely.  I remember one time when a teacher taught us rotational conics in a grade 11 math class and even though I did not have the math knowledge to know about "the rotation matrix", I still found it intriguing and it really peaked my interest.  That teacher also said that this is something I will learn in second year university math so he gave me something to look forward to.

I think I was a lucky person to have been in classrooms where everyone loves math so that the teachers went at a pace that suited the fast paced classroom.  I think that a good math teacher is rare and I hope to change the stereotypes that math seems to have in the mind of high school students.

If I Talk to High School Math Teachers and Students, I Would Ask...

Teacher:

1. How do you deal with students who are not interested in math?
2. Do you have any unique or especially effective teaching methods you would suggest to us?
3. What aspect of the job do you find most difficult?
4. How many hours per week do you work and how is this time divided between prep time and class time?
5. What do you find most rewarding about your job?

Student:

1. What do you like most about math, why?
2. What do you like least about math, why?
3. What could be done in the classroom to make it easier for you to learn?
4. What would you like to see or to do in your math class?
5. What do you think of the math teaching you have had throughout school so far?

Richard R. Skemp - Do I Have a Relational or Instrumental Understanding?

I enjoyed the article, Relational Understanding and Instrumental Understanding by Richard R. Skemp of the Department of Education at University of Warwick, as it focuses on how there are two different levels of understanding.  Sometimes, people may be unconscious of which type of understanding they have of a certain subject.  Perhaps it is the lack of awareness that these two types of understanding exists that may lead certain people to learn only one way.  My interpretation of relational understanding is that this type of understanding is truly the state of knowing.  The word "knowing" in this context would mean understanding the origins or reasons why something is so in addition to applying the knowledge.  In other words, relational understanding is beyond just knowing the algorithms necessary to reproduce a certain answer.  Someone who only has an instrumental understanding would be someone who thinks they have the knowledge and even though they might have the ability to reproduce certain answers, they do not know why they are doing it.

Despite the article being informative, I think that the author missed a crucial point.  That point is that instrumental mathematics can be thought of as a subset of relational mathematics.  This means that if someone has a relational understanding of something, they will also have at the very minimum, the knowledge of someone who has an instrumental understanding.

There is a clear statement that relational understanding gives the student the ability to adapt to slight differences in scenarios, but I believe that sometimes, that isn't necessary.  For example, let's take a look at the quadratic formula.  If a person can use the equation, then they will be able to find the roots of every quadratic that exists.  In addition, if that same person was taught the scenarios for b²-4ac>0, b²-4ac<0 and b²-4ac=0, then there is nothing more that the quadratic equation can offer.  And in this case, instrumental understanding would span into relational understanding and ultimately, there would be no difference.

Last but not least, I think that the article could have finished with definitive solutions to allow teachers to teach mathematics relationally rather than instrumentally.  Of course, the first step is always awareness; knowing is half the battle.  But what about the other half?  Where can teachers, who want to improve on teaching relational understanding, start?  Especially since teachers already have the prior knowledge to have relational understanding when they are given information that would allow students to only have an instrumental understanding.  In other words, a teacher could be teaching students instrumentally, and the scary thought is that teacher may think that the material that is being presented will provide a relational understanding to the students.