Letters From the Future

Dear Miss L.

   I want to say thank you for being my teacher all those years ago.  I came into your class really not enjoying math at all and you helped me see that it is not all bad.  I appreciated how much you cared about me beyond how well I could do on a test.  You really took the time to see me as not just another face in the crowd.  You cared about how I was doing in and outside of class.  Even though I was never really great at math and didn't persue it any farther after your class, I left school with a more positive attitude about my strenghts and weaknesses.

Sincerely Student A


Dear Miss L.

   I am writing this letter just to let you know how I felt about you as a teacher.  You were one of my least favourite teachers and here is why.  You were often too focused on the little stuff like how an assignment was to be set up, what kind of pen/pencil I used.  That was never that important in the grand scheme of things.  I also didn't appreciate how fast you always went.  It seemed like as soon as a few people understood you were moving on.  I didn't like how it always felt like you were the be all and end all of knowledge.  It made it difficult to approach you if I didn't understand something.  I also felt like you were never as clear as you could be in your feedback to us.  Lastly it seemed to me that you favoured the females in the class and that was not very fair.  I hope things have changed over the years for you and that your students now are better off.

Student B


I think I am the most worried about being remember for being picky about the small stuff.  How an assignment is laid out isn't as important what they learn through it.  I am worried about being seen as favoring certain students over others.  I am afraid of losing that personal connection I have now with students when I eventually end up in a larger school.  I am also afraid of not having sufficient background knowledge to properly teach the subject matter.

Five Burning Questions - Assignment 1

Questions for Math Student:

1. What memorable method did a current or previous math teacher use that made the learning easier?
2. What memorable method did a current or previous math teacher use that made the learning fun?
3. Why is your favourite math teacher your favourite? What did they do differently than other math teachers?
4. Why do you like (or dislike) math?
5. How do you feel about the amount of math homework that you get?

Questions for Math Teacher:

1. How do you incorporate topics into your math class which show how the math applied to real life outside the classroom?
2. Do you include history of math into your classroom? How?
3. What types of methods do you use to ensure that the student’s homework or assignments are their own?
4. What is the most challenging part about teaching the subject?
5. How do you approach both the students who like math and students who dislike math?

Hong, Michelle & Nadine

Assignment 1 Report

Assignment 1 Report

(Group Members: Michelle Davis, Hong Jiang and Nadine Lundie)

PART 1 – Mathematics Teacher

We chose to ask our five burning questions to two different math teachers with varying experience. The first teacher interviewed had graduated from the UBC four years ago and has been teaching grade 11 and 12 math. The second teacher is the Senior Math Expert and has 30 years of high school teaching experience. We decided to ask two teachers with different levels of teaching experience to compare our results.

We found the answers were quite different in that the responses from the recent UBC grad were responses that we as teacher candidates might have thought of. On the other hand, the responses from the experienced math teacher were quite different and her methods unexpected. For example, we asked both teachers how they approach both the students who like math and dislike math. The newer teacher said that when she has a student who is only there because it’s a requirement to graduate and they are not interested in pursuing anything mathematical after high school then she simply tells them what they need to pass. She explains the requirements for them to get a specific grade and lets the students decide for themselves what grade they want. The experienced math teacher did not bring up the notion of ‘requirement to graduate’ and said that she shows students that math is more than computation. She believes that math is a fine art and compares it to music in saying that playing scales is not all music is. She says that she teaches from the premise that math is creative, efficient, effective and fun. She believes that all students can and should have an appreciation for mathematics even if they never plan to pursue it. She is not content to just let them be.

This premise also relates to how she manages to relate math to concepts beyond the classroom. She describes math as a way of thinking which helps with organizational skills, efficient procedures and problem solving. She goes on to say that this mathematical way of thinking is used even for daily things such as your cell phone plan or relationship issues. She firmly believes that math is more than just procedures to memorize and strives to make this come across to her students.

One thing our group found interesting was how the experienced teacher incorporated topics from the real world into the classroom compared to the newer teacher. Rather than presenting or telling about real world applications, the experienced teacher posed questions or problems for the students to think about. For example, using a parabola to represent a bridge or arch she would ask the students whether they could replicate a famous structure in a different location over another river of different width or to allow for taller boats. We found this very interesting because not only is she relating math to a real problem, she is also having the students try and solve it themselves. This would be a great idea for a group project.



PART 2 – Mathematics Student

We asked our five burning questions to a high school student who likes math and a high school student who dislikes math. When considering math a mere subject, the student said that they like math because there is either a right answer or a wrong answer, and there is no maybe answers. The other student said they dislike math because they feel it is too hard for them to understand and they wait too long to ask for help until right before the unit test. Our group was wondering if perhaps the teacher was not approachable enough for extra help, or if the student already established a sense of defeat about math.

We found it interesting that the students had similar answers as to what about a specific math teacher made them their favourite. Both the students said that the teacher made math fun, used good humor and brought jokes about math into the lesson. For example, one of the students said that their teacher gave the three different forms for the equation of a line names that were funny and non-math related to help students remember. The student who disliked math said their favourite teacher explained things in the simplest and easiest way and the student who liked math said their favourite teacher did things that were hands on and interactive. One of the students also said their favourite teacher let them watch “Finding Nemo” during class. It seems to us that it is much more about the relationship that the teacher built with the kids that made them memorable.

A few of the other comments we found interesting had little to do with the content of mathematics itself. The student who likes math said that her teacher cared, wanted to help, and made sure that the students were doing okay, and not just in math. The student who dislikes math said that their favourite teacher had a positive attitude. We found this intriguing that these characteristics are completely unrelated to the subject. We have been learning that being a teacher is more than knowing and teaching your subject matter. It is also about caring for your students and their success.

Of course the issue of homework came up with both students. They both said they did not much like homework, which is not surprising. The student who dislikes math said that if too many questions were assigned they would dread even getting started on it. It’s an interesting issue; how much homework is too much? How much is not enough? As the teacher how do you treat homework in the evaluation process?

Conclusion

This interview was very eye opening for all the members in our group. We can relate to the answers from the newer math teacher, although we aspire to develop the methods of the experienced teacher. We believe the confidence and creativity this teacher brings to the classroom comes not only with experience but also with constant reflection and adaptation.

We gained a different perspective by interviewing both types of math students. We saw that they had different concerns in areas like what made learning the easiest, but they had the same ideas about homework and why a certain teacher were their favourite. We learned that the teacher having a positive attitude and caring about their personal well being, which are both unrelated to math, are more important than we previously thought.

Micro-teaching Jive Basic Step

Mini-lesson Jive

Dave Hewitt Video

I have to say, I really enjoyed the video presentation on Monday.  It is such a simple way of presenting so many different aspects of math that some students find so difficult to grasp.  I really appreciated the fact that the tapping method can illustrate many so things like sequences of numbers, the properties of counting, the number line and its properties, positive and negative numbers, algebra, skip counting, etc...the list can go on and on.  It is such a versatile way of reaching students at any level of mathematics, not just grade eight students trying to learn positive and negative numbers.  I also really liked how the group dynamic worked with this method.  By the end almost all, if not all, of the students were participating and correcting themselves without fear of being laughed at.  There was less pressure for them to be perfect right away and if they didn't get something right off the bat that was okay.  There were encouraged to work as a team.  It was an us versus the math kind of thing and the math wasn't portrayed as something beyond their scope of ability.

One question I have is how can this type of method be moved into to more complicated fields, like geometry or trigonometry?  How can we make this type of method work just as well in Calculus?

Remembering Math Teachers

I have two different situations that come to mind when considering memorable math teachers.  The first was in high school with the three teachers I had for my whole high school experience.  The first teacher encouraged me to challenge myself by taking AP math in successive years; he knew I would have been bored and underchallenged had I stayed in the regular route.  The second teacher was just a strong teacher who explained things in such a way that I could easily understand them.  My final teacher, grade 12 and calculus, was a phenomenal instructor who was also very easy to approach and cared about us beyond simply what we did in his classroom.

The second experience that has had impact on me as a teacher came much more recently.  The last two years teaching in Calgary, I shared my classroom with the master math teacher.  The first year I was very resistent to her suggestions, especially if I had not asked for advise.  The second year I realized that she was just trying to help me become the best math teacher I could possibly be.  I enjoyed sitting in on her classes and seeing her at work.  Seeing how she inspires the students to do their personal best and not try to live up to anyone elses standard.  She is someone I truly wish to become like.  I still contact her often when I am need a word of encouragement.

Skemp Article

Relational Understanding and Instrumental Understanding - Richard R. Skemp

 Relational versus instrumental understanding is a debate that will continue for a long time.  It is an issue to which there is no easy answer.  Each approach has value in and of itself, but the reality of the situation is not black and white.  The need for relational understanding is apparent and necessary for a true understanding of mathematics, a true love and appreciation for it as a subject matter.  However, the reality is that the curricular expectations, student expectations, parental expectations, provincial expectations, etc...don't necessarily allow for the application of a relational approach.  There is too much in the curriculum to spend large amounts of time focusing on the connections behind the concepts.  Often the students do not want to know the "why"; they are content with the formula and that's it.  The best a teacher can do is strive to draw out those connections, whenever and wherever possible, that make math really meaningful without losing sight of the importance of instrumental understanding as well.  It is an ongoing challenge in my own career to try and mesh the two as much as is possible given the current environmental restrictions.