My Microteaching Reflection

           The overall feedback regarding my microteaching lesson was extremely positive.  Everyone felt that I successfully covered all the items in my BOOPPPS lesson plan and that my instructions when teaching had been clear and easy to follow.  One person did make a good suggestion that I bring in pictures next time depicting women wearing the sari both properly and improperly, so that they can get a visual idea of the difference between the two.  Another person thought I could’ve projected my voice a bit more at times but all agreed that they had really enjoyed the lesson and felt that it was really well done.

            I too was pleased with how I carried out my lesson.  Not only did they learn how to tie on a sari, I felt everyone took away a greater appreciation for the women who happen to wear one all the time.  The suggestion that I bring in pictures next time showing examples of what a sari’s supposed to look like when tied properly was a very good recommendation I thought and definitely something I will consider for next time.  My voice projection is another aspect of my teaching that I will try to improve on next time.  But overall I was extremely pleased with how my lesson went and I look forward to doing one again soon.

Microteaching BOOPPPS Lesson Plan

	What?	How Long?	Materials
Bridge	Discuss the different types of Indian outfits they know of and may have seen or worn before	1 min
Learning Objectives	To learn how to tie on a sari
Teaching Objectives	To appreciate the difficulty in tying on a sari
Pre-test	Ask how they think a sari might be tied on	1 min
Participatory Learning	Show them the steps in tying on a sari	5 min	4 saris
Post-test	See if they can tie the sari on again by themselves	1 min
Summary and Wrap-Up	Conclude by briefly reviewing all the steps and answering any questions they might have	2 min

STUDENT INTERVIEW REPORT

Group Members: Feda, Zhi Song and Mandeep

This interview was conducted with a three high school students from the west side of Vancouver. The three students with different age level, competency level and gender were interviewed in mathematics classrooms. Based on last year report cards, the first student H was a girl in grade 12 who was assessed as very good at math. The Second was a boy S in grade 9 who was assessed as excellent at math. The third was a boy G in grade 8 who was assessed as fair at math.

Despite the difference among these students, they all agreed about some common believes related to mathematics teaching and learning.

They all saw mathematics as useful in everyday life. However, they stressed the idea that only the basic mathematics is needed for that. They agreed that math is motivating when it makes sense and it is well understood. For these students a good teacher is the one who makes math fun to learn and explains it clearly.

An interesting point appeared through the interview was that two of the students, S who is excellent at mathematics and G who is fair, both preferred to work alone rather than in a group for two different reasons. While S thought that “working in a group would slow me down,” G commented that he liked to work “alone, because when I solve a problem it gives me the confidence that I did it without any help.” On the other side, H preferred to work in a group, because she thought that solving a problem could be a combined effort and that “ everyone is looking from a different perspective to solve the same problem.”

What was obvious from the students’ responses is that students learn differently and a teacher should be aware that different students have different needs. What a teacher could do in this situation is give the student some time to work on a problem alone and then assign them to groups. An excellent student like S will get the chance to help other students in his group after solving the problem on his own. A struggling student like G will get the chance to try to solve the problem alone and then get the help, if needed, from his friends. That might have worked well for G since when he was asked the question

Q: What do you usually do when you face a challenging problem

He answered:

G:Take some time to figure it out on my own then ask for help.

Another interesting result was related to the following question:

Would you rather have a teacher teaching you relatively easy stuff and give you an A- OR a teacher teaching you relatively difficult stuff and give you a B+

H: Depends if she is going to ignore the difficult stuff and then we miss important topics for the next year then I would rather get a B+ and learn the difficult

S: The more difficult it gets the less useful it is, so easy stuff with A-

G: I am not going to become a mathematician I only need to learn the basics so easy with A-

            For H who was preparing to go to university and knew that marks are important to get enrolled she was mature enough to realize that a good grade was not enough if that means she is going to struggle in the future by missing some important concepts. On the other hand, S and G cared about the mark the most because they had different needs and interests and they related to mathematics in a different way.

The idea of different students with different needs appear again here. Not every student wants to “become a mathematician” and not every student finds complex topics in mathematics as “useful.” Hence, when a teacher plans for a lesson she should take students’ different interests into account. A teacher should reach out to all students and make sure that everybody did understand the requirement for their grade level. Yet, at the same time, he/she has to motivate students and set high expectations so they will be pushed to do their best and not just settle with a minimum achievement. Being a good teacher is setting your students for success.

Student Interview Questions

Group Members: Feda, Zhi Song and Mandeep


Questions Asked in Student Interview:

What do you usually do when you face a challenging problem?

How often do you use mathematics in everyday life situations?

Do you prefer to solve problems alone or with a group?

What motivates you the most in a mathematics classroom?

What do you like/hate about mathematics?

What kind of math teacher do you dislike the most?

Would you rather have a teacher teaching you relatively easy material and give you an A- OR a teacher teaching you relatively difficult material and give you a B+ ?

What advice/suggestions would you give new math teachers?

TEACHER INTERVIEW REPORT

Group Members: Feda, Zhi Song and Mandeep

          This interview was conducted with a high school math teacher from the east end of Vancouver, where she has taught Math Essentials (Grades 8 through 10) for the past two years.  Much of what this teacher revealed in her interview confirmed what we’d expected to find in a typical math class.  In her interview, the teacher discussed how maintaining class discipline and getting her students motivated and involved in her class were often the most difficult parts of her job.  She found the students who were the most disruptive in her class often happened to be the ones who were struggling the most with the material that was being taught.  One way in which this teacher tries to address this issue is by giving all her students a clear set of goals and guidelines.  With these goals clearly defined, the students know what objective they have to work towards.  The goals may vary for each student; for some students, the goal may be to get an A as a final mark in the course, while for others it may be to simply improve their understanding of topics they hadn’t understood very well in previous years.  In each of these cases, the one thing this teacher makes sure to do is to ensure that each student is aware of the goal he or she is individually striving towards.  This way, the students can evaluate and re-evaluate themselves throughout the term or semester and reflect on how they’re doing towards reaching their goal.  The teacher found this method helped to enable students to take more of an initiative in their learning or “ownership of their own work,” as she likes to calls it.

            Another technique this teacher uses to keep her students involved in her classroom is giving her students different responsibilities.  These responsibilities can at times be academic (ie, giving out bonus assignments as a challenge) or they can be simple classroom tasks like writing the homework on the board, helping to hand out worksheets, etc.  What the teacher found with this approach was that students felt more engaged in her class and made them more comfortable to participate in class activities.

            A part of the interview that surprised us occurred when this teacher was asked which grade level she found most challenging to teach mathematics.  Her response of Math 8 was not entirely unexpected but her reasons behind this answer were interesting and something we as teacher candidates had not considered before.  The teacher found Math 8 to be more demanding to teach at times not because eighth graders usually have more energy thus require more attention; instead, the teacher found it more difficult to teach because in this grade, the teacher usually spent a lot more time teaching basic learning skills not directly related to math than she did at any other grade level.  Examples she discussed included teaching students how to write homework in their agenda, instructing them on how to take good notes, getting them to all show their work in a neat and organized manner, etc.  The teacher found teaching these skills ate into a lot of their class time, making it stressful for her to get her students through all the material in the curriculum.  We find this to be of interest because it was something we had not given any thought to until now

            In summary, we found this interview to be very informative and helpful to us as teacher candidates.  Teaching can at times be very challenging career but it is also obviously a very rewarding and enjoyable one as well.

Teacher Interview Questions

Group Members: Feda, Zhi Song and Mandeep

Questions Asked in Teacher Interview:


How do you balance authority and care?

What are the issues that keep coming back every year?

How do you keep the students involved and motivated?

Why did you choose math teaching as a profession?

How do you cater for individual differences?

For student teacher, which grade level is more challenging to teach, grade 8 or grade 12?

Assuming you are a sponsor teacher, what would you do if a student teacher makes a conceptual mistake in your math class?

Assuming you are a sponsor teacher, in evaluating a student teacher, will you value instrumental teaching ability over relational teaching ability or vice versa?

When students do not respect you in your class, what do you do?

What do you find is the most challenging part of being a math teacher?

What in your opinion are some of the common mistakes beginner (math) teachers make when they first start teaching and what advice would you give them so as to avoid such mistakes?

Dave Hewitt Video

I was quite impressed with the teaching methods that Dave Hewitt presented in his video.  They were unlike anything I had ever seen before.  What I liked most about his method was how it forced students to do the math mentally as opposed to writing it all on paper.  I believe this is an important skill that one should learn but one that unfortunately is not often emphasized in classrooms.  Hewitt's method addresses this concern completely.  The only possible problem I see with his method is that if there was a student who wasn't following along with the rest of the class, he or she could easily remain quiet or just pretend to answer along and the teacher would not be aware that this student does not understand; however, I still found Hewitt's methods to be a fun and creative way to teach mathematics, something that I'd definately like to try for myself!

Memorable Math Teachers

I was lucky enough to have had great math teachers throughout my school years but my most memorable math teacher would undoubtedly be my third grade elementary school teacher.  She was the first to instill in me a love for working with numbers and appreciation for the world of mathematics.  I remember her as being the first of my math teachers who did not simply teach straight from a textbook.  She would often come up with her own problems for us to solve which tried to incorporate other material we were learning in other subjects at the time.  She never relied on using just one method when showing us how to solve problems either, as she was usually able to illustrate several different ways to solve each question.  I can specifically recall a time when I struggled with division and simply could not understand the textbook instructions on how to divide.  My teacher drew a number of small shapes on a piece of paper and had me put them into groups of 2, 3, 4, etc., in order to demostrate how division worked.  For the longest time, picturing those shapes mentally and putting them into groups was the only way I was able to answer division questions.  It was of great help to me throughout my early school years.  Today, as a future math educator, I still think back to this teacher and feel that I cannot thank her enough for all the help and guidance she provided me in my early math years.

Relational and Instrumental Understanding

     I agree with the overall point of view Richard Skemp presents in his article regarding how there exists two types of understanding, relational and instrumental, and that the relational approach is the better of the two; however, I don’t share Skemp’s opinion that instrumental understanding isn’t really understanding at all but rather “rules without reasons.”  Though the relational approach provides a more complete “schema” of mathematical understanding for students, for many people the instrumental approach is the first step towards this relational understanding as this approach allows for an easier introduction of new math material than the relational method.

    I also think Skemp’s article downplays the effectiveness that the instrumental approach has towards helping students learn and understand mathematics.  For most people, learning math only occurs when they actually do math, ie, solve math problems.  In order to do this, there are at times certain rules that must be learnt first but once these rules are learnt, the theory behind where these rules come from, how they’re derived and why they work becomes much easier to understand.  It would be much more difficult for one to try to understand these explanations without having already learnt such rules.