My Math Teacher

I can not forget my intermediate  math teacher. He taught me for four years and I want to admit that I learned nothing those years. I was really struggling with mathematics and barely passed every year. That teacher was rude and inconsiderate. He only liked good students and forgot about the rest. We were scared to ask questions because if it was not up to his expectations he would make fun of you. The best thing for me to do was to stay invisible at the end of the classroom. I hated mathematics and hated mathematics classrooms. But what happened in grade 10 was not expected at all. A new teacher came to school and he was teaching our grade. His approach was the complete opposite and I actually started to get interested in mathematics to the extent that I planned to cover for the four lost years on my own. It took a lot of effort and hard work but I graduated with the highest mark in math 12 class. My passion for mathematics did not stop there. I finished my bachelor degree in mathematics and my master’s degree in math education and the plan is to become a teacher of mathematics and make a difference.

Letters comment

Teaching is a very rewarding profession when we make a difference in our students’ life. But, what could be heart breaking is when we find out, after it has been too late, that by doing our best to support our students’ learning, we actually accomplished nothing.

Reflecting on our own work constantly, while observing each single student closely and listening to what they say to us, is crucial to a teacher’s profession. When we look at our classroom, we should make sure that we are seeing unique individuals.

Imaginary letters

Letters background

I wrote an email to some of my students that I used to teach 10 years ago, to invite them to a teacher student reunion. I  was able to get their email address from some of their friends that I kept in touch with through the years. This is the reply I got from each of my students

Student A

Dear Ms X

I was so glad to hear from you. It has been a long time and I couldn’t believe it when I saw your name. I still remember the first day of your class when you came in and told us that math is beautiful and that you are here to show us its beauty. That sentence was stuck in my mind the rest of my high school years. I did realize what you meant through time. I actually majored in mathematics and now I am working on my Phd in mathematics education.  I feel that my passion for mathematics is due Ito being once a student in your classroom.

Yours sincerely

A

Student B

Hi Ms X

When I first got your email I did not actually recognized who you were until I read the content. It has been a long time, you know. I will do my best to attend the get together but I am worried that seeing everybody would bring bad memories.

My parents had to move at the end of that school year and I had to change school so I haven’t kept in touch with so many people.

I know you are wondering about the bad memories and I want to be honest with you because this is something I wanted to tell you for a long time. I hated your class and your teaching had a very negative effect on me learning of mathematics that year. I thought that you presented math in a very arrogant way. You were so sure about your positive attitude towards the subject and were so sure about changing our attitudes. You did not understand that not every student could see math the way you see it and we are different individuals coming with different needs and interests. You were too self-centered to realize that.

I know that you were a new teacher with a big enthusiasm to teaching but I hope that through the years you’ve come down to earth and have become more realistic.

Good luck

B

Battleground Schools: Mathematics Education

Summary

The article presents the battle around mathematics education between the progressive and conservative positions in mathematics education since 1900. While the first view supports a more conservative and authoritative way of teaching and learning mathematics focusing on facts and algorithms, the second view argues for understanding of mathematics concepts, and an exploratory and  inquiry-based mathematics learning. This battle progressed through three phases; (1) The progressive movement (1910-1940) associated with John Dewey movement to develop “Scientific and democratic thinkers” through inquiry and active learning. (2) The New Math reform movement (1960’s) that was based on the belief that mathematics curriculum should completely change to prepare students to become “the elite rocket scientists of the future.” The new math curriculum focused on bringing the university abstract topics of mathematics to teach in elementary and secondary schools. (3) The wars over NCTM standards (1990’s-present) are still going today with no present solution.  The NCTM standards recommended a reform in mathematics education through teachers ‘workshops and training and the inclusion of parents and technology. Despite the fact that the NCTM standards were originally welcomed by the government and teachers, an opposing right-wing conservative stands appeared in the mid 1990’s supported by religious figures. The public was divided between the two views which reflected the conflict between left and right wings’ political views.

My response

I was a teacher assistant in one of the elementary mathematics classes at UBC and I was surprised with the high anxiety that most of the teachers candidate had towards mathematics. It is a fact that kids are exposed to math-phobic teachers who lack confidence in teaching mathematics. That, of course, will affect students view about mathematics and about themselves as mathematics learners. It is true that we are trying our best to boost students’ confidence in learning mathematics but are we doing enough to boost teachers’ confidence?

Conversation with math teachers and students (Mandeep, Zhisong & Feda)

Students' interview report

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.

Teachers' interview report

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.

Micro Teaching Comments

                                   Balancing Objects

The group comments

The feedback for my lesson was very encouraging.  Everybody mentioned that the lesson was clear from beginning to end. The group enjoyed the lesson. They thought that it was a very hands-on activity. Everybody got to participate. They felt that they learned a new concept in physics in a fun way. Despite the fact that I mentioned verbally what we were going to learn, one person from the group suggested that she would have liked to see the structure already built at the beginning of the lesson so everybody would know what they are going to do. That is a clear indication that different students have different needs and learn differently and the teacher should be aware of these needs and structure his/her lesson to meet those needs.

My comments

I was happy about the lesson. I felt that it went really well. The group was excited to be involved. Everybody got the chance to repeat the process of building the structure on their own and was able to succeed at balancing the objects. The only thing I missed is the pre-test. It was embedded in the bridge rather than performed separately despite the fact that I planned for it in my lesson plan.

 It was great that we got the chance to look at the group feedback and to reflect on our own lesson at the same time. Part of being a lifelong learner is to accept people constructive criticism and to assess our own work constantly with the determination to improve and grow.

Burning Questions

Students

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

2) How often do you use mathematics in everyday life situations?

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

4) What motivates you the most in a mathematics classroom?

5) What do you like/hate about mathematics?

6) What kind of math teacher you dislike the most?

7) 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+

8) What advice/suggestions would you give new math teachers?

Burning Questions

Teachers

1) How do you balance authority and care?

2) What are the issues that keep coming back every year?

3) How do you keep the students involved and motivated?

4) Why did you choose math teaching as a profession?

5) How do you cater for individual differences?

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

7) Assuming you are a sponsor teacher, what would you do if a student makes a

     conceptual mistake in your math class?

9) Assuming you are a sponsor teacher, in evaluating a student teacher, will you value

     instrumental teaching ability over relational teaching ability or vice versa?

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

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

12) 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?

13) Is there anything you wish you’d known or been told about this profession before you began teaching?

14) In a class with students of all varying degrees of math skill, how do you plan your lesson/what methods do you use so that all students are included in the learning and discussion?

Dave Hewitt's video

Dave Hewitt's lesson was very impressive. His method is very creative and seemed effective. It made me realize that, it does not matter what technique or method we use to teach students, our main intention should focus on grabbing their attention, get them involved and make them the evaluator for their own work. However, for teachers to be able to use new techniques like Hewitt’s, they should have already mastered the subject matter and be confident and experienced enough to use different ways to teach the same concept. 

 I was just wondering when I was watching the video, If Hewitt was able to identify that every single student was actually involved. Usually, in a classroom, the same students would volunteer to answer the questions. So, how was he able to avoid that situation? In addition, when Hewitt involved the whole class, how was he able to detect that everybody did understand the concept so he was able to move on to the next concept?

MICRO TEACHING

Balancing Objects

Materials

A spoon

A fork

A match

A cup

Lesson Plan

Bridge

(2 minutes)

Who can tell me what a fulcrum point is?

(A fulcrum point is a point or support on which a lever pivots)

Can anyone give me an example?

(A balance, a seesaw...)

Today we are going to balance two objects on a fulcrum point.

Objectives (learning)

The student should be able to balance a spoon and a fork attached to a match on the edge of a cup.

Objectives (teaching)

Students will be engaged in the activity using the materials.

Every student will get the chance to try to balance the objects.

Pre-test

(1 minute)    

Each one of you will have a fork a spoon and a match.

Try to find a way to balance it on the edge of the cup.

Participatory learning

(4 minutes)

Let us try to do it together. We hold a spoon in one hand and the fork in another by their handle.

(I will identify the concave part of the spoon and the inner and outer prongs of the fork to the students).

Now, we insert the middle two prongs of the fork under the concave portion of the spoon and press firmly.

The spoon and the fork should make a V shape like this. We turn the V shape in a way that the open side is towards us.

Now, we insert the bottom of match at the bottom of the fork between the first and the second prong. The match should be facing you.

We hold the other end of the match and try to balance it on the edge of the cup. It works, yippee!!

Post-test

(2 minutes)

Now, let us take the parts apart and let me watch you do it on your own.

Summary

(1 minutes)

Can anyone give me more examples about fulcrum points and balancing object?

What can we conclude from that?

My response to “Relational understanding and instrumental understanding” by R.R. Skemp

I believe that both instrumental and relational understanding should be the goal of the teachers and the students in a mathematics classroom. The first involves knowing the “how” and the second involves knowing the “why”.  As long as marks take part in students’ assessment, and as long as we are bounded with time and the curriculum, instrumental understanding approach to teaching and learning will always be present in mathematics classrooms.

I was a teacher myself and my goal was relational understanding as well as instrumental understanding. I was teaching my students rules about how to solve a problem quickly to get to the right answer but at the same time I tried to relate the concept to other concepts in mathematics, to other subject matters and also to their daily life.

I see that teaching for relational understanding might be time consuming but I do agree with Skemp that it would save time on the long run because students will be able to understand new concepts quickly by relating it to previously learned concepts. They will also make sense of the new concept and will have an in-depth understanding of it when they can relate it to something they experienced in another course or everyday life.

The question I raise here is about the relation between the different way of teaching/learning mathematics and how students look at mathematics and at themselves as mathematics learners?