Reflection on Microteaching

In general, I think my microteaching performance was okay but I am not satisfied.  My biggest challenge in teaching is always my speech speed.  It is so natural for me to speak fast and often times I lose my listeners.  I knew that if I could speak slower and enunciated clearer, my intonation would be calmer and I would express myself better.  Before the teaching, my husband had suggested me to lower my voice to sound calmer and clearer.  I took his suggestion and it did work well at the beginning. However, when I realized that I was short of time, I started to speak faster and louder.  Another thing I didn’t do well was when I realized that I couldn’t finish my lesson as planned, I was panic and lost of my train of thought.  I think I really have to work on these two things to become a better teacher. 

One thing I did well was that when one of my classmates couldn’t follow me, I stopped and showed him once more how to fold the paper. I think this is where effective communication happens between the teacher and the learner.  As a teacher, the focus should always be the students.  In my opinion, it is better to teach half of the lesson and have all the students understand the materials than to finish the whole lesson but only have half of the students understand the materials.

 

 

 

 

Homework Geometric/Numerical Puzzles

When I first looked at this puzzle question, I just drew a circle and tried to match points. But I put 1 on the very top center and put 3o on it’s left. Then it became confusing. Although my intuition told me that 1 should pair with 16, I couldn’t be sure until I realized that I should put 30 on the top and divide by 2 to get 15 on the bottom of the circle. This reminds me of the clock! It should be an easy puzzle if I could think of clock at the beginning.

I noticed that if the total number of points divides by 2, we get an odd number, the pairs will be even and odd. If the total number of points divides by 2 and we get an even number (eg., 40/2=20), then the pairs should be either even & even or odd & odd.  However, if the total number of points is even, it is possible to create such a puzzle. If the total number of points is odd, it is not possible.

It is not a bad idea to give students some puzzles which are not solvable because the process of thinking is more important than the solvability of the puzzles. I have taken a puzzle solving course at SFU which I really enjoyed. One of the tasks we had was to decide whether certain permutation is solvable or not. In the end of the course, we were able to gain a concrete understanding of what makes a puzzle solvable and what makes a puzzle not solvable.

I guess what makes a puzzle truly geometric is the visibility of the puzzle. If we could see the puzzle through our eyes, we could have visual images and we can expand these visual images and solve some even more complex problems.

 

 

 

New BC Mathematics Pathways Structure

I used Tupper Secondary’s planning guide as reference and made the math pathway chart. When I looked at the chart, one thing I was hesitated to put on was the pre-requisite letter grades. What does it really suggests is that if you are not good enough in grade 10, then you cannot be good enough in grade 11 or 12.  I don’t quite agree with the implicit indication from these pre-requisites. I hope there is a way to mediate so that students can have other options when choosing classes.

Mathematics Pathway Structure- BC

The first term that draws my attention is “constructivism”. I just read an article talking about constructing cognitive and social constructivism teaching pedagogies in classroom last Friday in another class. I really enjoyed the reading and I learned that it would be helpful to incorporate constructivist teaching methods and practices to create an effective learning environment. Constructivism has two types. Piaget’s cognitive constructivism emphasizes on personal importance of acquiring knowledge.  He believed that humans cannot be simply given information, rather, humans construct their own knowledge through assimilation, accommodation.  Whereas Vygotsky’s social constructivism believed that social interactions is an integral part of learning.  He claimed that scaffolding and cooperative learning would have a huge effect on students’ learning outcomes. I think the two theories combined together will be the best approach in helping students to be successful in their learning process.

The second term is Individual Education Plan (IEP). I did a little bit research on IEP.  The plan is designed for students who cannot follow what is being taught in a regular class. It was created by a school team to address the learning needs of a specific student.  A student who receives IEP usually under a circumstance where all regular school avenues have been exhausted.  Some IEP students will also receive Ministry designation, which means extra funding.  For example, students who fall under categories A or B will receive double funding from Minster of Education. With these extra funding, the school is able to allot more resources to meet the IEP student’s individual needs.  

 

Homework Reading:

The Educational Imagination

The first stop when I read this chapter was when Eisner talks about how school course planning exerts an implicit impact on the students’ perception on the importance of each subject.  He points out the fact that arts “are generally taught in the afternoon rather than in the morning and often on Friday afternoon” which “reinforces the belief that the arts do not require rigorous and demanding thought and that they are really unimportant aspects of the school program” (Eisner, 1980,p.92).  It reminds me that when we look into the BC Curriculum, many artistic subjects such as visual arts, dance, music, drama are treated as “electives”, that is, they are usually not required for university entrance.  This implicit indication has a detrimental effect.  Although oftentimes students love taking these electives, but they don’t treat them seriously because they realize doing well on artistic subjects cannot lead them to a reputable university.  In addition, many parents also place bias towards artistic electives as they perceive art as an “unemployable” subject.

The second stop was when Eisner explains that the implicit curriculum can teach a host of intellectual and social virtues: punctuality, a willingness to work hard…, and the ability to defer immediate gratification in order to work for distant goals” (Eisner, 1980, p. 95).  Indeed, school is an intersection of society where students not only learn knowledge but also obtain social conventions.  These positive attitudes are not a formal part of the curriculum, yet student do learn and adapt them through education in schools.  What makes Ivy League Universities differ from the rest, in my opinion, is not the quality of education as almost all universities teach the same content for the same course in North America, it is the kind of students who possess broader visions and revolutionary minds which will exert significant impact on future societal change.

The third stop was when Eisner talks about the how curriculum should be designed in a way to cultivate imagination and develop productive thought.  In Eisner’s example, the poet e. e. cummings chooses joy over knowledge, and he would rather learn to sing than to learn from Einstein, Marx or Darwin (Eisner, 1980, p.101).  This reminds me of my experience in China when being taught one of the Four Great Classical Novels, Dream of the Red Chamber.  To this day, I was reluctant to take up the historical, social and political implications imparted by my teacher.  The curriculum requirement has forced the educators to explain the novel in such a way that every character was behaved with some political indication which really destroy the beauty of the novel.  

To connect Eisner’s perspective on the three curricula all school teach, I think we as future teachers really need to ponder on what we are teaching each day to our students. We need to constantly exam our teaching ideology and make sure we truly cultivating independent and critical thinkers rather than limiting their imaginations.

 

Reference

Eisner, E.W. (1980). The Educational Imagination: On the Design and Evaluation of School Programs Elliot W. Eisner New York: Macmillan, 1979. 293 pp, $15.95. Journal of Teacher Education, 31, 34 - 35.

 

                 Microteaching Lesson Plan- EDCP 342

 

Subject: Folding open-top box	Class: EDCP 342 Students	Date:  Oct. 14/20	Duration: 10 minutes
Class Composition:	26 students in secondary math cohort, some experience with paper folding

 

Rationale	·       To provide a hands-on learning experience for teacher candidates and to give them perspective on what it might feel like being a student in a high school classroom.
Learning Objectives:	·       Classmates will be able to fold an open-topped box through in-class demonstration. The goal is to through self- and peer-evaluation, teacher candidates are able to practice their teaching pedagogy, and exam and reflect on their strength and weakness in terms of teaching. ·       To learn how to fold an open-top box

 

Required Materials

·       Any paper (scrap paper, newspaper, construction paper, etc.)

 

	Lesson Components	Learning Activities	Time Allotted
1.	Introduction	·       A short story about the use of an open-top box	1 minute
2.	Demonstration	·       Demonstrate step by step folding procedure	2-3 minutes
3.	Guided Practice	·       Ask students to grab a piece of paper ·       Have students follow along with me in a step by step manner	6-7 minutes
4.	Summary/Closure	·       Extension ·       Summary: reiterate the procedure for the folding of the box ·       Reiterate that the box shape can be varied to suit your needs	1-2 minutes

 

 

Homework Reading:

Battleground Schools

One thing stands out to me is the traditional and stereotypic assumption about people who like mathematics.  Under this assumption, only nerds, absentminded professors etc. who are “unable to cope with human interactions” will study mathematics (p.393).  Granted, some extremely intelligent people are so frantic about mathematics that they choose to interact with numbers over human.  However, most of the mathematicians or people who are fond of math have no problem communicating or interacting with other people. They are not living isolated in another planet but having family and children just you and me.  Look at our math cohort, our professor and classmates are not only enthusiastic about math, but also enjoy the interactions with each other.  Every class, we are fully engaged in conversations on arts, society, environment etc.  All these conversations require the participants to be very compassionate and passionate.  Aren’t we best exemplifying that people who love math also love life?

Second point I want to make is the benefit of experimental and inquiry learning over instructional learning.  For experimental learning, there are lots of uncertainty and challenge to teachers and professors. We as teachers cannot plan everything ahead before classes start. Things could go wrong and we could lose control of the class.  What shall we do under this type of pressure?  Is second plan sufficient enough to remediate the damage?  Will I lose my credits in front of my students?   These worrying coincide with the concept of instructional leaning where obedience and authority are expected.

As soon as I read the section of The New Math, one thing drew my attention right away was the political influence over mathematics.  If we allow math or any science subject to serve for political purpose only, it is dangerous.  The human history has many to say about tragic events happened in the past when scientific invention was at the hands of political driven politicians.  The implementation of New Math program in my opinion is totally invalid.  The brain capacity of a child at secondary school level is not sufficient enough to comprehend those university level mathematical concepts and his logical thinking skill is not yet fully developed.  Not to deny there are math geniuses, most of the teenagers cannot absorb such complex and abstract mathematical concepts.  They might lose interest on math which is detrimental to their future learning process.

 

Reference

Mathison, Sandra & Ross, E Wayne. (2008). Battleground Schools.

 Without having the tool of algebra, it is more difficult to solve the problem for sure. However, it allows me to think more critically rather than just define a variable and write an equation and find the unknow. I actually had so much fun in the process of figuring out how to find the number of guests. I broke down the number of total dishes 65 into two prime numbers first. Then I tested 13 was too big for a sum of 65. It only left 5 to be tested. Finally I got the number of dishes offered under each category and find the least common multiple of 15,20, and 30 which is 60, the number of the guests.

Later on I realized that my method was not the best way to find the solution. All I need to find is the least common multiple of 2,3 4, and multiply it with one of the prime factors of 65.  However, I was more involved in thinking the relations among all the elements and how do they interact with each other. Although solving this problem with the absent of the algebra is not straightforward, it does serve as a critical thinking practice. I believe this kind of mathematical exercise is valid and meaningful in classroom teaching.