Battlefield Schools - A Summary

The article outlines two very different schools of thought in our education system, progressive and conservative. The conservative view on mathematics education focuses more on instructional and instrumental understanding of the material. This view sees that answers and facts are the way to teach math, treating it as a means to an end. In stark contrast, the progressive view sees that the journey to the answer is much more important and experimentation and understanding is the way that math should be taught. The rest of the article outlines how these two have “battled” for supremacy in how mathematics is taught in the K-12 level.

The progressive movement of the early 20th century saw a realization that experimentation and exploration would lead to more democratic citizens. Educators like Dewey found that, instead of dictating knowledge to the student, it was more effective to let students grapple with issues and problems and let them figure some things out for themselves.

In the 1960’s, a more abstract form of math, called the New Math, permeated the mathematics curriculum of the day. The launching of Sputnik into space meant that America was losing the space race and it was imperative that students in the secondary level ought to be trained to become future rocket scientists. This was seen as very radical and unhealthy for the state of mathematics education as it was conservative idea parading as a progressive one. It also did not account for the fact that not all students wanted to get into Mathematics and Science after finishing secondary school. Lastly, teachers could not teach the material at all because they were educated in a totally different than what the curriculum outlines.

In the latter part of the 20th century, the 80’s and 90’s, a third movement caused a great shift in mathematics education, the Math Wars. Conservative ideas of mathematics education were being branded as right-wing and radical while relational understanding and progressive ideas were seen as more desirable. These ideas are what we would see today happening in our current curriculum.

Conversations with Teachers and Students: A Group Retrospective.

From our interviews with the teachers and students, we got a good sense of what to be aware of and how to better ourselves in becoming effective instructors. Though some of the ideas from the teachers and students are different there are a few things that stand out. Firstly was the provincial and its seemingly “narrowing way of teaching”. Both teachers agreed on this and though both wanted to expand the students’ understanding of mathematics, the provincials restricted them into just teaching rules and equations. One of the teachers even just referred this method of teaching as “training” the students into passing tests and exams. This evidence of training even shows up with the students’ answer on how important they think high school math is later on in life. They were trained to thinking that it’ll be very useful and even if it is in certain areas, they couldn’t really explain why or where it would be important.

Another difference that stood out was the analytical versus computational component of mathematics. The students all agreed that they rather just learn the equations and they don’t need to know the concept whereas the teachers were fully for analysis and expanding those equations. It seems like the students have been so immersed in the computational part that they don’t see the other alternatives and are seemingly dismissive of the idea of analytical math. So we thought that’s something that we as teacher candidates are probably going to struggle with, trying to broaden the students’ minds even though they might just want the equations.

The most significant thing that we found through these interviews is the similarity in both the teachers’ and the students’ response on how to engage students. They all agreed that to be able to engage the students, teachers must be energetic and be relational with the students. The students must be able to be comfortable with the teacher and like the teacher in order for “something to stick” with the students. At the same time the teacher must show that they are enthusiastic with the subject in order for the students to feed off that excitement and be attentive to the teacher. This above all else is what engages the students. From our interviews with the students, they remember more of the teachers rather than most creative lesson they’ve been taught. They learn better from the teacher’s attitude towards the subject rather than “gimmicks” to making learning math fun. That’s why one of the teachers always tried to eliminate the idea of math being tough and always stayed positive.

Conversations with Teachers and Students: An Individual Retrospective.

In the past few days, I have had a chance to reflect on the recent events that my group and I had with the math and student teachers we chose to interview.

In interviewing these groups, I found that there is a certain difference with what the students expect from the teachers and what the teachers expect from the students. The teachers we interviewed try their best to engage the students by including more relational oriented material. The students, however, wanted more instrumental learning because of provincial exams. In that note, the teachers found that they did end up teaching for the provincial examinations. With the death of the provincial exam would be a greater change in curriculum.

I think now that my job, as a teacher candidate, is to be able to find a happy medium between what the students want and what the teachers would like to teach. Reflecting on these interviews has given me an idea of what is expected of me as a teacher by the students and what I should expect of myself as a teacher for the students.

The Two Most Memorable Teachers in My Life

The first teacher I'd like to talk about is Michael Bennett. I had him as a professor for two courses at UBC and the reason why I found him so memorable is because he knew his subject but he wasn't so encumbered by formal mathematical writing. He would talk about squares of numbers and write them out literally as boxes. I found that quite novel, clever, and amusing. It got the point across. Also, he always knew how to get a student interested in his subject matter by his energy in the classroom. All in all, he made two seemingly difficult subjects enjoyable because of his teaching style.

The second math teacher I would like to talk about is Don Furugori. He was my high school math teacher for grades eleven and twelve. He always seemed to teach the material well enough so that an expected mark would be achieved. What I do remember from taking his classes was that it snows a lot in Ottawa. That really summed up his teaching style: very tangential.

Using Research to Analyze, Inform, and Assess Changes in Instruction: A Mini Commentary.

I felt empowered by Robinson’s article. I feel that her article was basically a success story of how one can change the dynamic of the classroom for the better after years of a certain way of teaching. Also, since she’s fairly new to the profession, I can relate to her better in the sense that I most likely will end up the way she ended up during her first four years of teaching simply because it is practical and that I would probably need to gain more experience before I can start experimenting with lesson plans. Ideally, I would like to start out with the kind of lesson plan that she implemented after her research but I won’t really know how that goes until I actually start teaching.

With respect to the topic of research, which she mentioned quite often in her article, I once heard that “if you know what you are doing, then you are not doing research”. I believe that to be true and that her research endeavour was started off as an experiment. She really didn’t know what to expect from changing her teaching style and she does admit that she was quite surprised with her results.

Overall, I think her article was very revealing and touched on very well how a teacher should always be developing his or her practice. Creating an engaging environment like that will create less stress for the teacher in the long run because there is less to worry about and if all works out like she outlined in her article, students are learning. If students are learning, then her job is a success.

Micro-Teaching: A Review

On Friday, September 18th, my peers and I got into groups of four to five to do some micro teaching. Here is a summary of what my peers and I thought about my mini lecture on the basic rules of composing photographs.

After reading what my wrote about my micro teaching session on how to make a compelling photograph, here is what I found for each section:

Bridge

They found my bridge to be concise and to the point.

Learning and Teaching Objectives

They found my learning objectives to be clear and well understood.

Pretest

My peers found my pretest to be very seamlessly integrated with the learning objectives and the bridge. They found that my use of visual examples via a laptop computer to be very well done

Participatory Activity and Post-Test

All my peers found my activity and post test were, again, seamlessly joined together and found the constructive criticism that I provided useful.

Summary

Was labelled as ‘good’

Strengths

They found that my session was well structured and flowed very well from one part of the lesson plan to the next.

Also, my use of examples and feedback during the post-test were mentioned to be quite good

Weaknesses

It was felt that, during the participatory activity, a single subject should have been used. I had let the students decide on what subject that he or she would like to photograph.

One of the more tactile learners would have preferred to touch the cameras I had brought while I was lecturing

Lastly, and most importantly, it was mentioned that I used the phrase ‘you know’ quite a bit. Notably, it stopped towards the end of the lecture.

Given that, here are my own thoughts about my micro teaching session:

I liked the fact that my microteaching session flowed seamlessly between through the BOOPPPS lesson plan. I quite enjoyed the fact that my peers had a hard time distinguishing where one section ended and where another started. I liked that I gave the students a chance to apply what I had just talked about by letting them take my cameras and shoot photos. All in all, I think that those aspects really worked well for my lesson.

Unfortunately, like all lessons, there were quite a few things that went wrong. Most of these things involved my own speech. I found that halfway through a sentence, I would say “umm” or as a peer noticed, “you know”. I tried my best to avoid such phrases but I found that I was speaking faster than I could generate words to express the ideas that I was trying to convey. As well, I feel that I had brought up too many topics to think about in a 10 minutes mini-lecture so I could not properly go in depth with the details. That is, I could not fully explain relationally why a compelling photograph had the elements I outlined and I feel that this made my micro-teaching lesson much weaker than I would have liked.

BOOPPPS Lesson PLan

In preparation for the micro-teaching assignment tomorrow during MAED314A, I have prepared a simple lesson plan based on BOOPPPS to outline what I intend to teach during tomorrow's activity.

Composition. How to Shoot a Compelling Photograph.

Bridge

• Everyone loves to take photos. With the dawn of the digital camera and websites to share photos like Facebook and Flickr, how do you create photographs that stand out from the rest?

Teaching Objectives

• Find balance between instrumental and relational teaching of proper composition in photography.
• Engage the students’ interest in the subject matter.
• Learn from the students too. That is, learn different opinions on what makes a good photograph.

Learning Objectives

• Students should have a basic and working knowledge of proper composition.
• Students will learn about lines in composition using some sample photos.
• Students will learn how to lead the viewer’s eye with lines.
• Students will learn the ‘rule of thirds’
• Students will learn to be more comfortable with ‘getting close to the subject as possible’ to fill the frame of the camera with their subject.
• Students will learn to shoot from unusual angles.

Pretest

• Show two photographs to the students.
• The photos are to have the same subject but one is improperly composed, while the other is properly composed.
• Ask the questions: “Which photograph do you find more compelling? Why does this photo stand out more than the other?”
• Segue way into discussing the learning objectives with the students.

Participation

• Students will be given one or two minutes to take photos of a subject of their choosing using concepts outlined in learning objectives.

Post-Test

• Check to see if students followed ideas that were discussed in the learning objectives.
• See if they applied the ‘rule of thirds’
• Note how ‘full’ the subject is in the frame of the photograph and if the student shot the photo at a clever angle.
• As an added bonus, the photos that the students took will be sent to them by the teacher via email.

Summary

• Reiterate the basic rules of composition discussed in the lecture
• Describe more advanced composition techniques such as ‘depth of field’ and ‘shutter speed’.

Relational or Instrumental? A Commentary on Skemp's Article

For our first MAED314A assignment, we were asked to write a short commentary on an article by Richard Skemp on instrumental and relational understanding of mathematics. As well, we were asked to choose 5 quotes from the article and comment on them.

Commentary:

In reading Skemp’s article, Relational Understanding and Instrumental Understanding, I was able to fully realize concepts that I had encountered in my own time of learning mathematics. Skemp makes note of two ways of understanding mathematics and says that both ways of understanding have merits. I’m inclined to agree with Skemp in so far as both types of understanding are necessary to be able to effectively teach mathematics. I feel that a compromise between the two schools of thought are necessary to cater to the minds of each learner in the classroom. I would like to say, however, that I would much rather prefer the relational way of understanding mathematics because I have always felt that, in the long run, it is simpler and more useful. Given that, instrumental learning and understanding of mathematics has its merits and I believe that Skemp has covered those merits quite well in his article. I agree that it is faster, simpler, and provides immediate satisfaction than its relational counterpart. As such, I am inclined not to simply dismiss this way of learning. The bottom line is that I agree with most of what Skemp has said in his article and that I, myself, have learned quite a bit through reading and digesting the ideas inside it.

Quotes:

“That he is a junior teacher in a school where all the other mathematics teaching is instrumental.” (11)

In some merits, Skemp is right. A junior teacher will find it difficult to apply a different teaching style in a school where the vast majority of teachers support a certain style. But my question is, why would it be difficult? Why can’t the junior teacher be a catalyst for change? There isn’t really a concrete reason why the junior teacher should teach a certain way. Unless maybe his or her job depended on it.

“From the marks he makes on paper, it is very hard to make valid inference about the mental processes by which a pupil has been led to make them”(12)

From the meagre amount of marking that I’ve done, I am inclined to agree. While it is easy to spot a mistake that a student can make and correct it, it isn’t always clear to see what the student was thinking while writing down the solution to a problem.

“So far my glowing tribute to mathematics has left out a vital point: the rejection of mathematics by so many, a rejection that in not a few cases turns to abject fright.”(12)

I hear this all the time from other students. “Math I hard. Math is scary.” Partly the reason I wanted to get into teaching was to help prevent this sort of mentality.

“At present most teachers have to learn from their own mistakes” (13)

I don’t yet know whether or not I should agree or disagree with this statement. I am inclined to disagree given the amount of support that a teacher has at his or her disposal. Besides, a teacher can learn from other teachers’ mistakes too.

5. “…nothing else but rational understanding can ever be adequate for a teacher.” (11)

I wholeheartedly agree with this statement. As discussed in the article, instrumental understanding is generally superficial and a teacher with superficial understanding of the given material, regardless of subject matter, cannot effectively teach.