Micro Teaching Reflection

I thought our lesson went over really well overall. We kept student's interest levels up through the whole lesson. I think people were enthused by the historical perspective, as well as the problems we did in class and assigned for "homework."

Although people did enjoy themselves there were many complaints about our lack of clearly prescribed (to the students) learning outcomes. So, most people didn't see the mathematical reasons for the exorcises. We also ran short on time which cut off a lot of the discussion we were going to have about error, methods, and everyday applications. Oh well.

I wonder if our "class" had a copy of our lesson plan as the lesson was being taught would the feedback be better? I think that it would be easier to see where people's lessons went off course if we could see what that course was supposed to be.

As for my thoughts on our presentation, I'm feeling much more comfortable in front of the group. It's funny how when I started juggling everybody immediately started to pay attention. That may be something to think about. From there, I definitely felt the compression of time. What I'd wanted to be a leisurely discussion ended up being a rushed presentation. I hope to learn more about this time management thing in the classroom over the next couple of weeks.

Simmt Article

What is "citizenship education?" Or rather, what is the goal of "citizenship education?" I only ask because I'm not quite sure. In my mind the goal should be to create citizens who are empowered, citizens who are not easily exploited, and citizens who are informed (to name a few criteria). Part of this is being able to follow and critically examine current events. Is it possible to understand completely a budget and its effect on your life if you can't understand what the numbers mean? Clearly no. So how can one be informed for elections if they are innumerate? They can't. This is just the very minimum that one should be learning from math class. As Ms. Simmt stated in the article, math is much more than just numbers and facts, it is a way of critically thinking and problem solving. It seems to me that these are two goals of education in any subject area. So if one of the goals of other classes is citizenship education, then that goal is shared by mathematics.

Micro-Teaching Number 2

Lesson Plan:

Learning Outcomes: Be confident in making estimations, understand error in estimation, problem solving.

Hook: Fermi brief introduction and story about estimating TNT in atomic bomb. Talk about in everyday life when we use estimation: tipping, tax, time, distances (driving).

Pretest: How many 10-dollar bills would it take to cover the surface of Canada? Answer: 950 trillion!
Canada: 9 984 670 km^210
Dollar bill: 1.05*10^-8 km^2
950 trillion.

Lesson Part 1: Understand the problem -> Think of a plan -> Carry out the plan

Go through the example and how we would solve it using those three steps.

Activity: In groups of 3-4, hand out one problem to be solved by the group in the same way we have just shown. Each group will have basically the same problem, but one group has access to computers, one has access to calculators only, one has no computer/calculator, and one has limited information from the problem. Question: How many songs does a radio station play per week? Groups 1-3 will be told it is a classical station.

After 5 mins, have groups share their answer and how they got it. After they've all shared talk about error and which group they think was closest in their estimation.

Post-Test: Assign a few problems for homework.

Summary/Conclusion: Scientists often look for Fermi estimates of the answer to a problem before turning to more sophisticated methods to calculate a precise answer. This provides a useful check on the results: where the complexity of a precise calculation might obscure a large error, the simplicity of Fermi calculations makes them far less susceptible to such mistakes. (Performing the Fermi calculation first is preferable because the intermediate estimates might otherwise be biased by knowledge of the calculated answer.)

What if not?

The applications of the "what if not" (WIN) strategy are many when it comes to math education. One thing that I have always advocated (although not really had the chance to practice yet) is the value of allowing kids the opportunity to feel like they're discovering something for themselves. WIN type questions allow for this to happen. By carefully posing your initial question or problem you can allow students to lead themselves to desired learning outcomes via exploration of the possibilities of the original question. As shown in the text, even a "simple" theorem can lead to an endless rabbit hole of new inquiries in to diverse and sophisticated branches of mathematics. Sure, some of the topics may not be valuable to a grade 8 student, but recognizing the relationships between the legs of the triangle and the hypotenuse (ie, what does a^2 + b^2 < c^2 mean?) is really useful. And, who's to say that explorations of Number Theory or Abstract Algebra would not be interesting to some learners. In our Education Education, there has been plenty of talk about asking the right type of questions when teaching class, WIN questions help to give us a path to some of these questions.

Strengths:
-Revealing the depth of even simple math problems.
-Self exploration of the subject.
-Interesting discussions could abound.
-Room for learning from "failure."

Weaknesses:
-A topic could be lost in the sea of questions.
-Student's/My mind could be blown/melted by ensuing puzzles.
-It is more difficult to ask WIN questions than it is to not.

10 Burning Questions

1. If there are remaining questions/observations that are results of the initial problem, what is the best way to illicit discussion about them?

2. There is little insight without the proper questions. How can we be sure we're asking the proper questions?

3. Is there value in have students pose classroom problems?

4. Assuming a rather strict background in mathematics, how does one broaden questions appropriately?

5. This seems to be how social sciences are approached (i.e. which questions can be asked). Any thoughts?

6. Should there be a limit to the questioning that students can do?

7. If a line of questioning goes off topic too far, what is a good way to regain the topic without killing the creativity involved in the process?

8. I also find that fairly illuminating questions come from the untrained eye.

9. If, like in the example of Euclid's 5th axiom, it can take thousands of years to ask the right question, how does anything get done?

10. After posing 9 questions, I fear that my view is fairly narrow. How can my eyes be opened? Can you point me in the direction of some good resources?

The year, 2020. This is your life!

Note from a student who liked me:

Mr. Bouey is the best! No, it's true. Today when we came into class he was wearing suspenders, as usual, and was listening to some weird music that I didn't like at all (I think Mr. B hates music). But, every class is super exciting. We are always working on fun puzzles in groups or whatever and he always makes them apply to whatever we're studying that day. The other day we did in class presentations on "famous" mathematicians. I chose Alan Turing, he ate a poison apple and invented the computer. All my other math classes were total lamesville but this one's total funtopia (not all the time, sometimes he's super boring).

Note from a student who hated me:

Mr. Booby, is the worst! I don't see why I need to learn this stuff. My old math teachers just gave us the formulas and stuff so that we could just solve the problems in the book. This guy makes it way more difficult than it has to be. Why do I need to know what Algebra is? I want to be brain doctor. You don't need this stuff for med school. Also, he dresses stupid, listens to bad "music", and is old old old (I mean, all his hair's grey). Here's my point: I wish he would just lecture and give us the notes so we'll know what we need to for the provincials. My sister had him and did really well on the provincials, but she must have done a lot of work on her own.

I think that my enthusiasm for the material will be helpful in getting students interested in the material. I also hope to be able to find ways for the students to gain a deep understanding of the material that will lead to success in math as well as other subjects. Clearly I'm afraid I will alienate some of the students.

Dave Hewitt Reflection/Memory Challenge

I probably should have written this a lot sooner 'cause my memory is not so hot. But. . .

In class I stated that I liked the way he introduced the idea of algebra. After all, algebra is just the language we use to express mathematical ideas. This is a hard message to convey and he made it seem like the kids had "invented" the idea on their own. I have always found one of the most rewarding aspects of mathematics is that sense of discovery. I didn't get to experience that feeling until I was in University but these kids are getting that chance in class every day. But, I have already said all of this.

I thought it was interesting that many of my classmates were concerned with the lack of note taking. It didn't seem like the kids couldn't take notes if they wanted to. I got the impression that they didn't really need the notes. If they did "need" the "notes" from the day, I'm sure there are pages in the textbook, or handouts that explained it. The point of the lesson is a fundamental understanding of the subject matter. Once one has the fundamentals down their math skills can flourish through practice/rehearsal.

What I wonder is how does, one arrive at these lesson plans? It is hard to imagine since we haven't even written the basic lesson plans yet, or taught the basic lesson plans, or had a chance to modify the basic lesson plans. I hope that I have at least one idea that is as good as Dr. Hewitt's.