Assignment 2 - Personal Reflection

I would like to do my reflection in two parts, a) on our lesson plan; and b) on my personal performance in delivering the lesson. 

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I would like to stress that I learned a lot from my peers in putting together a lesson plan, and I really like our lesson plan (which regrettably I wasn't contributing much to; it was my group members who came up with those ideas and activities). And you may check out what a simple lesson plan I was producing for my non-curricular micro-teaching, which make a good contrast with what we made for this group project. 

So before we deliver the lesson, I was super excited about our lesson plan, and no surprise that once we realise the plan in a classroom, things didn't felt as perfect as I expected to be. 

One limitation I found is in assessing and providing feedback. Since it's a Math 8 class, I won't be having student doing a lot of homework/individual work. But I should have accurate knowledge about where they're at as a teacher. Then I believe in-class activity time would be crucial for me to assess and provide feedback. In the micro-teaching we did on Wednesday, we (me, Damanjit and Shannon) were all circling around the room and check-in with students during activities, and that's one thing I really liked about our lesson plan. But imagine in a regular Math 8 classroom, a 80 min lesson, although I would be able to allocate more time to the activities, there will be more students in the room, and I could hardly help and assess every student in the room. 

Another notable unexpected happened is the confusion between volume and area. The confusion arose from the water demo we played in the lesson, which we were intending to derive the Pythagorean theorem from. This confusion is was also mentioned in the feedback we received. If this arose in a 80 min lesson, I think I would facilitate the students to think/discuss about it. But for our 15 min lesson, we didn't have enough time to resolve this confusion completely.

From the feedback provided by our peers, one of them was suggesting providing motivation behind learning Pythagorean Theorem. And this is an advise that I am not sure if I agree with. I would suppose that the motivation would be to find the missing side in a right angle triangle, but what percent of our student would be motivated by that? I feel like it is more natural, that we first derive the theorem from observations, and then talk about the implications of the theorem. I would like to know what other people think about this. 

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In terms of my performance as a teacher/speaker, there's a specific thing I'm feeling regretful from my performance on Wednesday - I couldn't wrap up the lesson nicely. I was giving the last part of the lesson, and when I knew that is almost time, I asked for any final question (which was nice), but after that I was kind of frozen. We have planned for further contents and activity (including stating the algebraic form of the theorem), and I had the chance to signposting, saying for example "we will be doing ____ and ____ in our next class."

Moreover, I really want to work on my teachers' voice and confidence. I want to be a good speaker. I might want to start with practicing a loud and clear voice. 

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Here are the forms we collected. I am sorry that I didn't complete the form for my group. I didn't forget about it but just struggled with it. I hope what I wrote above is adequate for cover up for that. 

Assignment 2 - Curricular Microteaching Lesson Plan, Oct. 15th

 

Micro-Teaching Reflection, Oct 1st

On Oct 1st, we did our non-curricular micro-teaching. My micro-teaching was on how slugs mate. Overall, I am quite satisfied by how I was able to deliver the contents, despite that there was some moments that I couldn't organise my sentence very well. 

My biggest mis-plan was on timing and pacing. I think I end up finishing everything I prepared to talk about in 7 minutes. Luckily, the 3 minutes left was mostly covered by answering the questions students brought up. 

There is a specific part that I want to reflect on. At the very beginning of my micro-lesson, when I asked my students what they know about slugs and how they mate, Danielle answered with significant prior knowledge on this topic - they knew that slugs are hermaphrodites and they hang and intertwine when mating, which surprised me. I then felt like the beans was spilled, I was a little panic, and I kind of started to rush through. However I could have respond that "Oh excellent, we will definitely go into what you just said.", and encourage more input from the other students. 

If I was to deliver this micro-lesson again, I will try to slow down the pace. Especially in the beginning, since there was only 4 audiences, I could have ask students to share their prior knowledge or any thoughts they have on slugs one by one, which can make them feel more engaged in the lesson. Also, by knowing how each of them feel about this topic, the languages/narrative I use to explain the mating process could be tailored. Moreover, JJ's feedback also echoed this pacing problem, as he point out that I might want to take more pauses to make sure the audiences are following. 

Other than JJ's feedback, both Danielle and Snow pointed out that there could be some participatory activities. Indeed, I was quite obsessed with all the contents I wanted to deliver, and ended up giving a lecture-heavy lesson. It would be interesting to try incorporate some activities to the lesson. 

Below are the assessment sheets (from my peers and myself). 

Reading Response - History of Mathematics Education, Oct. 8th

My first stop was at where the reading depicted the character of a stereotypical math person. I laughed. Apparently, the people I meet in the mathematics department during my undergrads, instructors or peers, they don't really fall into that stereotypical description, while they express their love to mathematics. 

Then, I read the next bullet point, which says there are a lot of positive social valuation in claiming incapable of doing math. I laughed again. And then I thought that indeed, there could be a "safer space" vs "braver space" when it comes to expressing one's affection toward math. The math department in universities, are probably the "safest space", whereas it will be more difficult for people to share their enthusiasm about math in a place that we would expect the majority is feeling relatable to each other by sharing their math phobia.  

The third stop I had was at where The New Math was recounted. Bourbaki group's rejection of teaching geometry was quite shocking to me. And the term "abstract" in that passage confused and bothered me. I am not sure if we are saying "abstract" to refers to a property of being "alike" to the field of abstract mathematics? Does less visual just means more abstract? According my general understanding to the term "abstract", although I think it's true that a lot of people find geometry more "intuitive" or easy to understand, but I don't think geometry is anything less abstract than algebra in nature. Therefore Bourbaki group's advocate kind of sounded like an "algebra-elitism" to me, which some people who are better at algebra (over geometry) view themselves as elite in the field simply because they are the minority. I think I just couldn't see the reason why they thought algebra would better prepare students to become future rocket scientists. 

Reading Response - Lockhart's Lament

It was a very interesting and exhausting reading. I was surprised by Lockhart's energy in that article. 

I agree that the way we construct the curriculum or the way we perceive math education is making a lot of kids who could be passionate about math to find it boring. I personally didn't find math class that boring, but I totally see that boredom in many students. 

There was a lot of questions and objections in me as I read, but most of time they are addressed later in the article. I think overall there were a lot of things I didn't emotionally relate with him, but his arguments were still convincing to me. Just as an example, I don't think I find as much as enthusiasm in mathematical problem as Lockhart find; while I think the satisfaction I find in learning and using "rigorous" mathematical language is more than what Lockhart's would expect. But that satisfaction, indeed, might not be about mathematics, but rather about linguistic?

I really appreciate that he provided a very clear image to how math should be "taught" if we perceive math in his way - that there's no such a thing called a teaching method, but just a honest relationship. I really enjoy this idea, since I'm more interested in relationship building rather than comparing different teaching method. 

I also found his whole point about how a "mathematical problem" is crucial very inspiring, including his argument of technique in math should be learned in context. I think that is something we can try to incorporate in teaching. Apparently it's not likely that we can have the students to work on a single problem for days or weeks, but it should be possible to try to expose students with more "context". 

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Comparing with Skemp, Lockhart's criticism towards instrumental teaching of math aligned with Skemp. And very interestingly they both wrote about analogy of music class taught in "math style". 

Micro-Teaching Lesson Plan - How Slugs Mate, Oct. 1st

How Slugs Mate - Lesson Plan, Oct 1st. 

1. Lesson objective: To learn about one of the two major ways which slugs mate (the overhanging style)

2. Structure:

    ① Ask students to share any prior knowledge they have about slugs and their mating (1-2 min)

    ② Explain what does "hermaphrodites" means, and the different ways for slugs to reproduce. (1-2 min)

    ③ Show an illustration of overhanging mating of slugs, and ask students to come up with description and interpretation. Then briefly explain the illustration. (2-3 min)

    ④ Explain when and how apophallation happens (1-2 min)

    ⑤  (Optional) Talk about how slugs may control when to fertilise themselves (1 min)

3. Materials: 

    ① Illustration(s) that shows the mating process. (Graphic representation is crucial for this lesson, while students may feel uncomfortable with pictures of slugs. Therefore illustrations are used.)

    ② My passion

Assignment 1 - Personal Reflection

In my past engagement with mathematics, I was mostly focused on the arithmetic side. This project was a great opportunity for me to look into a different facet of math. Designing and creating the artwork with Tiffany and Ross was a lot of fun. In this personal reflection, I would like to go into some thoughts I had during this process. 

As we finished preparing all the triangles we wanted to have on the faces of the flexagon, we were going to glue them onto the stripe. And how we orient these triangles was crucial, since we had to make sure the patterns come together when we fold the stripe into a flexagon. We (mostly Ross) experimented on a marked up flexagon, to figure out the orientation of the patterns in stripe form. The product was the stripe shown in the pictures below. Looking at the rules we found, we were trying to form interpretations about why the patterns has to be in this way (e.g why when the rhombuses point up and down on the stripe, they can form a star once folded into a hexagon). I found this process of seeking rules, and then gaining insights by looking at them was very much like what we do in math. 

The next step was to glue the triangles onto the stripe, and I was really concerned about the spacing between each triangles. The first flexagon we made, was made of thick card paper, and turned out pretty tight and difficult to flip (until we beaten it up). In a video I watched on Youtube about making a dodecahexaflexagon (so embedding 12 faces into a hexaflexagon), considerable spaces were placed between each triangles, to allow covering up the thickness of embedded layers. Having layers of fabrics glued together would similarly create some thickness, hence I proposed to space the triangles as we glue them. We chose this space to be somewhere around 1 cm (without any effort to calculate or justify the number), as shown in this picture:

The final product we got, with some disappointment, was very loose. (The positive side was, it was indeed very easy to flip!)

Looking back to Borcherds’s work again, I was so amazed by the precision of their work. I wonder what kind of math and planning have Borcherds done in order to achieve that precision. 

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Overall, I think my biggest take away from this assignment, was how we can gain enthusiasm with playful puzzles. I found that enthusiasm from my peers playing with flexagons, and I also found it inside me when I engage in the presentations from other groups. I am quite confident that most student would enjoy these playful activities we had in our classes this week, if offered in a non-evaluative & in-class manner. But I think the challenges would be, how do we draw connections to the BC curriculum, and how do we manage to fit these "extra" activities into the limited lesson hours.

I think even if we cannot afford a fantastic project/activity, it's still very nice to simply show students some artworks related to math. For example, when we talk about radical numbers in class, we can show students the artwork which JJ, Snow, and Katarina's group have chose and presented, and ask students what they think about the art. Or, when we talk about irrational numbers, we can show students the artwork which Juma, Jimena, and Shannon have presented. (However the enthusiasm you get in an art/craft-creating activity would be missing.)