Assignment 3

 Here's the link to my final unit plan. 

https://docs.google.com/document/d/17E4Z3prEM3N1UDLRx0aiYqEn6CDnrVCNJKnAt2ani-s/edit?usp=sharing

Please check-out all the tabs in the document for the lesson plans and worksheets. 

Unit Planning Draft, Nov. 26th

 EDCP 342A Unit planning: Rationale and overview for planning a unit of work in secondary school mathematics

Your name: Sissie He
School, grade & course: Math 9

Topic of unit (NOTE: This should be a unit you will actually be teaching on practicum!):

Exponents and Exponent law; Rational Numbers

 

Preplanning questions:

(1) Why do we teach this unit to secondary school students? Research and talk about the following: Why is this topic included in the curriculum? Why is it important that students learn it? What learning do you hope they will take with them from this? What is intrinsically interesting, useful, beautiful about this topic? (150 words)   Rational numbers are quantities we use in real-life (counts, prices, ratios, measurements, probabilities etc.). Understanding and being able to perform calculations between rational numbers are an important part of numeracy.  This is also an important unit that allows students to practice conversion between different forms of the same number (decimals, proper fractions, improper fractions).   Learning about powers and exponent laws helps students to understand properties of multiplication and division. It allows students to develop understanding in how mathematical laws model general patterns in calculation, and prepare students to understand exponential growth/decay. Exponents are also foundational for polynomial and probability, which are a part of Math 9.

(2) A mathematics project connected to this unit: Plan and describe a student mathematics project that will form part of this unit. Describe the topic, aims, process and timing, and what the students will be asked to produce, and how you will assess the project. (250 words) Project on Powers and Exponents: Students are expected to work either in pair or individually.   There are two versions of the project which students can pick from: 1.      From Powers to a Work Step 1: Pick a base, and pick at least five powers of that base. (e.g. 3^0, 3^2, 3^5, 3^11, 3^12). Step 2: Observe and research, what thing in the world may be (roughly) in each of the power you have? Come up with one (or two) item(s) for each of your powers. Step 3: Create a piece of work that includes all the items you have, by either: a) write a story, b) record yourself telling a story, or c) create a visual artwork.   2.      From a Work to Powers Step 1: Pick a work that you love or you are interested in (e.g. A book, A movie, A game, A musical etc.) Step 2: Pick at least five items from the work. Step 3: Estimate their quantity using five different powers of the same base. Write a few paragraphs explaining how did they estimate the powers.   The project will be introduced to student when they learned about what is power and zero power. They will get in-class time to work on this project. By the end of any work block allocated for this project, students will be asked to write an exit slip on what they have done in that block.   ------------- Reflection: After hand-in the project, the students are asked to 1.      Write down 4 things they learned (math or non-math) through this project 2.      Reflect on what they liked/disliked about this project and why   Assessment: The project will be assessed using proficiency scale based on whether a) the powers are reasonably estimated, b) student showed meaningful reflection on their learning.

(3) Assessment and evaluation: How will you build a fair and well-rounded assessment and evaluation plan for this unit? Include formative and summative, informal/ observational and more formal assessment modes. (100 words)  Formative assessments: The classroom is constructed around the use of students working in group on vertical erasable surfaces. Vertical surfaces make student’s work very visible to the teacher, and will be the main tool for teacher to formatively assess students. When vertical surfaces are not used in a lesson, exit slip could be used in complementary.     Summative assessment: Students will be assessed summatively through the project, a few quizzed and two tests.

Elements of your unit plan:

a)  Give a numbered list of the topics of the 10-12 lessons in this unit in the order you would teach them.

Lesson	Topic
1	(2.1) Introduction to power and exponent
2	(2.2) The zero exponent, power of 10
3	(2.3) Order of operations with powers
4	(2.4) Exponent Laws - Product of Powers and Quotient of Powers
5	(2.5) Exponent Laws - a Power of a Power, a Power of a product, a Power of a quotient
6	(3.1) What is a rational number & ordering rational numbers
7	(3.2 & 3.3) Adding & Subtracting rational numbers
8	(3.4 & 3.5) Multiplying and dividing fractions and mixed numbers
9	(3.4 & 3.5) Multiplying and dividing decimals
10	(3.6) Order of operations with rational numbers
(11)
(12)

 

Lesson plans: https://docs.google.com/document/d/17E4Z3prEM3N1UDLRx0aiYqEn6CDnrVCNJKnAt2ani-s/edit?usp=sharing

Reading Response - Textbook and Math Learner, Nov. 17

Through the reading, I found the distinction of thinker imperatives vs scribbler imperatives very interesting. Other than the inclusive/exclusive connotation discussed in the article, I thought that given the wide-spread math anxiety, we might want to use more thinker imperative, in order to encourage students to consider themselves as a capable thinker. 

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As a student, I think I liked textbook. The formulas, worked examples and practices were all very helpful to me. The only problem I have with them was their volume and weight. Since I really wanted to work on my homework with the textbook in my hand, and I didn't want to bring it home, I never do my math homework at home (I did them after school or during other classes). I think at that time, I totally considered learning math as an purely individual process. To some extent I still think in the same way. However now I have been working as a tutor, playing a role in one's learning, it seems like "learning math is an individual process" sounds less valid. 

Combining with the questions asked in the reading, I am reminded about two things. The first one is one of the FPPL, which state that "learning is holistic, reflexive, reflective, experimental and relational." The second one is the sociocultural theory (we did in EPSE 308), which consider learner's interaction with a more knowledgeable individual as an important pathway of learning. I think textbooks may serve as the knowledgeable individual figure. Then if, the students have anybody/anything else that can play that role when they are learning, I guess textbook is not needed.  

Promoting Flow - Nov. 17

Personally, flow is something I'm seeking. I have been struggling with staying focus in the past years (I was excellent at focusing on task when I was kid). I think what is blocking me from entering a flow is always an anxiety about time (e.g. how long would this task takes me? what else I would have to do after this?). When I really can't focus and I really need to, I write a brain dump. But I only do it when I have to, because writing brain dump takes time and energy (hence thinking about writing a brain dump also cause me anxiety). 

To create flow in a classroom, I would say it's difficult but possible. 

After my first teaching during my short practicum, both my FA and SA were telling me that I might want to talk less and give students more time. To be honest, once I start to talk, I struggle with keeping it short. I feel like if I'm going to explain something, I got to make it clear, because leaving students confused will make them feel helpless. 

I have been consistently thinking about how to navigate the difference between tutoring and teaching in a classroom. (Rephrase: how is teaching a class even possible??) Thinking about flow gives me a little push. To promote flow in a classroom, I might should just consider myself as a host/MC. I introduce the topic, provide prompts, and try keep people on the right track - this idea creates an anxiety of "isn't that just leaving out the teaching role?" in me. I think what I truly concern is how to create confidence and positive belief in students. If I see students engaging with math with confidence and motivation, I will be more than comfortable to leave them struggling on their own. And as a direction toward that, I am thinking about joy pedagogy (Kevin was showing us videos on this topic on Wednesday, and I really liked the idea there). 

Giant Soup Can Puzzle, Nov. 12

This puzzle didn't provide any specific number, so I started with researching numbers. Numbers I got are:

 a). Standover height of a M size bicycle: ~78 cm 

b). The diameter: height ratio of a Campbells soup can: 1:1.5 

       -  I found a hidden storage taking the shape of a Campbell's can and its dimension is 3"to 4.5" (on amazon:  https://www.amazon.com/BigMouth-Inc-Campbells-Chicken-Valuables/dp/B01H456RXC), I wasn't sure if that actually reflect the real dimension, so I measured it roughly using a picture and it was actually about 1:1.5

c). Amount of water needed to put out a house fire...

    -  I saw a few sources are saying one gallon of water put out 3 square feet of fire (one of the sources is https://kiserrenovations.com/how-much-water-is-used-to-put-out-a-fire/). The average house size in Canada is said to be 1948 square feet (https://worldpopulationreview.com/country-rankings/house-size-by-country). I would simply assume that one whole house is on fire in average. Then the amount of water needed is 1948/3 = 649 gallons = 2457 L.

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Estimation: combining a) and b), I need to estimate the dimension of the water tank. 

 I realised that measuring the diameter is very difficult from this picture, so I choose to measure the height of the can. The estimation is height of the can = 5*standover height of the bike. 

Then, h = 5*0.78 = 3.9 m; d = 3.9/1.5 = 2.6 m; 

Calculating the volume of the tank: 

V = pi*r^2*h =20.7 m^3 = 20700 L. 

--> There is more than enough water.

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I will share a puzzle on the tangent of "tank". 

This is a picture of a liquid nitrogen tank on UBC campus, with the B/C block of Chemistry building in the background. 

The question my friend actually asked me when we were walking in and out the building (we were having  MATH 320 in this building) was, "if this tank explodes in front of us, would we be suffocated before frozen, or frozen before suffocated?". Unfortunately for our purpose here, this question is too challenging to be answered properly, and may not be appropriate for a class setting, since there are deaths caused by liquid nitrogen leakage. 

A possible question would be to estimate the weight of the liquid nitrogen in the tank, which require students to research on what percentage of a liquid nitrogen tank is usually filled (the tank should not be 100% full). 

Reading Response - Arbitrary and Necessary

I think what I am inclined to do is establishing the notion of convention in classroom, so whenever I inform the arbitrary, students know that what I'm telling them there are conventions in mathematics and they are expected to know it, remember it, and use it. Similarly when teaching something necessary, I would like to prompt them that those things are deducible. However I don't think it is realistic to not "give" students any necessary and have them com to know it by themselves.

I feel like I just wrote something really boring above. I think I totally agree that the awareness of what is arbitrary and what is necessary is very important for both teachers and students. But I am not sure how can I encourage that awareness effectively. Maybe incorporating some visual aid? (e.g. box all the arbitrary using red throughout the materials or in-class writing)

I think everything just comes down to how can we help students to understand the math. Since even when students know the presence of necessity in what we teach, they often end-up thinking "but memorising is just easier for me."

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.)

Assignment 1 - Group Documentation

Members: Sissie He, Ross Kagna, Tiffany Williams

Original artwork: Fabric Hexaflexagon by Jill Borcherd

We chose this art work because we thought it would look visually appealing to the kids and would be easy for the kids to recreate with their own twist on it. For example, for us, we tried to make it our own by choosing different patterned fabrics for each face (Tiffany was especially proud of the side with apples and oranges because my friend made a joke earlier that week about comparing apples and oranges!). We also used fabrics Sissie already had, which might make for a good project on upcycling fabrics for the kids to find materials they already have but that might have gone unused and forgotten otherwise. Other than fabrics, papers, stickers, or other materials might also be used, as long as they are thin and gluable. 

We first started by making samples using paper. This first sample got beaten up pretty quickly as Ross was mapping out the sequences. In this first sample, we had to make sure our trig (!) ratios were right for our equilateral triangles, which might serve as a warm-up reminder of what the kids might already know about trig for us to evaluate how familiar they are with trig concepts (ie. the 2 to sqrt3 ratio). 

Here are some other samples we made, both for ourselves and for our peers to play with:

Sissie made the brown paper samples for the interactive activity of our peers playing with the faces and trying to figure out Tuckerman’s Traverse—the fastest way of getting to all 6 faces by mapping out the sequences of the faces they get to. We hoped this would be a gentle introduction for the kids! 

A struggle we initially encountered as a group was finding specific instructions to the strip of triangles that the kids would be able to follow and understand; we were kind of just folding it until it looked right at the beginning! Ross was folding it a bunch of times to work this out.

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Then, for the replication of the artwork, Sissie found a strip of fabric, on which we pasted the different patterned fabrics for the various 6 faces. Since the orientation of the faces mattered, we wanted to be thoughtful in choosing which patterns we used for each of the 6 faces, and careful in the way we glued them to the longer strip of fabric. For example, in the mapping of the faces, since 1, 2, and 3 occur the most frequently, we chose to focus on making the patterns for those the most visually elaborate and interesting. 

We used lace, floral, and polka dots for Face #1, apples and oranges for Face #2, and apples and gingham for Face #3. Then, we laid them out to make sure they looked appealing. After experimenting with a sample on which we drew different coloured stars to determine the correct orientation of each equilateral triangle on the long strip of paper, we carefully stuck the patterned fabrics in the correct position on the long fabric strip. After this, we folded the long fabric strip, as we had done with the paper samples! And we were done!

The Locker Problem - Sept. 29th

 I started tackling the puzzle by thinking about what happens to a specific locker, for example locker #1 or #1000, since I thought these numbers on the end are easier to figure out. I then realised that locker #1 is only going to have their state changed for once (by the first student), whereas locker #1000's state is probably going to be altered for many many times, including by the first and the second student. 

I then tracked down the first few lockers, what happens to locker #2, #3 and #4. I realised that a locker's state will be altered when, and only when, the count of the student is a factor of the number of the locker. The first student were to alter all the locker's state, was because 1 is a factor of every integer from 1-1000. 

Thus I could deduce that, by the end, a locker will be closed if it has odd number of factors (e.g. locker #1), and it will be opened, if it has even number of factors (e.g. locker #2). 

To figure out which numbers have odd/even number of factors, I considered a few numbers, such as 8, 9, and 12. I found that the factors mostly comes in pairs, with the exception of squares, which introduce duplicated factors. 

Thus, I could conclude that, from locker #1-1000, any lockers with a perfect square number will be closed by the end, that's #1, #4, #9, #16......, and will be opened otherwise. 

With the aid of technology, I figured that the largest perfect square within a 1000 is 31^2 = 961. Hence there will be 31 lockers closed by the end. 

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Overall I think my strategy was to start with considering specific examples, particularly the easier ones, to figure out the pattern. 

Favourite and Least Favourite Math Teachers - Sept. 17th.

It’s quite difficult for me to come up with my favourite and least favourite math teacher. For my least favourite, I would collectively say the math teachers I had in elementary school, which I think there was 2-3 of them, and I only have the blurriest memories about them. One episode I remember from then is when we were learning the multiplication table. To make sure we were memorising the table, we were assessed on the table every class. The things goes like, we start with a student sitting in the corner of the class, students are asked to stand up and recite the few rows from the table that come after what the last student recited. And we go around the class. I was very shy and reserved at that time, as a result, although memorising the table wasn’t too challenging for me, being assessed in front of the whole class was a very anxious experience. Especially since the teacher was being intimidating.

I think I understand the reasons behind her intimidation. Actually, the majority of teachers I had in my elementary school was employing intimidation as a strategy for classroom management. To me, I am pretty sure I have always been on the very sensitive end of the spectrum, their intimidation was a form of aggression. These experiences are definitely the reason I want to be a friendly and approachable teacher, but also the reason I struggle with drawing boundaries. 

When it comes to my favourite, I would say is my math teacher who taught me from grade 7-12. At least she’s the person came into my mind when I think about “my math teacher”. She wasn’t a very warm and friendly type of teacher, but she was very prepared and responsible - those are some qualities that I really admire about her. I very much want to be as prepared to teach as she has always been.  

Reading Response - Three Curricula, Sept 15th.

 This was a really condensed reading. What I really resonated with, from the article, was the questioning towards the exclusion of certain studies, especially law. For example, we all know a thing so called "marriage" since we were in the elementary school, and that most of us were told that it is something virtually everybody is going to come across in their lives. But marriage is actually, to a large extent, a legal contract, which the young are very often not taught about what exactly is that contract about. It was quite upsetting, when I read Eisner wrote "We teach what we teach largely out of habit". In BC, we have Law Studies 12 as an option of social studies 12, which is great. But I think the importance of law education, is likely more than just an option which students may take in their grade 12. 

There were also quite a few thing that I've rarely thought about, highlighted by Eisner in the chapter. One of them was the effect of fixed timetable education to student's working habit. I've never really reflected upon this fixed-timetable-scheme in education system, and I can hardly comment on it yet. But indeed, sub-dividing a day into multiple fixed sections to work on multiple subjects, does not sounds necessarily like the most efficient way of learning or working in general. And this connects to Eisner's argument of, how the fixed forms and patterns we teach in school might constrain students instead of inspire them. This reading made me ponder about, how may I encourage students to learn creatively in my class, instead of having me "teaching" them how to use the "tools". To some extent, aren't all assignments essentially constraining the way students learn?

Reading Response - Instrumental vs. Relational Teaching, Sep. 10th

I will start with a few things that I enjoyed about reading the text. I really liked how Skemp started with introducing the idea of faux amis. Two faux amis I found very interesting in math, while difficult to explain to student, are "general" and "always". Also, I found the music class analogy which Skemp made very interesting. It makes me think about how in junior level of math class, almost all kids seems to be capable of doing those arithmetic. But once "x" and "y" are introduced, to some students, the same operations somehow seemed like a new set of operations to learn. 

An idea that I always kind of had in mind is that, often mathematical insight comes after performing mathematical methodology repeatedly. Because, this is the case for me. But as I entered university, I learned from my study buddy that, some math learners really struggle on solving a problem unless they have understood the methodology offered relationally, which is totally not the case for me. I was so good at imitate whatever was done in an example on the textbook and get the right answer without understanding any principle underlying. After realizing that some people need principles before methodologies, I start to believe that both instrumental and relational explanation are needed in teaching. I recognize the value of "instrumental teaching" as described by Skemp, because as a prevalent idea, "math is a tool". When students ask me why they learn "pre-calculus", well, I answer, "because calculus is very useful in many discipline, so you might want to prepare for it". But at the same time, mathematical insight is, almost self-evidently, what we really appreciate and eager to share with others. And of course as Skemp has pointed out, it benefits students in long-term. Combined with all the situational factors Skemp has outlined, I think a mix of instrumental and relational teaching is the direction that I would like to go for.