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."