Reflection on the Battleground Schools Reading.

The analogy of school as a battleground, fighting against the negativity surrounding mathematics from conservative teachers, students with preconceived notions of mathematics, and the general public's views of the irrelevance of mathematics was quite eye-opening.

I felt that this reading was directly related to the reading comparing Instrumental vs Relational ways of understanding that we read earlier this year; comparing a superficial knowledge of "how" to do something to a deeper understanding of "why" you are doing something. This reading really exemplified the comparison by bringing in the notions of conservative understandings and progressive understandings of math.

The Progressive Movement emphasized a teaching philosophy that allowed for student experimentation and I fully agree with it. A student's learning should be dictated by his or her own desires and interests. A teacher is there to moderate and facilitate. A teacher should guide and lead, not direct on a singular path. Blind obedience is not how you build life-long learners.

The New Math Movement is an interesting one. The sudden outcry for a stronger emphasis on mathematics in the classroom is such a stark transition from the negative preconceptions seen in generations before. Their push for understanding over fluency is agreeable to my view, but their demand for strict and rigorous mathematics is a lot higher than what I desire from my students.

Math Wars is just a cool name. The ongoing debate of where the curricula of math and science should stand is one to keep an eye on as it progresses in the current era.

Reflection on Microteaching: Popping

In general, talking and teaching about dance is always fun. It's a great way to get students active and embrace their silly side while also creating the opportunity for them to find a great new hobby/passion in life!

Everything in the 10 minute lesson went pretty well, everyone was engaged and participated. The problems basically stemmed from my end of the lesson. I wanted to have music playing to demonstrate the moves with a rhythm, but the speakers were not cooperating. Moreover, the video that I wanted to show as a closer for the lesson would not buffer for a little bit. But these events just helped me solidify the notion that a teacher need to be flexible in the classroom. If things aren't going according to plan, you CANNOT just plow through and try to make your "perfect" lesson plan work. Be flexible. If the music isn't working, make your own. If the students aren't engaged, ask them what would be better.

It's important to be honest with yourself and honest with the students. You have a plan, if it's not working, change it. You are human, make sure the students know that. That way, you'll build a connection with them.

Lesson Plan for "Hitting"!

Math Lesson Plan:

Objective:

·       Teach people about the different ways to “hit” in popping

o   Arms

o   Core

o   Chest

o   Legs

Strategies to help people learn:

·       A hit is a quick flex and release of muscles in an area of the body

·       A good way to learn is to flex for 2 seconds, release for 2 seconds, flex for 2 seconds, etc

o   As you get used to this feeling, you can flex and release for 1 second each

o   Then just keep getting quicker and quicker

·       Some people like to learn how to hit each individual body part separately before combining them all

·       Others prefer to learn how to hit all simultaneously, just depends on the person

How to start (hook):

·       Show them what “hitting” on a beat is, maybe bring some music

Materials needed:

·       A phone or a laptop or anything with speakers! And a song with solid instrumentals

Assumed prior knowledge:

·       No previous dance experience required! Just willingness to participate!

Time (for participatory practice):

·       Due to the nature of the lesson, participation will be throughout the lesson

Development of ideas/skills:

·       Explain what it means to hit a beat, to “hit” on rhythm with the music, either to a snare, or to a base kick

·       Different ways to hit

o   Hitting and stopping

o   Hitting and bouncing back

o   Hitting and continuing motion

·       Active and continual participation by students as I explain step by step how to do these things

How to assess the learning (informal/formal):

·       Visual assessment of whether or not people are doing it properly, or are at least improving

·       Recognition of different beats and when to hit a bit

Ending:

·       Show a video of Michael “Onion” Kim from Skillz for Billz to show what hard hitting can look like

Application, further directions:

·       This technique in dance is really great because you can practice anywhere! While you wait for the bus, while you cook, while you’re walking to and from places! Practice practice practice!

·       Next time: isolations!

Campbell's Soup is a Problem!

Judging from the picture of a regular Campbell's can, where the letters are oriented and how large they are compared to the can itself, one can assume that the height of the bike is roughly one third the length of the diameter of the large Campbell's can. Further, one can estimate the height of the bike to be 3 feet. Thus, the diameter of the large soup can looks to be about 9 ft. Since the height of the Campbell's soup can appears to be twice the diameter, we can assume that the height of the large soup can is around 18 ft. Using these dimensions, and the formula for the volume of a cylinder ( Volume = pi*(d/2)*h), we calculate that the total amount of water that the large soup can can hold is pi*(9/2)*18 = 254.5 cubic feet.

Thus, our estimation of the dimensions o the large Campbell's soup can is 9 ft in diameter, 18 ft tall, and can hold up to 254.5 cubic feet of water. Converting this volume to liters, we have that it can hold roughly 254.5*28.3168 = 7205.75 litres of water!

Letters to Mr. Mak

Letters to Mr. Mak (10 years from now)

              Letter #1 from the happy student:

Hey, Mr. Mak, long time no talk! I’m just finishing up university right now (not a math degree, mind you), and I thought I’d shoot you a message. I want to thank you for making math entertaining and always making the class laugh. You made us all feel individually important and capable of learning new things that we found difficult in life. Personally, I want to thank you for listening to my problems that I was going through at the time (sorted out now), and then for convincing me to go talk to the counselor once you were feeling a bit over your head. At the time, I was a little hurt, but I see now it was the right choice. I’ve been able to be self-aware of myself and been able to overcome both academic and personal struggles over the years. So, just in case you’re questioning your life choices or whether you’re doing good things at your job, I thought I’d just say thank you for everything.

Letter #2 from the not-so-happy student:

Hey, Mr. Mak, I’m actually getting my teaching degree right now and am just reflecting on your teaching style from 10 years ago. Please, take no offense, but I always thought that you were too silly in class and didn’t focus on the course material enough. You didn’t emphasize certain mathematical terms and vocabulary enough, so when I went into university math, I didn’t understand a lot of what was being said. It sort of seemed like you wanted to be liked more than you wanted to get us prepared for exams and tests and things.

 

Reflection: The good letter is emphasizing my strengths of connecting with students and being approachable. The bad letter is stressing that I don’t want to prioritize entertainment OVER learning the material in class; I need to maintain control of the classroom while still being entertaining.

Excuse me while I reflect on my Math-Dance presentation...

            Combining math with dance was quite the experience. We had some issues deciding what aspect of math we wanted to emphasize in our dance. We came down to either combinatorics or geometry. Focusing on combinatorics, we decided to use different parameters to classify what a “handshake” could be. We asked ourselves questions like these (and more): does a handshake need to be between two people, does a handshake need to involve same or different hands, does the handshake need to only include one hand from each person? We decided that, under different parameters, you can increase the number of possible handshakes. Moreover, that we can calculate the number of handshakes using combinatorics; I have two hands to CHOOSE from, and then I CHOOSE one of my partners etc.

Regarding potential math learning elements, this activity is a good way to introduce the concept of combinatorics and counting to a class. It gets them involved, active, and thinking creatively and abstractly. More importantly, it gets participants to implicitly use the principles of counting without having to lecture them about the concepts. Using this activity as a hook, it allows a student to understand the notion that they are ALREADY capable of doing math, and even further, that they are ALREADY doing math. It’s our job as teachers to just solidify those concepts and make sure they stay crystallized in students’ brains.

Dance can be used in many different lessons in math. Geometry sections can be livened up by doing different dances with arms and legs. Musical chairs (sort of a dance) can be used to actively illustrate examples of counting how many ways a group of people can sit in a line. Active learning, through dance, is a great tool for teachers to use. Math is typically looked at as a boring, sit-down-and-write-notes kind of class, but with dance, we can slowly reverse that preconception.

Dishes Problem

I first started this problem by looking at the lowest common multiple of 2, 3, and 4, simply because the restrictions state that every 2 people have to share a dish, every 3 have to share, and every 4 have to share, thus the total number of dishes has to be a multiple of 2, 3, and 4.
The lowest common multiple is 12. With 12 people, and the restrictions on dishes, that makes 6 dishes of rice, 4 dishes of broth, and 3 dishes of meat. That totals to 13 dishes for every 12 people.
If I recognize that 65 is 13*5. That means 5 groups of 13 dishes, and subsequently, 5 groups of 12 people. Therefore, for 65 dishes, there must be 5*12 = 60 guests!

I don't believe cultural context has any effect on this problem. The fact that I'm working on this Chinese problem from the 4th century in 2015, not knowing anything about Chinese culture is testament to that. The problem itself, when translated, can be done in any language, in any location, at any time period. It's timeless for a reason!

Commentary on MathThatMatters

The proposal of a new way of looking at teaching math is very much what IB stands for. The interdisciplinary approach to mathematics by intertwining current events of social justice and politics is an effective and very important method to get students more interested in the topic. They need to see that math is everywhere. This is a good way to do so.
I particularly enjoyed how the author weaved in other teachers' responses into the article and responded to each with optimism. They were all valid concerns and were addressed appropriately. In fact, in my IB training, where we must integrate similar styles into our lesson plans, I have been struggling with many of these same questions. Will my students have the capacity to learn the math as well as connect with social justice issues around the world? Am I sacrificing skills they could gain in order to make the subject more interesting? I hope not. I hope that this method encourages students to be more optimistic about math as a whole, that they can go into their next math class without the preconceived notions of "I'll never use this in real life" or "I can't do this, it doesn't make sense".  I want to create learners: people that aren't afraid of a new challenge, people who are determined to overcome obstacles, people that can take a topic and expand on it to make it more worthwhile.
Open-ended assignments allow students to use the math in their own areas of interest. This tailors the math to each individual student at their own learning pace and skill level. It's an elegant solution.

In summary, this proposal of a reformation of the way mathematics is taught is something that excites me. It's something I truly believe in, and believe that it is the solution to reshaping how students view math. I will be utilizing this strategy in my classroom on the first day of practicum, I assure you.

Pro-D Day!

On October 23rd, I will be attending an IB cohort conference with my MYP Inquiry class and the DP Inquiry class. I am very excited.