Ever think of the guy who gets paid way too much for having painted a random splatter on canvas? Yeah, well maybe I could make a splatter too. Heck, you could make a splatter. But could we each recreate the exact same splatter? Visually, PROBABLY. With technology these days there’s really no excuse. But what if art isn’t something that’s completely visual? All those moments, events, thoughts, and feelings that came before the splatter, gets somehow imprinted into the splatter and that’s why rich people pay what they do for a kindergarten-style drawing that you or I could make on canvas for just the low low price of ten bucks a pop. Now, how that emotion (or at least the essence of it) gets captured onto splatter and subsequently transferred to another human being is beyond me. Perhaps some of us are just not privy to it. We’re not on the same wavelength. What if understanding emotions from art was just like being able to tune in to the right frequency?
So, what is art?
Art is truth. My truth. Your truth. A shared truth, or a hidden one. This summer I went to the Brooklyn Sketchbook Museum. I was skeptical at first. I wanted to “learn things” I countered to my travel companions. Let’s go to the Natural History Museum, I offered. Let’s learn the history of the world! Then comes Chloe, knocking me out of my reveries about traveling back hundreds of millions of years to see the journey of earth through time with, “Honestly? It’s just going to be a bunch of stuffed animals...”
Some people are right.
But some people will also never understand how underrated a bunch of stuffed animals are.
Against my better judgement (or so I thought), we went to the Brooklyn Sketchbook Museum. I picked up a sketchbook, not really knowing what to expect… and I had the most incredible journey. A glimpse. It was a glimpse into Neil’s life. I had never met Neil, but I now held a fragment of him in my hands. Neil sketched the female figure. A worthy pursuit, I might add. But it wasn’t that Neil was drawing naked or half-naked or semi-clothed or whatever-you-want-to-call it women, but it was the fact that Neil shared some part of himself – in the very unique combination of lines and colours he created. His artistic DNA, so to speak. This unique combination of lines and colours was how he, Neil, tried to recreate the world that he saw, and to tell the truth as it was for him. But no matter how true to form your art is, you can never capture it without putting YOUR personal stamp on it. I had a sample of Neil's artistic DNA, and it was thrilling.
You could tell when an artist was just in their infancy in the way they presented their work. You could literally feel when the work was just a cry for attention, a mushroom experience (some would literally tell you what drug they were on), or a genuine piece of who they were. Sincerity comes through in different ways, and it’s hard to explain how I knew that certain pieces contained sincerity or not, I just did. So, art is truth in the moments we try to capture.
After Neil, the I swam through a dozen more like water, but there wasn’t enough time to see them all. Hundreds upon hundreds of sketchbooks, like personal diaries, await in the shelves. Let me tell you a little bit about what I'm thinking and feeling, they beckon.
So, Art is truth, and art is emotion.
Above all, art is patience. Art is staring meticulously back and forth from your reference photo to your sketchbook and hoping you didn’t miss a splotch of colour here or a rounded-oval thing with a dent in it there. It is sitting still and forgetting about the time. It is meditative. It’s letting your hands “flow” so you’re not creating too-rigid lines. It’s using the smallest amounts of pressure, creating the faintest outline that only you know is there, and, bit by painful bit, going over those draft lines over and over until you’ve got the curve just right, the proportions just so, the negative space right where it needs to be. This is art.
These were also the reasons I started to avoid art. The experience, though seemingly unobtrusive and perhaps a little mundane, started to leave me feeling raw. It became a competition with no one in particular and it seemed crucial that to compete meant I had to win, or don’t compete at all…
This is a crippling viewpoint to have about art. While I doubt everyone experiences this, I do recognize that some might feel that way towards other things. That too, is crippling.
Sorry I don't have all the answers.
So I was lucky enough to have the opportunity to teach in the Head Start summer program at my international school here in China. The program is intended to help students going into high school to gain exposure to full English immersion classes in Math, Science, Socials, and Language Arts. I taught four blocks a day for 70 minutes each. Each class had anywhere between 12 - 16 students. Ten days straight; on the one hand, no break (kinda brutal), and on the other, open curriculum (YES! Free reign).
I had lofty plans. I'd been refreshing myself on Jo Boaler's work about mathematical mindsets (see my previous ramblings here). I was going to do a little study. Please note that I do not have any experience whatsoever doing educational research. While I have a general understanding of the scientific method, I was mostly doing this out of pure curiosity and a desire to become a better teacher.
Like all good mathematicians and in the name of good science, it was perhaps inevitable that first time was not the charm, and rather than have a very successful, replicable study, I instead gained some knowledge about how I might proceed in the future. Nice.
Content that I had planned to cover in 10 days would have taken closer to 18. The students had an incredible range of English speaking ability, with drastically varied dynamics between groups of students. The schedule did not operate on a cycle, so I saw the same group of students at the same time each day, which definitely influenced their learning experience. For instance, Group C who were absolute angels and ready to learn each day in my first period class were exhausted by the time they got to third period, which led to more behavioural problems in the classroom.
Group A: A challenging group. I saw them the period right before lunch each day and there was a group of four students who were unable to sit still and wandered the class during inappropriate times, such as in the middle of me giving instructions. I lost my cool on this group; shame on me because I wasn't able to regulate my emotions and respond calmly to the situation. Just to clarify, a "losing my cool" moment for me doesn't mean shouting or yelling, which is neither helpful nor productive. I simply raised my voice to get the students attention. But, in that moment, I had lost my cool because I let the students dictate my response rather than carefully assess the situation and respond calmly and accordingly.
Group B: Did absolutely anything in their power to NOT pay attention. Would whine anytime I introduced a new activity. Would put their heads down and sleep in class. I saw this group after lunch each day, they were my last and perhaps most challenging class because of the incredible amount of sleepers and students who wanted to do absolutely nothing. There were definitely some gems in this class that would have benefitted from being in a group with other, more responsive students. Lots of patience and flexible teaching strategies required.
Group C: The first group I saw each day and by far the best group. Students had a decent command of English and I rarely had to repeat myself. They would listen and follow instructions the first time. Students would always do as they were asked. The challenge with this group was pushing them to work slightly beyond their zone of proximal development.
Group D: A diverse group with students who always wanted to be two steps ahead, students who needed a lot of personal assistance, students who got distracted easily, and students who were happy with just coasting along.
HOW I COLLECTED DATA
I used Boaler's Mathematical Mindset Teaching Guide as a self assessment tool for how I was and was not strengthening growth mindset culture in my math classroom. I wanted to focus on changing students' inclinations towards math learning, challenging those who believe math is a subject that defies creativity and passion, and pushing those who already saw themselves as "math" students to expand their definition of what math is. With the help of my math mentor, I settled on collecting data through a mindset survey.
Students took a before and after survey. I added two prompts on the after survey that required students to provide written answers to the following:
- What I think math is...
- How math class makes me feel...
A source of error here is that for students with low English level, they may not have fully understood the meaning of the statements they were agreeing or disagreeing with. Another possible source of error (though unavoidable) are those students who "did" the survey by randomly clicking boxes just to appease their dear teacher.
HOW I TAUGHT
I chose content from YouCubed's Week of Inspirational Math. I chose these tasks because they were all low-floor, high-ceiling tasks and were designed to build good mathematical habits of mind. For example, on day 1, we did an activity called "Four 4's" which encouraged students to think creatively and work collaboratively to come up with as many expressions as they can that equal the numbers 1 - 20 using only four 4's and any mathematical operation of their choice (see picture below).
Other activities we did:
In terms of assessment, I wanted to stay as far away from tests or quizzes as possible. Instead, I focused on providing students with specific, written feedback on their journal entries, group quizzes, and one final presentation at the end. I wasn't concerned so much with what they knew, but rather the process through which they were learning and engaging with the material.
Select responses to "What I think math is"
"The most important things we need to learn"
-"Have unlimited creativity"
"Subject between creative and and teamwork"
"is very interesting. make my brain growing"
"Math makes me hate and love"
Select responses to "How math class makes me feel"
"Moer interesting than chinese class"
"It may not very interesting, but OK"
"happy that I learned a lot"
"I feel very good, I meet very good teacher also know the very good friend in the math class"
"I feel happy when I fiand the ancer"
"Good! make me more confedent"
WHAT I LEARNED
A majority of students already had tendencies towards a growth mindset in mathematics, perhaps as a result of the general high regard Chinese people hold for mathematics as a subject. For the most part, students liked math and saw themselves as capable of achieving if they worked hard enough. Of the 59 students I taught, a small number of students (three or four) were of the opinion that they were "just not math people" and were extremely hesitant in trying.
In the end, I can't really say definitively which factors of my teaching influenced (or failed to influence) a stronger growth mindset towards maths. What I do know is that the switch to low-floor, high-ceiling tasks was extremely freeing -- for me and for the students. It allowed us to take a concept or idea as far as we wanted to go. There was no script or prescribed problem set that the students had to work through in increasing levels of difficulty, but rather a greater depth of thinking, and the time and space for that thinking to happen. Despite (or maybe thanks to?) the lack of testing (there were none), students still engaged with the tasks and content at high levels, drawing conclusions they might never have done with a pre-made worksheet of the skills they were supposed to practice.
By building a stronger focus on increased depth of knowledge, it then follows that a necessary norm to advocate would be that math isn't about speed. When people refer to themselves as not "math people", that's usually what they refer to, the fact that they aren't fast at mental arithmetic. But math is so much more than that.
In all, while it is hard to say from the students' perspective whether or not they appreciated a stronger switch to teaching with mathematical mindsets in mind, I know that for me it resonates as a noble endeavour. Yes, it is much easier to write a test and spend 70 minutes of your life making sure no one cheats. But take that same test, rip it up, and replace it with a diagram, an equation, a single question, a blank sheet... and possibilities begin to emerge. Some groups may reach a higher level of understanding and some may not, but then again, we teach students, not subjects.
I recently attended a professional development session led by a colleague titled, "How to Make Any Worksheet into an Escape Room," which helped us experience an escape activity from the student perspective. It was the bomb. Dot com. The session touched on ideas expressed in this article, which happens to share the same title.
Two weeks later, I ran an escape room in my classroom. It was the most fun I'd had all year.
Cue intro. Goal: Answer the question, "what is life?" Other than that, I gave my students VERY little prompting. I figure I'd let all the mysterious new locks that had been placed in my classroom do most of the talking.
In order to answer the question, they need to collect all four puzzle pieces, which eventually led to this:
The escape activity was designed to work in a linear fashion, so students had to unlock each combination in sequence in order to get to the next clue.
Clue 1: Integration
Students were given a numeric code that had to be converted to a word after correctly solving the given integration problem.
The answer was "SNACKS," which happens to be a location clue, leading to the refreshments centre where I provide students with water, tea, and snacks. The answer to the first clue was hidden under the snack basket. Many students got stumped at this point and wasn't sure what they were supposed to do (I didn't give them ANY other instructions). Once they got going, however, they really got into the flow of it.
Clue 2: Derivatives Matching
I used a matching activity here from Flamingo Math (teachers pay teachers) and students had to find the four digit number code based on the highlighted boxes. (So they didn't actually have to complete the entire matching activity).
Clue 3: Find the Mistake
The answer: Students convert correct answer into letter code to unlock the letter lock.
Clue 4: Calculus Crossword
The answer: Highlighted in invisible ink are the words TRIAL.
A couple observations:
A great format for STEM OLYMPICS
The same colleague who lead the Escape pro-d was also part of the planning committee for our first ever STEM Olympics (shout out to my buddies Flower, Jeon, Im, Yin and Patel if you're reading!).
ROUND 1: Unlock one of three boxes
ROUND 2: Gain 5 points in a trivia style tournament
While it does take some time and planning, the escape room format is a great way to review and preview content for a unit or course. I like that it is completely student driven and there is a great deal of collaboration that happens. The novelty factor with the physical locks also played a great role in keeping students interested and engaged, although it is possible to adapt this activity to be completely digital (Onenote or Google forms).
Since then, I've created two other escape activities with my classes. They're a lot of fun to make and the possibilities for clues and questions are endless! This is definitely an activity I'm going to keep using in my classes.
It's amazing to think that I'm now in my fourth year teaching internationally. People often ask me what it’s like to work overseas. Friends and family back home are always curious about where I might end up next. This is my life now, I'm a nomad!
In all honesty, when I graduated teacher’s college, I panicked. Having been a part of the concurrent education program at Queen’s University, I was in a class full of driven and hard-working individuals who always had a plan. Everybody in the program (or so it seemed) knew they wanted to teach, and they pursued that goal relentlessly. By the time February rolled around, a lot of people had already gotten offers or had jobs waiting for them. By the time I graduated, I had nothing.
Knowing what I know now, finding yourself jobless after graduation is completely normal. What felt like weeks of unemployment was actually mere days. What seemed like dozens of personalized cover letters and job applications was probably more like five or six. In fact, it took me about two weeks to get a job. I wasn't picky, knew I wanted to be overseas and it didn’t matter where. So when the opportunity presented itself to teach in Kazakhstan, I went for it. One job interview later, and I was preparing myself for life abroad.
I only stayed in Kazakhstan for a year. The contract itself was a dream (great pay, light workload), but my gut told me it wasn’t the right job for me. When I decided I wouldn't return for a second year, many experienced teachers cautioned me I would never find another job with the same benefits and salary, and they’re probably right. But I left. Eventually I ended up in Korea. Long story short, a very different experience from Kazakhstan! The work hours were longer, the work was more taxing at fraction of the pay, in a city whose standards of living were much higher, but it felt more real.
Eventually, I left Korea too. That’s a whole other story. Now I’m in China… a place I never thought I’d end up working. A place I never had any desire to work in. I just felt like too much of an anomaly – “Who is this girl that looks Chinese but cannot speak the language and behaves differently from us?”
When I think about my experiences growing up as a Chinese-Canadian, I carry a lot of guilt and shame. It feels like there is this great burden to fit in and be accepted into different social groups, but also pressure to live up to your family’s expectations and pass on the culture, traditions, and language to the next generation. If I leaned too much to the left, I was too jook sing (roughly translated as “kid who betrays one’s cultural roots”), and if I leaned too much to the right I was considered too much of a FOB (“fresh off the boat”). Rather than living up to my cultural/familial expectations (whether spoken or implied), I tried to run away from them. I decided that being an outlander in a country where I am very clearly foreign would quench those weird notions that I had about fitting in once and for all. I would work anywhere but China, I decided. Oh the irony.
I’m happy to report that these feelings of guilt and shame have mostly subsided, or at least, I have come to a peaceful cohabitation agreement with them. In fact, being in China has helped me feel more connected to my culture and my family. I’m even taking Chinese classes again! For me, that is a big frickin’ deal, and this time, a step in the direction I want to take.
This summer I enrolled in a course called, "How to Learn Math for Teachers," taught by Professor Jo Boaler, a Professor of Mathematics Education at Standford University. The course brings together best practices from research on brain growth and classroom techniques for anyone who's curious about engaging students in mathematics education.
One of the course modules talks about creating or giving students tasks with a growth mindset framework, which has the following components:
2. Different ways of seeing
3. Multiple entry points
4. Multiple paths/strategies
5. Clear learning goals and opportunities for feedback
The example that is given from the course is as follows:
Without any numbers or formulas, describe how you see this shape growing.
A teacher might ask, "There are more squares in case 2 than in 1, where are they? There are more squares in case 3 than in 2, where are they? Describe what you see."
Go ahead and try this task on your own first. Watch the video to see examples of different responses (skip to 3:50).
This type of task is referred to as a "low entry, high ceiling" task, as anyone, regardless of their skill level can engage with the question, "How do you SEE this pattern growing?" and the question can be extended to higher levels. youcubed.org has tons of videos, teaching resources, and research papers that challenge the status quo on what it means to be "mathematically minded". Check them out!
I decided to try a similar task with my Pre-Calculus students in China, and picked a pattern from Fawn Nyugen's site visualpatterns.org
Based on my students with Chinese students thus far, many of them are quite baffled whenever they get an open task like this. They are used to the typical, "how many squares are in the next case? The 100th case? The nth case?" type questions and so my challenge was really to get them to train their brains to operate different ways with respect to math. This took time. Two classes in fact, but it was worthwhile.
Here are some answers that students came up with (I posted 6 copies of the same image and challenged my classes to fill all 6 with different representations).
(From top to bottom, left to right) 1. "Raindrop" method. Squares fill in from the top. 2. "Bowling Alley". Squares being pushed up from bottom. 3. Squares pushed in from the left. 4. L-shape 5. Rotating Left/Bottom 6. "Negative Space" the missing squares form the same number of squares as the previous case.
After, and only after students have had a chance to visualize the problem, and see other representations of the same pattern in multiple ways did I have them attempt to come up with a formula for the n-th term.
Most students were able to set up a table and saw that the difference from one case to the next increased by 1 each time:
But only a few students were able to break it down further. A message I kept telling my students, "If you're going to fail, fail differently each time!"
It turns out that most of these students had been exposed to Gauss' summation before. Those that did were able to find a formula for 1 + 2 + ... + n, but the challenge with this pattern is that we start at 3.
Another student used the "square" representation as a part of his proof but isolated the last row.
Looking at the diagram below, we see that the total number of squares can be represented by (n+1)^2.
Ignoring the last row, we see that the number of actual squares and "negative space" squares are equal. The total number of squares (excluding the bottom row) is therefore given by [(n)(n+1)]/2.
Putting both these parts together, we get that the total number of squares for case n is:
My favorite proof thus far, though, is this one:
-Take the square representation, ADD another layer
-Now we have a rectangle with equal amounts of actual squares and "negative space" squares
-The resulting formula is just the area of the rectangle divided by 2
Even though this material isn't explicitly stated in the curriculum documents for this course, it was a valuable exercise to have done with my students. I had a few students approach me after class, eager to show me their proofs and what they had discovered. Throughout our whole discussion, I never gave students any answers, but focused on process. This is a message I want all students to internalize when they leave my classroom.
Never in my life did I ever imagine myself teaching in China, and yet, here I am for a second year at that! Below are images of welcome packages I put together for the members in the Math Department this year, which includes:
- A door sign with the teacher's name, room number, and teaching schedule
-Stickers, 'cuz duh
-Coffee, a key element in sustaining the life force of a teacher
-A pack of cards, essential in any math teacher starter kit
-A math puzzle, fuel for the brain
I'm super happy with the way they turned out, and I'm looking forward to a good year ahead!
This year I'll be teaching Pre-Calculus 11 and Calculus 12, which I'm both excited and nervous about! It's been years since I've taken Calculus and this will be my first year working with twelfth grade students (I've been doing a lot of review this summer on Khan Academy). Here's a fun activity that I found on Kate Owen's blog that I plan on using this week with my Calculus 12 students. It's a great way to review concepts and vocabulary from Pre-Calculus to see what students already know and remember from the course.
I've added some modifications and created an accompanying PPT that's a full lesson, all ready to go. Scroll down below to access this resource :) I'm a big believer in sharing teaching resources for free, and this is my way of giving back to the online teaching community that has given so much to me. Huge shout out to everyone in the #MTBoS, I love this community.
The activity works as follows:
1.Students it with a partner, shoulder to shoulder.
2.One person faces the board, the other person faces away.
3.The person facing the board will be the explainer.
4.The person facing away will be the grapher.
Warm Up: Teacher does warm up round with the students, describing a basic graph (ex. linear function) and students attempt to draw it in their notebooks. Discuss: What prompts were useful? Is there something the teacher said that could have made it easier?
The Activity: (see above)
Exit Ticket: Given a picture of a graph, students are to write a description that matches it in as much detail as possible.
Extension: Students draw a graph and write a corresponding description. Scramble the results and have students match them!
Eddie, you inspire me.
Day 4 - Ancient Cities in Mandalay
For our final day in Mandalay, we opted to hire a private car and paid about 35 000 ks for a "three city tour". As it is common for taxi drivers to advertise private tours of the surrounding area, it wasn't necessary for us to book ahead. We had collected a few business cards from taxi drivers during our first few days in the city and opted to go with the driver who seemed the friendliest and spoke the best English.
For our first stop, our driver took us to a monastery in Mandalay where we had the opportunity to speak to his friend, a monk who teaches English there. We were shown around to various buildings (the dormitories, dining hall, study halls...etc.) and learned about life in the monastery. Becoming a monk is a well-respected and esteemed route to take for boys and men of all ages. A family's status is elevated if they have a son who decides to become a monk. Of course, not many choose to stay one, some quit years, months, weeks, or even days into monkhood, which is not uncommon. At one point, both our taxi driver and tour guide (whom we would meet later in Bagan) had taken up monastic life.
At the monastery, we met an especially charming and charismatic young monk who went by the name of "Drake." Funnily enough, we would later run into "Drake" again three days later in a totally different city, at sunset, on the top of a temple, where he would re-introduce himself as "Maha Raja," and add us as Facebook friends. To this day I am still not sure if he is using his real name.
We were told to stay for the monk procession, in which 1000 monks would line up according to rank and seniority for their second and final meal of the day. If I'm completely honest, the sight made us feel uncomfortable in comparison to our calm and quiet morning around the monastery. In an instant, the empty streets became crowded with tourists, with their big cameras, tablets, and cell phones; we witnessed a few elderly women handing out sweets and loose change to the younger monks, perhaps out of charity or something else, I don't really know. It just seemed like such strange way to sensationalize their lunch time... It was good to finally get out of the crowd.
Next, our driver took us to a location where they made longyis, a long sheet of cloth commonly worn as a skirt by both men and women in Myanmar. We were shown how the longyis were woven and taken to a nearby store were they could be purchased. Sarah suspects we were taken to what is known as a "tourist trap," but heck, it was cool and we bought one for ourselves anyways.
Afterwards, we ate lunch at a restaurant of our driver's choice. The food was pricey and not particularly noteworthy.
Like Mandalay Hill, U-Bein bridge is a popular tourist destination at night time, as people like to go for the sunset. We decided to go earlier in the day to avoid the crowd. Here, we purchased some coconut ice cream (DELICIOUS) and walked about halfway across the bridge before turning back... on account of some uncomfortable cat calling. We weren't dressed in scantily clad clothing by ANY means but my Sarah does happen to have strikingly blonde hair and fair skin which drew a lot of unwanted attention. We definitely had to check our privilege at that point.
PRO-TIP #1: Please don't do what we did and walk the entire length of the bridge! We missed out on exploring Amurapura city as a result, but we ended up having a great day regardless (read on to find out!)
Now at this point we had been to half a dozen temples and seen a ton of pagodas so if you can forgive me, I do not recall the name of the temple our driver took us to next. The highlight for me, however, was watching the line that quickly formed as soon as Sarah agreed to have her photo taken. One, led to another, and then another... People wanted group shots and individual shots. Blonde, white-skinned, and beautiful, Sarah quickly became a hot commodity! (Only 2000 ks for a photo with this beautiful foreigner! Anyone? 1000 ks special discount just for you!)
Having my friend taken from me for photos would be a common occurrence throughout the entire trip. Me, on the other hand, being of Chinese descent, and having been told I have a face that can pass for a variety of Asian ethnicities, was able to (at times) conspicuously blend in with the crowd.
The next part of our journey would be my favorite in Mandalay. That was our brief tour of the ancient city of Inwa.
Once we arrived, we hired a horse cart and driver to take us around the Ancient City (~9000 ks). It's possible to do on foot, but you'd need at least two hours and we were running short on time. He took us to a few notable locations before dropping us off for the last ferry back.
PRO-TIP #2: Keep in mind most places you visit will require you to go barefoot (temples, pagodas, ruin sites...etc.), so bring comfortable shoes that slip on and off easily!
On the way back, we saw a little boy and a dog at one of the ancient ruin sites.
It looked like they were friends.
(The dog was likely a stray).
But still, it was a fine friendship.
We decided to explore the area.
But we noticed that someone kept showing up in our photos...
"Follow me!" he said.
And so we did.
And saw the most breathtaking statue.
There was something about the way the light fell, the little boy giggling and running around us, the other little one who turned out to be his brother, prodding us along, telling us to climb here, sit there, pose like this, not like that... Making faces at us when we did something they didn't like and giving us the thumbs up when they deemed we had the perfect pose...
We had so much fun running around with those two that we didn't even break a sweat when they eventually busted out their post-cards and offered to sell us some.
What fine salesmen they turned out to be.
NEXT UP: Bagan!
This past February, I took a trip to Myanmar with my good friend Sarah. As we were both teaching in Shanghai at the time, we wanted to take this opportunity to explore Southeast Asia during the Chinese New Year holiday. We visited Mandalay, Bagan, and ended our trip in Yangon.
Day 1 - Mandalay
We landed in Mandalay at around 3pm on a Sunday. The airport is fairly small and underdeveloped. Depending on the time you arrive, there may or may not be services available. From what I remember, the only place that was open at the time was a shuttle service and a money changer.
Our priorities for the day: get to our hotel and get food! We exchanged what RMB we had in our wallets and took a taxi from the airport direct to our hostel, the Moon Light Hotel, which cost maybe 30 CAD (for reference, the exchange rate at the time of our travel was about 1 CAD to 1000 MMK).
We stayed at the Moon Light Hotel for 3 nights, which cost us about 50 USD. The hotel is very new, staff are extremely friendly, and breakfast is included.
If you haven't traveled Asia before, some of the imagery you encounter can be pretty jarring. While our hotel was tidy imitation of some Western hotels, just outside you can see signs of impoverishment; unpaved roads, large piles of garbage, stray animals, and the like. Not a vacation destination for the faint of heart.
For dinner, we walked to Mingalabar, the #1 rated restaurant on Trip Advisor in Mandalay, and boy - did it live up to those standards! For bout 15 CAD, we had a beer, lime soda, soup, rice, a main of lamb curry, and dessert. The main course comes with all the side dishes you see below, the idea being that you can customize each bite according to your taste preference. The side dishes they serve vary from night to night, but ours featured peanuts, fish, potatoes, cauliflower, a shrimp paste, and some raw vegetables.
A word of caution...
Our biggest mistake on this trip was not bringing enough CASH! We had read online that there have been many improvements in the big cities in terms of ATMs being available. Having come from China, both of us have UnionPay cards that are accepted at many ATMs throughout Myanmar, according to research. We did not, however, factor into account that these ATMS may not be regularly maintained, so many that we visited were out of cash!
[For some mysterious reason, I was not able to withdraw ANY money on my UnionPay card, but luckily Sarah was able to to do on her Canadian bank card.]
Long story short, to avoid running into this issue, I would recommend bringing enough cash with you to last the trip. But beware of pickpockets, especially in touristy places!
Day 2 - Mandalay Palace
Our second day was spent getting acquainted with the city, hitting up every ATM we encountered, and getting SIM cards. I would highly recommend getting a SIM with a data plan for your travels, as it makes life significantly easier (access to GPS, Trip Advisor, etc.) SIM cards are fairly cheap and top ups are easy to come by (most convenience stores will have them). Popular carriers include Oredoo and Telenor.
In the afternoon, we asked our hotel to help us call a taxi to take us to Mandalay Palace. If you call a taxi through your hotel, the prices are usually set (though still very reasonable). If you choose to hail your own transport, usually there is a bit more room to negotiate. Keep in mind that these are not "taxis" in the Western sense, but rather random strangers you're waving down in the streets who happen to have a car and want to make a few extra bucks driving people around.
To get into the Palace grounds, you need a visitor's pass. You'll be asked to leave your passport with the guards in exchange for one. We did not have our passports with us, but luckily, they accepted Sarah's drivers licence (phew!). In the area surrounding the palace there's a park and some temples and pagodas. We just walked around and took our time exploring the area.
At one of the vendors, a girl offered to paint our faces with thanaka, a yellow-white paste made from tree bark. We later learned that wearing thanaka is like putting on clean clothes; worn by people of both genders who may perceived as "unruly" if you did not put it on, though trends seem to be changing in the big cities.
In the afternoon, we ate at a restaurant in town and freshened up at the hotel before heading out again in the evening. We went back to Mingalabar (which means "Hello" in Burmese) for dinner, and walked to the bar across the street for cocktails.
Day 3 - Mandalay Hill
Early next morning, we had breakfast at the hotel and took a taxi to the Lion's Gate entrance of Mandalay Hill. Mandalay hill is a popular destination at night time, as many tourists often go to see the sunset. I found the views in the fresh morning air just fine, and seeing as there were hardly any people around during the hike up, wonderfully peaceful.
You'll know you're at the top once you reach the giant escalator that takes you down Mandalay Hill. We opted to take a shuttle down for 2000 ks instead.
Final verdict: Mandalay Hill is a must! Definitely enjoyed our morning hike. We took our time, and stopped a lot to take photos and enjoyed the scenery.
I can't remember what else we did in the evening (ate food somewhere definitely), but the morning hike did take up a lot of our energy. A day well spent overall.
NEXT UP: A private tour to the ancient cities in Mandalay (click here for Day 4 details.
Oh Polynomials. My least favourite unit by far in the Foundations of Math and Pre-Calculus 10 course I am teaching. Find the greatest common factor, least common multiple, factor these trinomials, collect and simplify like terms, the swimming pool has a width of 5x + 1 and a length of x + 2… YAWN.
How can I frame a boring, completely algorithmic and skill-based unit into something that's relevant and meaningful for my students? I am borrowing Dan Meyer's definition for relevance here.
It Begins with a Question…
A colleague asked me today, "How much time do you have for homework at the end of class?" This was a surprising question to me, and as I thought back over the 10 day unit, my answer was almost none. The question sparked a great dialogue between us about our approach to teaching the same content in our respective classrooms. It really made me think. I realized that while I still dreaded teaching polynomials, I had found a way to improve the way I taught it from first semester that required less rote work and more thinking.
One thing that has not changed, however, is that I avoid teaching FOIL method like the plague. It only works for expanding binomials and does not apply for polynomials with more than two terms. After I read this article I was convinced I would never need FOIL in my classroom:
For a good laugh:
Some things that came up in our discussion:
1. Algebra Tiles
Definitely a hate-hate relationship. As a math teacher, I am obligated to entertain this idea and I do admit it has its benefits, especially in lower level math classes when students are initially being exposed to distributive property and the like. The problem, however, was that my students were already armed with the skills and knowledge of multiplying and factoring polynomials. Moreover, the limitations of using tiles far exceeded the benefits, in my opinion. Algebra tiles do NOT work for: polynomials higher than degree two, multiplying more than two polynomials, and multiplying polynomials with more than three terms. This meant that it took more effort for students to understand how and why it works.
Nevertheless, we spent a few classes examining algebra tiles and their usefulness. Rather than approach it from the typical standpoint of using algebra tiles as a manipulative, I wanted students to see the link between the algebraic and pictorial representations of polynomials. This took work and was not as straightforward as it seemed. A big takeaway for me was that students gained much more out of the experience when they were able to physically manipulate the tiles and arrange them into their "factored forms." Last semester, I "taught" algebra tiles by merely showing them examples and drawing them on the board. It took a bit more prep, but this semester I printed eight sets of tiles (positive and negative) in my classroom and had students manipulate them instead.
If we were to spend any more time on the unit, or if this was a lower grade level, as an enrichment activity I would have students discuss the limitations of algebra tiles and look for ways to address them.
2. Picture Talks
I like to use Sarah VanDerWerf's Stand and Talks as a format for students to discuss picture prompts. I find that the buy in for engagement is much higher when the prompt is linked to physical movement. My favourite questions for photo prompts are: "What do you notice?" and "What do you wonder?"
What are my photo prompts, you ask?
That's right. Algebra tiles.
Goals for students:
I like this activity because it is easy to differentiate and works well as a "minds on" for any topic. Asking students a general question like what they notice/wonder means that lower ability students can comment on ANY aspect of the photo (e.g. "there are blue and green rectangles") while higher ability students can be pushed towards making observations based on any mathematical patterns or relationships they observe (e.g. "the green tiles represent positive polynomials and red tiles are negative").
3. Factoring Method - Criss Cross or Sum Product?
I've had the great fortune of only having one prep and a spare block this semester (for friends and readers who don't teach, that's teacher jargon for FREE TIME, kinda. The details are not important). Anyway, I've been making drop-in's to my fellow colleagues classrooms with my new-found "free time" and one thing I picked up was the importance of proper SEQUENCING. For instance, a natural progression for factoring trinomials might look as follows:
That, together with a quick exercise on sum/products, helped me push students towards seeing the relationship between the factored form of a trinomial, and the sum/product method.
I prefer this method over the traditional "criss cross" method for a few reasons
Which One Doesn't Belong? (WODB)
Fantastic activity for building up thinking skills and vocabulary. Each student picks one of the expressions and must argue why that one doesn't belong.
"27x^2 doesn't belong because it is the only expression that has a coefficient with a perfect cube"
"45x^2 doesn't belong because it is the only expression that has a coefficient with 5 as one of its prime factors"
More WODB prompts can be found here.
How it works: One student is chosen to stand/sit at the front of class facing the audience, they are in the "hot seat". Behind them, a vocabulary term is shown for the rest of class to see. Students in the audience must help the student in the hot seat guess the vocabulary word by miming, explaining the definition, or giving examples. They may not use any part of the word in their explanation.
Modifications: Differentiate by giving students the option of bringing a "cheat sheet" of vocabulary terms with them. Prepare students for the activity by giving them cross word or fill in the blank exercise reviewing the vocabulary words for the unit. An "expert round" can include vocabulary not on the cheat sheet. "Challenge round" can be facing a peer or the teacher. Can play in teams or as a class.
his activity was shared by a good colleague of mine. To get BINGO, students must find one "expert" in the classroom to answer each question on the bingo card until all the questions have been answered. The student who answers the question must sign their name. A student may not be asked more than once to answer the same Bingo card.
Teacher, Friend, Adventurer. (Not necessarily in that order)