# Visibly Random Groups

Peter Liljedahl‘s work on Building Thinking Classrooms has been extremely influential in the education world. In his research, he discusses a collection of high-yield strategies that teachers can employ to help learners engage with work in the classroom and become better thinkers. They are sorted on a continuum of ease of implementation and “bluntness” (requiring less/more fine tuning).

When I first stumbled upon his research (hat tip to the Global Math Department), I immediately began to experiment with the two moves that were the easiest to implement: Visibly Random Groups and Vertical Non-Permanent Surfaces.

I created Seat Finder cards that I would hand out to my students at the beginning of every class as I greeted them at the door. The Seat Finder cards had various algebra problems on them whose solution corresponded to their group number.

The idea behind this is to help build a classroom culture where students are working collaboratively, and not just with the same people the entire year. In theory, this works great, however, I hit a few kinks along the way. The first kink was that I was not beginning my lessons with “good tasks” at the time (see here for some examples). Second, it quickly became exhausting and time consuming for students to find their seats in this manner each day. I also noticed that students would try and surreptitiously swap cards so they could sit with their friends. Rather than building that culture of community and collaboration, I was battling my students about compliance issues.

So, to alleviate some of these problems, I switched to weekly seat changes, and eventually settled with a change once per unit. Rather than assigning each student their individualized Seat Finder problem, I gave each student a playing card instead that corresponded to a group number. Rather than writing the group numbers on the tables, I opted for math problems whose solutions corresponded to group numbers instead. I created a set for different units of study that we looked at in our classes, which are meant to be solved relatively quickly.

I found that having one problem per table helped students get into their seats more quickly, and they often helped each other if some students were unsure of how to solve the problem.

Note that while students seats stayed the same for the course of a unit, they were still expected to work with others on various tasks I assigned during class. This gave them the comfort and consistency of knowing where they were sitting from day to day, but also the ability to interact with a variety of classmates.

# 2019-2020 Year End Reflection

I remember sitting at a meeting table at my school in Suzhou, China late January earlier this year when a colleague said, “Heads up, there’s a virus going around in Wuhan. Very contagious,” and thinking something along the lines of “Well, at least we’ve got our Chinese New Year holiday coming up. Let’s cross that bridge when we get to it.” I was, absent-minded to say the least.

Two weeks later, nobody could wander into a public space without a mask, long distance buses stopped running, temperature checks were imposed at major transportation hubs, and cars were restricted entry into locations outside the jurisdiction of their licensure.

2020, I imagine, has not turned out to be the year many has expected it to be. I write this four and a half months after the World Health Organization declared the Novel Coronavirus disease (COVID-19) to be a pandemic.

This dramatic turn of events has had me feeling like the entire world is just holding its breath. For a while, all we could do was observe and wait, not fully willing to settle into what was slowly shifting into our new normal in hopes that we can just pick up where we left off pre-COVID.

By the time Semester 2 began mid-February, I was “temporarily” residing back in Canada. For safety reasons, the school re-opening date was to be pushed back two weeks. Teachers were told that online learning would only be temporary (lasting no longer than 2-4 weeks) to accommodate for rapid changes in travel plans and quarantine measures.

Our school eventually re-opened in May, but by that time, a majority of our teaching staff were out of country and had no way to get back in. China had already closed its borders and our visas suspended. All we could do was wait. I ended up teaching the entire semester online, with many changes and adjustments that had to be made to teaching style, content delivery, and assessment along the way.

Despite the many barriers that were imposed upon us, I remind myself that I still have a lot to be grateful for. I didn’t chance to say goodbye to my students in person, but we found new and different ways to connect online. We missed out on a ton of live in-school events and activities like Pi Day, the graduation ceremony, the school-wide lip dub, sports competitions, but that didn’t stop us from celebrating student achievements through their virtual counterparts. I lost my job too, but at least now I have an opportunity to start fresh. When one door closes, right?

## Looking back

When I started the school year, one of my professional goals was to be able to get into more teacher classrooms, of all different subject matters, to learn from and observe my colleagues, and to get teachers in my classroom as well. It was my way of taking small steps towards making #observeme more of the norm at our school.

As a department, we worked on re-vamping the way we structured our classes and assessments using principles from cognitive psychology to better help our students learn and retain information (I wrote about it here).

We experienced many successes in our first semester, but still had a long way to go in terms of finding our groove. When COVID hit, I knew we all needed a new goal: find ways to help us and our students successfully navigate the world of online learning.

## Starting from ground zero

If I’m honest, for a long time it felt as if we were just keeping our heads above the water, struggling to balance between the uncertain timeline imposed by COVID, as well as expectations from the school, students, parents, and ourselves. Even though we were working long hours, none of us truly felt like we were operating at 100% capacity. A jumbled mess now laid in place of the clear path (or so it seemed) that was once before us.

THE CHALLENGES:

• Several cheating and/or plagiarism incidents took place with course assignments
• High student absenteeism rates, especially at the beginning, which led to snowball effect of select students continuing that trend to the end of the year
• Inconsistent scheduling (due to various factors)
• Difficulty communicating with some parents and students

WHAT WORKED:

• Developing a consistent school-wide plan for scheduling, parent and student communication
• Keeping platforms for communication and e-learning consistent.
• Incorporating interactive and collaborative elements in online synchronous lessons (e.g. Padlet, Nearpod).
• Eliminating heavily weighted timed assessments (such as unit tests and final exam) helped alleviate pressures associated with adjusting to an online learning environment. Students had more time to work on fewer graded assessments, thus increasing the quality of work to be handed in.
• High success and engagement experienced with implementing open tasks on Flipgrid.
• Moving from weekly to bi-weekly quizzes to help with student workload.
• Maintaining a positive mindset and staying flexible and adaptable to changing circumstances (school policy, overall outlook of global health crisis… etc.)

SUGGESTIONS FOR IMPROVEMENT:

• Keep graded assessments to a minimum.
• Opt for more open tasks, collaborative projects, or project-based and/or problem-based learning
• Develop, communicate, reinforce and continually PRACTICE norms for successful online learning
• May need to rethink mandatory synchronous live lessons. Issues of access may make this a non-equitable practice that may hinder the success of certain students. Providing equitable asynchronous learning options is ideal for ensuring equal learning opportunities for all.

## Closing thoughts

For a long time, I was in denial. The practical me jumped in headfirst and did her best to adjust and adapt to changing circumstance, whereas my less practical self refused to accept that this is really happening. Yet, neither of those selves are helpful. In thinking about the past, or worrying about the future, I forget to live in the present.

# Talk Less, Ask More: My Goals and Set-Backs

This week I’ve had some great lessons, and some awful ones. Looking back at what I had done differently in the good versus not-so-good lessons, I realized that one of the biggest differences was the amount of “telling” I was doing in one class versus another. It didn’t matter that I had amazing visuals and was super enthusiastic about the content I was teaching; if I talked too much, students would start to zone out. Compound this with the fact that we are distance learning and all of my students are English language learners, we now have wi-fi/connectivity, audio, and language learning issues all thrown into the mix.

The one who does most of the talking, is doing most of the learning.

(Something I’ve heard from multiple sources throughout my teaching career)

At this point, I have to slap myself on the wrist because I know better, so I need to do better.

In yesterday’s class, I consciously made an effort to talk less and ask more questions. I also explicitly told my students that my goal as a teacher is to never tell them an answer, but to just show them the way. Classic case of easier-said-than-done.

I realize, with a sudden mixture of nervousness, trepidation, and excitement as I’m writing this, that this might be the first time in five years of teaching that I have really made a conscious effort to take Cathy Fosnot’s advice to heart. She writes,

Don’t try to fix the mathematics; work with the mathematician. The point is not to fix the mistakes in the children’s work or to get everyone to agree with your answer, but to support your students’ development as mathematicians.

Cathy Fosnot

On the surface, I’d like to think I was doing my best to project a calm, neutral tone as I jotted down notes while students shared their thinking. I wrote everything down, regardless of whether their strategy was “right” or “wrong”. Meanwhile, it felt like Hermione Granger was living in the back of my mind jumping up and down going “Pick me, pick me!! I know the answer!!” Talk about my “rescue the student” instincts being on overdrive!

In the past, I would have eventually given in to those instincts and immediately correct any mistakes that came to my attention. I tell myself that this is okay, because if I don’t, my students will continue to make those fundamental math errors, divide by zero, and initiate the end of the universe as we know it. I also think that deep down, that hidden behind this instinct is fear, fear that I can’t help them get where they need to go without just giving them the answer. Although, impatience is an equally guilty accomplice here in my crime of robbing students of a perfectly good learning moment.

This time, however, I tell myself a different story. I learn to trust myself and my students a little bit more by just letting them get where they need to go, in their own time and in their own way. This too, is a little scary.

## The Lesson

To add some context, here’s a bit about how my lesson went.

The goal of today’s lesson was to introduce the idea of trigonometric identities, collect some strategies that may be helpful in identifying whether a given statement is true or false, and then work on moving towards what it means to rigorously prove the truth or falsity of a mathematical statement.

I began the class by doing a modified version of an “Always, Sometimes, or Never True” activity with radicals (trying to introduce some interleaving here) from the Mathematics Assessment Project and called it “Truths and Lies”. I asked students to tell me which statements they believed to be truths and which they thought were lies, and to share their thinking on Padlet.

After about ten minutes of individual think time, I selected a few student strategies and had students explain them to the class. Here’s what we came up with:

Strategies Used:

• Plug in a number for x and check to see if both sides are equal
• Start with LS or RS, use algebra to show it is equal to the other side
• Assume the statement is true. Square both sides of the equation. (If both sides are equal after squaring, then the statement is true).

Next, I showed them this image about the different Levels of Convincing from Robert Kaplinsky’s site.

We then revisited each strategy and I asked students to mentally place each of these strategies fell on the spectrum of least to most convincing. Ideally, I would have given more time for students to really think this part through, but since we are doing distance learning, I was eager to get to the real meat of today’s activity, which was to prove trigonometric identities. From there, I took on the role of prosecutor and started to stir up some trouble.

For instance, in statement 1), we can demonstrate the statement is false by finding a value of x that shows LS does not equal RS, however, I argued that x = 5 worked, so wouldn’t that make the statement true? What I’m getting at here is that I want students to be able to articulate what exactly are we asking when we ask whether or not a statement is true? That it must be true all the time? Or only some of the time?

Then, I attempted to tackle the “squaring both sides” strategy… Couldn’t we also use same reasoning to show that 1 = -1?? (Can you see why?)

At this point something really amazing happened, and that was when a student interrupted me and said, “Ms. Soo, I just thought of another way to explain this!” The student was able to connect what we were doing to our study of transformations of functions from a previous unit.

I couldn’t —

keep my poker face, that is. This was me:

For the remainder of our lesson I had students work independently on the following:

My goal for them was to use different strategies and methods to try and “prove” or “justify” which were truths and which were lies. Students always have the option of messaging me privately for hints or advice if they were stuck, very few did.

After about 15 minutes, I asked students to send me pictures of their work and we could start talking about some strategies they used. The one mistake I see students make when “proving” trigonometric identity is to start by assuming the statement is true and start manipulating both sides of the equation.

Instead of telling students WHY they can’t do that, I referenced my earlier example of how, by the same logic, we can prove that that 1 = -1 and asked them, WHERE did the mistake occur?

Let’s assume. the statement 1 = -1 to be a true statement.

Next, let’s square both sides of the equation. Doing so, I get

1=1

Therefore, it must be the case that 1 = -1. (End of proof).

Getting students to where I wanted them to be was really challenging because many were focused on the math, and not the logic of the argument itself. They focused more on the operation of ‘squaring’ and how we need to keep in mind both positive and negative square roots, which is certainly a valid piece of mathematical insight, but again not where I needed them to be.

Since we only had about 5 minutes of class left, I decided to pause the discussion there and ask students to write me a 3 – 5 sentence of the strategies we used to justify whether a statement is true or false.

## What Went Well

I stuck with my goal.

## Where I Need Help

Right now, students still don’t understand what a proof is. I want students to be able to articulate that while plugging in values, and graphing both sides of an equation are helpful strategies to show why a statement might be true, they don’t constitute enough rigour to show that a statement is always true.

How do I get students to this point without just handing them the answer? How can I do this effectively in an online setting? They also have a common assessment (assignment) coming up in which they will be asked to prove trigonometric identities, and the quickly approaching deadline makes me feel anxious to default to just tell students the answer.

# What I’ve Learned from Online Teaching

I’m no expert, but the COVID pandemic has given me the prerogative to scour the interwebs for useful tidbits on maintaining lively and engaging online lessons. In the last three or so months, I’ve created at least half a dozen new teacher accounts on educational sites and platforms; some of which I use moderately (EdPuzzle, Padlet, Flipgrid…etc.), a few that I use religiously (Zoom), and still others that I’d like to experiment with some more (Nearpod, Brainingcamp).

Transitioning to full-time online teaching has been a process of repeated trial and error, and a test of patience and flexibility in learning to adjust to changing circumstances. I’ve definitely made more than my fair share of mistakes, but here I’ve compiled list of tips and tricks that I’ve found useful for teaching online. Some of these are obvious and are good practice in general, and others are things I’ve learned along the way or things I wish I had done sooner. If there are any tips here that you think I missed, I would love to hear about them in the comments!

Delivering Live Lessons

• Look AT the camera, not your screen. An easy one to remember for more formal settings, like online interviews, but also at an important one not to miss with your students too. It shows them they matter, you care, and gives them a sense that you are watching.

Left: Even though I’m looking at my students on screen, I appear less engaged. Right: Takes some getting used to, but this one has more of the right feel to it.

• Display your daily agenda, and deadlines on your screen like you would in your regular classroom. This develops helps consistency and create routine for you students.
• Always pair visual and verbal cues. If you want your students to respond to a question in a group chat, or complete an activity, make sure they can hear and see the instructions, as some may experience audio or internet connectivity issues. (Good practice in the regular classroom too).
• Allow longer than normal wait times. Again, expect a lag between the time you pose the question to when your students actual hear it.
• In general, I’ve found that live lessons take MUCH longer than a regular class. Plan more than you need but expect to cover less.
• Engage students as much as possible. Q&A sessions can get tricky in an online setting and plain old cold calling… well, gets cold. In the next section, I’ll take about some low stakes methods to ensure that students aren’t just tuning into your lesson, only to be playing League of Legends off screen.
• Start easy. Rather than dive right into the deep end with new content, a class-wide discussion…etc. why not begin with a warm up question? I like to start class with an attendance question that each student will answer (a tip I picked up from my VP). This gives me a quick and easy way to check-in with my students, they get to learn some information about each other, and it allows time for mentally transitioning into learning mode.

Keep in mind it DOES take time to check in with each student individually, so think about the type of question you want to ask, and whether or not you will give each individual student air time, or have them all type their answers into a shared document simultaneously.

• Record your lesson and upload the video for later access. Zoom does this automatically, but there are plenty of free software out there for you to record your lessons. We are an Office 365 school, so I upload my recorded lessons onto Sharepoint for any students who missed a class.
• Get a drawing tablet! Perhaps this goes without saying, but it is really difficult (in my math class at least) to pair visual and verbal cues when I can’t draw or write on the board. Having a tablet helped alleviate that issue.
• Something I wish I had done is model to students how e-learning works. Sara Van Der Werf talks about this in detail here.

Increasing Engagement

• Set the expectation that students need to turn their video cameras ON right from the get go. This one may not work for everyone due to issues of access, but I found that in my classroom engagement is much higher when my students and I can all see each other. Not to mention this gives me a better way to gauge how they are responding to the lesson.
• Don’t just lecture. If you are having a live session, use this time to build in as much interactive elements into the session as possible. Information heavy content can be recorded and made available to be accessed later.
• Make PARTICIPATION, not evaluation, the norm. I thought that I would need to incentivize participation with marks (like marking Flipgrid responses), but looking back I don’t think this was the right move. Whatever platform(s) you are using for online engagement, use these early and often, and keep them low stakes.

Assessment

• Assessment is not the same as evaluation. Assessment is timely, and gives us a way to gauge where our students are at and for us to figure out how to get them to where they need to be. Assessment needs to happen early, often, and BEFORE evaluation.
• Prioritize the learning itself, not the marks. I know from personal experience, this can often feel like an uphill battle, not only against whatever policies that have been set, but also against yourself. We’ve been teaching and learning for marks for so long it is easy to forget that the goal of knowing the Pythagorean theorem, or understanding transformation of functions is not so our students can pass the test, but because there is genuine enjoyment to be had! (This point deserves its own post).
• Eliminate timed tests and quizzes (as much as possible). Ask better, open questions instead (OpenMiddle, Which One Doesn’t Belong, Number Talks…etc.).

Tools and Tech

• Less > More! Really. This one was a biggie for me. Trying to do too much will only drive you crazy. While there is a ton of useful tech out there that can dramatically up our teaching game, it can also be time consuming to learn a new tool. Start small.
• It’s not about the resource, but how you use it (check out this podcast, episode #70). Contrary to the last point, don’t let the fact that there is so much tech out there stop you from exploring a new tool. Yes, choice paralysis is real, but at some point simply sending your students links to Khan Academy videos ain’t gonna cut it.

Finally

• Remember that kids have lives outside your classroom. This one is so important, even in a non-COVID situation, but nothing is easier to forget. I often get offended when kids don’t remember deadlines or to submit work, but the reality is that my class is NOT the centre of their universe and I have to be okay with that.

# Empowered Problem Solving Workshop: My Takeaways

I love it when professional development is purposeful and practical.  I’ve been following Robert Kaplinsky for some time now and finally decided to enrol in his Empowered Problem Solving Workshop.

I don’t have time for problem solving in my classroom.”

TRUST me, I’ve been there. The first time I ever taught Calculus, my talk time during an 80-minute block was probably at 50-80%. It was awful, I was so dehydrated. It also didn’t help that I did not have a strong enough grasp of the material that I could deliver problem-based lessons with any sort of confidence. I was simultaneously teaching and relearning the material myself so how could I expect my students to develop these deep understandings when I was barely keeping my head above water?

Looking back, I realize that trying something is always better than nothing.  Problem solving isn’t something you do “if you have time for it,” like at the end of a unit. Because you know what? You’re never going to have time for it. You’ll always feel like the time could be better used for review, a project, to reinforce a skill…etc. Problem solving is not something you should “make time for”, it needs to be integrated into the content we teach. I would argue that the heart of mathematics is problem solving. The sooner we realize that math isn’t just about getting the right answer, passing a test, or even getting into university, the sooner we can teach in a way that honours what doing mathematics is truly about.

My students lack the basic skills and understanding to do these types of problems.”

If that is what you’re thinking, know that I too, have had this same thought. Herein lies the beauty of problem-based lessons: students don’t need to be pre-taught skills or content, they can learn them along the way.

“I’ve tried problem solving before and it doesn’t work. Students just want to be told what to do.”

Guilty. I’ve been there too. It’s not going to be perfect the first time you do this. Students WILL resist, and you need to persist. If you don’t genuinely believe that problem solving is worth the time and effort, your students won’t buy into it either.

When I first tried problem-based lessons, I did not spend enough time anticipating student responses and was taken off guard by solutions or strategies I hadn’t thought of. I tried to lead meaningful discussions about student work, but because I wasn’t getting the engagement I wanted, sometimes ended up making the connections for the students (I’m still working on scaling back my “rescue the student” instincts). Success, however, comes in small doses, like getting a student who normally never raised their hand to try a problem on the board, or maybe just seeing a decrease in off task behaviour.

Teaching problem-based lessons takes effort, from the student AND the teacher, but that is precisely why its so awesome. Students aren’t just passive recipients of knowledge, and teachers don’t need to spoon feed their students.

## My Biggest Takeaways

1. Problem-solving: Just DO IT!

2. Be deliberate about how to facilitate meaningful discussions in math. Often, we get to an answer and that’s it. Full stop. Getting to the last act of a 3-Act Math Task doesn’t mean that the learning stops there. Here is a wonderful opportunity to discuss various approaches to the problem, potential sources of error, limitations of our mathematical models, and to make connections between different solutions. This is an area where I feel I need the most practice, and it is also most difficult to implement during this time of online learning due to COVID-19. I’m limited by the fact that I cannot circulate the classroom or peep over students’ shoulders to see where they are at, but I am trying to find alternative ways to connect.

Here’s a snapshot of me working out a selection strategy for sharing student work, and anticipating questions that might be helpful to ask:

3. You can always add information, but you can’t take it back. Dan Meyer refers to this as turning up the Math Dial. Robert Kaplinsky talks about “undercooking” our students (like you would a steak). Ask questions in a way that ranges from least helpful to most helpful to give your students a chance to make connections for themselves.

4. Ask yourself “Why” more often. Why am I doing this problem? To introduce a new concept? Get my students used to productive struggle? Problem completion?  Be intentional about the purpose of your lesson and what can be realistically achieved.

5. Ask better questions. Shallow questions tend to lead to false positives. A student may appear to have procedural knowledge, fluency, and conceptual understanding, when in reality they are just good at replicating the work that you do (me in school…). You might be asking, “How do I really know if my students have the components of mathematical rigor?” Check out Robert Kaplinsky’s Open Middle problems and Depth of Knowledge Matrices.

# Finding Culture as an International Educator

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.

# Reflections on My First Semester Teaching in China

Semester one of my first year living and working in China is officially over! Since my last post about the first day of school, I realized haven’t blogged at all this entire semester. I am a little disappointed that I had skipped through all the middle bits, but regardless, here we are.

This past semester I taught Math 10 and 11 of the British Columbia curriculum at an international school in Suzhou, China. With the exception of a handful of students, all of them are English Language Learners. Some might argue that this does not pose a big problem in mathematics, since the language of mathematics can be viewed as a combination of abstract signs and symbols separate from the English language.  The problem is, it is one thing to understand mathematical ideas and concepts, but another to be able to communicate them. Someone who is well versed in a mathematics should theoretically be able to describe the same concept in more ways than one – numerically, algebraically, graphically, and verbally. Mathematicians strive for precision in expressing ideas, and this is not always simple. Aside from students having to approach mathematics from an ELL standpoint, the issue is compounded when you consider all the ways in which ambiguity arises in the English Language. Take for instance the word “and”; conjunction in mathematics is commutative (A^B is the same as B^A), but you can see from the example below that “and” in everyday English is not commutative.

The sentence, “John took the free kick, and the ball went into the net,”  would have a very different meaning if the conjuncts were reversed (Devlin, Introduction to Mathematical Thinking).

For my most challenging students, the issue wasn’t so much as getting them to communicate their mathematical ideas well, but getting them to communicate at all. For students with extremely low level English ability, being afraid to speak or ask questions in class was a huge roadblock in developing  a good grasp on the mathematics we aim to study. The most frustrating times were when students didn’t even bother to try. Perhaps this has something to do with being in a culture where “saving face” is important, but students were sometimes so afraid of being wrong that they left entire test pages blank, multiple choice even! (Yes, I know, I was stunned!) You’ve probably heard this a million times but I’ll say it again, mathematics is not a spectator sport! You have to do it to get it, like riding a bicycle. (Am I preaching to the choir here?)

My biggest goal this semester is to get students talking more. About mathematics. In English. A large part of my success will depend on how well I set up a classroom culture of trust and acceptance. This is huge. If I have any hope of getting students to share their original thoughts and ideas they need to know they are safe doing so. Luckily, I’ve got some ideas to help me get started, but the rest will be trial and error (as is most of my teaching anyway). I also plan on working in a slower progression at the beginning of the year to first get students acquainted with some of the language used to describe mathematical expressions before we dive into what exactly mathematics is. With any luck, every student will be able to describe, in English, what we are learning in any given unit.

Things That Went Well in Semester 1
1) I finally found a groove! Lesson planning no longer takes up hours and hours each day (#win), and I also have a nice support network of experienced teachers to draw ideas from and borrow resources from. Establishing daily routines early on in my classroom (and enforcing them!) also worked wonders.

2) Brain breaks. I was a little hesitant about these at the start since they seemed silly and unnecessary if the lesson is well-chunked. I learned early on though, not all lessons are made equally and some days really are a drag, especially when are teaching 80 minute blocks. Taking a short 5-10 minute break to stretch/play a game/go on your cell phone provides both myself and the students some much needed refuge from a long period of work.

3) First week activities. As I mentioned earlier, setting up a warm and inviting classroom culture is key to being able to get students to talk more math, and learn more in general. I spent about a week doing activities and playing games related to math with my students last semester before I started diving into teaching any curricular content. I plan on spending about the same amount of time, if not more, this coming semester settling in with my new classes.

# Goals #sundayfunday

I’m participating in the #sundayfunday blogging initiative within the #MTBoS community.

1. Build a thinking classroom.
This isn’t a new goal for me, but something I’m always trying to do better. In teacher’s college, I was introduced to the phrase “Explore First, Explain Later” in my Introduction to Biology Teaching class and this is something I try to incorporate into my math and science classes every single day. The concept is self-explanatory; students are given a chance to explore, investigate, and uncover ideas within a particular topic or concept prior to taking formalized notes. This teaching methodology is congruent to the constructivist theory of learning which states that “that learning is an active, contextualized process of constructing knowledge rather than acquiring it” (learningtheories.com).

“Exploration” can take many forms; investigation, experiments, noticing and wondering… however, something I’m keen on devoting more time to in my planning and lessons is developing the question. Daniel T. Willingham writes about this in his book Why Don’t Students Like School, “Sometimes I think that we, as teachers, are so eager to get to the answers that we do not devote sufficient time to developing the question.” I’ve really been following Dan Meyer’s lead on how to do this; his blog post on “The Three Acts of a Mathematical Story” are a good place to start.

Peter Liljedahl also hosts a free webinar on how to build a thinking classroom, available here

Visual summary of Peter Liljedahl’s research, as summarized in a sketch note by Laura Wheeler.
2.  Get students to talk more.
​It is so easy to just fall into a routine of lecturing/note-taking followed by independent (usually textbook) work, but I eventually want to create an environment in which students manage themselves. This begins by getting them to talk more, exchange ideas, and share what they already know. Some things I’m excited about trying in my classroom are Stand and Talks (Sara VDW), and talking points (adapted from Lyn Dawes).

3. Do fewer things better.
When I first started my student teaching, it consumed my life. Go to school, plan for the next day, sleep, and repeat. I stopped exercising, watching TV, hanging out with my friends… and basically anything that was not work-related. I could’ve used an old lesson plan my associate teacher has taught before; I could’ve downloaded lesson resources online; or I could have picked one really good question and focus the class on that for the entire period. There were a million things I could have done better, but no. Instead, I scoured dozens of sites for lesson ideas, worksheets, and activities before creating my own unique cocktail using an amalgamation of the best ideas I had gathered. I made my own worksheets and presentations because I wanted things done in my own exact, particular way. Planning  a single lesson would take me hours – this is not sustainable!

I know better, so I’m going to do better this year. Angela Watson’s keynote presentation for the Build Math Minds Virtual Summit really helped me refocus and re-evaluate my priorities. I’m going to invest my energy in doing the stuff that matters, and NOT because:

• Of peer pressure “Everyone else is doing it, so I’d better do too!”
• It’s tradition “We do this every year, so we must do it this year!”
• It’s instagram-worthy “OMG this will look so cute when it’s done!”

Instead I’ll only commit my energy to doing something if:

• It will help me help students engage and interact with the subject in a meaningful way
• I believe it is the best use of my students’ class time
• It is something I am genuinely excited about trying in my classroom

Three things I’m going to start doing now to achieve this goal:

1) Manage my time by setting a timer for the tasks that need to get done, and stick to it. Whatever gets done during that time doesn’t have to be perfect or have beautiful fonts and layouts, it just needs to be good enough
2) Reduce my workload by only formally assessing student work if I believe it is a TRUE reflection of student learning.
3) Increase efficiency by delegating tasks to students, like self-marking formative assessments.

# Mindset

Picture a circle on the center of a blank page. Along the circumference of the circle are six spokes, evenly spaced. If you were to write down one word for each of the spokes that defined who you are, what would you write?

For me, these words are: female, older sister, Chinese, Canadian, teacher, learner… These are important parts of my identity, they fundamentally shape who I am and how others view me, however, if I am not careful, they can also label me and lock me in. We all have assumptions about ourselves that can hinder us from reaching our true potential. To be more specific, I recently had a conversation with a good friend of mine who told me about an article she read that said the reason why many females are overqualified for their jobs are because women tend not to apply for a position if they feel they do not fulfill all the requirements, whereas males will if they feel they fit most of the criteria. I wondered how many opportunities I missed because I told myself I wasn’t good enough to try.

I recently interviewed for a position that required teaching AP physics. With my measly, almost-two years of full time teaching, and zero experience with physics (or AP for that matter), I definitely did not think I had all the requirements for the job. But I thought about what my friend told me, and I said- to no one in particular- “Heck, what do I have to lose?” Lo and behold… I was stunned when I landed an interview… and even more amazed when they called me back for a second one.

If such a small shift in my thinking could have led to such a significant outcome, no doubt this can apply to all areas of life and learning as well. I am currently reading Mindset by Professor Carol Dweck. I wonder a lot about how I can help my students uncover the hidden assumptions they have about themselves in order to develop a growth mindset. We talked about what it means to have a fixed versus growth mindset at the beginning of the year and what that looked like for different people. We explored the nature of science and how important it is to acknowledge failure in science. We discussed our ideas about how success is like an iceberg; magnificent and grand on the outside, when in fact much of it is submerged and hidden below the surface. I try to make it real for my students and have them connect it to their own lives, but most of all I’m trying to build a classroom culture that enables them to feel safe taking risks, making mistakes, and to fearlessly embrace new challenges. I struggle with this every day. Sometimes I feel like I am making good headway, and other times I feel like I’m picking my students up by the feet and trudging  them through the mud, shouting, “Come with me! There is a light at the end of the tunnel!!! Just keep moving!”

And with that last bit of imagery, I shall kindly remind myself that learning is a process, and that we each move on our own time.

When I think about Carol Dweck’s research on mindset I am reminded of my grandfather, who, throughout all the years I have known him, has shown me in his own way that it is NEVER too late to learn a new skill or to grow your mind. When I was eight or nine, I remember grandpa practicing to get his truck driver’s license. He had only been in Canada for a few years at that point, had never driven a truck before, did not have access to one, and was unable to take lessons, but that did not stop him. He took us out to Canadian Tire and bought a toy truck with remote controls. I remember watching him maneuver it around the carpet in his bedroom, studying it from different angles, gathering information about the spacing, and so on. He practiced like this diligently for days before his driving exam. Even I tired of watching the little truck move around in endless loops, turns, and parking maneuvers, but grandpa always aimed for perfection. This was the type of man my grandfather was.

I used to hate going to Chinese school on the weekends, but grandpa insisted that I persevere because he was afraid that I would lose my heritage and that my future children would forget their ancestry. This thought frightens me also. I never used to think learning Chinese was very important. I just knew how going to Chinese school made me feel – stupid and inadequate. It was like being sent to a correctional facility for not being born to the right circumstances. To hide my feelings of inadequacy I worked even harder to get good grades. I memorized difficult words, I practiced spelling them out over and over, and people told me how smart I was.

It wasn’t until one day my grandpa said something to me that I finally was able to breathe. I didn’t even know it then, but I was suffocating. I had been trapped by the need to prove how good I was, that I too could read and write, two things that seemed to come so effortlessly to others. I used to cry myself to sleep because it seemed that no matter how hard I tried or how much I worked at it, I would never be fluent in Chinese like my family. So, when grandpa said those words to me I knew the facade was up. I didn’t have to pretend anymore. He said, “Even if you are not very smart or talented at something, with effort and practice we can make up for the things we lack. This is me, your grandfather.” And then he said, “You and I, we are both hard workers, no?” I will never know what prompted grandpa to say those words to me, but I just know that when he did, at that very moment, I felt true clarity and a huge sense of relief. It didn’t matter that I wasn’t great at something, what mattered was that I tried.

# A Collection of Moments

For the last two months at my new school, I have been devoting so much of my time and energy planning and preparing that I haven’t really been enjoying the actual teaching. This past weekend was the first weekend where I hadn’t felt pressure to do something – I could just be. Sure, there was marking to be done and rubrics to be made, but I no longer felt the urgency of it all. I simply existed. I was just another presence in the universe with no agenda or ulterior motive. It sure felt great. I had a life again, and it was mine. For the first time in a what feels like a VERY long time, I did not put my students first.

That much needed mental break was just what I needed to be able to step back and appreciate all the good things that had been going on in my classroom that I subconsciously chose to ignore. It’s ironic really, that choosing to be a good, well-organized, and prepared teacher for me meant being less emotionally available to my students. An odd realization to have, but a necessary one.

Teaching is very much a collection of moments, and if I’m not careful they quickly slip away and are lost to the busy hum of school life. Yet, it is precisely those little moments that make teaching so extraordinarily wonderful. You never know when it’ll happen, but when it does, it is magical.

Today, a student of mine, one who is not particularly keen or motivated in school, who frequently falls asleep in class, and is usually late, RUNS into my class at lunch time  and excitedly yells, “MS. SOO I’M HERE! CAN I LOOK AT THOSE FLOWER PARTS UNDER THE MICROSCOPE?”

​Me on the outside:

“Why, yes good sir, you may examine those flower parts under the microscope.”

Internally:

“OMG, YAAAAS!!!”

Music to my ears.

# Burnout

Taking some time to hike through the Autumn scenery in Sockcho, South Korea.

As we near the end of October, we are finally starting to get a semblance of the Fall weather one would expect back home in Canada here in Seoul. As the leaves begin to fall, so too do my spirits in dreaded anticipation of the dark winter days ahead…  I still spend long hours at my keyboard typing away and planning each day’s lessons in detail. So many thoughts run through my mind I’m surprised I get any productive work done at all.

Slowly, I have begun to settle into a routine of work, eat, plan, sleep, repeat. Little perturbations in this routine are often accompanied by feelings of guilt. I know in my mind that there will undoubtedly be many mistakes in my teaching and yet I still find myself trying to avoid them all. Slowly, I’ve let myself forget what it’s like to spend an hour each day exercising and working on my health, or letting my mind just wander.

How will I ever learn to enjoy the moment when I’m always thinking of the future?

I’ve decided to start small. Today, I have dedicated some time to write in my blog. Tomorrow, I will make time to exercise in the morning. This week, I’m going to dedicate an hour each day doing something solely for me and recharge. This girl needs some #solitude.

# Geeking Out and Freaking Out About School

“Summer’s off.”

“All the vacations!”

“Only work 10 months of the year.”

Anyone who’s ever cited the above reasons for why they became a teacher is a liar, and anyone who assumes the above is actually true has clearly never lived with a teacher. While I can confidently dispel the myth that teachers do not live at school, I cannot say that the dwelling of a teacher (or any educator, for that matter) has not effectively become a school, in the sense that the “teacher hat” rarely ever (truly) comes off.

While I’m sad to say that my year of teaching mathematics to a brilliant group of students in Kazakhstan is now over, I am happy to report that I will be working as a science teacher at a Canadian international school in Seoul, Korea come Fall.  Currently unemployed, I have been spending my summer months contemplating the new school year to come. As a new teacher, I get thrown with a lot of advice:

“Make learning interesting”

“Don’t just lecture”

“Whatever you do, don’t smile until December”

“Whoever said not to smile until December is throwing out a bunch of bull-crap”

I mean, all this advice is helpful in some way, but mostly, I worry. I worry because I know that the advice usually stems from some past experience; perhaps my adviser has had a brilliant teacher in the past and wants to give me some insight on best practices, or maybe the experience was so traumatic that it is a warning against what I might become. I know, and am reminded every day, that teachers have a tremendous opportunity to influence the lives of their students, whether its for better or for worse. I would be lying if I said that thought has never kept me up at night.

So what does a young, novice teacher like me do during their free time? Well, this summer (like the last, and probably for many summers to come) has been filled with a lot of reading; books about science education, classroom management, cognitive psychology, teaching and learning . . . you name it. Books, and also a lot of web-surfing in search of inspiration and ideas for the next school year. The great thing about being a teacher today, versus 50 years ago even, is the incredible, vast, and extensive amount of information available literally (excuse the cliche) at our fingertips. With the advent of online textbooks, YouTube, massive open online courses (MOOCs), I really have no excuse for not knowing better. The issue now becomes knowing how to efficiently and effectively conduct searches, filter out the big ideas, and not get caught in fun  yet unproductive Pintrest spirals, or the ever-so-looming YouTube vortex.

A sample of my summer reading.

I find myself constantly striving to be perfect. I work, rework, and surgically remove minute details in my lesson plans until I am convinced they are just so. Then along will come some new insight I’ve read in a book or online article and I will repeat the process all over again. I worry about many things:

Will my students find this topic interesting? Can they relate this to their own lives?
What will they remember 10 years from now?
Is this an example of content-based, activity-based, or inquiry based teaching?
How can I work towards developing lessons that are more minds-on rather than hands-on
How can I better scaffold this project to ensure top-quality work?
. . . and so on.

The result of all this worrying is twofold: 1) my brain is now attempting to process more information than it can actually take on, and 2) very, very slow progress with my unit planning. I realize that I need to just give myself permission to just be okay with being a novice. I mean, there really is nothing more liberating than knowing you are not the best and that it is okay (splendid, even) to keep learning – that is a belief I want to instill in my students too! Of course, knowing all this, it is still a constant struggle to be mindful of it, and I am sure I will be reminding myself (and my students) of this more than once.

So here’s to wanting to be a great teacher, but okay with being good (modest?) one (for now).

Privilege is like an invisible door. You can walk right through it and never realize it’s there until it shuts close for somebody else.

My grandmother never went to school past the age of ten. She’s a little too loud and boisterous at times, is never afraid to speak her mind, and to my family’s embarrassment, can always be found haggling shamelessly with local shopkeepers to maximize savings. To some, her behavior may appear crude, but to me, my grandmother exemplifies the kind of rare and selfless individual who gives so much of herself away to help others that she’s perfectly content with just being happy that others experienced success from her sacrifices.

Grandmother never went to school past the age of ten. Being the eldest of three children, she stayed home full-time to look after her younger siblings. Born and raised in a time and place where getting an education was considered a luxury, my grandmother never had the chance at a post-secondary education, but I did. I am afforded so many more opportunities because of the country of my birth and the situation of my upbringing.  It took me a while to realize it, but the success I’ve experienced in my life was as much pure luck as it was hard work. I was born into a privilege that my grandmother did not have and I have the chance to do something about it.

Inspired by my grandmother, I adopted a simple classroom activity about privilege from an article I found here. ​

I remember talking excitedly with a friend about this activity and the powerful messages it sends about the concepts of privilege, equity, and equality. I was not a teacher yet, but I was keen to start  building the foundations for a classroom environment structured around social justice. My friend considered this for a moment, then said to me, “It’s a great exercise. But the problem with these types of activities is that it can’t just be about awareness. Okay, so we all have privilege to varying degrees, some more than others – so what? The question you need to ask next is: ‘Now what can we do about it?’” I took her suggestion to heart and asked my students exactly that.

With some help from a colleague, here is the follow-up activity I presented to my students:
1. Draw it- draw a picture to show what you would do to solve this problem.
2. Share it- share your solution with three other students in the class.
​3. Write it- Now that you’ve listened to others’ solutions, write down a few sentences to add to your solution.

Despite the language barrier, my students surprised me with their many insightful  responses. See their work below:

Instead of sitting in rows, we should aim for a more optimal arrangement.

Even better, perhaps we should all be equidistant from the bin.
Sometimes, we need a little help from each other.
Or maybe each person should be given multiple chances.
Or what if… we each had our own bins?

# Alfie Kohn: Rewards and Competition

A question I’ve considered many years: Why is it that so many of the tasks we perform in our culture – at home, at school, at work, at play – are set up […] where most of us can succeed only at the price of another’s failure. – Alfie Kohn

Alfie Kohn is one of my heros in the field of education. He is an American author and lecturer on topics pertaining to human behaviour, parenting, and education. His website contains a series of links to articles he’s written, books published, his personal blog, and a series of “online freebies” (e.g. video/audio).

In the video below, Kohn speaks to a group of educators about the effects of competition in the classroom (my thoughts here). To put it simply, competition kills creativity; it teaches students a “sink or swim” attitude and that one’s success comes only at another’s failure. He argues that competition is never the optimal arrangement. In contrast, cooperation and collaboration lends itself to better attitudes and results, both in the classroom and in society as a whole.

As an aspiring educator, I couldn’t help but also notice the way Kohn engages his audience as well. He skillfully navigates the content of his lecture while drawing his audience into the discussion as well. He starts by surveying the audience to see what their professions are, creating a simple but effective connection. Then, he provides an example of a study having to do with competition that yielded some fascinating result, and prompts the audience to think about why those results may have been produced. He gives the audience a chance to discuss their thoughts with someone near them, and takes some time to talk about other relevant observations he’s made on the topic before getting the audience to share their responses. That way, he sets the stage for the depth and type of responses expected of his audience, and they also get some time to refine and further develop their responses before sharing with the larger group.

Watching and listening to Mr. Kohn speak is such a privilege. He’s funny, insightful, and thought provoking. Definitely worth the watch!

# Rewards and Vacuous Praise

Think back to your days in the elementary (or even secondary) classroom. I’m willing to bet that most of you will be familiar with some version of the controversial reward chart as exemplified above. What are your thoughts? Do rewards work? What has been your experience with rewards in the classroom? Go ahead and think about this for a minute before you read on.

Pintrest board on reward systems.

I distinctly remember the day my grade five teacher decided to implement a “Merit Points” system in our classroom. There was a blank chart on one of the the side walls with each of the student names listed in rows, and empty boxes for check marks next to each name. Our teacher explained that these points will be very difficult to earn and would only be awarded for “exceptionally good behaviour”. None of us really knew what that meant, but I was interested in seeing how this would play out.

After our return from recess that day, the class began filing in when all of the sudden Mr. R yelled, “EVERYBODY FREEZE!” And so we did – “Megan has earned her first merit point. She picked up a piece of garbage that wasn’t hers – WITHOUT BEING TOLD TO DO SO.” Man, I thought, if that’s what it takes to get these merit points I’d better pick up every single piece of garbage I see, but only when I’m not being told to do so.

As the year wore on, Megan, a naturally kind-hearted person and good friend of mine, began accumulating more and more points. Eventually, there was no way to catch up. A large portion of the class had no points at all! Naturally, I stopped caring – what was the point? I was never going to get enough merit points to win the prize, and it didn’t matter if I did good deeds outside of the classroom because Mr. R was never going to see them anyway.

What I Know Now:
I watched a lecture presented some years ago by Aflie Kohn  as a part of the MacClement Lecture Series at Queen’s University. To answer the question, “How do we create kind, compassionate, and caring children?” he asks us to consider the following question, “How can we destroy a child’s inclination to care?” The answer: competition and rewards.

Grades, stickers, praises, money, are all forms of rewards commonly used by parents and teachers – these are thought to encourage positive behaviour when in fact research shows the opposite effect to be true. Providing extrinsic motivators (i.e. rewards) for what are inherently intrinsic values and behaviours (compassion, resilience, grit…) simply does not work! Extrinsic and intrinsic motivation are inversely related. According to Kohn, research shows that children of parents who frequently use rewards tend to be less generous than their peers.

Thinking back to my grade two classroom, the only thing that the Merit Points system did was reward the students who were already good. While I was motivated to “try” for a short period of time, I quickly reverted back to whatever I was doing before once I decided it was a waste of my time.

Praise can be similarly perilous to your child’s development. If you are like me, you often get annoyed when others give you empty praises like, “Good job!”, “You’re awesome”, or “You’re so smart!”. Not only do praises like these provide no context or constructive feedback whatsoever, they can also be detrimental to a child’s confidence, grit, and self-esteem. This article (“How Not to Talk to Your Kids”) does a good job at explaining the basics. In general, kids who are praised for intelligence over effort tend to give up more easily on tasks that they believe they have no inherent talent for. Specific praises like, “I like that you moved on to the next question when you got stuck,” are key to providing students helpful strategies to succeed.

In general, I think that rewards can act as good short term motivators for getting necessary but uninteresting tasks done and out of the way, like rewarding myself with candy for completing  chapter readings for a course I don’t enjoy for instance. However, in the long term, rewards can hinder a child’s development of good attitudes and behaviours and should generally be avoided.

Once children hear praise they interpret as meritless, they discount not just the insincere praise, but sincere praise as well. – Judith Brook, New York University Professor of Psychiatry