Turn Your Classroom into an Escape Room

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:

• DON’T set letter locks to be something obviously related to your subject. I stupidly set mine to be “MATH” and had students guessing random four letter words rather than actually engaging with the problem sets that I had worked so hard to create! (I later changed the combo to “BATH”)
•  On that same vein, you can set a rule so that students can only attempt one combination at a time.
• There’s always that one kid who examines everything with the UV light… so I ended up writing a few random messages around the class not related to anything but just for giggles.

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

• Event began with nine teams of four
• Students work in teams of four, they have a choice of which question set they would like to work on, however, once a box gets unlocked, then that box becomes unavailable
• The question sets corresponding to each box cover a different range of subjects (ex. Box A might cover Math 10, Science 10, Physics 11 and Chemistry 11 while Box B might cover IT 10, Math 10, Science 10 and Math 11).
• Inside each box are a series of “advantage cards”
• Only the teams that unlock the boxes proceed to the next stage of competition

ROUND 2: Gain 5 points in a trivia style tournament

• Each box contained a specialized advantage card that can be used in round 2
• Advantage cards may only be played after the question topic is revealed and BEFORE the question is revealed
• Examples of advantage cards: skip the question, make the question worth double points, invite an expert to answer the question
• First team to 5 points wins
• Remaining teams compete for second place

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.

Visual Patterns and Mathematical Mindsets

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:
1. Openness
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.”

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
 Wondering if there’s a way to embed LaTex code into my blog… (AKA me trying to be more tech saavy) (Please excuse the crappy graphics, I did what I could with Powerpoint…)
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.

Intro to Probability and Counting

Lesson Theme: Introduction to Probability and Counting
Prerequisite Knowledge: Permutations and Combinations

Here’s an activity that I introduced to four groups of tenth graders in a recent unit on probability:

 The instructions. Students working to crack the code!
• Give each team a travel lock and a different hint. No communication between teams are allowed. They have two minutes to try and “break the code” and find the combination that opens the lock.
• The reveal: show the class all the different tasks they were given. Ask: Did each team have a fair chance of winning? Which team do you think had the highest chance of finding the combination? What about the lowest? What strategies did each team employ to try and crack the code?
• Have students support their answers by calculating the number of possible codes for each lock. Each group needs to commit to an  answer by writing it on the board. (This ensures the type of “buy in” necessary for students to invest in the problem).
• Have groups come up one at a time to explain their calculations.
• Have students find the the probability that each team breaks the code on the first try, introducing notation along the way (e.g. “P(A) = probability of event A”)

​Provide minimal guidance as the groups decide on the number of combinations for each scenario. I made an exception for students who asked clarifying questions, such as:
– Are there any repeating digits?
– How many digits repeat?

The hints are open to interpretation on purpose in order to get students thinking about the sorts of constraints they would need to consider when calculating the total number of outcomes. The discussion phase of the activity provided a rich opportunity to address student misconceptions about permutations and combinations, as well as the importance of reasoning, i.e. Does this number make sense? Is this estimate too high or too low? How does this number compare with my initial guess (intuition)? What if there were no constraints, what would the answer be?

The Solutions
TEAM GARRY – 3 digit code, repetitions allowed. This hint is not much of a hint at all. “Repetitions allowed” could mean that there may be or may not be any repetitions in the code. So, one possible answer is simply 10 x 10 x 10 = 1000. There are ten ways of picking the first, second, and third digits.

TEAM ORVILLE – 3 digit code, no repetitions. This narrows the playing field a bit. 10 x 9 x 8 = 720. Ten ways to pick the first digit, only 9 choices left for the second, then 8 for the third.

TEAM APRIL – 4 digit code, numbers 2 and 3 appear in the code.
(a) This would be significantly easier if the ONLY numbers in the code were 2 and 3. There are only 4 possible combinations, which are easy to figure out by hand: {2323, 3232, 2233, 3322} or
4!/ (2! x 2!) = 4.
(b) With repetition. There are 4 ways of positioning the “2” in a four digit combination. For each way that the “2” has been positioned, there are 3 ways to position the “3.” In total, we can arrange the digits “2” and “3” in 4 x 3 or 12 ways. If repetition is allowed, the total number of combinations would be 12 x 10 x 10 = 1200.
(c) Without repetition. Similar to above, except that once we have found a placement for the “2” and “3”, there are only 8 and 7 digits left to choose from respectively. The final answer would be
2 x 8 x 7 = 672

My notes and observations:

• Having done a previous unit on permutations and combinations, students tended to misuse the combinations formula without fully understanding what it actually helped us find  (e.g. 9C3 gives the total number of ways to pick three objects out of 9, when order does not matter)
• While this did not come up in our discussions, you may choose to ask the class, “What types of combinations would you say are safe to rule out, or eliminate?” [EX. People are less likely to pick combinations that have just one repeating digit like 000, or consecutive sequences such as 123]
• For lower ability groups, it is advisable to go through the solutions one at a time rather than all at once. Give groups the option of revising their original solution, agreeing with another group’s solution, or arguing another groups solution after each round of explanations
• Depending on the depth of discussion, this activity can range from just 10 mins to 40 mins

Tis the Season of Marathons

I ran my first ever half marathon today in Almaty, Kazakhstan and set a new personal record of 02:06:28  in 21 kilometers. To me, this record is less of an indication of the time and effort I have put into training, but instead it represents the numerous voices of encouragement and motivation from strangers I have met in a strange land, all of whom I am now proud to call friends. Without them, I’m not sure I would have ever participated in a marathon in the first place!

Origin Story
When I first arrived in Kazakhstan, several of my colleagues had already participated in the Almaty marathon the previous year; some ran the 10K, some did the 21K, and a select few opted for the full 42K. As they each recounted their stories of training and triumph, I got a sense of the camaraderie and unity that was borne  out of the journey they all shared as they strove to push mind and body to new heights. I wanted in. Over the next few months, I found myself training harder and running longer distances than I have ever done in my life.

I shared many eventful runs with my training and running partner, Orville, who is, to put it simply – a black man in Kazakhstan. The local people tend to gawk at him with mixtures of fascination and awe. He is always being honked at by passing cars, interviewed by local television stations, and requested to have his photo taken (with or without permission). Orville regards his famed status with  much grace, which I greatly admire. It makes me uneasy to see the way people behave around him just because of the color of his skin – but I diverge.

Today, records fell. Legs sore, body fatigued, and yet my head is above the clouds. I am extremely happy I was able to meet such a great group people and be able share this moment with them.

Pre-race photo op with Team Angelina, Dave, April, and Orville.

Racing to the finish. Photo courtesy of Forest Dweller, from Adelaide.

Doin’ the Bolt with my brother, who sometimes refers to himself as Will Smith.

Do Nows

I have been doing a lot of reading (self-help mostly) and thinking (about the future) lately, though none of this has resulted in any sort of definitive action. This past week has been filled with many ups and downs, and it was one of those weeks that felt as if the downs tremendously overshadowed the ups. I have behaved in ways in which have made me ashamed of my character – I gossiped, and I complained – a lot. I am also guilty of being a massive consumer; a consumer of lies, outrageous acts of injustice, and rumor. I am sick of the complaints and I am tired of the negativity. It is time to break myself out!

I briefly thought of titling this blog post “Commitments for the Future” but that  just made it sound vague and ironically non-committal. The future can mean tomorrow, or it might be some abstract entity far off in time and space. In the end, I resolved to come up with a list of “Do Now’s” (so named after a common teaching strategy described in Teach Like a Champion by Doug Lemov). As a good friend once advised me, “New Year’s Resolutions are a scam. If there are things you really want to commit to doing, then they should just be ‘goals.’ You don’t have to wait for a new year to start living the life you want,” (his approximate sentiments in my words).

Without further ado, my current list of Do Now’s:

1. Create more, consume less.
2. Stop complaining! Nobody wants to hang around a killjoy.
3. Drink more water.
4. Eat more fruits and vegetables.
5. Train for a half-marathon. (Run a half marathon before the end of the year).
6. Implement a “no eating out week” at least once a month.
7. Stop eating at least three hours before bed! Otherwise your sleep will be uncomfortable and your belly will feel like a stack of bricks (I know this from experience).
8. Work to pay off student loans.
9. Invest in a retirement plan before the year is out.
10. Read at least 10 minutes a day.
11. Level up in adult-ness. (Work in progress).

Admittedly, the goals themselves need some work in terms of specificity, timeliness, and a way of measurement. But hey, I think it’s a good start.

Silent Teaching

For reasons I still do not fully understand, my grade 10 classes were combined with another teacher’s classes today. Classes are 80 minutes each, and are split up into two 40 minute blocks. I spoke to the teacher of the other group beforehand, and from what I could tell from her limited English (and my non-existent Kazakh), it seemed like we would each teach a 40-minute lesson to the combined classes. It was not until the lesson began that I realized this teacher wanted her group to work separately from mine. The lesson ended up being a disaster, a huge flop, an extreme “UGH” moment if you will, and one that I’m not too proud of. It felt like I was trying to teach against a storm. I felt disrespected by the other teacher and students in the room because they were being extremely noisy while I was trying to get through my lesson. I asked them to quiet down a couple times but then the noise level would eventually go up again.

Thinking back, I wish I had been more adamant on insisting that I kept my classes and never combined groups in the first place. Again, for reasons I cannot explain, it seemed imperative to the other teacher that we kept the two groups together. So by the time my second class came along, I devised a new plan. I was better informed the this time around. I knew I had to share the same physical space with the other teacher and her students, and I knew that there would be at least minimal amounts of talking. I also knew that I didn’t want to enter in a shouting match with the other class (fighting fire with fire just makes a bigger fire). Instead, I tried my hand at silent teaching.

I left the following note up on the board for my class at the beginning of the lesson:

Our goal was to prove the six basic trigonometric sum/difference of angles identities today.

The Results –

What Worked:
The silent teaching definitely got the students’ interest and forced them to keep an eye on the board so that they could keep up with what was going on. A few students got the idea and were able to explain verbally what I was trying to do non-verbally – and English is their third language! (So proud!) The other class was noticeably more quiet this time around, and without me having to go into a shouting war with at least a dozen other voices, the noise level was much lower in general. I also noticed that some students from the other class were intrigued by what we were doing on the board, and stopped to observe our lesson. Once all six trigonometric proofs were finally complete, I gave a dramatic pause, and POOF – I got my voice back!

Me but with clothes on.

What Didn’t Work
The students who are less visual were really craving verbal explanations. While classmates volunteered to help explain concepts to those who didn’t understand the first time around, two students told me that they still felt really confused after the lesson. I wish I could find a way to make this a less teacher-centered lesson, and create more opportunities for students to get involved. I did call a couple of students to the board once I felt they got the general idea of the proofs, but I was not able to assess all my students one-on-one. An exit slip would have been useful had time permitted.

Next Steps
I’ll try my hand at silent teaching again in the future, but I’d like to find ways to create even more student involvement. Our topic this time was the sum/difference identities for trigonometry and it was very theory-heavy. Next time I think a topic (or even short demonstration) that is more straightforward to understand will be more effective with this teaching strategy. Also, I resolve to make facial expressions more dramatic for a fuller effect!

Other Notes
I later realized my big dramatic moment at the end wasn’t as dramatic as I had hoped. I called a student up to the board to complete the last proof, and it wasn’t until after I “regained my voice” that I realized there was a major sign (+/-) error!

On Symmetry

Here are two interesting questions I posed to my students in our unit on the transformation of shapes.

(1) Playing card (on right): Where is the line of symmetry?

I handed each pair of students a printout of the king of hearts and asked them to identify the line of symmetry.

(2) M.C. Escher (below): Is this drawing symmetrical? Why or why not?

It may be a good idea to preface both of these questions with, “What is symmetry? Give an example to support your answer?”

 We are working on math journaling in my classroom. I use these journals as a way to assess my students’ prior knowledge, gain feedback on my lessons, and to give individual feedback. As my students are all English Language Learners, and this is one way for them to build up their written communication skills.  I currently do not use any rubrics for their journal entries, though it may be a possibility for the future. I try to get students to write in their journals about once a week. This frequency of journaling works well, so that it is not seen as
tedious, and it gives me some time to respond to all their entries.  I try to vary the writing assignments as much as possible to add interest to the lessons, and students are encouraged to include pictures or diagrams to support their explanations.

The Solution:

Both the above questions are meant to test how well students understand the idea of symmetry. Symmetry is any transformation that leaves the original shape or object unchanged.

(1) In the playing card example, students often say that the line of symmetry is horizontal, vertical, or diagonal. In fact, there is no line of symmetry – as that would indicate reflective symmetry (mirroring an image). The type of symmetry exhibited on a playing card is rotational symmetry by 180 degrees (or point symmetry), meaning that you can cut the image in half at any angle through the centre of rotation, and the two halves will look exactly the same upside down. (I actually got my students to cut their playing cards in half at different angles to illustrate this property).

(2) Most students are likely to state that the drawing does not exhibit any type of symmetry at all. Again, students at this stage tend to be familiar only with the idea of reflective symmetry. I will accept their answer as long as they provide a suitable justification. However, what I’m trying to get across with this question is that tessellations (translating an image/object) are a type of symmetry also. This creates a nice lead in to further discussion on  geometry as it relates to art, or vice versa.

Photo from: mathisfun.com

Inverse Functions and Cryptography

Here are some teaching notes on a recent lesson I did on inverse functions with my group of grade 10 students.

Learning Objective: Understand the definition of inverse functions and their relevance to everyday life.

1. Setting the Stage with Office Supplies
Beginning the day’s lesson with a “picture talk” can be a good way to get students to practice using subject-specific terminology. The pictures can be controversial, or you may choose to pick analogies relating to the topic of discussion, like the one below for instance.

Inspired by a photo I found on Pintrest. (Click to follow link)

I find that leaving the questions open-ended gives students more freedom to get creative with their answers.

A series of open-ended questions you might ask:
What do you think  ‘x’ represents?
Predict: How do you think this photo relates to our new topic?

Teaching Notes
A lot of my students like to shout their answers out loud when they get excited about a topic, which tends to drown out the quieter students and does not give them enough time to think. But sometimes, I get excited too and I basically just end up shouting “YES!” while enthusiastically pointing and staring  wide-eyed at the students who yelled out the answer I was looking for. “The answer I was looking for” – which meant ignoring all other answers that may have added important insight to our discussion. Such habits are dangerous because they tend towards a classroom environment in which it is not safe to take chances or make mistakes. When I  dismiss wait time and only acknowledge the quick answers, I am effectively giving everyone else the permission to shut down and stop thinking.

To combat the issue of the shouting-the-answers-out-loud thing, I introduced this image by inviting students to take ten seconds (any more and they would have shouted the answers anyway)  to silently look at the picture and gather their thoughts about it. When ten seconds had passed, I asked them to share their ideas with the person sitting next to them when they were ready.

2. Lesson Objective and the Enigma Machine
​​By now, it is likely that students have guessed that the lesson has something to do with “functions” and “opposites.” At this stage, I presented the day’s lesson objectives and key terms (with translations), along with a dashing photo of Benedict Cumberbatch in “The Imitation Game.”  I gave a brief synopsis of the events in history in which the movie is based, and explained how it related to our topic of inverse functions. In retrospect, I probably should have posed this as a question instead: “How do you think this relates to our topic?”

3. Intro to Cryptography
Next came the fun part, and what formed the bulk of the lesson. The students worked  pairs and were asked to  decode a hidden message within a twenty minute timeline. The less hints you give, the more challenging the activity becomes. (You can download the activity page along with my teaching notes below).
Once the twenty minutes are up, you’ll see some students scrambling to finish decoding the message. Debrief the activity with them. Discuss strategy- for instance, how were they able to determine the cipher? Follow up- how do you think Alan Turing and the British Intelligence were able to crack the unbreakable code? (May choose to show video clip of the relevant scene in the movie for dramatic effect). Extension- What is the probability of randomly guessing the code correctly? What assumptions do you have to make in order to do so? (Can also relate topic to permutations and combinations).

Teaching Notes:
I downloaded a 20 minute digital countdown timer and added it to my ppt so students can keep track of how much time they had left for the task. If you have any English Language Learners in the class, it may be helpful to post the English alphabet on the board as an added hint.

4. Consolidation
I ended the lesson by asking students to write a short journal entry relating to the picture shown at the beginning of class. I think a better journal prompt would have incorporated a debriefing of the cryptography activity. The students’ journal entries  gave me individualized feedback on how well they understood inverse functions and the composition of functions. A common mistake I noticed was mistaking the concept of reciprocals with inverse. Some students wrote that 2 and ½ were “opposites”, and therefore the inverse of each other. Something to address in my next lesson.

On Teaching in a Vacuum

Earlier this week, our school Principal passed away. The announcement of her death was sudden and unexpected, and the impact it has had on our school staff and students has been tremendous. We were called into the assembly hall mid-day to be given the news.

It felt surreal as I stumbled back out into the hallway, surrounded by my teary-eyed and visibly distressed colleagues who were deeply impacted by the news. As teachers, we are always told that our jobs are not just about teaching and that we must simultaneously act as parents and counselors – those words never felt truer. “Put on a brave face,” I told myself as I headed to my next class. But as soon I saw the look on my student’s faces I knew I could not leave the matter untouched. Grief has a way of hitting us in strange and unexpected ways; I surprised myself when I got a bit emotional while speaking to my students. I told them that they had a right to feel whatever it was that they were feeling, and that it was okay to cry, to feel sad, or to even feel completely unaffected.

It is moments like this in the classroom that remind us that no matter the amount of resolve and strength you have as a teacher, you are, and can only expect to be, well, human.

A Lesson on Permutations

My lesson on permutations was inspired by this post by Dan Meyer. I teach a group of very bright and mathematically inclined students at our school. While my students’ computational abilities and mathematical knowledge are almost second to none, a majority of them tend to lack skills of inquiry and critical thinking. This is due to the fact that the curriculum is dense and completely knowledge driven, which leaves little opportunities for linking (making connections) or creativity. I believe the second culprit of this phenomena is the post-Soviet style culture and traditions in which the Kazakh education system is rooted.

I see that my colleagues are under constant pressure to deliver heaps of content from a prescribed curriculum which is flawed to begin with. To provide some context, one term is roughly 6 weeks long. In those six weeks, we typically cover three units of work, with a prescribed 12-16 hours of teaching per unit. The end of each unit is followed by a formative assessment (1-2 hours). This leaves 10-14 hours of actual instructional time, of which is no where near enough time to cover all the topics we need to cover AND engage students in meaningful inquiry-based projects.

As a result of the limited time constraints, we are basically teaching one new concept a day. The students, meanwhile, are left to soak up as much as they can (like sponges that retain very little water, or knock-off expandable water toys that actually stay the same size) before the end of term summative. Add to this the other 7-10 classes the students are required to take, and you can see the students have  an enormous workload. They are in school six days a week, at least 9 hours a day. There’s just no time! The default solution? LECTURES.

There aren’t many opportunities for engaging students in rich learning tasks, but I try to squish in bits of it whenever I can. As I said, my students are extremely gifted but are used to thinking in terms of algorithms and formulas, so I often get a lot of blank stares and a lot of “Why are we doing this?”  when I engage them in conceptual thinking – which is exactly the point! “Why ARE we doing this?” I ask, and that really grinds their gears! Slowly but surely, the students are getting used to this rather “oddball” tendency of mine (in their p.o.v.) to turn things around put the onus of learning on them. And golly I think it’s working!

So anyway, here’s how I began our unit on Combinations:

Photocredits to Dan Meyer. Lesson possible due to his establishment of the “rule of least power.”

I placed students into groups and organized a placemat activity. Instead of me asking the questions, I wanted to know what opportunities the students saw when looking at this picture.

How much combinations can be made sum of digits in each number is 53?
– How much combinations do we have if key consist of 3 digits?
– What is the possible length of the hardest password?
– How many possible variation of making code with all numbers (all numbers can be used one time, and must be used)?
– How many numbers that password include?
– What is the probability of randomly unlocking the lock?
– How many explosive charges are required to blow it?

As I ponder this list I see a rich minefield of opportunities before me. Within a five minute brainstorming session, my students touched on permutations, probability, and of course, “real-life” problems.

I put “real-life” in quotations here because I believe the relevance of math to everyday life is relative. My version of “real-life” is different from my students, and I certainly don’t expect all my students to be making calculations with factorials on an everyday basis. I was blunt with my students, though I certainly didn’t mean to be… it sort of just slipped out. “Some of you might never use this again in your lives,” [cue snickering, whoops], “but…” There’s always a “but” of course, and I’ll leave it to you and your imagination to fill in the rest of the sentence.

Once the snickering subsided, I proceeded to introduce factorial notation. The sequencing worked out beautifully because once the students were familiar with factorial notation, we revisited the lock picture and the students were able to derive the formula for permutations themselves! All I did was ask “How many possible combinations are there?” and students were quickly able to discover that we needed to define more parameters in order to answer the question. E.g. How many digits are there in the code? Can numbers be repeated? Beautiful!

At the end, I gave them the following exit questions:
1. Define permutation, in your own words.
2. Give an example (not used in class) of a permutation problem.

I was surprised at some of the responses I got. First, I learned that the class had a diverse understanding of the word “permutation” (I never actually gave them a definition), so now I know where the gaps in my teaching were. Second, not only did their examples show me the depth at which they understood the topic, but some students were able to accurately predict the types of questions we would be covering in future lessons. So instead of using textbook questions, we can explore the ones they came up with in class. Brilliant!

On left: confusing the word “permutation” and thinking it synonymous with “repetition.” On right: a student’s take on the classic playing card questions.

On left: still need to work on precision of language in coming up with a solid definition for the word permutation, but good effort. On right: Good to see the key word “order” being used.

﻿The Teacher Trap

I somehow always manage to fool myself into thinking that knowing is the same thing as doing.

​Many new teachers get too caught up in the trap of wanting to be well-liked by their students. While there are good reasons for the “students don’t learn from people they don’t like” argument, I don’t think that being well-liked by your students is a key attribute of a good teacher. As long as we make teaching about ourselves, we are losing sight of what is important for the students. At the end of the day, it isn’t about how much they like me, but how much they learn from me. Despite knowing this, I still find myself looking to gain my students’ approval, because deep, deep, deep, deep, deep down, this is what it feels like to be the “cool/fun teacher” that everybody wants to hang around with: ​

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It’s like that one tiny sliver of light you see at the end of a long, dark tunnel that says, “You’re still relevant! We need you!” The one great paradox of teaching that I feel will probably haunt me for years to come is trying not to take defiant behavior or ill-intentioned comments personally when I genuinely care about about my students and want to do good by them.

At one extreme, trying too hard to be the “cool teacher” means jeopardizing my professional boundaries and compromising the integrity of my classroom. We’ve all heard this in teacher’s college, “Be friendly, but you are not their friends.” Of course, being totally impassive to your students feelings about you does not work either; at this extreme you risk being completely detached from the process of their learning. Maybe then the key is not to gain your students’ approval, but their respect and trust – a much lengthier and more complicated process…

Yesterday I taught a lesson about Euclid’s theorem of proportional segments in right angled triangles (a wordy way of saying, “the geometric mean of a right angled triangle is the altitude from the 90 degree angle to the hypotenuse.” OK, I don’t think that explanation was any actually better).  For my starter activity, I gave students three red right angle triangles and one blue rectangle. The triangles can be rearranged to fit inside the blue triangle. I wanted students to use this fact to help them prove the similarity of all three triangles.

The idea was to use the rectangle to show that all three triangles shared common lengths and angles, and hence, are similar. It was an activity that combined spatial geometry and logical thinking. I was quite proud of the lesson and thought that this would be a good activity for students so they could play around with the shapes and see their proportions.

Then one of them said, “This is so boring. Why are we doing this?” Those words cut through me like knives. Talk about being impervious to student comments.  I did not know how to respond to that statement so I ignored it and instead asked, “So have you figured out how to fit all three triangles into the square?” and I moved on.

But really, that comment affected the whole tone of my lesson. Instead of giving students the freedom to make their own discoveries, I spent the rest of the lesson trying to defend and prove the value of my starter activity. I ended up doing most of the work, and I let the students get away with passive note-taking. [Ugh! Seriously April, stop being such a pushover.]

​Next time I will STAND MY GROUND, and no matter how long the awkward silence, or how much the students refuse to think critically, I WILL eventually get it out of them. They’re here to learn dammit, and I’d better make sure they are they ones doing the work. I hope to eventually gain my students’ trust; trust that I have their best interests in mind and will plan and deliver meaningful lessons and activities for them. Until then, I suspect  I will have to deal with a lot more resistance.

Ms. April

I don’t teach for the vanity, and let’s face it – teachers do not exactly have the best reputation these days. Something stupid about money-hungry fiends who take up way too much of the taxpayer’s money, blah blah blah. It’s not like we are educating the future citizens of the world or whatever, so no big deal. For the record, it is a huge burden to teach kids stuff they will never use in real life. Even textbooks have to work extra hard with their fancy graphics and enticing fonts to convince children that modeling the shoulder height of a male African elephant is an example of using cube roots in “real life.”

​Note that the problem states “a male African elephant,” as in (singular) male African elephant. Why the hell does nobody ever care about the female population? What made this particular male elephant so special that he can have his shoulder height modeled by a mathematical function? Won’t the other elephants feel left out?

Some days I feel as if I am teaching from inside of a five foot thick cinder block that’s been buried ten feet underground. A few sympathetic students will strain their ears and squint their eyes, but no one is really listening.

Other times my lessons go so horribly that I wish I could morph into a bird and fly away. At least that will be more exciting than what my students will have to endure. There are moments when I forget that teaching is not the same thing as learning, and there are instances when I  knowingly commit the heinous crime of giving my students the “I taught it so you should know it” attitude. I know, I’m awful.

I have been told that it can take years to make a difference in someone’s life, and most of us do not have the privilege of witnessing that change. I have also been told that making a difference in somebody’s life can be as simple as handing out a lollipop.

My personal “lollipop” moment.
My “lollipop” moment happened on my graduation day.

Four years ago I was an orientation leader for the incoming class of con-ed 2015, Queen’s University. A couple of us volunteered to write letters to future members of the con-ed family that year. I had a lot of fun with those letters and wrote them on hello kitty paper and decorated the margins with stickers from my personal sticker collection (of which I am very proud of). Only one person out of five responded to my invitation to email any questions or concerns they had to me. Orientation week came and went, and for a while, that was that.

In all honesty, I had forgotten all about those letters. But one of those letters had been sent to a young man named Mike. Mike went on to become the Rector of Queen’s University in 2014. On the day I received my Bachelors of Education, I walked across the stage of Grant Hall to shake the Rector’s hand. He leaned in and said to me, “April I just wanted to tell you that you were the one who wrote the letter to me. The one with the hello kitty stationary and all. I wanted to tell you what a difference it made.” I was so shocked I nearly pushed him off the stage (okay, it was a gentle nudge, but my family members who were watching from the balcony swore that it looked like I punched him in the shoulder).

That story still gives me warm fuzzies every time I think about it. Who would have thought that a letter I wrote, and purposefully sprinkled with tacky looking gold-trimmed stickers would have been something that could ever have an impact? I mean, okay, I doubt I drastically altered the course of his life by sending him that letter, but I will be forever grateful to Mike for showing me what I difference I have made.

To quote Drew Dudley who quoted Marianne Williamson, “Our greatest fear is not that we are inadequate. Our greatest fear is that we are powerful beyond measure. It is our light, and not our darkness, that frightens us.”

Sometimes our students have small ways of telling us we matter, and they will come at moments when we least expect it. On Friday, I complimented a student for the cute stickers she had on her notebook. Surprisingly, stickers are not easy to come by in Kazakhstan, and if you know me, you will know that I am a proud owner of a shoe-box full of stickers that I have been hoarding since I was seven. Today, that student came to school with a pack of happy face stickers. She gave them to me.

So, to my fellow teachers who may feel discouraged, worn out, or overworked, I say – teach on! Follow your guts and stick to your principles. Teach because you matter more than you know. Teach because you are powerful beyond measure. Teach because you have the courage to teach.

And most importantly, teach because there might be stickers involved! (Ok, not really, that was a bad joke).

On  Friday, a few of my grade 10 classes began the new unit on “nth roots.” My “lesson planning” currently consists of getting orders from my co-teachers on what they expect me/us (?) to cover the next lesson, me taking pictures of the related work pages, subsequently decoding these work pages which are all in Russian via an online Russian keyboard, and then translating them via google translate.  The process looks something like this:

Step 1: Obtain photos of the exercises my co-teachers would like to cover for the next lesson.

Believe me, I am not exaggerating when I say that these are all to be covered within one forty minute lesson. Oh, and have I mentioned that the curriculum here is about a trillion times more advanced than the Canadian one? Units covered in the grade 10 math curriculum include sequences (okay, so far so good), nth roots (seems alright, until you see what types of questions the students are expected to solve), properties of functions (don’t see this until gr. 11 in Canadian curriculum), vectors and equations of a line and circle (gr. 12), reciprocal functions (gr. 11/12), trigonometric functions (gr. 11/12), probability (at grade level), modelling mathematics (11), transformations of shapes (11/12), combinations (12), and finally, logarithmic and exponential functions (11/12). My first reaction was shock and awe, and I think those are still accurate descriptors for how I feel now.

Step 2: Convert questions to an electronic format.

Typing out the questions via an online Russian keyboard.

Step 3: Copy and paste Russian text into Google translate. Pray that the translation is comprehensible.

Okay, I’m guessing that’s the Russian to English translated version of “evaluate.”

Step 4: Do the work! –> Understand it! –> Master it!

Sometime in the distant future: Actually plan the lesson!

Teaching is a deeply humbling pursuit. No matter how much I think I know, I discover that there is always more to learn. Sometimes I feel silly taking notes in class while my co-teacher is teaching. Sometimes I think I hear them making fun in their native language. But I persist anyway. I am here for the students and I will put in my best effort, even if it means looking “stupid” in front of the kids. I want to show them that it is okay to struggle and that everyone will at least once in a while. I am not just here to teach Math, I am here to teach the students. Besides learning a bit of math, I hope that my students learn the skills of patience (because math has a reputation of creating short-tempered monsters), persistence (do the work, and the payoff will come), and that mistakes are okay (life is messy)!

The Art of Packing

Okay, I know this is way late, but I thought I would compose a list of my packing successes and regrets: a) for future reference, and b) for anyone who might be considering travel/living abroad.

Some things I was glad I packed:

• Travel sized versions of important toiletries (e.g. shampoo, conditioner, toothpaste), and full sized versions of my skincare routine.
• My pillow. I’m particularly picky about my pillows (essential to a good night’s sleep in my opinion!) so having a good one that reminded me of home home went a long way in making me feel more comfortable in my new home.
• Comfort food. It was a last minute decision, but I’m so glad my friend convinced me to bring some before I left. Even though there are lots of neat and tasty treats you can buy here in Kazakhstan, there’s something about having a sense of familiarity when you are craving sweets that makes the transition better. Besides, the labels are all in Russian, so a lot of shopping has been pure guesswork at this point.
• Plug adapter and EXTENSION CORD. By far one of the best tidbits of packing advice I read online. Saves you from having to buy multiple adaptors. Just make sure the plug for your extension chord is compatible with your adaptor before you leave… mine was not. #travelnoob
• Unlocked cell phone. As soon as I arrived, the school provided me with a sim card with a pay-as-you-go plan. Calling and texting is super cheap in KZ, the teachers tell me they spend an average of about 5 USD a month on their plan.
• A good quality camera. Excellent for documenting my travels and sharing it with friends and family, but extremely useful for taking pictures of important landmarks so I don’t get lost!
• Photographs from home. I printed out a few of my favourites before I left and packed them with me. It’s nice having some personal things make an unfamiliar place feel more like home. As an added bonus, pictures are light and barely take up room in your luggage.
• Over-the-counter medicine. I packed a few of my favourites like Tylenol, Buckley’s, and Neocitrin. Lately, I’ve noticed many students who have been absent due to illness, and a fair bit of sneezing and coughing at the school. I’ve actually caught the sniffles myself so it is comforting to know I have a supply of some medicine essentials to keep me functional. Going to the doctor’s in any foreign country can be difficult if you do not speak the language.
• A fitted blazer. A must for any professional wardrobe. The fit is key; if the blazer fits too big or too small it will look sloppy and unprofessional. (Shout out to my homies Dan and Shlow for helping me shop for wardrobe essentials before I left for Kazakhstan!)

Some things I wish I brought:

• A good quality travel back pack. When I read that the people in Kazakhstan value being “well dressed over comfort,” and then received confirmation that this is in fact true of everyone at the school I’m working with, I thought, “Screw it. I don’t need a backpack anymore! My student days are over! I’m getting a good quality purse instead.” So much regret…
• A good-quality, broken-in pair of runners. I decided to bring my lightweight sports shoes to avoid having to carry my bulky runners, but since I’ve arrived here I joined a running group comprised of a few international staff, and after going out on a couple of runs I realized that having a solid pair of running shoes makes a big difference in keeping your joints healthy and limiting the amount of blisters you will get!

I’ve been able to purchase all other things I need here for low to mid-range prices so thankfully my list of packing regrets is not sky-high. To give you an example, I was able to purchase the items below for about 20 USD in total, which amounted to less than \$2 an item.

My shopping haul consisted of: yogurt, toothpaste, shampoo, conditioner, cola, lotion, rice, a plastic container, biscuits, and laundry detergent.

Adventures in Kazakhstan – Getting The Job

Before the school year came to an end, I spoke with a school counselor in regards to my worries about finding a job and having to fend for myself in the adult world. I asked for some practical advice on the job hunt/interview process, and the top five pieces of advice he gave me were:

1. Get a LinkedIn account.  It really works! Exhibit A: my current job. Unlike visiting individual job search sites that add spokes to your wheel, networking is like adding entire wheels to each spoke (see diagrams below).

 Type of connections individual job search sites offer. Networking opens up more connections.
2. If you have an online or phone interview, don’t wear pants. Check out my version of “letting it loose” below.

An interview is already nerve-racking enough. Loosen up!
3. Always follow up. Call, email, or send a card to your interviewers to thank them for their time, and this could also be a good time to ask for feedback about the interview.

4. Practice, practice, practice, practice, and practice some more! There’s no way you can prepare answers to every single possible question they will ask you at an interview, however, you can think about situations in which you’ve exemplified a certain skill that’s relevant to the position, and practice telling that story in a clear and concise manner. If you’re like me, not practicing prior to an interview will only end one way:

Word vomit.
5. After you’re done school, take some time to relax and do NOTHING (easier said than done). Then devote a good two weeks to the job hunting process – it’s a full time job!

So, it turns out I didn’t have to spend the full intensive two weeks job hunting… I was haphazardly updating my LinkedIn profile when I saw that a friend of mine whom I worked with two years ago made a post about teaching positions available at his school. I sent him a message, and a few emails, a lesson plan, resume, and Skype conversation later, I managed to get an interview with the school!

The interview was an important deciding factor for me, because it gave me the chance to ask the interviewers about the school culture, some of the things they enjoyed most about the school, and some things they thought could use some improvement. Their responses were genuine, and they didn’t give me stock responses that made me want to cringe (“Oh the students are great, yeah, really great! [Full stop. No further explanation provided]”). Another thing I appreciated was the fact that the school sent me a sample copy of the contract to review right when they gave me the offer instead of swaying me into an agreement before I could review the terms and conditions for myself. (SIDE STORY: During my time of post-grad panic, I accepted a part time position as a tutor for a tutoring company that was a two hour bus ride away from home. It wasn’t until after the first training session that the employer revealed to me that training was unpaid. Which, isn’t the worst thing if that was the whole story, BUT I was expected to attend monthly training sessions (an additional 5 hours a month, not including the induction process), AND that bit of information just happened to have been left out of the contract.)

Tangents aside, because I was able to see myself working well with the people at the Nazarbayev Intellectual School in Taldykorgan, KZ, because they had been honest and professional in their dealings with me, and because I knew I would have at least one friend at the school, I decided to take the job.

Of course, my family insisted that I also do a sh*t ton of research before committing myself to the position, so I did my due diligence and asked as many questions as I could before accepting the offer. After that, the rest of the summer was spent vegetating at home and gathering all the paperwork that was needed to obtain my visa.

Up Next: Adventures in Kazakhstan – Getting There