How not to have a ‘teenage debate’

I work with teens and most of them love arguments and debates [i love debates as well!] But debating is a form of art.  Some of my students have not mastered it yet, so they often end up having a ‘teenage debate’. A ‘teenage debate’ is a discussion where participants criticize each other instead of each others’ ideas, blame each other for not understanding their points of view, and  – most importantly – everyone is very poorly informed about the topic of discussion. Another characteristic of a ‘teenage debate’ is that it gets started to procrastinate on some real tasks that the students have to do at a given moment.

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Essentials for a freelancing math teacher

I’m a math teacher and a graduate student. I don’t teach at a public school. Instead I teach at special programs for gifted children, or work with children individually. I guess that makes me a freelancing math teacher. Continue reading “Essentials for a freelancing math teacher”

Fields Medal Symposium 2016

There’s no Nobel Prize in math but there’s a Fields Medal which is given to mathematicians under the age of 40 for their outstanding achievements. Every year Toronto’s Fields Institute hosts an annual Fields Medal Symposium to honor one of the medalists. This time we have Prof. Manjul Bhargava  – a number theorist born in Hamilton – is the honored guest.

Prof. Bhargava is the first Canadian born mathematician who received the Fields Medal! This makes this year’s symposium even more special. There were no empty seats in the Isabel Bader Theatre where the Public Opening of the Symposium was taking place yesterday evening. The audience was composed of professionals from a variety of fields and students. Prof. Bhargava’s talk was engaging and accessible for everyone in the audience.  Colorful diagrams and interesting facts about nature that he mentioned were especially appreciated.

We brought our Math Circles class from UTM to the public opening. This was their first time attending such a large event.  Luckily, they enjoyed the talk and the festive atmosphere around the Public Opening night.  Moreover, they even had a chance to take a picture with Prof. Bhargava!

Prof. Bhargava will be giving a special lecture for high school students this evening at the Fields Institute, but unfortunately I will not be able to attend it, cause I’ll be teaching my own students.

If you want to find out more information about the Fileds Medal Symposium, click here:


Math Snippet: Graphs, Instagram, Internet


I’m taking an online course on graph theory now and the lecturer is so good that listening to him is like watching an engaging movie.  His language is simple enough and he does not assume any previous knowledge of higher level math (just high school knowledge). For now, here are some very basic snippets about graphs:

Imagine we have a classroom full of desks that can seat two people.  We could represent people as dots (vertices) and connect these dots with lines (or edges).  We have created a graph that provides us with information about the pairs of students, the ways they are paired up.  More formally, graphs are structures that describe pairwise relationships between objects.

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Math Anxiety Inducing Phrases

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I became a contributing author for Lifehack.Org

Here is my first post about math anxiety inducing phrases that all of us should avoid when talking to kids about math or academic subject matter in general. would not appreciate if I just pasted my post here, but in short, whenever you  talk to kids about anything math related, avoid emphasizing that math is only for the ‘geniuses’, that you were ‘never good at it’, and that it is ‘too hard’. You never know how these phrases can be misinterpreted by kids, and most likely they will be used against you (or against math and other academic subjects) at some point down the line.

Do you know anyone suffering from math anxiety? Were you anxious about math when you were at school?

Teaching an online course: Online Math Kangaroo Enrichment Classes

This summer I have been teaching a Online Math Kangaroo Enrichment Classes for grade 4.

In each class we looked at several core concepts and then solved numerous problems that resembled problems from Math Kangaroo Contests.

Teaching an online class was a new experience for me and I am extremely happy that i had a chance to try it.

The trickiest part about teaching an online class was finding an effective way to communicate with the audience.  This challenge, however, could be resolved by asking the students to ‘raise their hand’ (by clicking an appropriate icon) and typing their questions in the chat window provided.

I found that giving the audience plenty of time to think about each posed question on their own.  Providing sufficient time allowed the students to understand posed problems and to formulate meaningful questions afterwards.

This summer the audience was quite active and well prepared for each class.  Although the group of students was quite diverse in terms of academic background and age, everyone caught up to the same speed and academic level very fast.

I am quite proud of my students and I wish them the best of luck in their next academic year and the upcoming Math Kangaroo Contests!

Although the summer course is over, please see the related information at  and stay tuned for information on further classes


Classroom Adventures in Mathematics Summer Institute 2014

Last week Department of Mathematics of UofT welcomed school teachers and teachers in training for a week of professional enrichment – Classroom Adventures in Mathematics Summer Institute 2014.  UofT faculty and graduate students spoke to the teachers about enrichment of traditional curriculum for students of different ages and academic backgrounds as well as highlighting the wide possibilities of interdisciplinary studies of STEM subjects.

Please see to read more about the covered topics and stay tuned for the videos of selected lectures that will be posted soon!

Meeting experienced teachers from local school boards was an invaluable learning opportunity and I am very glad that I could be a part of the program!



Canada Math Camp 2014


Last week I had a pleasure of being a camp coordinator of Canada Math Camp! Working at a camp is always intense but very exciting.  Although it can be tiring at times, I can’t wait to do it all over again already!

Canada Math Camp is for students who achieved high scores at the Canada Open Math Challenge (COMC) or for those who were recommended by their mathematics teachers or other members of the mathematics community.

Check out our daily updates here:

General information about the camp can be found here:

If you re feeling nostalgic for the last year’s CMC camp, CMC 2013 info and daily updates can be found here:


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Geek Street Fair powered by Google – Toronto Distillery District


Last Thursday I, along with a great group of volunteers, had a pleasure to participate in the Toronto Distillery District Geek Street Fair powered by Google.

The event was designed to demonstrate how fun and exciting STEM subjects can be.

Read more about this event at out new website at

Math Kangaroo, Mentorship, Girls in Gear

It has been a long time since I posted any updates, and I want to thank all the guests who have been reading my webpage during that time.

Here are several events that took place recently:

Mathematics Kangaroo Contest took place on March 23rd across Canada.  All three University of Toronto Campuses were involved.  The students and the staff had a great time! Visit to register for the 2015 Math Kangaroo Contest!


Math In Motion…Girls In Gear  (April 5th).  It was a great honor for me to be one of the guest speakers and to teach grade 9 students about ancient calculation aid – abacus. Then they even made their own abaci and took their creations home!

Girls also braved the Design Challenge task that required them to build a container for an egg that needed to be thrown off the third floor! Guess what – most eggs survived this adventure without a slightest crack!


Mathematics Mentorship – Poster Presentation Event. 25 high school students were paired up with UofT Math department graduate students and professors for a semester-long mentored studies.  The students demonstrated their newly acquired knowledge during the end-of-the-semester poster presentation session.  Please see the details of other outreach programs offered by the U of T Math department at


Kangaroos are coming!!!

Last weekend all of the University of Toronto campuses hosted the last preparation session before the Mathematics Kangaroo Contest of 2014! The students and the instructors had a great time. The kids couldn’t wait to write the contest!

The contest will take place tomorrow! Math students all over Canada will be writing it. If you are planning to participate, you still have the entire Saturday night to try some of the contest problems from last year.

You can find them here

Good luck for tomorrow’s contestants! Have some good night sleep and we will see you on Sunday morning!

Math and Comp. Sci. High School Teachers’ Workshop

 Today I was honored to be one of the speakers at the Math and Comp. Sci. High School Teachers’ Workshop at the University of Toronto at Mississauga.

Here is the link to the workshop program

I was speaking about methodology of history of mathematics, math education reforms in the US and in the USSR and various ideas that modern teachers can  draw from them and successfully use in the modern classroom.

I could not only attend one other talk –  Nifty Computer Science Assignments by Daniel Zingaro – and it was a great! We learned about various ideas for assignments that stimulate the students to go above and beyond the course content.  


Happy Pi-Day!

The Math Kangaroo Camp is over, and I have to say that it was an absolutely amazing March Break week! The weather prepared a surprise for us on Wednesday – 10 cm of snow in just several hours, just when all of us thought that the spring is on its way.


Then on Thursday the temperatures dropped drastically, but the Math Academy students braved the icy wind and went on a mini Filed Trip to the Fields Institute.

Friday – Pi-Day! That is a great rhyme, and certainly a great way to end the March Break week!

Congratulations to all of the camp participants and instructors! Can’t wait till the Summer Math Kangaroo Camp already!

Math Kangaroo Campers get antiquated with Platonic solids

Math Kangaroo Campers were making platonic solids this morning. They did a great job! See the pic at

Math Kangaroo March Break Camp 2014 has started!

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I am so excited to be working at the Math Kangaroo March Break Camp and Math Academy this week! The camp started out on a great note. For instance, grades 4 and 5 started their day by looking at crocodiles from a mathematical point of view! Picture can be found here:

Fields Institute wins!

Last week, and the week before, we were visited by a group of students from St. Andrews Junior High School. They chose to come to the Fields Institute even though they could go to the Playdium or any other place in Toronto for their activity day!

I gave them a mini lecture on history of calculation devices, and then they created abaci from scratch. Here is a link to their photo:

Science Unlimited


This week I am working at the Science Unlimited Summer Camp at U of T (

Every day packed with experiments, mini research projects and tours of UofT’s best research facilities.  Every department involved in the camp (Mathematics, Physics, Forestry, Chemistry, Astronomy, etc) has impressed the students with something unique and totally different from a usual high school curriculum.

If you want to know the details of our whereabouts, the daily updates that I have been writing are posted on

Stay tuned for the rest of the week!

WHERE pigs fly…

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When was the last time you have seen a piggy with wings? I have seen one this morning! And, as you see, I have a picture to prove it 🙂

I am working at the Math Kangaroo Summer Camp at U of T right now and it is housed right next to a physics lab.  This morning when we came in to set everything up, this is what we found in that lab: a flying pig and an airplane.

So next time when you tell someone that you will do something only when ‘the pigs will fly’, be careful! They might bring you to this physics lab!

If you want to see the live updates from the Math Kangaroo Summer Camp at U oft, go to

Work day of a mathematician

 “What does a usual work day of a mathematician look like?” (grade 8 student)

“Unlike writers and novelists, mathematicians do not even publish their work too often. What do they do all day?” (grade 9 student)

“What do professors do when they are not teaching undergraduate courses?” (grade 11 student)

“How do researchers manage their time when they do not have strict deadlines to follow?” (grade 11 student)

“How do co-authors work together when a lengthy research project needs to be completed?” (grade 9 student)

These are some of the questions questions that I often hear from high school students and even from junior undergraduates.  Most students do not observe mathematicians at work too often, so their questions are perfectly valid.  Every student knows what a shoe maker, a chef or a painter does because they see the direct products of these people’s work.  The situation is different with mathematician because often the outcomes of mathematician’s work cannot be immediately observed. Thinking about problems and experimenting with various solutions could take days, weeks or even months! Many attempts to solve a problem could fail.  Extreme persistence is needed to keep going forward and to avoid quitting. So, really, how do mathematicians keep themselves on track every day? How do they stay productive and motivated?  The answer is different for every mathematician. For example, here are some strategies for balancing academic work and hobbies that professor Andrei Kolmogorov and his co-author professor Pavel Alexandrov practiced:

First, they chose a pleasant setting to work in.  Both professors adored nature and often spent 3 to 4 days of the week outside Moscow in a cottage near a small river. Second, professors placed great value on physical activities to keep their minds fresh.  Their day usually started at 7am with various sports-related activities.  Both preferred taking walks and hikes every day after lunch (2pm) and short walks before bed time (10pm). Third, Kolmogorov and Alexandrov dedicated lengthy unbroken time periods to their research (usually from breakfast till lunch and from 3pm till dinnertime).  Fourth, both researchers did not neglect their shared hobby – music, and dedicated some time to listening and discussing various records every day. Fifth, professors aimed to get about 10 hours of sleep every day.  That often included short naps during the day.  Of course, when their research was going especially well, they altered their schedule and often spent entire days discussing the solutions to the posed problems.

In summary, in order to stay academically productive and motivated, try following these five simple suggestions:
1)      Find comfortable setting to work in
2)      Find common interests that you share with your co-author and dedicate time to pursue these interests
3)      Exercise regularly and get plenty of fresh air
4)      Get enough sleep!
5)      Organize your day in a way that will allow for lengthy unbroken work periods
6)      Be flexible in your planning and don’t hesitate to change your routine!
What do you think of these tips? Would you dare to try living several days by this demanding schedule?

Note: most of the information about professor Kolmogorov’s work habits was taken from the interview published in the “Quantum” (Квант) magazine in 1983.

The original version in Russian can be found here

The image is taken from

Canada Math Camp

This week I have been working with the Canada Math Camp (

Here are the daily news updates that I posted on the CMC website



photo from