Unprecedented v/s New Normal

I have probably heard ‘new normal’ in the last 3 months as many times as I have heard ‘unprecedented’ in the last 13, and it is scary.

The world went through an unprecedented time in the last 1 year and forced all of us to change the way we interact with people, do our jobs, do grocery shopping, protect ourselves; basically survive. We realized the importance of societal responsibility and mental health, the prevalence of racial injustice and economic disparity and our vulnerability as human beings.

Today, at least in the United States, we have enough vaccines that we can once again hug our grandparents, hang out with our friends and plan for having all students back in our classes.After almost a year, we transitioned from thinking about surviving an unprecedented pandemic to figuring out our new normal. But, are we really going back to new normal or just reverting to old normal?

Can we take a moment to reflect on everything we did last year and see what we would like to take with us to the new normal?

I can start…
I hated teaching on zoom but I love the chat feature. It gives me an opportunity to check in with students individually without anyone knowing.

I don’t think I can teach without desmos anymore!

I missed seeing kids in person but I know some students thrived in online learning because they did not have to worry about pressures of physically being in school, they were much more comfortable in their own space.

I am devastated by all the racial hate around us but I am proud of the way students showed leadership about educating themselves and people around them, by organizing peaceful and safe protests and demanding concrete actions from our leaders.

Last year we had to slow down, take a breathe and figure out what our priorities are. I prioritized relationships over content, rigor over volume, conversations over independent work, mastery over speed and I think I want to continue doing that next year too. But this is not possible if my new normal has to include everything from the old normal too. Something has to give.

To all the leaders out there, every time you say new normal and have certain expectations/suggestions for the new normal, don’t forget to clarify what we are replacing, otherwise it is very easy to revert to the old ways and  forget that we saw racial injustice and achievement gap and inequity in every possible way around us, and then the world really would be crumbling in more ways than we can count.

Talking about January 6th

What kind of week it has been…

I am neither the first nor the last person to feel this way. It is difficult for me to put into words the emotional rollercoaster this past week has been.

The week started with the anxiety of teaching from the school building for the first time in 10 months. Then came Wednesday when this roller coaster really picked up speed. In the afternoon, when the news of the riot at the Capitol came out, I was in shock…at a loss of words. I could not process or understand what was happening. All the hate in the videos and pictures being reported was not sinking in.

Next came the feeling of double standards. Would we have reacted the same way if people in front of the Capitol were a different color or have a different religion? Did the law enforcement not remember the way they reacted to Black Lives Matter protests just a few months back? Wasn’t this so much worse?

A few hours later came the understanding of how this riot should not be called a protest…should not be compared to a protest. It was an attempt by an angry mob to inflict harm and spread hatred because they did not like or agree with what the majority wanted.

All of this happened while I was worrying about how to process this with my students the next day…how would my students of color respond? How would I explain to my students that a riot is different from a protest and that this was a riot? Would I be able to find the strength to be vulnerable enough to let them know that I am grieving with them…for the attack is on the democratic values of this country and this country belongs to ALL of us. How could I make sure that we talk about not just the political nature of this attack but also its racial and anti-Semitic ramifications? How could we use this lesson to unite us instead of divide?

When Thursday came,  as always, my students gave me hope…hope in their understanding…hope in their empathy…hope in their willingness to lead…hope in their hope…

We, as a community talked, processed, vented and healed bit by bit.

By the end of the day I was exhausted and emotionally drained, but one thing kept nagging me…

People in front of the Capitol building that day were mostly white(as far as I could see in the news), and most of them must have gone to schools and had some education.Did this mean we, as a society, are failing our children? How is it that with so much focus on diversity and anti racist practices in schools there could be so much hate and segregation? 

This weekend I did some  research into education resources pertaining to teaching students about race and race relations in this country. What I found is disappointing but not surprising. In the past decade we, as educators focussed so much on how to teach students of color that we forgot to talk much about how to teach our white students that they are part of the problem and that they can and should be part of the solution. We have numerous books, videos, articles and classes on how to teach/interact with students of color but what about our white students? How do we explain to them the idea of white privilege without turning them against people of color? 

Understanding our own biases and learning to become an ally is a journey every educator and every person should take, but how do I convince my students that ALL of them need to start on that journey sooner rather than later?

My experience so far…

I am 8 weeks into Remote Teaching this year. I have to admit it has been an adventure…
I have heard many people say this and I have to admit, it feels like the first year of teaching (and since my first year of teaching was not that far back, that is saying something!). 
As daunting as this task seemed a few months ago, I was also kind of excited. I felt like this is the year I can change things, because everything was changing anyway…
The more I thought about planning for this year, the more I reflected on what had not been working for me in the past and how I could change that.
I strongly believe that every student, every person is a math person but I always get a lot of push back about it. Last year I realized I have to convince not just the students that they are mathematicians but also their parents. The other part was to convince my students that math is beautiful and logical and so very useful. This article on abakcus.com helped me find words for my thoughts.

What I figured out was that I need to work on changing mindsets, of students and adults. I had to show them the beauty of math and its usefulness, I had to show each and every one of my students that they are mathematicians and to help them experience what a mathematician does. I had to do all of this while teaching them remotely, getting to know them and hopefully while teaching them the curriculum as well… a daunting task. 

I usually spend the first 3-4 weeks of school on community building. The only difference this time was to translate some of my usual activities online or find new activities which would get at the same thing. My objective for this first month is to get to know the kids, have them get to know each other, build a classroom community of learners and to show them that math can be fun, logical, have multiple paths to the same or different answers…
As usual, I relied heavily on my ever helpful colleagues and the amazing MtBos community. I could not have made it through these crazy times without these pillars of support.
Here is a list of activities I did to help set up my community of learners. Please feel free to suggest, modify or ignore this list:

1. Name tents : This is one my favorite first week activities, It takes a few minutes everyday but I get to learn a lot from the responses my kids give. I adapted the desmos version that Sara VanDerWerf has, changed the prompts to things I wanted the kid to answer and made sure I gave each student some feedback for the next day.

2. Google Calendar birthday invite: I wanted students to get used to using google calendar. To that end, I had all of them send me an invite to an event on their birthdays. Now, not only do they know how to set up the events but I know all their birthdays

3. Getting to know some Mathematicians: I got this idea from Howie Hua and adapted into google slides where each student upload their picture into a frame which says ‘I am a mathematician’. They not only write about themselves but also comment on each other’s slides, which helps them get to know each other..

4. Quick math conversations: This was a math twist on speed dating (again thanks to Howie Hua). I would highly recommend this activity for anyone trying to get the kids talk in breakout rooms.

5. Ultimate tic tac toe: A highly strategic game in which students can get competitive really quickly. Once they figure out the consequences of their moves, they have to really think about each step.

6. 20 words/phrases: In this activity, I asked students to list words/phrases which come to their mind when they think of a math class. Then we striked out and replaced the words/phrases we did not want associated with our classroom. This showed me not only what their experience had been but also what they are most worried about. This is another gem I adapted from Howie Hua.

Alongside these basic activities, I added in some logical math problems from my WarmUp folder. I have not collected them over the years from other teachers, different websites, brilliant.org, etc.
My students work on these problems individually but then we share all the different strategies they used to come up with answers. I do not tell them the right answer till everyone has had a chance to share their strategy. I believe this helps them see that it is ok to make mistakes and explaining their thinking helps them learn.

All of these little things, little activities, feedback loops and moments of connections are now paying dividends. Most of my students now look forward to sharing their strategies with their peers. They are not afraid to admit or point out a mistake respectfully, most importantly, they like to explore math for exploration sake. 
Very recently, while reviewing rules of exponents, we came to zero exponent rule. One of the students asked me why is that true. I used the ‘catch and release’ technique and posed the question back to the class. Very soon, the entire class was involved in a discussion about it. In 20 min, they were able to prove the rule and I could not have been prouder.
These small moments of victories are what keeps me going and makes me smile. I hope all the educators out there gets to experience the same joy!


Happy Father’s Day!

A few weeks ago, a student came to my office hours (distance learning!) and asked me for help with a problem. She told me she is stuck and doesn’t know what to do. I asked her to try the problem right then. Miraculously, she solved the problem. She said, “Ms. K, I should just do all the problems sitting in front of you. You don’t even say anything but somehow I am able to do the problems when you are there!”

Her statement took me back to my childhood. I used to often joke with my Dad that I should just carry his picture to all my tests because I can always solve the problem when he is around. He never used to tell me how to fix my mistake or what the mistake even was, the most guidance he would give me was to point me to the part of the problem; beginning, middle or end; and even that was rare. He would just sit there and watch me flail….and miraculously I learnt to swim. 

Thank you Dad…

What he gave me was so much more important that instruction or motivation. He gave me BELIEF….My father, with no background in teaching or education, was the definition of a Warm Demander. He, through his action and his words, taught me to believe in myself and my ability. He also instilled in me this unwavering belief that he will be my Champion if I need someone to push me and my Cushion who I can always fall back on.

That is the kind of teacher I aspire to be…but how? What can I do to make sure ALL my students BELIEVE…In this world where they are told everyday not to believe…not to believe in themselves…in the society…in the news…how do I show them that I believe in them and their abilities? That they should believe in themselves?

Instead of a final exam, I asked my students to reflect on their learning this year. Francis Su inspired me to focus the reflection on the virtues that math can instill in us. My students reflected on their perseverance, curiosity, thinking for oneself, creativity and their idea of beauty. Here are some of their responses:







These reflections showed me just how much my kids have grown over this past year…how much they have learned and how ready they are for the future.

As the school year is ending, I think, it is time for me to reflect as well. Reflect on what worked this year, what did not. Was I able to instill belief in some of my students, who did my strategies work for and why? I don’t have answer to all these questions…yet…but I will keep looking and experimenting.

For now, I would like to wish all Fathers and Father-like-figures,  a very Happy, Peaceful and Joyous Father’s Day. You are more important to us than we let on! Keep believing in us so that we can believe in us!

Looking Forward…

As I sit in my makeshift office, instead of jumping around in my classroom, trying to plan activities which can engage my students from afar, I can’t help but think about how my students are dealing with this isolation and fear. I am sitting in front of my computer trying to come up with a list of objectives and time and again I keep coming back to critical thinking and problem solving instead of algebra and geometry as objectives for my lessons.
Everywhere on the internet I see people talking about the growth of the COVID-19 virus and how to turn it into a lesson or activity and all I can think of is the need for out of the box thinkers and problem solvers in this world. That is not to say that understanding the growth pattern is not important but I believe it is perhaps more imporatant to analyze what we could have done as humans to help the situation, what we can do now.
That is what I want to teach my students. That is the lesson I would like us to take from these unprecedented times. This is the time for us to be creative, to be courageous, to collaborate, to find peace and beauty in things we usually would not…
I can not think of a better medium than mathematics to do just that. I am taking this time to prepare, for whenever I see my students, to teach with a focus on life skills. I am taking this time to solidify my resolve of not getting bogged down by the need for tests and quizzes, but create assessments which teach my students the life skills I want them to leave school with, be it partner tasks or project based assessments, or designing a solution for a real world problem. I am taking this time to teach via exploration, to focus on inquiry more than the procedure. 
If you can think of any activity, lesson, assessment idea which I can use for my high school students, I am all ears. Please reach out. We are in this together. I would be happy to brainstorm ideas.

What do you think of mathematics?

Is it easy for you or hard? Do you think it is important and why? Is it procedural or creative? Is it logical or intuitive? Is it abstract or concrete? Is it something you want to learn or something you have to learn? These are the questions I wanted answered when I asked my students to do fill in this free write using the essay “A mathematician’s Lament” by Paul Lockart.

What I received was an insight into their thinking…how they perceived math and math education. Everyone agreed math is important to learn but most of my students said we have to learn because that is what society (colleges, parents, peers) deems important. They did not see how it related to real life or whether it could ever relate to something they would care about. As an engineer and a math teacher, that was heartbreaking for me. 

Now it was my duty to show them the wonders of math and its connection to their lives. Everything from game development to art projects to collecting and analyzing data about the community, it was my duty to show them the mathematics I love. I have strived to do just that this past year.

Lately, my students have been working on art project using demos. We are learning about functions and they are exploring different functions and their domains and ranges to show their creativity. This is an opportunity for them to tell me what they are passionate about and why.I have one student making a scaled working model of the solar system because he wants to be a astronaut and another drawing a beautiful whale because that is her favorite animal in the world (after cats :)). One student is tracing one of her actual sketches using functions…I knew she was artistic but I did not know she drew such beautiful sketches. 

This project is reaffirming my belief in project based learning…not only because these kinds of projects gives me a chance to learn more about my students but also because they are a more realistic form of assessments. Life in the real world is rarely about taking a test but often about applying everything you learned to different situations

I would be doing the same free write with my students at the end of the school year…so that I can see how much we have all grown and learned

Are application problems the only way to make math engaging?

Every time I say to a group of math teachers that I want to make math more engaging in my classroom…inevitably the first suggestion has been to incorporate more real world applications. Great idea but what about the content areas which don’t have grade appropriate application problems…like complex numbers.

Complex numbers or imaginary numbers are taught in sophomore year but I am yet to find an application problem…engineering? Not everyone finds it interesting…

This year I decided I am on a mission… I will find a way to make imaginary numbers interesting and engaging. 

I started the lesson by asking the students about the need for  natural numbers and why as humans we started using them. The students went on an exploration of invention/discovery of numbers, specially zero. Then we talked about the advancement of the human race and our evolving needs.
There came a point when we had all the numbers we needed but humans started applying those numbers  in geometrical shapes and constructing buildings. That is when we felt the need for irrational numbers. On the other side of the world, Al-Khwarizmi was writing the Kitab al-Jabr to teach the world about algebra. 
I had the most insightful conversation with my students about this. We discussed need of math for survival and need of math for exploration and discovery. That is when I introduced the concept of imaginary numbers as a way for humans to explore equations which do not have real solutions. 
This was the first time not even one student asked me why we learn this…their reflection at the end of the lesson was positive, showed engagement and understanding. Most importantly, this lesson marked an important milestone in our learning community as a turning point for the need and importance of mathematics. 
This is not to say that connecting content to real world application based problems is not the way to make it engaging, but I think when we focus ONLY on that, we miss out on the beauty of mathematics, its logic, its patterns, its creativity and exploration.

New Year…resolutions…?HOPES!!!

As the year is coming to an end, I have been thinking about steps I am going to take to improve my teaching practices, to help all my students and to grow myself as an individual. Being a classroom teacher does not leave me with a lot of time and energy to think…I am hoping this will help me keep my priorities at the forefront of my mind…even when that’s the last place I look for them!Here is THE list!

1. Be Courageous: I will try not to be afraid of trying new things, of being open to more ideas. I will seize every opportunity I can, to get out of my comfort zone…whether that is trying a new teaching technique or talking about that technique in front of an audience.

2. Listen More, Speak Less: I will listen to my students more. Everything they say matter to me and I will make sure I give them every opportunity to express themselves…in class and outside. I will try to plan lessons which are more student centered and gives them the agency to inquire and explore. Instead of being a sage on the stage, I will be a guide on the side.

3. Homework: I will be more cognizant of what I am assigning as homework and why. I will try to get away from repetitive worksheets and focus on problems which form connections and are more open ended. Mathematical Mindsets (Jo Boaler) has made me take another look at ‘Practice makes perfect’  system I grew up with.

4. Assessments: I will revamp assessments of at least 5 units I teach. I want students to be able to show me their understanding and not just regurgitate the procedural knowledge. I worked on 2 units this year (Exponents and Probability), hope to work on a few more next year.

5.Leveling: I am not saying I will fix leveling in 2020, but I will work on it. This year I have struggled with its affects and causes, pros and cons. Next year, I will focus on what I can do about it…research, talk to decision makers, talk to teachers…I am open to all ideas.

Lastly, I will be KIND…to others and to myself. I will practice self care and I will take on only what I can manage. Easier said than done, when I have just agreed to teach a whole new course next year…

Make Math Moments Virtual Summit (Part 2)

Here are some more takeaways from Make Math Moments Virtual Summit. Please feel free to take a look at part one of my takeaways here.

4. Let me start with the session with Jennifer Withall. She is a pioneer of concepts based mathematics. She believes that information without intellect is meaningless. She is a great presenter and I walked away from that session reflecting about how I can incorporate more inquiry and discovery in my classroom, how I can focus more on student understanding along with the skill retention, how I can assess that my students understand the content. As Jennifer said, students understand the area of all rectangles and any quadrilateral can be derived from a rectangle. Taking a cue from that, I encouraged my students this week to derive the formula for the area of a trapezoid in multiple different ways. Later on I had students come up to me and tell me that this was the first time they understood where it was coming from. That is when I used Jennifer’s words: You should think about ‘what will I understand as a result of my understanding’!

5. Next session I would like to talk about is Sara VanDerfWerf’s session on Secondary Math Talks.  I have been following Sara’s blog for a while and it was an absolute delight to learn from her. Number sense is..”good intuition about numbers and their relationships. It develops gradually asa a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms” —Howden 1989
Sara strongly agrees with Howden and believes that math is the study of patterns. She wats students to notice, describe and generalize pattern. For a while I had been trying to do number talks in my sophomore classrooms. Some were going well, some not so well. After listening to Sara I realized, I need better norms and more consistency around math talks. Sara went over the protocol and norms she uses with math talks, which are as follows:


  • 1. Teacher poses problem
  • Pause and give student a chance to think mentally
  • wait for a visual clues that ALL students have some general idea 
  • Call for answers
  • Share their thinking and give evidence of their thinking6. Record their thinking


  • Nothing in your hands : Students are not distracted by papers or pencils or whiteboards
  • Knees pointing forward : They are doing some individual thinking 
  • No Blurting : Everyone is given a chance to think
  • Fist to chest : No raising hands
  • Thumbs up : Signal to the teacher that I have at least one way of solving the problem 

I was so excited by these norms that I used them the very next day in my classroom and the math talk went exponentially better. More students were engaged. Since I waited till everyone had at least one strategy, students felt they were more accountable. We could talk about the different strategies without the same 4 kids yelling out answers.My role in this process was, as Sara said, that of a facilitator, listener, questioner, learner and answer recorder. I have been doing math talks for the past few weeks now with some regularity. With one particular class I was struggling with the lack of number sense the students were exhibiting and I honestly think this is helping. Something I am struggling with now is how to get all students to participate and share, I don’t like cold calling but if I ask for volunteers, more often than not it the same students. Other than that I think my students are now more eager to explain their thinking, they are thinking and analyzing numbers and not just looking for procedures. They are becoming mathematicians!

6. Peg Smith, in her session, talked about ways of ‘Orchestrating Productive Discussions’. She is also one of the authors of the book, 5 practices for orchestrating mathematical discussions. I was very happy to hear that they have a book specific for high school students about orchestrating discussions in math classrooms coming out in spring. Peg was very articulate when walking us through the 5 practices in her session. Some of my notes from her explanation are as follows.

a. Anticipating: Think about all possible answers and questions.- Correct, incorrect, incomplete answers- What are you going to do when they do it?- What questions are you going to ask?- Which strategies will be most useful in addressing the math to be learned

b. Monitoring: Float around the classroom- At the end of period you should have a sense of who did what- Keep track of approaches that students are using

c. Selecting: Be strategic about strategies that are shared with the class.- Think about strategies and math that will be focus of class discussion- Make sure over time all students have the opportunity to be seen as the authors of mathematical ideas

d. Sequencing: Be strategic about the which order hte strategies are presented- Purposefully ordering the solutions that will be presented- Building a coherent mathematical story line

e. Collecting: Collect and cosolidate all ideas.- Ask questions that focus on mathematical meaning, link different strategies and representations-Make sure all students are making sense of the ideas

Towards the end, Peg mentioned Practice 0 which is setting goals and selecting a task (involves identifying a high level task that aligns with your goals and provides all students with access) which, as the name suggests, comes before all the other practices. You need to have a task with high ceiling and low floor which all students can access and then orchestrate discussions to bring about the best mathematical thinking from your students.

Combining techniques from Sara and Peg, I can see a significant improvement in discussions and math talks in my classrooms.

7. The finale of the conference for me was the session by Dr. Raj Shah. He is the founder of math plus academy and co-founder of global math project. The first thing that I remember from this session is, Raj quoting one of my favorite quotes about math. 

“Mathematics is a rich and fascinating adventure of the imagination”-Paul Lockhart

He then talked about how students are engaged in videogames and ways in which we can make learning math as engaging as playing videogames. He analyzed what keeps students engaged in games and talked about ways of incorporating those characteristics in teaching math. Here are the keys points he mentioned.

a. Math is intrinsically irresistible:

– Problem solving is the heart of mathematics
– Provides opportunities for perseverance- Students perform better on standardized tests
Problem solving is a means of learning math and not just a way of applying itWe just need to make math taught in schools more about problem solving and less about repetitive skill practice.

b. Everyone can do math:

Somewhere each one of us is going to fail at math whether that is in first grade or at PhD level. We need to make our students realize this too. We need to model for them that failing is ok. It is actually great as long as you can learn something out of that failure.

c. Teachers need to craft learning experience …like a video game designer:

Playing a game is a voluntary attempt to overcome unnecessary obstacles. Raj talked about ways game designers ensure that people would not just voluntarily, but happily and willingly play their games. They do that using the following techniques:

-Player has control of the action. (Can we make our students the Heroes and Heroines in their Math journey?)

-Always make you feel like you can catch the bus by making the 1st level of the game ridiculously easy (Can we design tasks which are accessible to all students?)

– It is fun to fail but only if the game seems fair and you have hope for success (Can we show our students that math is fair and logical and it can be fun to fail?)

– Descriptive feedback (Can we make sure students have answers to these questions?)

  • Where am I going?
  • Where am I now?
  • What is going well?
  • How can I improve?
  • What did I learn?

– Video games don’t take away their achievement:

When asked why they like video games, students generally say, video games don’t judge me!! (How can we ensure our students feel safe and comfortable in our classrooms so that they can take risks, collaborate and focus on solutions and not answers?)

I think it is time for me to quit saying that I get frustrated when all my students want to talk about is video games they play, and step into the shoes of the game designer and understand and design my lessons so that my students can be excited about them as well.

d. Learning starts with curiosity:

Raj said, “The biggest problem in education is the giving of answers to the questions which have not yet been asked”. I completely agree with his statement. So much so that this year, one of my personal goals was to not write on a students paper when explaining. I have stopped carrying a pen or pencil with me when I am floating in the classroom. I have become extra careful about asking guided questions to pique their curiosity as I also agree with Raj, that curiosity enhances learning and creating a gap between known and unknown in essential for that.

e. Math is best learned doing together (not being told):At this point, he mentioned the 5 Practices by Peg Smith and I was blown away by how the math educator community supports each other and learn from each other. He talked about the importance of collaboration and discussions and I was once again reminded of everything I learned that day from Peg Smith and Sara VanDerWerf

At the end of these 2 days, I had not done any lesson planning, I had not replied to any emails or graded any assessments or assignments, but I felt accomplished. I wanted some time to reflect about my practices through the various new lenses I had acquired. I felt like I learnt so much and I was eager to implement so many strategies and techniques in my classroom. That Sunday I did not have Monday blues, instead I felt like next day was going to be Motivated Monday

Make Math Moments Virtual Summit (Part 1)

My takeaways from a phenomenal learning experience…

A huge shoutout to Kyle Pearce and John Orr for organizing this wonderful learning opportunity for newbie educators like me who are eagerly looking for any chance to learn. The list of presenters was phenomenal and as much as I try, I don’t think I would be able to do articulate everything I learned.

Here is a little background about me and some idea of what I believe in and what I am struggling with:

I am a math teacher in a pretty good almost urban high school in Massachusetts, United States. This is my second year teaching math to highschoolers. I am an engineer by qualification and a teacher by choice. Actually, now I am qualified to be a teacher also but…you get the point. I have never been happier and I have never been more tired! I was not born or raised in the United States, so the education system here is fascinating and perplexing to me. The idea of no centralized education system is foreign to me and I am coping with the non sensical (in my humble opinion) standardized tests we have in US and the idea of standardized tests I grew up with in India. I am struggling with extra time as an advantage to a few versus the need of many. I am going back and forth on corrections on assessments and the false security it gives students and parents by inflating their grades. I see the need for better assessments and I see the need for fair assessments. I see the need for discovery and inquiry and I see the need for mental math and practice. I recognize the benefits technology brings and I struggle with putting it to best use. To sum it up, I am a teacher. I am constantly looking for ways to be better, at teaching, at understanding my students, at helping ALL of them, at being equitable, at being there for them, at finding time to plan better lessons, at executing those better lessons, at changing them on the fly and at being a happy, healthy individual.
As you can see from the rant above, I have a lot to learn (how to be diplomatic being one of them), I am eager to learn and experiment and I am willing to do everything I can to instill the love for learning in my students.

The Make Math Moments virtual Summit gave me such an opportunity. Since it was over a weekend and since it was virtual, I could sit in my study all day and learn from and interact with educators all over the world.

1. The first session I attended was Jo Boaler’s. She is a Professor of Education at Stanford university and a pioneer in math education with her work on mathematical mindsets with two phenomenal books about the same (‘Mathematical Mindsets’ and ‘Limitless Minds’). While listening to her, I realized that the the resource website (www.youcubed.com) that I have often used has also been developed by her. To anyone looking for engaging students, promoting critical thinking and problem solving skills, I would suggest checking this website out. It is a treasure trove of activities for multiple content areas and grade levels.
In her session, Jo talked about things we know about brain and learning in 2019. Here are some excerpts from her session. 
(i) Brain growth and change: Every day we wake up with a different brain. It is ever changing and growing, even for adults. Adult brain changes significantly every 8 weeks. Just imagine the potential of a school student.

(ii) Beliefs change the brain: What you believe about yourself changes your brain. If you think you can be good at math, there is higher chance that you would be. Also, growth mindset is important for productive struggle because it is easy to give up but persistence requires growth mindset.

(iii) Connected brains are growing brains: When we think in different ways about the same thing, we make more connections. Jo called this flexible, creative, elastic thinking. 

As an example, Jo used Cathy William’s Method of Diamond paper. In this method, Cathy asks her students to fold the paper like a diamond. For every problem, students are asked to give a visual solution, a different visual solution, to write a story, and to solve it numerically. This encourages elastic thinking and I think it also alleviates some fear around word problems that I encounter in high school students.One thing that stood out to me from this session is that Jo mentioned that when people are stressed, their working memory is blocked which means that timed tests are the enemy of creative thinking. How can we expect our students to think out of the box on a test when they lose points as soon as they start writing? This session left me wanting to read her books and also to start thinking about assessments. I am preparing student to take SATs and ACTs and APs but at the same time I am also preparing them to solve the problems of the world. Since this session, I have been thinking a lot about how to balance both.

2. Next came the interactive session with Hema Khodai titled, “Who is a mathematician?” Even though I thought I could empathize with so many of my students as a person of color with a name only few can pronounce properly, I came out of this session with a new found understanding of the importance of equity and identity in my classroom. Hema asked us to think about WHY we teach and reflect on how we encourage equity in our classroom. I was surprised to know that from freshman year to graduation, the half life of students is one year. This fact made me think about my actions which might make my students feel unwelcome and unwanted. As Renee Brown said, “Sometimes the most dangerous think for kids is the silence that allows them to construct their own stories – stories that almost always cast them as alone and unworthy of love and belonging.” Long after the session ended, I kept on thinking about ways to make my students feel welcome and worthy human beings and mathematicians. The stand out feature of this session was the Unforgettable video we saw. I have to admit that I saw this video multiple times and it resonated with me on so many levels. I personally know of people who changed their names when they came to the United States, so that it is easy to pronounce. I know of parents-to-be thinking about baby names which everyone can say so that their baby does not go through what they went through. I tell my students that they can call me Ms. K instead of Ms. Kant so that I don’t have to keep correcting them. For now, I have decided to stop doing that. I will model for my students the importance of identity. I will tell them my name and help them say it properly and then make sure I say their names the way they want.

3. James Tanton’s session, as usual, was creative, fun and informative. His perspective about math is at the same time both fascinating and baffling to me. To me, he is an extremely creative mathematician who is exceptionally adept at looking at the big picture of math education and at connecting various concepts across grade levels. The first thing I remember him saying is that Math is human! I have to admit as much as I love math and everything it represents, that would not have been my first thought about it. I would have said that math is logical, math is creative, math is honest, math is beautiful. When I thought back to what he said, it made complete sense to me. Math is all the things I think it is and that is what makes it such a human endeavor. It evokes human reactions in us. It makes us follow the rules and it makes us think outside the box. It makes us feel euphoric and dejected. Math is human!James then said that the first thing to do when you see a math problem is to your honest human self and to acknowledge the reaction that you have when you see the problem, be it happiness or confusion. After that he said, we just need to Do Something…Anything!
He then went on to talk about the 5 guiding principles of doing something: 

a. Don’t answer the question given to you…answer an easier one instead

b. A picture speaks a thousand words!!! Utilize the power of visualization

c. Work hard to avoid hard work. Think of strategies you can use to reduce the amount of work you have to do.

d. Seek the story behind the topic at hand.

e. Got haze? Walk into the hazy thinking. Do not be afraid. Sometimes it has to get complicated before it simplifies.

James demonstrated these steps by posing the question, ” How many degrees are there in a MARTIAN circle?”Using this seemingly innocent question, something you can google and find the answer to, he demonstrated how we can understand the concepts of degrees and radians and trigonometric ratios. Honestly, the next free moment I got, I went looking for his videos and books in which he talks about this concept again. I am yet to see a better testament to the importance of stepping back and looking at the big picture. What I walked away with from this session? All of us need to DO Something!!!!

Thank you for your perseverance in reading my thoughts. I will add more to this blog about some more amazing sessions I attended. Stay tuned!

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