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:

Protocol: 

• 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

NORMS:

• 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.

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!