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.