A British Math(s) Teacher now living in Indianapolis, USA, aiming to show my students how questions are often more important than answers. Presenter of the 360 Podcast, the MathEd Out Podcast and contributor for the Guardian Teacher Network.
Welcome to the first episode of season 3 of the 360 podcast! In this time of returning to in-person instruction during the global COVID pandemic, we chat with Brian Simmons, a mindfulness teacher and educational leader from Manhatten, NY. We discuss ways that we can use mindfulness and meditation to help us teach and learn well through this uncertain time.
About Brian Simmons from brian-simmons.org:
“I was an award-winning writer/producer for Comedy Central, and was suddenly struck down with a 10-year debilitating illness that changed my life trajectory. It sucked, but it was totally worth it.
Along the way, I learned very deep lessons about how Mindfulness and ancient wisdom can help a person exactly when they need it most – when life doesn’t cooperate. Today, I am an educational leader and mindfulness teacher in NYC, and I use this experience to relate directly to real people with no time for nonsense.
Regardless if you are a skeptic, seeker, educator or student of any age. When I was first introduced to meditation culture in the 90’s it made me cringe. It still does sometimes, but the practice of Mindfulness changed my life. And, it blew my mind. I believe it will do the same for you.
I’ve spent decades practicing fiercely with some of the best meditation teachers on earth. I’ve completed teacher training at the Center for Mindfulness at UMASS Medical College and am a graduate of the Community Dharma Leaders program at Spirit Rock Meditation Center in Woodacre, CA. I also serve on the teacher’s council at NY Insight Meditation Center in Manhattan and am a meditation teacher on the 10% Happier App. I’ve learned powerful techniques and perspectives that work, and I love sharing them with people.”
I’m planning out my start of year classes and it’s just beginning to hit me that I can’t do group work in the same way, and I can’t walk around the class in the same way, and I won’t be able to help a student in quite the same way. Students will be wearing masks, and will be sitting 6ft apart. With a strong belief in learning being a social activity, this semester is going to be like no other.
However, my priorities remain fairly consistent, although how it looks will be different this year, especially as I may need to be able to pivot between in-person and virtual learning for the foreseeable future. They are:
To give the students a positive and engaging experience of learning mathematics
To help students learn collaboratively
To help students to become learners, reflecting on their own progress and being able to adapt accordingly
In summary, my priorities for the year, whether in person or through the computer, are Connection and Reflection.
Connection: This will be especially true if we end up going fully online, but the more ways the students can connect with each other the better the learning will be.
Reflection: This has always been important, but in a time where we can not really meet with students one-on-one, we have to get creative in terms of helping students to reflect on their own learning.
Here are some tools that I will be using for student connection and reflection in the coming weeks:
Flipgrid is a k12 social platform where students can share videos with each other and with their teacher in a safe and transparent way. This is a great tool for general introductions, class social interactions, or creating reflection videos for assignments.
With some phenomenal options for sharing thinking between students and giving teachers full access, Desmos Activity Builder is a must-have in the connected math classroom. You can use one of the pre-designed activities from Desmos or other teachers (use this google search for better results from other teachers), or you can design your own from scratch, or using their hugely helpful templates.
They have taken follow-up discussions to the next level with tools to show aggregated and individual responses, as needed. You can anonymize names, or show named responses.
Desmos has put together some great webinars for you to get quickly up to speed on how it all works. And, it’s all completely free!
Designed by Mr. Craig Barton himself, Diagnostic Questions is a free tool that will give you some great data from multiple choice questions that you can set for students. I like that this software has the option to ask students to submit a summary of their thinking and not just to click on the ‘correct’ answer. This tool is easy to use, set up, and is completely free, giving you a lot of information on student mastery.
ASSISTments is a similar program that is more US based questions.
I reviewed Classkick a while ago, and although I haven’t used this for a while, it could be a great way to seamlessly transition between in-class and virtual learning. You can see all students working live on an assignment, giving them live feedback. There is the option for students to help other students, and with a pro account, you can export grade data, as needed.
When it is difficult to walk around the class room in the same way, Classkick is a great way to see everyone’s thinking without having to rely on multiple choice questions.
Padlet is a great way to organize student responses in a variety of formats including pictures, video, and typing. Useful for both in-person and at-home learning, it is a great tool for students to share ideas with each other, to work on a project, or to post questions. You can also see which student has viewed what if you need to ensure that everyone is engaged.
I hope this list helps you to start the semester/term well and for your students to feel connected and enjoyment in their learning. Feel free to write a comment below if you know of any tools that are a must-check-out for students to connect and reflect in the coming weeks.
Welcome to the first episode of season 3 of the 360 podcast! In this time of returning to in-person instruction during the global COVID pandemic, we chat with Brian Simmons, a mindfulness teacher and educational leader from Manhatten, NY. We discuss ways that we can use mindfulness and meditation to help us teach and learn well […]
If you were to search for the term ‘math games’ on google, you would get instant access to many sites where you get the chance to practice skills in the guise of a ‘fun game’. For example, in the game Candy Stacker, you get to practice pretty much any skill in any grade and it […]
Inspired by Robert Kaplinsky’s Problem-Based Learning Search Engine, I decided I wanted to create my own based on my favorite websites to check before starting every unit. The process is very simple but at the end of it, you come out with a search engine that will only search websites that you decide are worth […]
Originally posted on The MathEd Out Podcast: MathEd Out Conference 3.0: Going Deeper Saturday February 6th 2016, 9am-12pm Covenant Christian High School, Indianapolis, IN CLICK HERE to register your free place The first and second MathEd Out Events were so successful, we are doing it all again! Don’t miss out on your chance to meet…
If you were to search for the term ‘math games’ on google, you would get instant access to many sites where you get the chance to practice skills in the guise of a ‘fun game’. For example, in the game Candy Stacker, you get to practice pretty much any skill in any grade and it stacks cake on top of an animal until it reaches a candy. As with many of these games, it is timed, and you ‘fail’ if you get on wrong. These types of games reinforce the fixed mindset that is so often observed in mathematics classrooms.
There are better ways of building fluency and understanding of number. Number talks and Formulator Tarsia are just two great examples. But, are there activities out there that both have that gaming element, and help build a deep understanding of number while promoting a growth mindset, that depth is more important than speed? Thankfully, yes, and here is a list of growth mindset games that I love my students to play, either in a dedicated lesson or in those moments where you have 10 minutes spare. None of these will have timers or ‘fail’ notices. (Note: There are many great card, board, and paper games out there, but I am going to focus on online interactive activities for this post). Click on the images to go to the game itself.
Factors and Multiples (nrich)
This is probably my favorite of all, building sense of multiplication tables, but students also quickly come to realize that prime numbers are key in this game.
1 Player version: What is the longest chain you can make, clicking factors and multiples of the previous number (see the example in the picture). What is the longest chain that anyone can make? Are there numbers to be avoided at the beginning? Are there good numbers to start with at the beginning?
2 Player version: The winner is the person that can force the other player not to be able to build on the chain, cutting off all possible factors and multiples. Again, are there good numbers to start with? What are the key numbers to minimize the chances of losing the game?
Connect 4 Factors (Transum)
Another fantastic game to build a sense of numbers, factors and multiples. No timer necessary!
One Player Game: Fill the game board with the counters from both boxes. Avoid lining up four numbers with a common factor (other than one).
Two Player Game: Each player has a box of counters to choose from. Take it in turns to drop a counter into the game board. The winner is the first to line up four numbers with a common factor (other than one).
Broken Calculator (author unknown)
There are probably other versions out there but this one is the best I have found, even if is relatively basic. The idea is simple: Can you get the target amount using the keys on the calculator that are working. The levels get increasingly difficult, and it is a great way of building a sense of operations.
Double Take (Transum)
Similar to the popular game on mobile devices, this game builds a sense of base-2 numbers and exponential growth. This one is a favorite with the students. Try to encourage your students to think of and discuss strategies to get further than you would by just trying different ways.
Got it! (nrich)
A simple game with less than simple strategies. Once again, try to steer students to thinking strategically. Is there a better addition to start with? Is it better to go first or second? If you want a more challenging version of this game where you can’t choose the option that your opponent last chose, you could try transum’s 23 or bust.
Square it (nrich)
Not a number game, but a great strategy game nonetheless. Students can play either another person or the computer. They must claim all 4 corners of one square to win. Can blue always win? Is there a way to force this every time? What is happening in the middle of the game? What does the end of the game look like?
I hope you enjoyed reading about these growth mindset math games. What are your favorites? Comment in the section below.
The first and second MathEd Out Events were so successful, we are doing it all again! Don’t miss out on your chance to meet with others who are passionate about being the best high/middle school math teachers they can be.
The morning will feature:
Time for delegates to share ideas and top resources with table discussions including:
Using rich tasks to deepen understanding
How to go deeper with simple ‘skill practice’
Discussions with course specific groups (Algebra 1/Geometry etc)
The popular ‘resource symposium’, sharing all the resources we love best
There are just 60 places for this event. Register soon to avoid disappointment!
Robert Kaplinsky has worked in education since 2003 as a classroom teacher, district math teacher specialist, and University of California Los Angeles (UCLA) instructor. He graduated from UCLA with a Bachelors of Science in Mathematics / Applied Science (Computer Science) in 2000 and earned his Masters of Education in 2005.
He has presented and conducted professional development at across the United States and Canada. His work has been published by Education Week (2012 | 2015) and the American Educational Research Association (AERA). He has consulted for major publishers including Houghton Mifflin Harcourt and Pearson. Robert is a member of the National Council of Teachers of Mathematics (NCTM), National Council of Supervisors of Mathematics (NCSM), California Mathematics Council (CMC), Orange County Math Council (OCMC), and Greater Los Angeles Mathematics Council (GLAMC). He also co-founded the Southern California Math Teacher Specialist Network, a group that includes over 170 math teacher specialists from…
The visual pattern above is a quadratic relationship as the pattern grows in a linear fashion in two directions (It’s useful to talk separately about the width vs. length and then bring them together). The nth term is either (n+1)^2 or n^2+2n+1. Can you see both in the picture?
Let’s pause for a second. In 6th grade, I can use visual patterns to introduce the idea that a quadratic has two linear factors! I had HS seniors that struggled with this idea. I love this!
Next comes the coding. Again, we use CodeSkulptor to ‘skulpt’ our function in three lines: Input, Function/Output, and the display output command. The difference in this is that for exponents we have to use **.
Also, I get the students to Desmos to see if their prediction of the graph are correct. This brings up great discussions about why the graph is the shape it is in quadrants two and three.
I have also introduced the idea of an inverse function; using python to create a function that would enable us to answer the question: What step would contain 400 blocks? This forces the student to consider inverse operations and the fact that order matters. Here is the code (python reads from top to bottom so you can include this all in the one program):
The benifit of this has been less about coding or nth term and more about introducing the composition of functions. It also enabled me to run some rich lessons on the topic of ‘Straight Line vs. Curvey Lines – Who Cares’ exploring linear vs. exponential relationships with finance and population growth.
The effects of this series will not be truly measured until these students take Algebra, next year. However, my hope is that this will have given them a solid foundation for many of the concepts that they will study in the coming years. We’ll see…
To bridge the gap between pattern and function and following an online course I took with Rice University, I have started to introduce some basic coding. Python in particular. Even after one lesson of using coding and graphing, I have been able to have rich conversations about the differences between functions, input/outputs, the shape of a graph and the y-intercept. Here is the process I have taken them through:
Part 1: Have the students run through a basic (linear) visual pattern (from visualpatterns.org) using this sheet and reviewing using this slide:
The nth term for this pattern is 4n+1.
Part 2: I now challenge them that we can create a calculator for this pattern using the Python coding language. I use the free python interface CodeSkulptor (from Rice University) to do this. I take them through step-by-step with some great conversations about functions and inputs/outputs.
The nice thing about CodeSkulptor is that when you hit the save button, it creates a brand new URL meaning that each student will have their own URL to post and share.
They can then change the input and see clearly what happens to the output.
(Note: Lines with # are ignored by the interface)
Part 3: They then go to the Desmos Online Graphing Calculator and input the function y = 4x+1 to confirm or deny their prediction for the graph shape, from the start of the exercise. This is a great opportunity to talk about ‘step zero’ (as well as step -10 etc.) and why they graph is the shape that it is. I feel it is also important to stress the difference between 4n+1 as an nth term and y=4x+1 (which includes everything in between).
Their homework is simply to follow the steps with a different (linear) visual pattern and to share their CodeSkulptor URL’s and Desmos screenshots on the class’ wiki page.
For student assistance I created this video:
There are two main places that I would like to take this:
I’m really excited about where this journey will take us. My hope is, that as these students start Algebra proper, next year, they will have a strong sense of functions graphs and their connections with patterns and geometry. Here goes…..
Have you done anything similar? I would love to hear your ideas/thoughts in the comments section, below.
I used to teach high school. I would often see students who struggled to see:
How to generalize patterns and extrapolate
The meaning and usefulness of a function
That the cartesian plane was just two number lines stuck together, useful for comparing two quantities changing at the same time
The difference between a linear relationship and an exponential relationship
Thanks to teacher and activity creating genius Fawn Nguyen, we have a way to address this problem. I now run a visual pattern activity at the start of my lessons, every Wednesday. Just a few weeks into the semester, I am already seeing the above gaps filled!
We have started mainly by mainly using linear patterns with constant differences. Now that this link is pretty strong I have started to introduce increasing differences and they are quickly getting the idea of a curved relationship on the graph. I have created this sheet to help organize the students thinking. I give them 4 minutes to think on the problem by themselves and 2 minutes to discuss their ideas. Then as a class we ask and discuss:
Can you describe in words, how this pattern is growing?
What do you notice about the numbers in the table?
What would be a really slow way of calculating the number of blocks/objects in step 43?
What would be a quicker way of calculating the number of blocks/objects in step 43?
Using this rule, what would step 1000 look like?
If I saw a step with [ ] blocks, which step would I be looking at?
If I were to graph steps against blocks/objects, what would the shape be? Why?
Ext: What would step 0, step -1 look like?
I am quickly finding that, by accident, students are solving equations and building up a sense of the need for processes such as factoring, finding the inverse and finding the slope of a line. I have found I am able to coherently validate the need for calculus, 5 years before they take it. I believe this will really help my students when I run lessons such as Dan Meyer’s toothpick activity, later in the year. Sure this is just similar to the explicit/recursive rule section of particular algebra textbooks, spread over a year, but I think a regular discussion on this idea is crucial to making connections and getting the deep understanding needed for algebra and beyond.
I am excited to hear if it has made much of a difference, next year and into the future. I suspect it really will.
Jo Boaler is an author/speaker, and is Professor of Mathematics Education at the Stanford Graduate School of Education. Boaler is involved in promoting mathematics education reform and equitable mathematics classrooms. She is the CEO and co-founder of Youcubed, a non-profit organization that provides mathematics education resources to parent and educators of K–12 students. She is the author of several books including, What’s Math Got To Do With It?(2009) and The Elephant in the Classroom (2010), both written for teachers and parents with the goal of improving mathematics education in both the US and UK. Her 1997/2002 book, Experiencing School Mathematics won the “Outstanding Book of the Year” award for education in Britain. Currently she is the Research Commentary Editor for the Journal for Research in Mathematics Education.