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    • As teachers working in a system with a variety of constraints like time, standards and initiatives, how can we effectively make play a routine part of mathematics instruction?

      • First off let me say unequivocally that I have the utmost respect for teachers and the work they do. Their job is often thankless, definitely undervalued economically, and challenging. Balancing all the groups and goals, Americans especially, have put on schools has gotten to be a near 24-hour gig, and that isn’t good for anyone. Now, about play, a good friend of mine gave this response to your question, “How can we NOT incorporate play into the classroom?” to which, I give a hearty YES! 

        Play is the child’s job, the teacher’s job is to provide environments, opportunities, structures and values that incorporate play. By opportunities, I mean using games and puzzles, conundrums and paradoxes that intrigue the mind. This morning while thinking about this question a video came across my Social Media feeds that show a man (Tadashi Tokieda) pushing a large circular cork coaster through a small square in a piece of paper. He reveals the magic without hesitation, and the mystery is not solved but rather is enhanced. No child who watches this could help but wonder what is happening. Watch this video for yourself and see...you will know what he does...but you are likely to have more questions at the end than were answered. This is the heart of playful learning, where one idea draws out many many more. Look for opportunities like this.

        Create in your classroom, social structures that allow students to foster their creativity and to ask the questions that plague their minds. It is hard in the middle of a day where you know you have to get through certain aspects of the curriculum, resist that tyranny. Isn’t that the very goal of disruption? :) 

        Lastly, value laughter and joy in your classroom over everything else or well at least enough that you make daily decisions to be playful and allow playfulness. Shift the work to the child, let them accomplish their job description: Play.One other postscript to this question, I am reminded of the Latin meaning of “curriculum.” During the Roman Empire, horse-drawn carriages and carts were the means of moving goods and people. After dozens of years of trudging ruts would be worn into those famous “Roman Roads,” those ruts were called curriculae. Don’t fall into a rut.

    • What would be the first step in a teacher wanting to begin using the ideas in Math Recess?

      • Thanks Matthew for your great question. I'd like to say that my response would be definitive and declare that I hold the one true "THE first step," but will hopefully give you an idea for A first step teachers could take. Maybe start by committing to celebrating student questions more than student answers. When I made this shift in my teaching the joy and laughter in my classroom went upwards. Questions are more fun than answers because they are filled with fruitfulness and potential, while answers are pruned off thinking.

        As I said, this is just A possible first step, of course there are others that might be more fitting for other teachers, and for that I would like to ask the readers for their thoughts on this, collaboration is a great way to get at more truth.

    • There are successful education models around the globe that show the advantages of play and learning. What’s preventing the U.S. from adopting playful learning, and allowing for greater student agency?

      • Lil, your questions are always so insightful for your 12 years of experience, thank you for this one in particular.

        The U.S. is and has been suffering under a terrible misunderstanding of its place in the educational achievement world. This misunderstanding has caused many of us to spend way too much time in handwringing about our self-described mediocrity of late. Beginning in the hyper-paranoid Reagan era of public policy wherein the National Research Council coined the document "A Nation At Risk (ANR)," and continuing through to the Common Core State Standards response to the No Child Left Behind/Every Student Succeeds Act policies we have been frantically attempting to pull ourselves up by our bootstraps. We perceived ourselves as falling behind from our former glories and therefore in need of making ourselves over yet again.

        The data however does not support our misperceptions of it. The US is among the most diverse culturally, economically, and educationally populations in the world. Third largest in raw numbers behind China and India (which of these is the largest depends on which week you look), we boldly attempt to educate every single member of our population within a system originally designed to educate a very small, select subset of that population.

        I could go on and on about this but will try to focus more on your question of what prevents us from adopting a more playful learning model? In a word, FEAR. The ANR told us that we had in effect waged a war of mediocrity upon ourselves and those words have scared us so badly that we continue to flounder about for more and more control of our situation...not realizing that those fearful words were flat out WRONG.

        We as a culture need to come to grips with the real data that our achievements in education over time and populations is NORMAL (0,1) for one thing. Then look to other systems that are in fact achieving marginally higher in areas we would like to improve in, especially those that seem to graduate students who still enjoy learning after their 13 years of schooling.

        I said this recently to a group of educator friends and have decided to make it my schooling motto, "If a child graduates from High School less curious about the world than they entered it in Kindergarten, then schooling has failed her, we have failed her." If we set this as our standard to achieve and forego the relentless drive to over assess through over governing what happens in classrooms, we will remake our schools into places of joyful experience and exploration. This is what I think you are referencing when you speak of other countries who seem to have this attitude.

        Wow, sorry for being so wordy.

    • How would you describe the key attributes of great maths teachers?

      • Thank you Drew for this question. I have pondered this often and hope that I reflect what I am about to say in my own classroom. In no particular order than the order they tumble from my mind:

        1. Always continue in your own curiosity. Never stop wanting to know more about stuff in general and things your students might want to know about in particular.

        2. Follows from 1. Share your curious thoughts with your students. (I suddenly hear Crosby, Stills, Nash, & Young..."Feed your children well...upon your dreams...").

        3. Be fearless in the face of not knowing the answer yourself. And if you can't be fearless, be brave enough to live with uncertainty yourself. Teachers are not required to be the source of knowledge, rather they should be the source of questions, ideas on how to get to the answers sure, but not the repository of the answers.

        4. (You asked about maths teachers specifically I will try to focus there) Love your subject, get lost in it. Right now my co-author Sunil is writing a book he is titling "Down the Rabbit Hole..." a phrase we chose for a chapter heading in Math Recess. He is doing so to allow himself the space to get lost in the maths. Be curiouser and curiouser about things you thought you once knew.

        5. About that last point in #4. I have found through my 30+ years that there are always new ways to see the things that I once thought I knew completely. For instance, when I met Dr. James Tanton and started to experience Exploding Dots I came to a much fuller and richer understanding of the ideas of polynomials in general and the specifics of arithmetic. Two subjects I could have argued I knew A LOT about before. Or like in the past few months, Dr. Po Shen Loh revealed a method he was clarifying for himself for the first time, regarding solving Quadratic Equations, you can watch this here. Both of these mathematicians found new ideas for themselves within what is arguably "Elementary" mathematics. Never diminish the power of mathematical thinking.

        6. Study the history of mathematics. This is far more critical than I once believed. But maths are a human creation, and therefore have human stories that surround them. Knowing those stories helps to contextualize and demystify mathematics. Also, studying the history of maths is a fabulous means to celebrate the diversity of cultures within your classroom. This process is known in some circles as re-humanizing maths and I am fond of that characterization.

    • HAllum
      HAllumasked

      Did you and Sunil compare mathematical 'big ideas' between the US and Canada? What is similar/different?

      • This is also an interesting question. We spent a lot of time lamenting common problems such as the rise of reactionary factions in the math education community. In parts of Canada there are some serious conflicts between some vocal and contentious people as there are in the US. The struggle for equity and fairness is common to both our nations. Of course, you can imagine that his and my desire to see a more playful atmosphere in math classes are born from similar experiences, especially joys.

        The joy of seeing students find grandness and excitement in mathematics kept us both in this game. Children are the same the world over in this.

    • Do you see a role for Virtual Reality, Augmented Reality, and Spatial Computing in helping students relate to mathematical concepts in immersive environments? Do you have experience incorporating these technologies into your lesson plans?

      • I have seen some absolutely amazing applications of VR and AR in the classroom. For instance there are folks, especially in Europe it seems, who are creating immersive geometric experiences for learning basic Euclidean ideas. Picture this, you have your Occulus on and step into a world where you construct a triangle with one fixed length edge and opposing vertex on a line parallel to that edge. With your gloved hand you can slide that vertex along the parallel line, step through the fixed and stable area that the triangle encompasses, or even "throw" the vertex along your "infinite" line and watch all the effects of this sheering on the area in "real-time." You can do this with your whole body involved. A project I am particularly fascinated with is being run by Henry Segerman at Oklahoma State University. He and some associates have created a VR experience wherein you enter a universe that behaves in a locally non-Euclidean manner. In this world you can walk through six rooms that surround a single, shared corner, each of them at right angles to their neighbors. This world is based upon the Hyperbolic Geometric Axioms of space. We now have the ability to help students to literally embody their understanding of abstract ideas.

        @Brzezinski_Math on Twitter is constantly publishing video of how Geogebra AR (an app you can run on any smartphone or tablet) can be used to model an 3D object you like (for a quick introduction watch this short video he made a few years ago, then imagine how much better things have gotten since) I wrote my dissertation a few years ago now and its focus was on teaching geometry from a transformation basis. So this is an area of keen interest to me. Tim argues quite potently for the idea that transformations should begin in three dimensions rather than two because it is so easy now to implement, thanks to AR being so readily available and easy to use, plus it is just so danged cool creating a model of your Spiderman coffee mug on your iPhone.

        Regarding Spatial Computing, could you clarify what you are referring to? I have an idea but am uncertain that it aligns with yours.

        Thanks for these super interesting questions. We live and work in wildly interesting times when it comes to the possibilities of doing teaching better. I like that I feel guilty when I fall back to a Lecture - Take Notes model of a classroom (which is not evil just not the best way to learn 100% of the time, small doses only please). I think these tools can be used, like the tools of a pencil and paper, to enhance learning. Let's NEVER shy away from implementing them when we are ready to use them in an enhanced manner. As my friend Alice is fond of saying, "A PDF of a worksheet is just that...a damned worksheet. Paperless is not a pedagogy." We get to keep learning ourselves, so we can model it for our students. This is the very essence of playful learning.

    • Thank you by the way for such an in depth answer on Immersive tech in mathematics. I really enjoyed this. Regarding Spatial Computing, it is kind of a catch all but I think of it as a means to interact with objects/beings artificially through glasses, windshields, mirrors, or even holograms.