#InquiryMaths: Planning for Play as a Stance for Math in the #PYP ?
I’ve been binge learning through the online conference on The Pedagogy of Play. It’s been really inspiring for me. Last year, I felt like I was moving away from play-based learning and into more formally academic structures when I began teaching first grade. This has been a challenge for me because I miss the discoveries (theirs and mine!) and creativity that are natural by-products of a play-based approach. So as I embark on this school year, I have two questions that I am holding in my mind: How do I make math more fun and authentic? and How do I provide rich open-ended tasks that allow for multiple approaches with low threshold, high ceiling tasks?
These questions come from this quote from Jo Boaler, a math educator hero of mine.
Numerous research studies (Silver, 1994) have shown that when students are given opportunities to pose mathematics problems, to consider a situation and think of a mathematics question to ask of it—which is the essence of real mathematics—they become more deeply engaged and perform at higher levels.
― Jo Boaler, Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching
As I reflect on that research, I believe the answer to my questions is to play. Not just because it develops curiosity and self-expression, but it cultivates self-motivation and an appreciation for the pleasant surprises that our mistakes bring us in our learning process. Moreover, from Boaler’s academic point of view, “they become more deeply engaged and perform at higher levels”. Um…so why on Earth wouldn’t we connect play and math?
What is play? Play is the ultimate What If question in my mind because it allows us to explore with possibilities. Most Primary Years Programme (PYP) Early Years educators feel that the word “play” is synonymous with the word “inquiry”. As teachers, we can be intentional about marrying the joy of learning through play with our learning outcomes. I don’t think we have to suck the fun out of everything to make it “learning”; in fact, I think it has to be injected back into the process, especially when I consider that real * (think Albert Einstein and Euclid and Leonardo Pisano aka Fibonacci) mathematicians are exceptionally creative and playful with their ideas. (*Actually, I think ALL of us are REAL mathematicians, but not all of us embrace and delight in this aspect of ourselves).
So then if I approach inquiry maths through the lens of play, I need to consider ….
What tools can we use for play?
- Loose parts?
- Technology?
- Each other?
- Math resources (traditional, like geometric shapes, Unifix cubes, hundreds chart etc.?)
- Math resources (non-traditional materials that allow students to create. ie: a bridge)
What mathematical ideas can be developed and deepened through play?
I actually believe that most of the time, when we are authentically engaging in math decisions, we are not doing “number” and then “measurement” and then “data handling”–it’s not that discrete in real life and often time these strands are happening simultaneously and overlapping. Play expresses this transdisciplinary nature.
What language can I use to invite “playfulness” with math?
I think our teacher talk is actually a critical component of shaping our mathematical identities. Also, the enthusiasm I communicate, either through my speech or through non-verbal cues is something that I want to be mindful of. My favorite book that addresses this is still Mathematical Mindsets but I also love the simplicity of Peter Johnson’s ideas on language and I recently read In Other Words: Phrases for Growth Mindset: A Teacher’s Guide to Empowering Students through Effective Praise and Feedback which had a lot of gems in there that can be applied to developing our language around math learning. I’ve been ruminating over how I can embed more sophisticated math language in our classroom vernacular, especially with our English Language Learners (ELLs). I really want students to talk like mathematicians, explaining their algorithms and debating approaches to problem-solving in a way that is light and spirited as if we are having a cool conversation. I know that deepening my ability to express the “fun of math” is going to be an area of growth for me because I have been brainwashed into thinking (like many of us were) that math is serious and hard. I STILL have to unlearn this when working with older children.
How can I document their learning decisions so I can create more opportunities to engage, process and reinforce key concepts while also expanding their cognitive boundaries? Right now I am reading A Guide to Documenting Learning: Making Thinking Visible, Meaningful, Shareable, and Amplified by Silvia Rosenthal Tolisano and Janet A. Hale in the hopes of deepening my knowledge and finding answers to this complex question. I also find that this Math Mindsets Teaching Guide from YouCubed will be incredibly helpful in my professional learning journey.
So as I think about our first unit of inquiry in our stand-alone Programme of Inquiry (POI), I find this a wonderful opportunity to develop play as a stance to inquiry maths. Here’s the unit:
Central Idea: Exploring patterns and solving problems empowers us to think mathematically
An inquiry into how mathematicians . . .
1.Construct meaning based on their previous experiences and understandings
Make meaning from what they understand
2. Transfer meaning to connect and deepen their knowledge and understanding
Make connections to deepen their knowledge and understanding
3. Apply their understanding of mathematical concepts as well as mathematical skills and knowledge to real life situations
Use what they understand to solve problems
CONCEPTS – Connection Reflection
ATTITUDES – Independence Confidence
LEARNER PROFILE: Knowledgeable Communicator
I am considering what provocations would allow the students to “to show what they know”–which is really the essence of our first unit.
Before I do any provocations though, I have to survey and collect data. Nothing fancy, but I need to know their answers to the following questions and then analyze their answers to make informed choices on how we can create invitations to play in mathematics. Also, it helps me to assess the Key Concept of Reflection.
These are the open-ended statements that can help me understand where the students are now:
- Math is……
- Math makes me feel…..
- Math is fun when….
- I do math by…
- Math is everywhere (agree or disagree) because…..
Here is some of the brainstorming that I am considering for “provocations” to begin to shape our awareness in our daily lives and help create an authentic invitation to play. (By the way, this is my first thinking–I haven’t collaborated or researched with peers–so this is raw and rough ideas, happening in real time on this blog):
- The ole’ suitcase: Place inside a seemingly odd collection of items from everyday life that represent mathematical strands* like a pair of pants (measurement), a bottle of water (shape and space), a license plate (number and pattern), a bag of candy (data handling), a clock (number), a map (shape and space), some rocks or shells (data handling/number and pattern), some tape (measurement). Then have students pair up, select an item, and discuss the guiding questions. Record their thinking onto SeeSaw.
(*May I just say that I know that selecting those items and arbitrarily labeling them in particular strands is a bit comical because I know that the students will come up with more interesting ideas and connections than I ever will. But this is just an “accounting task” to ensure that, in my adult mind, I’ve covered all possible topics.)
The Guiding Question(s): If math is everywhere, then how are these things related to math? What math might someone have used to create these things?–What ideas were people thinking about when they made these items? (Key Concepts: Connection, Perspective)
The next day, we would need to share those survey results with the class so that students can start developing their identities as mathematicians. We’d probably come up with a display and have the students do a gallery walk and discuss what they noticed. Then I would set out these items and ask a follow-up question: If you were to sort these items, which things would you put together and why? (This is just to further identify the connections they’ve made)
Up until this point, I am just trying to kill two birds with one stone: plant a seed that math can be everywhere and collect data about their thinking. But now I have set up the opportunity to have purposeful math discussions through invitations to play. Of course, the types of tools and learning situations that can be engaged through play will obviously vary based on the survey and the data collected from the provocation.
But I think we could set up a variety of “challenges” or authentic contexts that can be steeped in play-based situations.
Example: The Challenge: Your mission should you accept it……
- Fill the cup: using a straw and this bowl of water, how might we fill the cup to the line?
Possible Tools: drinking straw, spoon, soap pump, timer, popsickle sticks, paper, pencils
Because I didn’t ask for a particular tool to be used, then this becomes a more open-ended task, allowing more choice and helps me to get data on the student’s thinking. This amps up the play quotient and math possibilities.
Possible teacher questions: What if you used a spoon (or straw, or soap dispenser, etc..), how might this change your results? How do you know that you have completed this challenge? How might you do this challenge faster? How do you think we could record your success?
This forward planning for a provocation and “play-storm” is really just the beginning. In less than 2 weeks, the doors will officially open and learning will officially commence for the 2018-2019. I couldn’t be more eager to approach this year’s learning with a dedication to play, taking their ideas and imaginings and connecting them to math learning that matters to them is going to be important and fun work. As I consider the possibilities with play, it gets me really excited. I hope, no matter what age we teach, educators see the value and need for play in developing mathematical thinking.
Developing learners as leaders is my joy! I am committed and passionate International Baccaluearate (IB) educator who loves cracking jokes, jumping on trampolines and reading books. When I’m not playing Minecraft with my daughter, I work on empowering others in order to create a future that works for everyone.
I know we have our checklists of paperwork that we have to stay on top of, but at the end of the day, I’d rather have teachers focused on making sure the kids have engaging, authentic and impactful learning and I have rarely found that paperwork inspires them to create that. This is especially true at PYP schools in which we have to reflect often on our students’ learning so that we can determine the next steps in their inquiries
And it’s poor form to throw teachers under the bus in front of teachers. Trust is so important in your work so if you undermine others, expect staff to lose their confidence in you.
Call me Old Fashion, but I prefer the personal touch of staff meetings over email any day. I like connecting with colleagues and having a common understanding of the events in our community and our school’s pedagogical approaches. Also, consider the fact that if teachers are more concerned with keeping up with emails, rushing to read them then they are not examining students’ work or reflecting on the discussions they had, then the focus isn’t on improving learning. We want teachers to be spending their cognitive power on making learning for students awesome rather than your 18-bullet email about professional development goals. Let that one sink in a bit. It’s good to have a weekly newsletter to communicate important things but if you find that your staff emails began as a couple of sentences and now is evolving paragraphs, then it needs a face to face. A quick and dirty chat will be more impactful than a back and forth conversation over the internet.
Go through news articles either on a social media news feed or through an internet search on a topic that is relevant and interesting to your students or controversial (ex: climate change). Have the students examine at least 3 websites or sources of information and put them through the filter of the 
I can’t believe they haven’t gone by the waste side yet, like horse-drawn carriages or 8-tracks. It doesn’t serve where we are in education and what we know about learning and teaching. And, as a parent, the letter A (approaching), M( meets) and E (exceeds) next to a subject area with a couple of sentences that explains the justification of those letters really doesn’t help me figure out how I can support my child. And, as a writer of those comments, knowing that parents are intended audience for these report cards, you end up summarizing the skills gained vs. the conceptual understandings–because at the end of the day, parents just want to know if their kids can read and do math up to the “standard” of their peers. So really, the report cards provide late feedback that schools may feel “report” the learning but ultimately doesn’t serve any of the stakeholders involved, students included.


A classic definition of a concept is an enduring understanding that is broad enough that you can transfer it across disciplines and time. But I’d like to add that a concept is something that makes you think, makes you wonder, gets those neurons firing. A topic fades from your mind, just like a rainbow after a shower–it seemed lovely at the moment, but quickly disappears from your memory. You see that quote from Chip and Dan Heath–our goal whenever we write a Central Idea is nearly the same–an idea so profound that an individual could spend a lifetime learning about it. This is why the PYP makes such a fuss about developing conceptual knowledge and skills. Learning facts and skills without a context is a waste of time and often evaporates unless we make units that are “sticky”. Concepts are like a bad rash that won’t go away. Concepts get under our skin and stick with us and reappear in new contexts that broaden our perspectives.
I’ve been examining standards and
This year a snowball has been building, from the “Me Too” movement to reading
And now I am seriously considering it–I’m sure to my team’s chagrin–to bring it into the curriculum. But this isn’t about the sexist commentary that I witness in an influential boy in our class, it’s also about “white-privilege”, classism and economic disparity that I have observed in silence as an international educator. Furthermore, I know that these topics may also touch a nerve in me–how do my own actions and words contribute to the –isms? I am just as much a student as I am a teacher in this sort of inquiry, recognizing that I am blind to so many things just because of the privilege that I have experienced in my life. There is something personal at stake when I start poking around these cultural “sleeping dogs”.
Yes, developing content knowledge and skills are really important, but what’s more important is the WHY that knowledge and skill are important. I think we can all agree that if you can google it, it shouldn’t be in a line of inquiry, let alone a central idea.
