Tag: growth mindset

#InquiryMaths: Planning for Play as a Stance for Math in the #PYP ?

#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 BoalerMathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching

loris malaguzziAs 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 ReflectionaflThese are the open-ended statements that can help me understand where the students are now:

  1. Math is……
  2. Math makes me feel…..
  3. Math is fun when….
  4. I do math by…
  5. 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.

 

If You’re Not Struggling and Embarrassed, then You’re Not Teaching Digital Natives.

If You’re Not Struggling and Embarrassed, then You’re Not Teaching Digital Natives.

Back in 2006, my 4th-grade colleague, Mr. Glenn patiently tutored me in using wikis and blogs. I gave it a whirl with my students but I really wasn’t very competent in my tech know-how to pull it off. Honestly, it took me YEARS before I’d get back on the horse again. Perhaps you can relate-As a teacher, you always feel like you are racing against the clock, trying to get all the standards taught and using tech just seemed so frivolous, so you forgo its use. I definitely suffered from technophobia as my awkward attempts caused more frustration than bore fruit. However, I didn’t stay marooned on this island for too long, as seeing my daughter engage with technology really compelled me to take a closer look at its use in learning. This blog actually is the outcome of this realization and it has evolved from an exploration and curiosity to my digital professional portfolio to being a reflective tool of my educational interests and practices.

I remember early in my teaching career a well-intentioned high school administrator told me that a “good teacher” can teach anything. I felt like a really terrible teacher for a long while, thinking that I was somehow grossly incompetent because I couldn’t successfully coach volleyball (never played it competitively) or teach Spanish (I studied French). It took me changing schools to see what ridiculous advice this was. But c’mon– Like who can teach cross-stitch or linear algebra without any previous knowledge or training?  Well, let’s just call bulls@#$t on that! And that is why this “good teacher” is a student rather than trying to wing it with a textbook. You cannot teach what you don’t have any experience in, let alone knowledge of.

So, later when I went back to 4th grade I realized that I had been digging up dinosaur bones for too long and avoiding technology. Yes, I could app smash and flip my lessons, but I really wasn’t moving my students from being “consumers” idare to teachnto “creators”, which is what I now define as the purpose of using technology in our classrooms. Plus, I really wanted to move them to the highest use of technology–Connection!-sharing their ideas and finding others in their “tribe” in the digital landscape. How could I possibly teach kids about stuff that I wasn’t actively doing myself? If I was going to get these kids prepared for their future, I had to be a 21st-century learner right along with them. I couldn’t possibly blindly ask them to create something unless I could somehow mentor them. That’s exactly when I started to get serious about blogging.

You see blogging is about one of the most humiliating things you can do, other than getting really smashed at a party and stripping down to your undies. Your ideas and thinking are “naked” and it has the potential to be seen by tons of people. You can sound like an idiot and these online ramblings leave a digital footprint. So, not only can your current boss and colleagues see what kind of fool you are, but your future boss and co-workers can too. But I have to do it because I want to teach to the future and not to the past. The expectations of my students to be creators are going to be higher since being “googleable” is a prerequisite for their job search. There’s no way I can teach them about digital citizenship and managing their online life if all I ever do is post an occasional Facebook update and never become a contributor to the World Wide Web myself. Seriously, how could I actually help them navigate these waters?

Now I’m teaching myself about podcasting. It’s not hard, but it ain’t easy. In case you were thinking about it, there’s all this stuff that you need to know about creating quality sound, editing tracks, uploading it onto feeds and publishing it. Plus you need to have graphic art for your podcast and I have to design a logo and description for it.  Geez! I haven’t used GarageBand in years and it is a heck of a lot more complicated than I remember. I’m harassing our music teacher to tutor me in making audio tracks and how licensing works in the recording world. There’s a lot about copyright that I don’t know about. And writing a script is not the same as writing blog posts, let me tell you. (As an avid podcast listener, it’s annoying to hear aimless talking. My time is precious, so if the podcast is a bunch of blah-blah-blah, then why bother?-right?!) I worked on my podcast this weekend and I sound like such a boob. But it’s my first step. I have to remind myself that everything is hard at first but eventually it gets easier and more fun. However, I’m hopeful that I can take this experience into the classroom. I really want to have my students create podcasts for kids. I think that would be so fun.

So, what about you?–are you rolling up your sleeves and getting your hands dirty with all this digital awesomeness or are you hiding behind your whiteboard and 3-ring binder? (No offense, but I see you.) I don’t think our children can afford to have Luddite teachers. Our world needs more courageous and tech-curious educators to not only help prepare them for their future but to help them create the future that they will live in.

 

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