Math Play in the Junior Classroom: Some General Observations

Before I start to document, I want to admit that I have not done as much around math play as I have wanted.  When I started to realize this, months ago, I felt guilty and upset with myself.  I had been so motivated and driven to really explore what math play could look like in a junior classroom.  Not only that, but after I decided what it could look like, I was eager to move my thinking into:

  • What are students truly learning and creating through math play?
  • What makes effective math play?
  • How can play develop math dialogue and thinking within math conversations and tasks?

Upon further reflection, I realized that I should not feel guilty or upset.  Letting the math play just be — play and mathematics — is an even better place to start.

Just about this time, this tweet from the awesome @Mathgarden (with mention of other amazing math leaders on Twitter), which seemed to give me new focus.  Let the play and the math be enough.

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Student Play:

I had a lot of ideas for what student math play could look like, but realized the new school year was fast approaching, and I knew I needed something more concrete to start.  Thanks to Sarah VanDerWerf and her idea of a math table, I started there.  I immediately created a space for students to explore and play with math.

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I randomly began to leave out math tools for students to play with.  No direction.

At first, students hesitated.  I don’t have a quantitative reason why they hesitated, but I can assume that perhaps they did not have much experience with free math exploration.

After time, students began to play.  I noticed they would go to the table as soon as they came in.  It was a great way to start the day for many of my students.  I also observed that if one student went over, it was only a matter of seconds before a small group would begin and dive into the play.

I started with select pattern blocks and small mirrors.

 

I used magnetic shapes next — oddly, I did not take any photos.  This is where my students started becoming comfortable with math play — their confidence and play began to expand.  I knew I had a winner when students were asking me to stay in for recess to continue their exploration.

I then discovered the great @Trianglemancsd and his amazing wooden creations.  My students adored — and continue to adore — our tiny turtles and our spiralling pentagons.

Turtle Work:

At first, my students had no idea what to do with the turtles.  They sat alone and untouched for about a day.  A few of my bound and determined students finally dove in.

My first student written tweet was the result:

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Here are some other tessellations my students played with:

Spiralling Pentagons:

Next, I pulled out the pentagons.  I thought students would go right for it, but there was still hesitation.  Again, once one started started to develop some designs, more followed suit.

What I Have Learned Through Student Play:

  • That play is different for each student.  I can confidently say every student has manipulated these toys at least once throughout the year;
  • Students have more persistence with problem solving.  Again, I can’t say there is a direct correlation, but since I have put out the play table from the ‘get go’ of the year, I can say that students ‘attack’ problems in math with a little more ease and confidence;
  • Collaboration happens naturally, and even if a student starts solo, another student is always entering and at least asking questions about the designs on the table (and, I admit, there might not be the most math-specific talk here, but there is definitely “What are you going to do next?”, “What about these that you left here?”, “Can I try something?”)

What I Need To Do Next:

…and these are crucial for the happiness of math to continue:

  • More time for play.  Students need more time, I need to provide more time for them to play, and give them more things to try and play with (how can I add numbers and number sense into my play table?);
  • Silently Observe:  I need to watch more, and take notice.  I need to step back and listen to the conversations around the math toys;
  • I need to start having students reflect on their play.  This can happen a number of ways:  Have reflection cards (or a Google Form ready for when students have something to say about their play), or talk to another student, or bring the conjectures and ideas they came up with into math tasks (“Remember when you were playing at the math table?  What did you do there that might connect here?”);
  • More creative tools for students to explore and work with;
  • Me asking more questions.  To start, as and after they play;
    • What are you thinking as you create?
    • What do you notice as you create (would be powerful to ask another student this question about someone else’s creation)?
    • What is your plan now?
    • What will this mean for future math play?

In short, I need to spend more time on math and play.  I need to be more cogniscent of my students and their play, and that it is being fostered as much as possible.  Math is play, after all!

Suggestions?  Please comment, or reply on Twitter!  I would love to hear your thoughts.  Thank you!

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How student and teacher learning interconnect

Before I start, I should say that this is a really rough reflective piece for me — and may not be super clear to you, dear reader.

The other night I was honoured to discuss my learnings and experiences teaching math at a Mathematics Part 1 AQ course.  I was worried I would embark exactly what I don’t want in my classroom:  That I am a keeper of knowledge, and I should be spreading it.

Instead, I wanted to go in and discuss how I have learned, which has made my students learn, and how student learning has made me learn.  I wanted to come from a angle that I am constantly and still learning, and here are some of the mathematical things I have tried.  Some worked, many did not.  But I am still researching, learning, and trying.

I talked to these lovely teachers about how they know they have learned, really learned, something.  We padlet-ed our thinking out.  Then I asked if they could tell me how they know their students have learned.  Interestingly, it wasn’t so obvious.  It brought up great discussion about how we can ask students how they know they have learned something, and odds are, we’d see some similarities.

In the curriculum, there are metacognitive expectations.  These are the challenging expectations that we feel come after a unit or test — what did you learn?  How?  But now I am thinking how I learn.  It’s not linear at all — I learn in bumps and starts, ebbs and flows.  So I wonder, can I not ask my students as they are learning to start considering how they know they are learning, and if not, what has to happen to help them learn.  Wouldn’t having them stop and pause and reflect as they are learning be powerful?  Do we give students enough time to really reflect on how they learn, and when they know they have learned (and this will be different for everyone).

This should be the same for teachers.  We should be constantly going through how our students learn, and how we are taking that knowledge and applying it to our planning and moving forward for our students to continue learning.

We as teachers, and adults, should realize that learning is not neat — it’s messy.  Full of buzz, and, sometimes, frustrating.

So, tomorrow, I am going to ask my students – How do you know you have learned something?  Really understood and learned something?  I know for a fact those answers will help me learn about them, and how they learn, and therefore, how I will teach.  I want to know more about the reciprocity of student and teacher learning.

 

What if Learning Goals were Learning Questions?

It was early and silent in my classroom.  I like to get in early (freakishly early, from my husband’s point of view) and putter.  As I putter, I look around my room, I reflect and synthesize what’s going on in my room.  I feel my brain expand in a long sigh; as all of my general worries and thoughts as a teacher stretch.

I was standing at my chart stand, one of my brand new markers in hand, curriculum open, and ready to finally consolidate our learning goal and success criteria for math.

I am not sure about anyone else, but I don’t give my learning goal or success criteria up front.  I do assessment for learning, I let students explore and investigate (probably the most common verbs in the Ontario Math Curriculum), and I listen to what students are saying first.

As they work, are they making connections between concepts?  Are they seeing how their estimates and thinking connect to the bigger problem I handed them?  Once I have heard the mathematical language I want, once students start talking in conjectures, then I pull out the expectations.

I write them, and we put them in student language.  We reflect, and we determine what it takes to be successful under that expectation and learning goal.  We keep re-visiting, and we change and morph this living track of our learning as we explore and learn more.

Anyways, back to me staring at my chart stand — I was recently doing this with Data Management, and following the EDUGains Scope and Sequence.  The idea of choosing the most appropriate graph for data found was the big idea.

And, instead of writing it in a “we will learn…” my gut instinct took over, and I wrote “How does organizing data effectively influence the reader?  What do I have to include in my graph or chart to ensure my reader understands my data clearly?”

Then, our success criteria would be the answers we had discovered.

  • Line graphs are better for data over time, as readers can see dramatic changes in data with ease
  • I want to make sure that my scale is representative of my data, and my reader can follow easily
  • Double bar graphs make comparing two similar data sets easily, and make the reader be able to find similarities and differences to make generalizations

Now, sure — this success criteria is massaged by me, but is generally the student ideas that have come up through our work.  But, really — doesn’t that question flow, make sense, to what we are learning in math?

But I panicked, erased it, and went back to a non-question. Because that would be wrong.

Now that I am moving into measurement, review of perimeter, area, and length with standard units, the same thing jumps to me.  I want students to understand the relationship between perimeter and area, and how this learning will lead them to area of triangles and parallelograms later.  So, the question, “What are the relationships between perimeter and area?  How does one relate to the other?”  seems powerful to me (Now, that’s not a perfect question by any means, but you get my gist).

Thoughts?

Estimating is justifying

Estimating to me means lots of visuals, lots of dialogue, and, generally, everyone feels safe estimating.  Estimation is a great way to start the year, and get the math talk flowing.  Also, it leads to the process of justifying.  Why and where did your thinking come from?  What do you consider a too high or too low estimate?  I can also throw in modelling open number lines, standard notation, familiarity and comfort with benchmark numbers (because generally kids naturally group in 5s or 10s), and – hey!  Even a little fraction talk (what if I had half?  Hmmm…the stadium isn’t full, I’d say there is about three one fourths present.  Does that affect your estimate?).

The power of estimation, and playing and thinking about estimation, is very powerful.  I find I can get a lot of information about the depth and perception of a students mathematical concept of number, and relationship between numbers, through estimation tasks.

I am going to highlight a few of the estimation tasks I did (and, honestly — they are not super amazing; they are just great for seeing student thinking).

I started out the year with one of my favourite tasks.  The classic Fermi Problem “How long would it take to sing happy birthday to everyone?” and right away the questions start.  “Wait, Mrs. Allum — who is everyone?”  “What do you mean ‘how long’?”  And I shrug, and pretend to go do something (OK, not quite, but I say, “well, what do you think?” and there is a moment of panic.  I remind them they have a group to help them, and sure enough, they are asking me for timers, and telling me that ‘everyone’ will be the members of this class).  And, as we know, once they start talking and thinking, they start coming up with estimates, or even better, questions for more information that would require their estimates to be more precise (my favourite this year was when I overheard one of my students say, “Hey!  Won’t it be different lengths depending on the lengths of people’s names?  Shouldn’t we factor that?”).

Then, I do the classic candy jar estimations.  Because, really — who doesn’t love candy?

 

This gave me a lot of information — how much of this estimation was just sheer guessing?  What strategies were students actually using?

We did a few classic estimate 180s, but I still wanted to get the justification of where their estimates were coming from.IMG_1026

So, I had a bit of a brainstorm. Rather than students estimating, I gave them 2 estimates to choose from, and then justify why they thought it was the better estimate.

We started with one estimate where students chose a side of the room.  See these Estimation slides for the bacon slide Estimation slides (thanks estimate180!), where I had students choose the amount, and then try to convince the other side to join theirs. We watched the third act video to see which side of the room was correct. Now students were beginning to understand they had to convince and justify their estimates to convince others, and to ensure their estimates were reasonable.

I then used the whiteboards, more photos, and a speed dating feel to the next task.  Students rotated around the room and looked at the photos, and justified their estimate (these photos are also in the aforementioned estimation slide folder).

 

The next morning, I had my students do an estimate match as they walked in the door.  One student got an image, and another student got a number.  Find your most reasonable partner.  They had to then share and justify with each other why they were the best match.  Some students even went on to discuss why it would be possible for more than one response.

Estimation Photo Match

I then went back to the estimation boards.  I wanted students to determine what they thought were the best justifications of the estimations.  I had them stick sticky notes on what they deemed the best estimates.  We decided as a class these would include:

  • A clear strategy that someone could follow and understand by reading it
  • using information in the photo to assist (size, shape, relation to another item)
  • they would consider the ‘unknown’ factors (i.e., if they couldn’t see all of the items, they would consider the amount based on what they could see).

I told the class we would look for clusters of sticky notes.  I took photos of the boards, and we discussed about why there were clusters.  These were the justifications that were the most clear and made the most sense.

 

So, I went back to the candy jars.  This time, students had to estimate, and write their justification.  I was curious to see if I would get richer responses — hoping for students to tell me they were grouping, considering and comparing size, and even using number lines.

Then I decided that students would decide who had the better justifications and estimates.  I typed up all of the sticky notes, and then gave them to groups anonymously.  Students decided and determined who won based on best justifications and estimates. They decided the criteria would be the same as earlier: A logical, clearly explained (there words:  I should be able to understand your thinking from your reading as if we were talking) justification.

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I have definitely heard a difference in students not only estimating and talking about number, but sharing how they know.  They are beginning to share their reasoning strategies and ideas, and I feel this time spent estimating will really help when we get deeper into computation.  It will increase their comfort with number, and reasoning through a problem.

The Power of Dot Number Talks

I was so excited to post about this, that I tweeted about it first, and I realize now that my tweet may have been a bit misleading.

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I didn’t really do dot number talks differently.  I just had students reflect on them independently today.

It all started with Jo Boaler’s inspiring 7 dot number talk that I watched over the summer.  Going into Grade 6, I was honestly skeptical about giving a subitizing task to older students.  I thought they would balk.  But when I saw the age of the students Jo Boaler was doing her talk with, I thought — yes!  What a great opportunity to start and structure Number Talks this year.  All students can participate, students will practice thinking, sharing, and explaining in a non-threatening way.

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7 configuration

I left it at that.  I did not realize how much I would get out of these simple tasks.  It ended up being one of the more rich tasks we did this week.  When two students fist pumped and said “Yes!” when I announced the second round of number talks, you know you are onto something.

I started my first number talk on the second day of school, and I did the basic 7 format.  My students enjoyed it, and by the end of the talk, they were naturally expanding on each other’s ideas, and talking readily about all the different ways they could see 7.  We ended the talk by consolidating – “Why is it important we see and understand that math can be seen and understood in so many ways?” I got quite a few blank stares, but a few students shared that when math became more complex, it would be important to be able to be clear in our sharing of ideas.  I told them to leave that question, think on it, and we’d return.

The third day of school I did a configuration of 10, and in my back pocket, I purposely built the configuration on the 7.  I was looking for my students to make the connection — could the strategies I used in the 7 dot talk help me with the 10?  I had planned to ask this, but was surprised when it was one of the first answers I got.  One student said they had built on what we had done with the 7 yesterday.  Without any prompting, there was the connection.  Students began to, naturally, start talking to each other about how they connected.  And then started sharing how else they would have done it in retrospect.  I got to sit back in wonder.  This is what all teachers dream of!

 

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10 configuration

That evening, I wondered something:  My students loved watching me draw what they saw and how they counted, but they also wanted to come up and draw what they did.  I decided I wanted my students to have more think time.

So yesterday I did an 11 dot number talk (you’ll see the configuration in the reflection sheet).  I put up the configuration quickly, and then told them to go into their own space and think about how they counted.  I then gave out this little exit ticket, and was amazed.

First off, I asked students to go and sit where they could think and focus.  Albeit I am not one for silence as being the utmost importance, but you could hear a pin drop.  Every single student was so engaged in demonstrating their thinking they were silent without me telling them to be.

Secondly, and more importantly, students drew and explained in many ways.  They also, without me even making the connection, naturally started breaking down the numbers into simple equations.

When I circulated and noticed this, I brought us back to the group, and asked that first day question again:  How will these strategies we use during number talks, and examining different configurations,  help us with more complex math?

Now the connection was made.  “Now I can see how the bigger number is broken down into smaller chunks, and it’s easier to work with”, “Once I can break down a number in a task, I can work through the math quickly, and know that my answer makes sense.”

So, math teachers, if you have not done a dot number talk yet, please do!

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High engagement
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Natural leap to making the image connect to number.

I am a teacher in Ontario, so…

with all of these articles (like here, here, oh, and yes — here), how can one not be aware and contemplative of the EQAO scores, specifically in Math.  As a grade 6 teacher, and as one of the many others who saw the Ontario results, the question, “What happened?” has been eating away at me for days.  Since then, “What happened?” has morphed into “What do I do now?”

Because, if not now, when?

However, before I discuss my thoughts, and, spoiler alert:  There is no one answer, I should probably do my best (within my knowledge) to give some information.

The Concept of “50%”:

I can see how the concept of “50% achieve” in Mathematics on EQAO a little deceiving.  Remember, these are those students who achieved level 3 or higher on the assessment.  It does not mean that 50% “failed”.  In fact, if we compare to the description on the provincial report card, a “C”, or, level 2, is:

“The student has demonstrated the required knowledge and skills with some effectiveness. Achievement approaches the provincial standard.”

So, in reality, this student has not failed.  They are approaching provincial standard.  I am positive when more specific scores are available, educators will find that many students will be ‘hovering’ in the mid/high level 2 range, and thus, in theory, students who are considered ‘moveable’.  Another question arises:  Why are these students not moving into the “level 3” category, and what do we do to help them get there?

The concept of “rote memorization”:

Now, let’s jump to another point that comes out in media.  As per Robyn Urback’s article, “rote memorization” seems to one solution that keeps popping up.

So, sure.  Let’s go with that idea.  Let’s ‘play’ as if we go ‘back’ to teaching rote memorization of mathematical facts.

Great.

Here we go.

OK.  So, what mathematical concepts (because, they are concepts!) can we actually memorize?  The first thing that comes to mind is multiplication tables.  I noticed in the comments sections of these articles was a concern that students could ‘not make change’.  Many people commenting were discussing specific instances where they were at the checkout, and the person working was stumped.  Sure, a concern for many.  We need to go back and memorize so that we don’t have this guffaw at the store.

Also, working flexibly with money and money amounts is something that is perfected with experience.  Those who work in the retail industry are going to have mental shortcuts for finding change, and are only going to become fast and fluent when they are constantly doing so.  The real-life experience is what makes people ‘fast’ at giving change and working with certain amounts.

So, we memorize our multiplication tables.  Heck, why not use what we know about multiplying, and apply it to division (it is just the inverse, right? Oh no! Wait, that won’t do.  Did you just learn math by making a connection between the relationships of operations?).  We can do the same for memorizing our addition and subtraction facts.  How high do we go?  Do we memorize a certain number by a grade?  For example, we all now up to our 12 times tables by grade 6?  That would be my first question.

Well that fixes that!  What else can we memorize?  Oh, some polygons! A triangle has 3 sides, it looks like this:

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See?  You memorized it.  Now you know triangles. I can do the same for other regular 2D polygons and 3D figures.

Now I can have you memorize some formulas.  Perimeter and Area for starters.

Great.

But what about the other strands and areas of mathematics students are to experience, and are to learn?  Interpreting data, for example.  I am not too sure how to have that become rote.  Every graph is different with different information, so strategies for reading and understanding the information given in a graph is going to change.  What about patterning?  Patterns change and morph, they can grow or shrink.  Sure, a simple pattern might be “decreasing by two each term”, but what about more complex, and geometric patterns?  You need to look at them, think, and analyze them.  Again, I can’t give you a one time formula to memorize and you know patterns.  For the sake of argument’s sake, there are math strands in the Ontario Curriculum that cannot be sheerly memorized.

Assessment Itself:  What are we wanting to assess?

If we continue the idea of making math completely rote, what would an assessment like EQAO look like now?  How would EQAO be laid out?  What would be the purpose of the assessment?  Would it literally be a table of addition, subtraction, multiplication, and division questions?  Would timing and speed be valued as well (meaning we add a timing element?).

Or, are we wanting to know exactly how a student is learning and understanding in mathematics?  If I go rote teaching, then really just making sure they have it memorized. Even then, someone will forget the formula, second guess their memory.  Will scores be that much different?  Maybe.  What exactly am I testing at this point?  Memory, or a student’s ability to process, problem solve, and use what they know about math in a new context?  Their application capabilities?  What is going to give me more information as an educator into a student’s understanding, and ability to process and apply math?

So, to get a little broader picture, I guess a word problem could be added.

Shavi bought $16.55 worth of goods at a store.  He gave a $20.00.  How much change should he receive?

No matter how much practice and memorization the student has done, what are they going to do now? If we have just been rote memorizing straight up math facts, some things are going to happen here:

  1.  They will struggle with what operation needs to be required here.  There is language that needs to be comprehended and deconstructed.
  2. Even with rote memorization, the decimal will be the hardship. No child can be expected to memorize whole numbers and all possible decimal number operations, too.  If I round the 16.55 to 16, subtract that from 20, my math will be wrong.  Suddenly they are going to need a strategy – yes, a strategy, to solve this effectively and efficiently.

So — here is what I am getting at:  Rote learning and memorization will not solve the EQAO problem.  Math is a fluid, flexible concept — it ebbs and flows depending on the situation the math is in.  One strategy will not always be the best dependant on what is happening.  Rote memorization will not  be the answer to all mathematical quandaries.  Will automaticity and fluency of math basics help?  Absolutely.  Will teaching completely in this manner ‘fix’ the issues of the scores?  Probably not.

What We Can Do Now:

So, now I have two things to say:

  • If math were completely rote in schools, would assessment practices such as EQAO garner any worthy information other than it was memorized or not;

or

  • If testing for a student’s mathematical thinking and application skills is what we are interested in as educators, and as a society at large, then rote memorization is not going to ‘fix’ very much, if anything.

What does need to happen?

Well, clearly many things.  If anything, the latest results tell us we need to keep looking deeper.  We are not going to have any one answer anytime soon.  We need to look at 3 big areas:  How students learn mathematics most effectively, how teachers know, understand and present math, and the developmental reality of conceptual attainment in mathematics.  There is a developmental piece for how students learn math – are we addressing this enough?  Maybe we need to really look at the curriculum and the test itself.

Either way, as a society, as educators, we need ask ourselves what are we looking for when we standardize test.  Are we looking for patterns into student thinking, application, and connecting ideas?  Or do we just want to make sure they can recite the multiplication table without skipping a beat?

How do I really effectively test a student’s actual mathematical understanding?  Once I have figured that out, what does it implicate for the teaching and learning of mathematics?

Mathematical balance is a phrase that pops into my head.  Giving students time to investigate mathematical concepts, but also giving them time to practice and become comfortable working with the ‘mathematical basics’.  As of the 2005 Ontario Math curriculum, this has always been the process of math instruction.  Never does it say “no longer do we teach multiplication tables!”.  A balance of both conceptual and explicit instruction is needed; and teachers need to know when to do which depending on the student’s needs.  Most of all, we want our students thinking.

If anything, EQAO makes us bring questions to the table, and requires us to really talk about what we need to do as educators.

 

The Classroom

So here it is:  A huge, massive room that I am lucky to inhabit.  In a week, 25 Grade 6s will live here, too.

One of my (many, many, many…I can’t write many enough) goals this year was to make my room purposeful.  I wanted to create a space that was open, minimal, and ready for student voice.  I’ll let the room speak for itself.

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The room itself:  First off, I am super lucky to have so much storage.  This makes the room seem less cluttered.  Because I have a lot of room, I made the seating on the left (as you can see with single, double, triple, and group options for students), and there are standing tables around the room.  I am lucky to have two guided table/areas, so my awesome SERT, Geoff Keen (@keenwlu28), and I can run guided practice.

The right hand side is ’empty’ and this will be our meeting area.  Students will be taught how to move their chairs to this area for read alouds, consolidation, and anything else whole group needed.

At this point, my bulletin boards are bare.  They will soon become full of student work, voice, and our learning together.  I want students to have a say as to what we decide to put up, and what we decide is valuable to our learning.

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White Boards/Verticle work space:

I had purchased these white boards last year, so thought I would prop them around the room.  Baskets of white erase markers are scattered, so students can collaborate on the white boards.  All of my STEM items are organized in the cupboards, for students to reach.

I have left our provocations on each work area, so students can enter and move toward what speaks to them on the first day as they enter.  I have left stickies and markers in the hopes some may write what strategies they are using, and what they are creating/building.  Some may or may not write, but that is ok for now.

IMG_0806Reading:  I am huge on reading, love it, and am passionate about reading.  I have many, many  books — all from my own collection.  I have organized them at the ‘front’, so they are easily accessible for students.  One thing I like to do is have students continue to add to the books as their interests become relevant.

IMG_0800Math Play Table:  This will be my math play table, thanks to sara (@saravdwerf)’s blog about creating a play table.  I am eager to see it start!  Thanks to @Trianglemancsd for the patterning with mirror idea — such a cool way to see symmetry, and depth of patterns.

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As students work, I will leave these very generic reflection prompts of their provocation/games to start.  Some will write, all will talk, and the practice of reflecting and making connections with tasks will begin!

IMG_0802Self Regulation:  A simple quiet area in the back corner for students who need a breather.  They can think here, read here, grab a clipboard and work here — but it’s also an alternate place for them to go if they need a little space.

I am happy with my skeletal plan, and ready for my student’s to add their mark.  This white board will soon be full of student thinking!IMG_0804

Defining Play in the Classroom

When one thinks of play in the classroom, one probably imagines this:

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This is actually my daughter playing at the Light Table at the Ontario Science Centre, but you get the gist.

Which, at least in my mind, generally includes:

  • Younger children;
  • Blocks, toys, and other items being used at the child’s digression;
  • The children are leading the play (and a teacher may be recording and observing the play for assessment purposes).

What you generally don’t see in the Junior classroom is this same level of choice in play.  Yes, you will see students playing games, whether games like Set, or online interactive games – and there is choice, there is generally an ultimate purpose:  A mathematical fact or concept that the game is being used to practice.

I am all for this – however, I was wondering, and what started this whole play in math idea, is if that same level of freedom on their play; the play would be the freedom and the driving force or catalyst for the math.

In my mind, here is where the focused and purposeful learning would happen:  By observing, and entering the play, and then challenging the thinking.  Sure, I run the risk of connections not being directly made to the math, but, I do hope that the play, that freedom and immersion, will lead to questions; to inquiries.  My job as an educator would be to find and rephrase the potential mathematics.

“So, what I am hearing you say is that you are wondering about…”

When I look up the definition of play, I find:

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However, for the purposes of school, perhaps we can add that challenge piece.  Ideally, the play would start out as recreational, and chosen by the child, but the challenges can be built, and the learning can connect.  Again, the play, in my case, is the catalyst for the conceptual learning.

So, perhaps I need to change the definition to fit education, and math:

Play in the Junior Classroom:

Engagement in a potential academically rigorous task that has the potential to catalyst (mathematical) concepts, and aid in the development of rich learning connections.

 

 

Purposeful Math Play in the Junior Classroom: Part One – Background Thinking

During my Math Specialist course, I focused my self-research on math inquiry.  I was lucky to have a course instructor who was quite experienced in this field, and I purposely chose to take the course under him (the great Matthew Oldridge) because I had been inspired by his Learning Exchange “Loving the Math, Living the Math” video series.  In the previous school year, I had also been inspired by Knowledge Building, and had started to think about making the link between the Knowledge Building ideas, and mathematics.  As luck would have it, Knowledge Building and Math was done for me.

After reading, and watching some videos, and talking to Mr. Oldridge and others who are  more experienced with mathematical inquiry, one question kept nagging at me:

How do I get my students to be mathematically confident enough to do true math inquiry?

I had attempted inquiry many, many times with my class this year, and it was a mix of fantastic, chaotic, terrible, messy, and sometimes just downright awful, and so I wondered how I could elevate my student thinking (this is a whole other blog post, really!).

So I started to look back — what could be missing?  What could I do better this year to engage and get my students to be critical math thinkers?  And not only critical math thinkers, but students who wanted to know more about math?  Delve deep into a math idea and really truly explore and learn?

For some reason, I started to read early years math articles.  I read blogs, watched videos — and I noticed something recurring:  These kids played with math.  Openly and genuinely played.  They were given time to play, to explore, to just…get messy with the math.

Could this possibly be what was missing with junior students?  Maybe there wasn’t enough time to play?

Yes, for sure, there are games.  Lots of games!  Card and dice games, coding and makerspace tasks, online games — my students generally loved these, but, were they being the voice in their math?  Yes, I always give choice in tasks, I was always giving options, and I had open and engaging tasks (I spent far too long spending night after night planning engaging math), but were they really exploring, deeply, the math?  And making the conceptual connections?

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Math “play” always had a clear math trajectory — students knew where they were going, and knew what was expected.  It took away a lot of the mystery and wonder out of math.

Sure, what I did was engaging — but the math was really ‘spelled’ out for them – they used the ‘play’ to demonstrate a specific concept, rather than the play being open, and students being involved in deep conversation, and coming to a realization of the math concepts the play demonstrated (*note:  I don’t feel there is anything wrong with the the former, I just feel I need more later!)

So, as my research continued, there really is nothing out there on free mathematical play and the junior student (and, by all means, if you have research, or have done choice mathematical play, send me your insights!).  This made me even more puzzled.  Was I missing something?

I am now embarking on a journey:  I am going to attempt some ‘free’ choice play in the junior classroom.  However, so far, this is all thinking, and nothing concrete.  There are three big questions:

  1. What will mathematical play look like in my classroom?
  2. How will I know if mathematical play is successful?
  3. How will the connections be made between the math play, and concepts?

This also leads to areas I need to think about even more:

-How will I set up play?  What provocations can I leave for students to truly explore?

 

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This quote, from Jo Boaler’s “Mathematical Mindsets”, is getting closer to what I am imagining as purposeful play in the junior classroom.

-What questions will I have to have ready to ask students for them to make mathematical connections?

Here is what I am hoping:

  1. Math play will lead to better math conversations between students; and more chance to experiment, and feel more comfortable experimenting;
  2. The math play will give tangible connections to concepts learned, to help with retention;
  3. Students will have more experiences seeing math as creative and fluid;
  4. Students will build math stamina, and, perhaps, be more willing to attempt challenging math problems;
  5. Students will increase their ability to reason and prove their math thinking.

My idea is to keep this blog going as I explore and research how purposeful math play in the classroom can look as I try this out!

The ‘First Day’

I am writing about the first day of school for two reasons:

  1.  In a month today, I will be standing (beside? next to? with?) ____ Grade 6 students.  To be perfectly honest, I am equal parts giddily excited (because I really love that first day buzz), and equal parts scared to death (because ‘what if?’ – and you can fill in the ‘what ifs’ as you will).
  2. Twitter is all about posting first day activities, suggestions, and ideas.

These two main reasons make me feel one thing:  Pressure.

The main pressure point is just that:  Coming up with an awesome day with a balance of engaging and thought provoking tasks, yet are not ‘too hard’, and tasks that are going to put my students in various situations so I can observe and learn about them as learners.

There is a lot out there.  Many ideas are fantastic, and make me go, “Oh! Yes!  I should do that!”.  Then I decided to stop.

One huge revelation hit me.

There are the other 179 odd days left of the school year.

Sure, the first day is important:  You give yourself a chance to show the students who you are, set expectations, and be their guide.  However, the same thing happens after the first day every year:  It’s 3:30, you are standing in your empty classroom, and, like a giant piano falling on my head (a la Looney Tunes), the sobering thought hits me:  “Right. I am doing this until June.  I have the rest of the year to get through.”

Don’t get me wrong.  Of course I curriculum plan, I look at my long range big ideas, I have a general idea of where my year is going to head (at least, I have thought about what lessons and tasks are going to take me, but there seems to be so much focus on the first day, that everything else becomes kind of blurred).

So, before I sit here and list all of the things I want to do on the first day, where I want to take my programming (more importantly:  talk about the tasks that are going to hopefully let me learn about where my students are, and then plan according to there interests/needs), I really need to think about the larger trajectory of my student’s journey, and really think beyond the first day.

And, the question now becomes:  Do I jump into math play right away (more on this later, with research, coming soon)?  Do I give a more Fermi-like task to decipher what estimation and numerical understanding (quantity, relationships) my students have?  Do I start a read aloud?  Do I jump into a Science unit with some inquiry tasks?

See?  Now I am looking at what my first week, month could look like…