The three part math problem in the play based Kindergarten environment

I have been teaching kindergarten for 10 years, and 4 years using the play based model.  I was introduced to the concept of the three part math problem about 8 years ago. Our school SIP plan incorporated the inclusion of the three part math problem as part of our mathematical instructional practices. It was an issue of some debate whether this could be successfully achieved in the KP classroom. Our KP team took the challenge and ran with it. We set up a program where we would introduce a math concept, put out manipulatives and grouped the students in mixed ability groups.  We would circulate among the groups and listen to their insights and ideas and help guide the lesson in the right direction according to our learning goal. We would then meet together as a large group and share our findings and talk about some of the strategies we used. Looking back, was there much differentiation of learning? Probably not.  Were parallel tasks offered to be inclusive of all learning styles?  No. Were we as educators cognizant of introverted students who were not comfortable working in groups?  Sadly, no.  

When I began to research inquiry based learning, and especially the Reggio model, I began to let go of my learning goals and see the math happen in so many unique and authentic ways. This is when I began to see how the three part model could still be honoured and modified in the play based environment. Explicit instruction does happen in the play based model; it just doesn't need to always be for a large group of students. Educators can still have learning goals, they just don't need to be for the whole class at the same time.

While students are immersed in play, this is what I see as the “problem solving” phase; when they take the mathematical concepts introduced to them either in a small group, or during large group instruction and apply it into their own lives in their own unique ways.  For example, when we introduced the concept of equality, some students needed the equal sign and created it with blocks, twigs and even their snacks. Some, preferred to use a pan scale, while others were not there yet and instead of balancing sets, chose to sort items. Some students worked together, while others chose to show their thinking on their own. The role of the educator during this problem solving phase was to keep the learning alive by providing materials to support the mathematical thinking, and asking questions and supporting the students’ thinking by giving gentle guided support.

The sharing part of the lesson can be a whole group consolidation, where students can share their learning with the whole class, guided small groups, or one on one sharing with student and teacher for those students uncomfortable with large group sharing.

What differs in the play based model, is that the learning can stay alive for a long period of time, infusing cross curricular learning.  The nature of the inquiry based classroom allows students who require more time to work out their mathematical thinking with the luxury of time. As well, those students who are ready to move on and take their learning to the next level are free to do so at their own pace and in their own unique way.  

In my opinion, the three part math problem is alive and well at the heart of the play based Kindergarten classroom.  It is through open ended learning opportunities, uninterrupted blocks of play, and opportunities to share and reflect upon student learning that students are challenged and encouraged to take their mathematical insights to levels we had never considered or dreamed of.

The Importance of Pedagogical Listening

A new year brings forth new possibilities...

      `It makes sense that our classroom environment is different this year as we have 14 new junior kindergarten students joining us.  We have to be cognizant of their interests, abilities, desires and wonderings.  We started off our year with just the "bare bones":  furniture strategically placed with a few intentionally chosen learning trays and materials.  As the school year progressed, we added to our centers to build upon the children's inquiries and learning styles.  For example, our dramatic play center has really evolved this year, mirroring a real kitchen with a real kitchen table, plates and utensils. These real items have been in direct response to the interest of a large group of students in our class and their desire to play "restaurant".  

Collaboration and respect are at the heart of our Kindergarten environment

... keeping our environment calm yet stimulalting can be a balancing act but this balance is one that we find both exciting and satisfying as educators.  

Light table provocation

We recently constructed a light table room for our kinders.  We had noticed through reflective documentation that this was an item that was rarely being visited in our kinder class.  We really thought about how we could create a provocation that not only honoured the concepet of the light table, but was intrinsically irresistible to our students.  We thought about several scenarios and locations.  We were cognizant of such things as traffic flow, sunlight and size.  After some serious brainstorming, we finally decided that we needed to move our reading corner to accommodate our new light table room.  We put up curtains so we had 4 walls, moved in some shelves to house our loose parts and then brought in the light table.  After thinking about it some more, we realized that this location would also be an excellent "safe place" for a child who needed some time to themselves, so we brought in our safe spot chair and books too.  

This whole process really makes me think about the value of reflective documentation.  If we (myself and Becky) had not taken the time to talk about our environment and look through our documentation we would have no idea that this valuabe part of our environment was being neglected.  

Reflections on Reggio... loose parts

Loose parts have become a very vital part of our "environment as third educator".  They fuel imaginative play, help prove our theories and inspire future wonderings.  I recently bought the book, Loose Parts:  Inspiring Play in Young Childlren" by Lisa Daly and Miriam Beloglovsky.  It introduces the idea of "what if" during play.  "What if..."  it's a powerful concept.  It makes me think of some of the great minds over the generations and how they dared to ask the question, "what if?"  "What if the same force that causes an apple to fall from a tree cause the planets to go around the sun?"  "What if I could talk to someone across the ocean?"  and "What if I could get my emails on my phone?"  

When we give students the tools and encouragement to ask "what if" we are creating the future problem solvers, inventors and theoretical thinkers of our next generation.  Loose parts can become anything to anyone.  It's all a matter of daring to dream and wonder.  

More reflections on introducing the equal sign in Kindergarten...

Our learning goal when introducing the equal sign was to dispel the myth of it simply representing an answer to an equation.  We purposely introduced it in conjunction with shapes as variables to make it “friendly” in terms of associating it with something the children already felt comfortable with and to help build the foundation of algebraic reasoning.  What surprised us was how the equal sign and fractions were intrinsically linked.  Representing half NEEDS an equal sign for the students to see how two halves can make a whole.  This concept seem to come naturally to many of our students when we asked them to show us “equal”.  Niko took a cracker and cut it in half and used his grapes to make an equal sign between the two halves.  This reasoning tells us that students are not only capable of deep algebraic reasoning in kindergarten, but much of this mathematical problem solving is naturally occurring around us and we are not paying attention, or naming the learning.  When we name the learning, we can then move the thinking forward and take bigger chances and broader our mathematical problem solving in areas we never thought possible in early learners. 

Pedagogical Documentation

I was fortunate enough to attend today's Pedagogical Leadership meeting with the focus on Pedagogical documentation.  We looked at the Capacity Building Series: Pedagogical Documentation Revisited.  It broke down documentation to 3 phases. 

1.  Observing and Recording Student Experience.  

My own documentation style tends to lean towards this particular phase.  I find that I am pretty factual and to the point when I record the learning happening in the classroom.  I try not to add my own personal inferences or opinions.  I was not doing this because I thought that this was the way I was supposed to do it, but simply because that is a reflection my of personality.  Here is an example of a recent documentation piece I produced:

2.  Interpreting Learning in Service Pedagogy.

This is when teachers interpret the documentation.  I see this part as "naming the learning".  If I was to look at the documentation in the above piece, I could infer that "B" is able to "pose questions and state problems as part of the design process".  "R" was able to "sort and classify groups of living and non-living things in her own way."  and "O" was able to "ask question about and describe natural  occurrances, using her own observations".  

3.  Respond, Share and Build a Culture of Inquiry and Collaboration.  

This is where I see myself reflecting on the documentation with the students and my teaching partners to see where we need to go next with each student.  How can we deepen the learning for the individual and what impact will this have on others?  This is where I see the documentation informing our practice... kind of like a road map of where we need to go next.  If I was to use the above documentation piece, I could say that we need to involve the students in finding the answers to their wonderings by building an environement that has the clues they need to solve their problems. We can put out provocations relating to the growth cycle, books about farm animals in both French and English which speak to what farm animals eat and we can work on sorting and classifying living and non-living things.  By sharing these next steps with my partners, parents and students we are building a culture of moving our thinking forward.  

New inquiry... new changes to our environment

We have a new inquiry... farms.  We could scaffold on this by talking about farm animals, but what I fear is falling back upon familiar and comfortable themes from our past Kindergarten program.  So, Becky and I are choosing to focus on the act of farming.  We are planting herbs and vegtables with the students and asked the students what they wanted to see in our classroom to support this new inquiry.   Some of our students asked for a "farmers market".  

They sorted our fruit and vegetable plasitc food and choose which baskets they wanted to use.  We will ask the students to label their farmers market and we will bring in some real vegtables and fruit to add to it.  We can't wait to see where the learning takes us...

CBC Radio: The Importance of Play!

Today at noon on CBC One, they did a phone-in show (Ontario Today) on the Importance of Play with guest Dr. Stuart Brown from the National Institute of Play in Los Angeles.  

Dr. Brown spoke of the importance of the "state of play" and how this unstructured, spontaneous play unpressured by time can help create important bonds between us, lessen anxiety and even reduce violence.  The 'doing' is more important than the outcome.  Dr. Brown talked about the difference between structured vs. unstructured play.  He pointed out that in unstructured play children get a sense of their own capacity when there is less parental involvement.  

One of the callers (Lisa) pointed out that Joy consists of 4 elements:  singing, laughing, dancing and playing.  She talked about how playing can actually reduce pain in adults and children.  Dr. Brown made the correlation with how this affects us at work.  If we are engaged in playful work environments, we reduce anxiety and see work as our "safe place".  This has a direct impact on sick leave in employees.  He used Google as an example of a playful workplace where employees feel valued and don't feel the need to take excessive sick days.  

Another caller, Katie (a child life specialist) said that play prepared children for an ever-changing world, spontaneous and unexpected.  She also spoke of the importance of improv and how this was a great tool to use with autistic children as it engages eye-contact, visual cues, and listening.  

What Becky, Sarah and I came away from the show with was that play doesn't end when you grow up.  Becky said that as adults, we are waiting for invitations to play.  We wonder if some of us are able to see those opportunities?

http://podcast.cbc.ca/mp3/podcasts/ontariotoday_20150417_92114.mp3

Reflections on Reggio...documentation

http://bpsearlychildhood.weebly.com/uploads/1/0/1/3/10131776/turnerkrechevsky.pdf

This is a great article on the Reggio Emilia approach and comments on each defining component.  I especially found the decription of how documentation informs practice and makes children aware of their own learning really insightful; how by looking back we are really looking forward!

One person's trash is another one's treasure!

http://www.nytimes.com/slideshow/2009/06/01/nyregion/0601-TRASH_8.html

An amazing article/slideshow depicting a Reggio-inspired preschool's use of recycled and found objects.  I'm feeling inspired!!!

Reflections on Reggio... Environment

It's funny how after you've worked with someone for almost 3 years how like-minded you become.  I asked my partner Becky this morning how she felt the environment was working in our room and she immediately responded, "it's not!".  She took the words right out of my mouth.  I feel that we have been focused so much on reflecting on inquiry and documentation in the last few months that we have forgotten some of the fundamental elements of the Reggio philosophy.  

How was our "3rd Teacher" working?  

Is our environment filled with natural light, order and beauty?

Does our environment have open spaces and is it free from clutter?

Does everything have a purpose?

Do the spaces encourage collaboration, communication and exploration?

Are there authentic materials and tools ready to encourage discovery and exploration?

After talking to Becky and answering these questions, we answered yes to some but no to more.  Things are beginning to look a bit cluttered in some areas.  There is not enough natural light and some items are getting lost in the chaos.  Some of the materials we have are not authentic or child-created.  I feel that we are not doing enough to "bring the outdoors in".  

This is something that we are going to focus on in the coming weeks.  We will keep you posted on our progress...

What is "self-active" play?

I recently read the book, "From Play to Practice" from NAEYC.  Near the beginning of the book, it talks about "self-active" play.  This is a term I had never heard before, but once reading about it, it seems pretty simple:  "self-active" play refers to spontaneous play in both children and adults.  This spontaneous play is in conjunction with the use of open-ended materials to support the play.  "The environment, the materials, and the children's natural curosity combine to activiate the brain to construct new meaning."  

I had often considered this type of play "open-ended"; we intentionally present the open-ended materials in hopes that it will spark the children's sense of curosity and initiate exploration and discovery.  

One of my personal discoveries is when we can set out a "provocation" with certain intentions or learning goals, and how the play always surprises us and takes us somewhere we had not considered.  That is the beauty of the Kindergarten program.  It gives us the freedom to look back and reflect upon the learning and name the learning.  I am always surprised just how many curriculum goals we achieve; so much more than or original leanring goals and always so much deeper and richer!  

Examples of our Math Trays in Kindergarten

Crayon Rocks

I just ordered these after completing an Ed Webinar on fine motor skills in children ages 3 to 6.  

"Fine motor skills: write outside the box".  I highly recommend it!  

GRIT

http://www.ted.com/talks/angela_lee_duckworth_the_key_to_success_grit

A question that we have been pondering lately in Kindergarten is why some of our students whom we classified as "devleping beyond" seem to struggle with some of the open-ended mathematical provocations in our kinder classes.  Why do some of the students whom we assumed were struggling matematically in such areas as numeral recognition, thrive and excel with these open-ended prompts? Is it due to GRIT?  

Kindergarten PLC today...

Today our kinder team met to discuss some of the learning from our k-12 math collaborative.  It was a great morning spent sharing and learning.  We started off the day viewing some of the Kindergarten Matters videos which focus on provoking an inquiry stance in mathematics.  This video spoke to many of us, and we connected to how the teacher responded to the learning by making a personal connection with the student.  We shared some of our personal stories of how we have pulled math from an inquiry such as in my room we brought out measurement when a group of boys built their own hockey rink. 

We reflected upon the car caravan problem that Helene Colombe assigned us back in January.  We had a deep conversation about mindset in regards to how the open ended nature of the problem spoke to many of our students who may struggle mathematically.  It seemed to allow these students an entry point which spoke to their personal strenths.  As well, we noticed that some other students who excell mathematically, struggled with the open-eneded nature of the problem; they needed a 'jumping off' point to get them started.  Diane Moore, an ECE member of our team, said that this was reflective of mindset; that the students who appear to struggle academically have to be more tenacious and persistent, thus creating a 'risk taking' stance in their approach to problem solving.  We all agreed that the kindergarten program, with its inquiry based approach, allows us to differentiate our instruction and environments to speak to wide and diverse audience of leaners.  

We also spoke about our grade one visit to Mrs. Pouliot's grade one class 2 weeks ago.  While we were there, our group observed their measurement centers.  We spent 75 minutes with the class while they engaged in their 5 centers.  Some of the observations that our group made after our observations were:  the learning was more student directed and less teacher initiated in grade one, there were certain expectations that the students knew that were expected of them before they left to centers in grade one, there were learning goals established before play in grade one, and the teacher had certain curriculum expectations behind her centers compared to in kindergarten, where the play is more open-ended.  We were also very impressed by the self-regulation that we saw during center time in grade one.  We saw evidence of collaboration and cooperation in the students.  

Lastly, we ended off by talking about the Capacity Building Series:  Maximizing Student Mathematical Learning in the Early Years.  This document gives lots of great examples of responding, extending and challenging in a math stance and some helpful tips when creating a math-rich environment.  

Our group plans on meeting again soon to discuss the results of our algebraic reasoning problem.  

The equal sign and early mathematics

I am part of the k-12 Math Collaborative and our last assignment centres around algebraic reasoning. My teaching parter, Becky, and I chose to focus on the idea of the equal sign and how it means the same, not answer.  This is a major part of algebraic reasoning.  I was talking to a grade 3 teacher at my school today about this and she said that this is one of the biggest stumbling blocks when she is teaching algebra problem solving.  I was thinking that if we in kindergarten can get the idea across to to our students about the real meaning of the equal sign in ways that are authentic and real world based, we can actually build the foundation of algebraic reasoning in children that they can access in later grades to take their learning further and deeper.
Mariam Small talks about this in her book "Great Ways to Differentiate Mathematics Instruction".  She says that "an equation is a statement of balance".  She suggests that using a pan balance is "an excellent model for the concept of an equation.  It helps students see what it means to say the sides have to be equal."  By using the pan balance in student-led play with loose parts, the students will be able to connect the concept of sameness to real-life scenarios.
I will post our finding soon.  I can't wait to see where the learning will lead us!

Welcome!

I have decided to start my own personal blog as a learning tool to help me document my personal learning as a FDK teacher.  I have been teaching kindergarten for almost 10 years now and this is my third year in the FDK model.  I feel that I have come a long way in the last three years as a FDK teacher.  I have learned about the Reggio model and have been fortunate enough to visit some Reggio inspired schools and daycares in both Ottawa and Boston.  As well, the inquiry model, which is the heart of the FDK program, is something else which I have endeavoured to implement. This model of learning is something which speaks to me personally, as it allows me to respond, extend and challenge the students in French and in a way that is personal and unique to each child.
Please join me on my journey!  I have so much more that I look forward to discovering!