Sunday, July 7, 2013

The Three Part Problem in Full Day Kindergarten

Over the past year, I have been fortunate to be a part of ETFO's Reflections on Practice action research program. I have spent the year learning what it means to conduct action research, how to do it, and follow through with it in our learning environment.

Action research is a way for educators to reflect, alter, and learn from their professional development inquiries. When I started with this project, they described it as "the pebble in your shoe" that you want to figure out and research. Action research is incredible to read and explore as well because the theories and learning is taking place in an actual classroom...what is better than that?!

Last year I had struggled with how to intentionally teach math to young children who come with varying academic and developmental understandings of math.

What we knew for sure was that the messages in Full Day Kindergarten around large group instruction are quite clear: maximum message, minimum time. Although this is a message for FDK, I would say that as we move forward in education - this should be the same message for all grade levels. The best instruction comes through learning centres, long uninterrupted periods of play, and intentional small group instruction.

Having taught in primary and junior classrooms, I have used the structure of the 3 part problem across the grades. I have found value in the structure and the process of this framework. The biggest challenge to 3 part problem solving in kindergarten is that it could not happen during large group instruction all in one day.

So...we formulated our action research question:
How would using learning centres and small group instruction on the working on it portion of a three-part math lesson impact the strategies Kindergarten students choose?

We began our research by looking at the "gurus" in early math research. Doug Clements was a reoccuring name and his messages focused around the need for balance in early math education. He explains that children cannot get all of their "math learning" through play. There is a need for intentional teaching (or formal math instruction) of certain math concepts.

Our Methodology:
1. We hooked the children (by connecting the problem to their interests, ideas, or familiar literature). We wanted to ensure that children felt connected to the problem that was being presented.
2. Learning Centre Provocation: we set out intentional materials for the children to solve the problem (as we progressed in this process - the children became a part of selecting which materials would support their learning)
3. During Learning Centres: variety of support systems for children (some 1:1 instruction/support, small group interactions, independent work) - we captured the learning through photos, videos (which I love!), observational notes, and work samples (when it made sense).
4. Reflection/Sharing: closer to the end of the week (or when interest in the problem began to fade) we would carefully select students and prep them to share their thinking with others. Although this stage was not the focus of our research, we learned so much about the importance of sharing and its benefits if structured appropriately.

As always there are children who may never choose to explore a math problem, so we invited them! I think it is important for educators to remember that it is always ok to invite children to join activities if you think it will be beneficial for them. However, it is of course always about balance.

We learned through this investigation that an adapted three part problem allows children in FDK to solve problems using a variety of strategies. Using this framework to structure problem solving, allows children to investigate and practice various strategies in a routine like manner.

We found that by allowing the children an extended period of time (Tuesday through Thursday), they were able to investigate and come up with multiple solutions to problems that were presented. The number of solutions and their depth increased over time.
We also found that when the problem was generated by the children or came up genuinely in play, the children were very motivated and interested in solving the problem.
Challenges We Faced:
One challenge that we both encountered was the intention to have children solve the math problems in small cooperative groups facilitated by a teacher. Many children approached the problem and immediately began to solve the problem independently. The interactions between peers in the small group setting was minimal without strong teacher guidance.
We realized very quickly that the ability to solve a problem with a peer was more of a problem than the problem itself. Rather than pursuing the teaching of cooperative learning, a skill that needs direct and explicit teaching, we chose to allow for groupings to be more flexible and the children could come and go from the learning centre.
When too many children were working on the problem at the same time we found it really difficult to capture their thinking and learning adequately. In order to capture their process of thinking, we had to observe the entire process. With an increased number of children working at the same time, some children lost interest and focus, other children needed prompts
Another challenge that we faced in working through our adapted model was the timeline that we initially planned. We felt as though having time lines was restrictive. At times interest levels in the problem began to wean before the end of the week and the need to share solutions arose a bit earlier than Friday. The timing needs to be flexible depending on the problem and the interest in solving it.
Similarly, the extended timeline also affected us as educators in that our time was consumed largely by supporting, observing, and documenting the children’s thinking in this process. Being so highly involved in this problem took away from other opportunities to engage with the children in play and assess other skill areas. Having a more flexible timeline and decreasing the frequency of problems will continue to provide children with enriching math problem solving opportunities and provide educators with more time to interact with the children in play and other areas.
Implications and Recommendations:
  • We have learned that the 3 part math model is applicable and successful in the FDK classroom. Children were able to come up with multiple solutions and used various strategies to solve open ended problems. It supports their mathematical learning and development.
  • As we continue on our journey in problem solving, we hope to develop strategies and ways to support students in learning cooperatively together. We will also work towards coming up with questions that may better lend themselves to encouraging cooperative learning amongst peers.
  • We learned through this study that many of the children struggle to verbalize their thinking when solving problems or explaining their solutions. We have begun to model and support the children in verbalizing their thinking and will continue to find ways to support them in this area.
All of this learning is almost complete - I am working with my partner Andrea this week to "finalize" our paper. I know this is a long blog post, but I hope that some of the learning allows you to make connections to the math in your own space.
I will create another post with some of the sample questions and responses from children to provide that context - this post is far too long as it is!
I think as I finish up this project it makes me think about how important it is as educators to zone in our own learning. Choose ONE thing you want to work on - set goals, research, try it out, reflect, change it, and continue that cycle. Taking the time to slow down and examine your practices, as well as making connections to research is a really helpful process!


  1. Very interesting article! The efforts that you put in to make sure that the kids are comfortably getting acquainted with education are just wow! I wish all schools followed this sort of junior kindergarten curriculum.

  2. Great article; I love your approach to reflective teaching practice. I wonder if you could share how you have tweaked your approach to using three part problem-solving. You mentioned in your post that you would like to adjust to having more flexible timelines and to having fewer problems. Has this worked for you? Could you provide a bit more information on how this looks in your classroom now?
    Thank you for all of your inspiration - I love to read your blog!!

  3. Hi Sarah - thanks for reading and sharing!

    We began to tweak our process last year, but are hoping to "sort" it out a bit more this year? Isn't that always the way?

    When we began we wanted to put out provocation on Monday and "wrap" up Friday. However we learned, similar to the rest of our room, it is important to watch the children and let them guide the timelines around it. If they are disinterested or really interested the problem/provocation could be left out shorter or longer.

    We had one problem out for about 2 weeks and one for one 2 days! Felt much less prescribed when we let go of timelines.

    Our goal this year is to hopefully capture problems naturally or have them connected to the children (aka "Spring Fair"). I would ideally like to see 1 or 2 problems a month (instead of the 4-5 that we were trying to cram in).

    Hope that is helpful - so glad that you enjoy reading the blog, I love having a place to share my reflections and learnings...and to connect with like minded professionals like you!

  4. Thanks for your reply Tracy! I am also trying to slow down a lot this year and let my observations of the kids and their needs guide me more. We are only a week into school - so far I am finding it difficult to resist diving in with my own agenda but I know it will be worth it!

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  6. Hi tracy
    I am so glad that I found this post on your blog. I remember you talking about doing some research into the 3 part problem in k and investigating what it could look like. I am wondering if you might be able to explain a bit more on how you introduced the problem..was it in whole group? did you write it up on chart paper with picture help? also did you have students share their work to the whole class?
    Thanks for your help

  7. Hi Jessica!
    It definitely depended on the problem that was posed. We had a few problems that were connected to books that we read as a whole group. Sometimes when the problem came from the children's investigations we would introduce the problem in a small group. Sometimes we would create an invitation and then share our thinking or responses in a small or large group.

    Generally, we stray away from large group since so many of the children are at very different stages of development and learning.

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