As we said in the section on literacy instruction, we believe so completely in the benefits of play-based inquiry and want our students to learn in an authentic and developmentally appropriate way, however, there are definitely advantages to gathering the students together for small group work that explicitly targets their particular needs. In Math too, it was difficult finding a balance between just-in-time teaching at play centres and pre-planned group work. What we found to be helpful was to use playful tasks from Clements and Sarama’s learning trajectories book (see below) as small group lessons. This way we can still capitalize on the children’s interest and they are relaxed, engaged, and receptive to learning.
We think that Sarama and Clements captured the dichotomy well – play that involves mathematics and playing with mathematics itself. (American Journal of Play Winter 2009 p 313-337)
The Play Interest or Inquiry as Starting Point
When we begin an inquiry or see that the students have a particular play interest, we consider which Math strand or strands would be a good fit for what we are pursuing and these strands become the focus of our Math lessons. For example, when the children were interested in butterflies we brought in patterning because of the patterns on caterpillars and on butterfly wings. When the interest shifted to Space, we moved to geometry since 3-D solids seemed natural – spheres (planets), cones and cylinders (rockets), rectangular prism (our box as a rocket in the dramatic centre) to name a few. During our Bee Inquiry, 2-D shapes popped up, first as hexagons and circles in the large honeycombs we had. We plan lessons with an interest/inquiry led strand or strands so that we can be sure that we meet the needs of all our students and we can, through tracking, ensure full participation. However, these lesson-focussed strands are never the only strands addressed in our room. Through the play, every strand and the processes will be met as teachable moments present themselves.
Whatever the interest, there is always a link to Math. Whatever the strand, there are always the seven processes to consider to further math thinking and reasoning.
The Five Strands and the Seven Processes
When we’re teaching Math, we have to keep in mind that we are not only teaching a particular strand of Math but we are also helping the students use the seven processes to acquire and apply mathematical knowledge and skill. Much of the time this means we are asking open-ended questions to prompt for the meta-cognitive or reflective piece. They may have to explain or justify their thinking. How do you know…? Could you do that another way? But sometimes it also means we have to support the students with strategies. We have to introduce the young students to tools they could use, as well as support and question them as they learn to choose the right tool for the job. Problem solving strategies have to be taught and encouraged. We have found that many of our students have trouble just learning to listen to the problem and figuring out what the problem actually is. Having them slow down and restate the problem in their own words helps. They also have to be taught different ways to represent and communicate their learning.
For more information on the 5 strands and 7 processes see the Math section in the document below:
Whole Group Instruction vs Small Group Instruction
In Math, we generally begin with a whole group lesson. Our learning from our own Math Inquiry has convinced us that either starting with some really rich children’s literature or starting with a provocation linked to our current interest or inquiry will fully capture the interest of our students. (see the section on Our Math Inquiry for more information and a list of books we used) The books we choose or the provocations we present will allow multiple entry points so that everyone will be able to participate. Our whole group lessons are short and are intended to generate interest. Following this lesson, we invite the students to try what we have been discussing as they play. For instance, if we have just been learning about 2D shapes, we might ask the students to look for shapes in the environment as they play and to record how many they see if they wish. As educators present in the centres, we are turning the children’s attention to what is around them and asking open-ended questions to extend their understandings. During the sharing time at the end of the play period we will ask students to share some of the learning that we observed and want to highlight.
A New Inquiry
We are forever indebted to our very fabulous Math consultant, Anne Harding. She has been there for us from Day 1 and we can always count on her for thoughtful advice and sound pedagogy. We are excited to be working with her again on another Math Inquiry. This time, she has introduced us to a text by Douglas Clement and Julie Sarama titled Learning and Teaching Early Math the Learning Trajectories Approach. We love it because it clearly lays out the skills that young children need to dig deeper into mathematical knowledge. It helps us more accurately assess where our children are as individuals in their Math learning and provides some instructional tasks to help them consolidate their learning and move forward.
We first started using this text while learning about linear measurement. It helped us discern what we should be teaching and what we should be looking for when assessing the students such as – Does the student start and stop at correct points?, Are there gaps or overlaps as they measure? Are they using measurement units of equal size or are they mixing sizes? (eg. Cubes and links)
The information we learned helped us assess our students and place them under a developmental indicator. (progression is not linear) From there, we could concentrate on the tasks listed to help our students gain more understanding.
Small Group Work
During the play period following the math lesson, one of us will usually extend learning at the centres while the other works with small groups of students to address particular needs. To do this we set up a centre with one of the tasks that is outlined in the Clement/Sarama text and invite students to work with us. We have a list of the students that we want to see here in order to extend their math knowledge but others are welcome to come also.
One of the tasks that the children really enjoyed was called “What’s The Missing Step?” This involves stacking cubes like stairs from 1 – 6 cubes. When one of the “stairs” is removed, the child has to guess which one is missing and explain how they know. There’s that processes part!
In the centres, the other educator is using our assessment knowledge to extend the learning of the students.
Most of our students fall within 2-3 indicators of each other so as long as we can keep accurate and available records of where everyone is, we really only have to deal with 3 or 4 developmental levels within the class so we can readily know what we want to target for each level. Within each level, we can pull students together in different groupings. That is, the groups don’t have to be fixed such as the blue group or the green group. If we have 12 students working at a particular level, we can group them in a more natural way providing we track them well. We can take a look around the room and call students over to us who may be transitioning activities or who would be receptive to a change in activity. This way we are not interrupting anyone who is deep in their own learning. It’s tricky, but manageable.