Problem solving In Kindergarten
What does it sound like?
We know that to start we have to know our students. We have to have some kind of diagnostic assessment to give us a starting point. But then what?
Some people are very familiar with the format of a 3 part lesson but how do we make it work in K, especially knowing there can be a huge gap in numeracy skills and also based on what we know about oral language and young children’s abilities to receptively process information?
The 3 part lesson consists of:
1.Setting the context
2. Working on it
3.Congress to share thinking.
Working closely with our math consultants I have discovered that problem solving has to look a little different in K. Setting the context and establishing the focus can
definitely be done as a whole group. Where is gets tricky is when we want students working on it. I have found it is more manageable with most problems to have smaller numbers of pairs working on the problem, with the expectation differentiated based on the needs of the students. In other words I don’t have all students working on the problem at the same time. This allows me time to
move about asking questions to a selected number of pairs on a particular day, documenting with a flip camera or ipad as I go.
Many SK’s would be working with larger quantities, with the expectation of recording their findings to share. JK’s who need extra practice with early numeracy skills, including stable order, one-to-one correspondence, and
cardinality, might simply be challenged to count and compare a given number of objects.
Students are paired based on similar abilities. I have also learned that even though pairs are working with the same manipulatives, when recording information students need their own paper to work on. At this stage if you only give one paper you will find that students will pick their own corner of the paper to record rather than recording together.
The goal is to have students explain how they know what they know. Some will do it orally and others will record their information to share during the third part of the math lesson. In K we will call it our math meeting rather than a congress, since again it won’t be whole group but rather smaller groups based on their level of understanding. The idea of the math meeting is to have students:
1. share (express) their thinking
2. listen and respond to others
3. begin to question/clarify information presented
In the area of oral language these skills move in a hierarchy and this is a huge step so it is extremely important to be aware of the amount students are able to
receptively process (i.e. too much talk from a peer can have the same effect as too much talk from an adult. Some students can lose focus because they cannot
receptively process the amount of information being presented).
The hardest thing with the problem solving model is to avoid the “ tell.” When I see a student struggling with a concept, miscounting a group of objects, or struggling to record in an efficient way, my immediate reaction is to want to ‘help’ fix the problem. However in doing this I am taking ownership of the mistake or the documenting, and research shows the student won’t question the adult if I suggest how to correct (fix) it, even if he/she doesn’t see the mistake or understand why. The goal is to encourage peers to gently challenge each other, and/or to offer to assist a peer by reminding him to count slowly or hold his finger to help him tag the objects as he counts.
Hopefully this helps clarify some thinking around problem solving in kindergarten.
I thought I would include an example of one of our problems for you to see:
At Christmas time we had a food drive at our school, collecting food for our local food bank.
Many of my students brought in food to contribute. I always try to make the problem something that is meaningful to our team (Team Jellybean) and our school and this was a perfect fit.
We wanted to let the local food bank know how much food they would be getting from our classroom.
The first thing we did was the students as a group were given the opportunity to see what had been brought in, to spread it all out, talk about the different kinds of food and eventually they ended up naturally sorting the food into various groups.
Students shared their thinking as they physically manipulated cans, boxes and packages into different groups. There was some modelling of counting, one-to-one correspondence, and cardinality, all by students during this initial meeting.
That same day 4 pairs of SK’s were each given a group of tins and asked to record their findings, showing how many. (In the photo I actually had 3 SK’s with similar abilities working together with quite a large number of cans of
Notice they all came to an agreement as to how many.
Notice to the use of dot plate formations in their recording, something I have NOT modelled for them nor have I suggested they use. That has come out of group
discussions connected to ideas of how to record efficiently as a mathematician.
The math meeting had 3 students selected from the groups working on the problem the previous day. These students shared their findings and their strategies for recording.
On that same day I would also have another 2 or 3 pairs working on the problem while I document their conversations and learnings.
Math meeting for pairs from Day 2.
I may only have one or two pairs working on the problem and their math meeting the next day would be a very small group.
Here you see two little girls working on tagging and counting to figure out how many. I can tell you now that the number of objects was actually too many for the one little girl but she had her peer (whose abilities are a little bit higher) to help her, coaching her by modelling tagging and counting.
Problem solving in K is an ongoing journey for me and my students. My intent is always how to make it meaningful and purposeful while working on early math concepts.