One of the things that is fascinating about using open-ended provocations in mathematics is that every experience with the materials is so different. Materials are chosen intentionally and often set out together to suggest an investigation but where the students take things makes it their own and often goes much deeper with the mathematics than what we may have intended.
Earlier this month I spent part of a morning in Stephanie Merrick’s kindergarten classroom at Hamilton elementary and the students had been using the materials from the Reggio-inspired measurement kit. The students in the class listen carefully to each other and are experienced with engaging with materials both independently and collaboratively.
I did a short mini-lesson on comparing linear measurements reading a book called Big and Small that compares different sizes of animals. We discussed how the term “big” is too general and that we need to use more specific language like longer, taller and shorter when comparing, I then modelled this using a set of matryoshka dolls, ordering them and using the comparative language. The students were then invited to use the materials and investigate measuring and how to compare measurements.
The provocations placed out on the tables…
And the students began measuring and talking about their measurements. We also placed some tubs of materials on the carpet. One student sat down not the carpet and started measuring his leg with cubes which then inspired others to measure parts of the themselves.
This pair of students lay down the panda matryoshka dolls and measured their lengths with gems and then recorded the measures.
As the girls were undoing the pandas to put them back together as a set, they began filling them with the gems they had been measuring with and wondered about the capacity of each doll.
During this visit I had a Queen’s student working with mean she interviewed Stephanie and captured some of her thoughts about teaching mathematics through Reggio-inspired practices. Specifically, Stephanie was asked how she thought student learning was affected.
- “Having everything hands on and play-based lends itself to extension. It lends itself well to students finding their own extensions”
- The practices and materials help students, “learn where they are at. If students are ready to learn more, they will explore it naturally.”
- The teacher noticed that it “takes away from my own micromanaging as they find where they will go next independently.”
- “It is engaging.”
- “It is easy to say to students ‘can you show me that in a different way with a different material?’” and the practices and materials provide these prompts.”
The students were engaged with the materials for almost an hour. During that time both Stephanie and I were able to sit alongside every child in the class and capture a glimpse of their understanding about measurement. The current prescribed learning outcome for measurement in kindergarten here in BC is: use direct comparison to compare two objects based on a single attribute such as length (height). Every student in the class was able to compare two objects (ie. two ribbons, two of the matryoshka dolls, their legs or arms, etc) and use the specific math language of taller. longer or shorter. Many students demonstrated understanding well beyond this outcome and measured using non-standard and standard units and were able to explain the differences in lengths or heights of the objects they measured using units. For example, one of the matryoshka dolls was eight cubes tall and another was four and a student said that the taller was was four cubes taller. As Stephanie suggested in her comments above, the provocations and materials provided the opportunity for students to extend their own learning.