Cultivating Learners Through Mathematics

How does Math Learning look like in our classroom...

The learning environment is set up to create opportunities for choice, collaboration, personalized learning and inquiry. More specifically for mathematics, our hope was to broaden understanding of what mathematics is and what the teaching and learning of mathematics can be. We wanted students and teachers to see math all around them and be inspired to think about mathematics in different ways – to see mathematical ideas in the materials, in pinecones, in buildings and structures, in images of our community, in art, in stories.

We have intentionally curated both mathematically structured materials like pattern blocks alongside materials often known as loose parts such as ribbons, gems, rocks, pinecones, etc. We also have art materials available to the students such as paint, clay, yarn and wool so that students can express themselves and think using different languages. Students also have access to various tools to support their investigations such as measuring tapes, grids and ten frames. 

The learning environment is intentionally flexible with choices in seating and tables available for both students and adults. Interestingly, although we have some chairs available, most of the students have used them, preferring instead to stand or sit and lie on the carpet or use pillows. We have observed the flow of movement in the space and intentionally have large open spaces for students to move through. Shelves filled with baskets of materials are open and accessible to students. Students can choose the materials they want to use and take them to where they would like to engage. We took doors off of some cupboards to create more open shelving. Provocations are set up on tables for students (and educators) to inspire mathematical thinking and inquiry. We always like to say 'art of teaching mathematics' – the intersection between what we are noticing about our students and the curriculum. This intersection is the lived curriculum of the classroom and our role as educators is to focus on a pedagogy of noticing and listening – being present and paying attention to our students and then being responsive. Our yearly math planning last year focused on five key elements of early mathematics: counting, subtilizing, decomposing numbers, spatial sense and patterning. 

Other teachers often notice the collection of numerals we have in baskets and trays on our shelves. We are always on the lookout for numerals in dollar stores, thrift stores, etc... Students use them in their play and investigations, ordering them, using them to label/represent their collections or sets of materials or to use as purposeful numbers in their creations (addresses, phone numbers, parts of a story, etc).

Here are 'Instructional Resources' for Math Learning that we often use in our class:

https://janicenovkam.typepad.com/reggioinspired_mathematic/instructional-resources.html
Reference:
https://blogs.sd38.bc.ca/sd38mathandscience/2017/06/11/the-studio-at-grauer/

Why Mathematical Routines...     

• Regular practice that has multiple entry points, open-ended, and personalized
• Helps to build a mathematical community
• Collaborative 
• Encourages mathematical discourse
• Responsive
• Focus on a pedagogy and noticing and listening
• Focus on number sense, mathematical thinking and reasoning

Evidence From Research Readings...

Monograph #59
Making Space for Students to Think Mathematically

Dr. Christine Suurtamm, Brenna Quigley, and Jill Lazarus University of Ottawa
Reference
http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/WW_SpaceThinkMath.pdf

Shifting from evaluative listening to interpretive listening can help a teacher decide how to respond to and support mathematical thinking. Many of An- gela’s questions provided her with opportunities for interpretive listening: “Can you explain this to me?” “What made you think of unit rates?” “What did you find out when you did that?” We saw her make strong use of these opportunities as she used student responses to these questions to further probe their thinking; each question she asked depended on the student’s previous response.

When using questions to elicit and respond to student thinking, consider that:

Asking questions, listening, and responding to student thinking promotes group interactions and enriches students’ mathematical under- standing.


Asking questions that facilitate interpretive listening will prompt student thinking and will provide opportunities to listen to that thinking.


Asking good questions, can help to elicit student thinking.

Teachers can foster mathematical understanding by ...

• providing a safe space for taking mathematical risks, allowing for exploration, and promoting collaborative learning

• presenting rich problems and encouraging high-quality student interaction

• creating a math talk learning community

• asking good questions and listening to student thinking