As you may know, District 30 adopted a math curriculum and a set of materials that place a strong emphasis conceptual reasoning. Our program is rooted in the concrete, pictorial, abstract (CPA) approach developed by American psychologist Jerome Bruner. Each year since, our teachers have worked to refine their instruction and evolve their math workshop to accommodate students of all ability levels.
I have the distinct pleasure of seeing students at Kindergarten through 5th grade wrestle with big ideas in math each and every day. For example, I observed Kindergarten students generating different ways (i.e., number sentences) to get to 20 using wooden number racks this morning. While the students were giggling with excitement, they were also building deep number sense. This afternoon, I observed 3 student struggling with exponential growth. The teacher asked them if they would rather receive a one-time payment of $1 million or a penny that doubles every day for a month. The students played with this until they figured out the equation.
As Stanford University Professor Jo Boaler has argued, math is a set of big ideas and connections (see her graphic below). When math is taught exclusively as a series of procedures or methods, students miss what makes mathematics a cohesive whole. If you are interested in the topic, I recommend her article, What is Mathematical Beauty? Links to additional resources and other related reading are included in the reference section. Of course, her book “Mathematical Mindsets” and her Ted Talk on math potential are also fantastic.