CGS Professional Development Blog

Conceptual Understanding in K-6 Math Series with Cathy Fosnot by Amanda Jackson, Peter Dieter, Brad Strohschein, Leith Monaghan, and Shauna Pascoe

Posted on December 9, 2016 at 2:24 pm

The grade six team is taking part in the three-part series on conceptual understanding in mathematics. In part one, we explored mathematics understanding and how it is developed in the classroom. We began the day by looking at the Russian Peasant Algorithm and developing models to explain why the method works. This activity led into some great conversation about what conceptual understanding is and what is meant when students are asked to show or use a variety of strategies. We also reviewed some learning landscapes and considered how to use these learning landscapes to develop rich problems that are approachable by all students.

When students are asked to show strategies, what we are looking for is for them to show their conceptual understanding. Learning multiple different procedures is not the intention and does not develop conceptual understanding. For example, a student may decide to explain a multiplication procedure using an array model. Being able to work flexibly with numbers and visual models builds both conceptual understanding of mathematic concepts and numeracy.

Learning landscapes are visual models that show the big ideas of mathematics learning. As educators, we can use these models to understand where are students are in their understanding and how we can help them develop on the landscape. Learning landscapes are organized by conceptual understanding and include helpful models teachers can use to support that understanding. It is important to consider the development of mathematical understanding as a complex landscape when planning learning experiences for students.

Future learning of this series will focus on assessment and instructional practices. We look forward to this work and using this learning in our classrooms.

SHIFT Lab by Zoey Graf, Richard Shewry, Kim Larson, Lindsay Sanden

Posted on December 9, 2016 at 2:21 pm

2016-2017 – Year Long Experience


The weeklong SHIFTLab intensive was an engaging experience in which teachers, administrators, museum personnel and others involving in education took a journey through design-thinking, empathy and transformation of learning spaces.
–Human-centered design is a methodology for investigating how design can engage stakeholders, build empathy and solve complex problems
–Empathy is a corner-stone to working with design-thinking concepts and moves design into the human realm
–Looking at educational spaces from new perspectives allows for transformative thinking

This experience was highly collaborative and encouraging of authentic connection-making to foster idea generation and utilize the strengths of the unique individuals involved. The facilitators are exceptional at creating a safe space for failure and possibility. Divergent ideas allow participants to consider a variety of perspectives and impossibilities. These impossibilities, through play and experimentation, did on occasion become prototypes.

Things we are thinking about throughout this year-long experiences.
–How can I create opportunities to grow capacity for empathy and appreciation for authentic self?
–How do I help students write deeply and insightfully, after empathizing with historical texts?
–How might we create human-centered experiences that cultivate empathy in our community?

Any SHIFT Lab attendees are keen to talk design-thinking and empathy. Please seek us out for encouragement, resources and excitement.

Excellent Resources

D.School – design-thinking resource

IDEO – design-thinking and creativity

Creative Confidence – Great reading to support design-thinking and creativity

Compassion • Integrity • Collaboration • Courage • Curiosity • Democracy • Diversity