READ ME Picture This Spatial Learning in math and science

These Grade 4 students have been studying multiplication. They build, explain and compare arrays to build a conceptual base that includes imagery for thinking in “units” not singles. Multiplying by 3 or 4 or 7 is a growth by a factor or unit of 3 or 4 or 7. Cuisenaire rods are an effective model for demonstrating multiplication because they are built as units. As student build with them they are challenged to see the growth in Units, not by ones.

Students build and match FINGERFOLDS to equation cards (answer included) so that they MATCH the correct FACT to the IMAGE.

FINGERFOLDS ARE a hand held reference tool to support understanding.

Once students “know” some of the facts they challenge each other to remember them.  The two students you hear are explaining to me how they understand the task of practicing.

PRACTICE SHOULD ENGAGE THE BODY, MIND AND SPIRIT. If you have to think, reason and manipulate things you are more likely to remember long term. That includes students actually being able to explain how the practice is set up and what it is accomplishing.

VISUALIZATION IN LEARNING MATHEMATICS HAS BEEN IGNORED FOR MUCH TOO LONG. Why do we make it so hard to learn when imagery makes it so easy to ENGAGE and then to REMEMBER.


THIS IS PRACTICE that I have playfully termed: FingerFolds…. because you can manipulate the distributive property at your fingertips.

THERE IS not a lot of benefit in practicing something you do not understand.. You waste brain power trying to remember what to do… if you were involved in building the understanding of what to do…. then you are practicing something you understand over and over. Now if you practice that thinking in collaboration with a partner you have company and a little competition and a space for innovation and personal mastery.

Use visual artifacts,  PUZZLES and FINGERFOLDS to help students stay engaged in their practice. Students control the level of Differentiation

BERCS CARDS are all about VISUAL SPATIAL REASONING being embedded in the learning, experiencing and assessing.


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The cards are starter tools, they open the door to student driven investigations. Or can be used as REALTIME ASSESSMENTS


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Layer in the complexity.