Member reflections on spatial reasoning articles, books, and resources.

Please add your own.

"Recognizing Spatial Intelligence." Scientific American. November 2, 2010.
by Edward Schroeter
This article gave me pause to think about all my mechanically gifted high school friends whose skills were grossly undervalued and ended up in the 2-year trades program, but might have gone on to win Nobel prizes. This article explores the failure of schools to value to spatial intelligence and the importance of paying attention to spatial reasoning.

"While those with verbal and quantitative strengths have opportunities to be identified by standardized tests or school performance, someone with particularly strong spatial abilities can go unrecognized through these traditional means. A recent review, published in the Journal of Educational Psychology, analyzed data from two large longitudinal studies. Duke University’s Jonathan Wai worked with two of us (Lubinski and Benbow) and showed how neglecting spatial abilities could have widespread consequences."

learning and teaching early math_2nd edition.jpg

Focus in Kindergarten: Teaching with Curriculum Focal Points

by Wilma Armstrong

By Karen Fuson, Douglas Clements, Sybilla Beckmann Kazez
Series Advisor: Jane F. Schielack

The article I read was interesting because it discussed what they are calling 'Focal points" - key learning that is important at different ages. The table provided in the article was informative beginning with spatial tasks preschoolers should be able to do as compared to a child in kindergarten or grade one. The chapter is from a book. I will need to go back and find the title of the book. I will send the article via our emails because I can't seem to load it here.

According to the publisher, the book describes and illustrates learning paths for the mathematical concepts and skills of each prekindergarten Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate understanding, stimulate productive discussions about mathematical thinking, and provide a foundation for fluency with the core ideas. This book also discusses common student errors and misconceptions, reasons the errors may arise, and teaching methods or visual representations to address the errors. Because learning paths cut across grades, related Focal Points at kindergarten and grade 1 have been included to clarify how prerequisite knowledge in prekindergarten contributes to later understandings. Focus in Kindergarten, one in a series of grade-level publications, is designed to support teachers, supervisors, and coordinators as they develop and refine the mathematics curriculum

Building Blocks and Cognitive Building Blocks
by Kristine Swift

This article explores how children use mathematics independently in their play, how adults support mathematical development through play, and touches on some of the equity issues around mathematics.

My big take-away: Theorems in Action can become Theorems in Thought – if we help children to mathematize (OR notice and name the learning?) **Children intuitively demonstrate mathematical reasoning to solve problems during play. One example – a boy who moved *both* ends of two long block closer together in order to fit short blocks across the gap. He was demonstrating knowledge of parallel lines.
“Many children intuitively use concepts of parallelism and perpendicularity just as this boy did. Such ideas have been called “theorems in action” (Vergnaud 1978)…..
…Unfortunately, the same boy who by his actions seemed to understand that parallel lines are always the same distance apart may not understand these concepts when he arrives in middle school. If he is not helped to mathematize his theorems in his actions, they will not become theorems in his thought.” p 321

Other take-away information:
Math is a big part of everyday play: in 15-minute videos of recorded free play of four and five year old children, “Overall, the children showed at least one instance of mathematical activity 43 percent of the time they were observed.” p 315

Researchers coded Math demonstrated in free play by 4- and 5-year-olds into six categories: (pp 314-315)
  • Classification
  • Magnitude
  • Enumeration
  • Dynamics (? I believe this is transformational geometry)
  • Pattern and Shape
  • Spatial Relations