Category: Explorations Guide

Our Partner — ERC

ERC Educational Resource Consortium

We’re suggesting a “New Architecture” for learning – one that foments deeper and more naturalistic intellectual engagement, provides flexible yet durable structures, proven inquiry practices with a “tool kit” for student and teacher success, and a vision of personalization that is far more than “blended learning” or the pursuit of “competencies”.

“Proper Questions”

“If I had an hour to solve a problem and my life depended on it, I would use the first 55 minutes determining the proper question to ask, for once I know the proper question, I could solve the problem in less than five minutes.”
Albert Einstein

Single Concepts

It is surprising how life loops around returning to similar, perhaps familiar would be a more appropriate word, ideas. My first foray into developing curriculum using technology started in 1968 at a company called Ealing in their Film Loop division as their physical science and math editor. I was to teach single concepts, as we called them, to students on silent films. The technology, a clever relatively cheap system developed by Technicolor, was designed to make film so easy to use that students and teachers could use it by themselves. In Jr. and high school I was one of those techies who set up and ran movies for teachers carting in and threading those hefty 16 mm projectors. I immediately saw the advantages of this new simplified technology.

I was also well aware of its drawbacks — silent, small image (super 8mm), just 3 ½ minutes in length, fragile, and relatively expensive media. These constraints made the task of developing single concept films, where images had to tell the story and words acted as captions, a great learning experience. I had to present ideas visually and not verbally, a new and demanding task for a former teacher used to standing and delivering to high school physics students. This was an even greater challenge in that era when textbooks, whose name well describes their form, were sparsely and poorly illustrated.

I had no choice. Text on film either as silent movie “cards” or captions over images wasted valuable film. I had to learn a new discipline, to picture a concept or tell a story with pictures and not words. I have always considered the opportunity to master this skill one of the great good fortunes of my life. You will, I hope, see in these Labs powerful visualizations of single concepts that your students can build their problem-solving abilities upon. And despite the lifting of those film technology constraints, the need for visualization and limited verbalization remain keys to student conceptualization and attention.

Science of Patterns

“The rapid growth of computing and applications has helped cross-fertilize the mathematical sciences, yielding an unprecedented abundance of new methods, theories, and models. Examples from statistical science, core mathematics, and applied mathematics illustrate these changes, which have both broadened and enriched the relation between mathematics and science. No longer just the study of number and space, mathematical science has become the science of patterns, with theory built on relations among patterns and on applications derived from the fit between pattern and observation.”

Lynn Steen, Science 1988

Why Spreadsheets?

9 reasons spreadsheets should be the mathematics engine of choice in schools.

  1. Spreadsheets are equity platforms available to all students at no cost. They can give every student a fresh start in math.
  2. Spreadsheets from Microsoft, Google, and Apple are ubiquitous, easy to use, powerful, and part of a suite with common, familiar, supported interfaces.
  3. Spreadsheets are the tools students will use in their workplace as well as school for relevant real learning.
  4. Spreadsheets are not just computational tools, they are visualization, interactive, and data science tools.
  5. Spreadsheets are function machines using functions and functional thinking to build and work with models essential to all STEM projects.
  6. Spreadsheets are the financial and business communities goto program, central to modern financial literacy.
  7. Spreadsheets are coding platforms easy to use for computer science beginners and powerful enough for serious programming.
  8. Spreadsheets are sharing applications enabling and encouraging students to work together online for group problem solving.
  9. Spreadsheets have a huge support network of videos, templates, and help available on the Web.