003*25 x 7 eds 2 copy milkin

                               STEM Without Boundaries

                                                          Pre-K and Up  

                                      S3 Cognitive Tool 

                               (low-tech / high-yield, cost-effective)

STEM development should be about power -- first, the power of abstract reasoning and then its practical application -- right from the beginning.


The GAO report [4/10/13] on STEM education announced that few of the "complicated patchwork of overlapping programs" are ever assessed for their effectiveness.

"Knowing this, why do we consciously put our nation at a disadvantage by failing to provide a strong STEM education for as many students as possible?  By failing to improve access to STEM, especially for under-represented groups such as girls and minorities, we are compromising the ability of our youth to compete for the jobs of tomorrow."                        

                                           Rep. Marcia Fudge, Chairwoman, Congressional Black Caucus (4/12/13)

Sprovides clear connections to curriculum outcomes by critical and measurable early exposure to the core of Science, Technology, Engineering, and Mathematics:  a self directed visuospatial tool.

Key to scientific literacy for all students, not just the gifted.

Reasoning about reasoning;

The reciprocal influence of Hands and Mind; 

How to think;

Develop and shine discretely.

                Cognitive Strengths -- Unseen, Unrewarded 

                                       Cognitive Payoff

The intersection of "general cognitive fields, illustrated by the Sreciprocity of Hands and Mind, and its epistemological premise (made tangible within a cubical field), and the newest research on manual and mental rotation, not to mention common sense, asks serious questions regarding the present love affair with computer learning and the avalanche of effectively unassessed implementation in the national STEM efforts -- with profound consequences for children, particularly in the early years.  

The Soffers answers in terms of manual and mental rotation benefits perfect for the acquisition / discovery of subtle cognitive skills, by teacher and student alike. Unlike formal disciplines / learning systems, there is no peer pressure to underperform (a fundamental survival skill in many schools).  Here, girls and minorities, for example, are on a level playing field.

In many cities a child spends more time dealing with negative peer pressure and ducking bullets than thinking about learning, and making a future -- a deadly, paradoxical environment.  

It is not impossible to make a difference with such a child -- but the children need to be spotted and given a voice in their development and its assessment, some way of communicating, "I'm smart" without making enemies.  Hands and Mind discovery with a simple tool is what Sis all about:  

Facilitate the engagement of what Einstein called Combinatory Play.


“The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined... this combinatory play seems to be the essential feature in productive thought before there is any connection with logical construction in words or other kinds of signs which can be communicated to others."

                                           Albert Einstein:  letter to Jacques Hadamard,

                                                     The Psychology of Invention in the Mathematical Field, 1945 

S3 is about pattern, "'voluntarily' reproduced and combined", the rule which governs a system or phenomenon, exactly like numeric, musical, or visual relationships -- and its simultaneous mental and manual rotation.

S3 simultaneously demands a spiral of pattern recognition (inductive - abductive / deductive flip-flop) while impeding it (gestalt figure / ground illusion flip-flop) introducing error (intermittent reinforcement), exciting curiosity:  a topology of paradox.

S3 is transformative, a kick-start, a self-generating, self-sustaining, escalating causal loop, a cycle of cognitive development where the manipulator is both agent and object of change.


"[The universe] cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word." 

                                                                       Galileo Galilei, Opere Il Saggiatore, 1623



A networking system that leverages full-spectrum cognitive / perceptual processing, learning algorithms, and the art of design with an emphasis on advanced thinking; reciprocity of Hands and mind.

                                     The Dialectic     


Reasoning about reasoning.

The reciprocal influence of Hands and Mind. 

How to think.

Develop and shine discretely.

          "Are Constructivism and Computer-Based Learning       

                            Environments Incompatible?"

"Calls for the widespread use of computer-based educational technology often justify themselves by the potential to support some version of constructivism, seen to be a major improvement in education over more behaviorist or information transfer notions of teaching. The strong claim that computer-based educational technologies are inherently constructivist cannot be sustained because current technology largely fails to provide four key components of a constructivist environment: an engaged learner, hands-on interaction with the materials of the task, an authentic problem-solving context, and human interaction during the learning process….”    

     Stephen Gance:  "Are Constructivism and Computer-Based Learning Environments Incompatible?", 2002

Arbitrary barriers between school subjects restrict the development of abstract reasoning.  A paradigm shift, a change of assumptions is needed.

Low-tech and high-tech.,%202006)(ISBN%20080774722X)(O)(209s)_MPop_.pdf

"The DNA of any great teacher is their ability to personally engage each student where they are and move them along a learning trajectory that taps into the student’s intrinsic motivation, learning style and capacity.  This kind of x-ray vision into the unique learning strengths of a student becomes increasingly difficult to manage and track as you add more students and impossible for a single teacher in charge of 20+ students. However, we can bring the powerful attributes of our learning management systems that engage learning online, one student at a time. Additionally, ... equip teachers with data on how their students best learn so that they can focus more on the magic that only their physical presence can provide. By leveraging technology in the classroom, we can finally realize the ideals of an egalitarian system wherein every student excels because every teacher is properly equipped.

                                                                                        Sajan George, Matchbook Learning

                Marriage of Constructivism and Computer Learning


Math is the power of ideas: the interplay of structure / space / change / quantity, etc.  Not “a way of measuring.” 

For example, the working assumption that “Math is a way of measuring” 

is the dumbing down of math, the weakest foundation possible  (BCM policy guide headline, link below).   

                   Children's Museums / Advocates:  STEM


                                                May The SBe With You    

                                                   A stronger foundation.

                                      The Equalizer.       The Upgrade.

© Michael S. Sommer, Ph.D. 2015