STEM Without Boundaries (STEAM)

This is the story of the Sommer Cube (S3), a cubical maze module — leveraging binary and analogical reasoning as both classic toy and cognitive tool (developmental and research).  Analytic and holistic thinking; a competition of rational (programming desired logic functions) and nonrational.


Because there are so many issues involved, across so many disciplines, and so many constituencies with competing agendas, we need to get back to learning / development basics:  full-spectrum human / machine study, coordinated long-term involvement of Brain and Psychology Sciences.

Not to mention innovative     research on spatial cognition and documentation on the transfer of skills and logic acquisition from S3 to STEM:  knowledge transfer, very important to document claims for already jammed instructional time in K-12 curricula.  "Recognizing Spatial Intelligence", SCIENTIFIC AMERICAN (2010) 

It’s about the need to eliminate STEM / STEAM bias against "girls and minorities” by illuminating a side of the manipulator often not otherwise seen.


STEM development should be about power -- first, the power of abstract reasoning and then its practical application -- right from the beginning (bottom-up, in addition to top-down).  Spatial processing  -- (teaching and learning).

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.

Slearning / development research is a first step toward rigorous, scientific demonstration that  STEAM is as effecitve as STEM, and why.

                                                           The Equalizer

                                  Full-spectrum Cognitive tool and Classic Toy


"At present, it seems that inadequate attention is being paid to the teaching of STEM in early childhood education. Less than 5 percent of time in formal early childhood education settings is devoted to STEM learning, according to research presented at a recent conference on fostering STEM trajectories organized by the Joan Ganz Cooney Center and the New America research institute.”  

                                                     Rafiq Dossani, Integrating STEM in Early Childhood Education 

STEAM / STEM is really just about people of good will seeing the issues from a richer perspective, the larger whole — It should not be (but it usually is) an argument; it should be a coming together within the constraints of whatever budgets are in play.  An opportunity for innovation. 

"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)


It’s about adaptation to uncertainty:  unleashing the instinct to think, with Hands and Mind; play, with freedom of means and ends, and why it is important, in scientific terms.

Science Technology Engineering Mathematics in a low-tech / high-yield, cost-effective format, where questions of function, role and position determine meaning.  What seems to be not understood is that science is a question, not an answer — any child knows that.  

An exoskeleton, with form and space consistent with Gestalt Illusion and Architecture. Thus, it is analogical in nature.  However, the exoskeleton also circumscribes a system of linkable tunnels which depend on the Law of Gravity.  Thus, it is also binary in nature.

What does Sdo?

It kick starts intuition, the nonrational. 


“While all children would benefit from from play with the S3, its potential contribution to the cognitive development of girls interests me most. We now have substantial research evidence indicating that females lag behind males in certain spatial abilities beginning in early childhood and persisting throughout the life span—a gender gap that contributes to wide-ranging differences in cognitive capacities and opportunities, from everyday map-reading to entry into careers in physical and engineering sciences.  We also know that spatial skills respond readily to relevant experiences, with improvements in performance often larger than the sex differences themselves. The S3 is an ideal context for providing such experiences.

“The S3 is also a wonderful means of stimulating adult-child and child-child engagement and in an open-ended, mentally stimulating, endlessly fascinating pursuit.  Children benefit enormously-from such collaborative endeavors, both cognitively and socially.

"I'd like to see the S3 in every preschool and elementary school classroom, and in the home of every family with young children.”  

                                                   Laura E. Berk, Ph.D.  Child Development, 8th Edition(April 10, 2008, cc m.s.)


                                                      Laura E. Berk, Ph.D.  Child Development, 8th Edition (April 10, 2008, cc m.s.)

It’s about Challenging assumptionsintegrating concepts that have been carefully examined in radically different fields.  

It’s about how to think.  Reasoning about reasoning.  Key to scientific literacy for all studentsnot just the gifted.

It’s about developing and shining discretely (spatial cognition strengths become self-evident to all — without negative peer pressure). 

The reciprocal influence of Hands and Mind; 

Thus, S3 is about the need for more learning proficiency than problem solving competence:  situation awareness, creativity, and the careful construction of logical arguments, and their limitations.

Knowledge generation that manipulator can both express and demonstrably use -- avoiding what Whitehead called “inert ideas” -- propositional knowledge that the student could express but not use.


Thus, in operational terms, Swith its nested reference frames creates an interdependence of analogical and binary reasoning, transformation to higher and higher levels of abstraction, much as algebra (“al-jabr”:  reunion of broken parts) converts geometry into algebra (and vice versa) with the Cartesian Plane.    CHALLENGES / GAMES "Spatial ability and STEM:  A sleeping giant for talent identification and development.

Toward understanding cognitive development by capturing patterns of changing analogical and binary abilities.  Complex and real world stimuli. 

Scientifically verifiable Spatial Thinking   (space, representation, process:  multifaceted, interconnecting competencies, human and robot) tools and learning opportunities are needed, for teachers as well as students, diagnostic as well as development.

                                                      Pre-K and Up  

                                                          Informal Reasoning:  "Use it or lose it”.


It's about exploration of deep causal structure.

Sachieves this by leveraging full-spectrum cognitive / perceptual processing, advanced thinking and intuition (essential for  Science Technology Engineering Mathematics, STEM, and its inseparable partner the Arts -- therefore STEAMwith Hands and Mind, and self-reflection



A simple block and ball networking system which leverages full-spectrum cognitive flexibility / perceptual processing   :  learning algorithms, and the art of design, with an emphasis on advanced thinking and intuition -- and self-reflection (not "mere facts", but principles); functional relations, particularly goals and feedback (What information is relevant?  What are my assumptions?  Are they justified?)

It's about uncertainty as tool:

CONSTRUCTION LOGIC BLOCKS, a cognitive tool for the education-minded consumer.   

S(a motile) is a work of art of bare utility, like mobile and stabile, a machine which offers abstraction of form and function, as well as cognitive payoff, for the manipulator.

Thus, it’s about Fine Arts and Cognitive Philosophy.

Exactly the thinking of  Albert Barnes (and John Dewey) (SPACE AS ART).  Science / art as an integrated whole:  

"— scientific method as intelligence in operation, art, education — are all bound together in A SINGLE ORGANIC WHOLE. To put the matter in other terms, all genuine experience is intelligent experience, experience guided by insightderived from science, illuminated by art, and made a common possession in education."

                                                                                  Albert C. Barnes (regarding John Dewey's philosophy)


                                                  S3 Day at Pennsylvania Academy of the Fine Arts 

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

                     The Smart Block.

                                                      Binary and Analogical Reasoning

                                                      (switch from fixed to changing values).

                                                      The Upgrade.     

              Low-tech / High-tech Interface (TUI) Assessment

                        (physical cubes, etc., with input / output devices)

                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 [emphasis mine] 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 levels of abstraction, pattern, "'voluntarily' reproduced and combined", the rule which governs a system or phenomenon, exactly like numeric, musical, or visual relationships; patterns of thought (and their systematic breakdown -- learning requires negative knowledge), intuition, under simultaneous mental (rational and nonrational) and manual rotation.  Apex reasoning, patterns of thought exceeding the parameters normally experienced in logical operations:  where the strategies and tactics are evolutionary.  

S3 simultaneously demands a spiral of pattern recognition, inductive and abductive intuition) and deductive flip-flop, while impeding it (gestalt figure / ground illusion flip-flop) introducing error (intermittent reinforcement — reversal learning":  analogical reasoning, instrumental learning), exciting curiosity:  a topology of paradox.

S3 is transformative, a kick-start, a self-generating, self-sustaining, escalating causal loop, an evolutionary 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.

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.

"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

                          Full-Spectrum Cognitive Partners



                                                    (VIRTUAL REALITY paths confirmed)

Sis about simultaneous mental (rational and nonrational) and manual rotation, giving form to binary and analogical information, a coupling between physical objects and binary information where bits are directly manipulable and perceptible. 

In other words, the S3 physical state embodies the binary state of the system, as well as the analogical. (think Tangible User Interface -- TUI)

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  (common mistake:  BCM policy guide headline).   

(Arithmetic is a way of measuring -- math is about, patterns, thinking, and its application to formulate and problem solving; when presented in this way it can be fun, and rewarding.)   


                   Children's Museums / Advocates:  STEM

                       The Equalizer.      The Upgrade:  Hands and Mind.



© Michael S. Sommer, Ph.D, 2018