Five Pillars of Neuroconstructivism in the Brain by Tracey Tokuhama-Espinosa, Ph.D. March 2017

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v. June 2015 rev Mar 2017

Elegant Complexity: The Theory of the Five Pillars of
Neuoconstructivism in the Brain
By
Tracey Tokuhama-Espinosa, Ph.D.
March 2017

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Figure 1. The Five Pillars Model, Tokuhama-Espinosa, 2015

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Table of Contents
Chapter 1 Elegant Complexity: The Five Pillars .........................................................5
Introduction .............................................................................................................................5
Evidence for the Existence of the Five Pillars.......................................................................6
The Pillars versus Traditional Domain Areas of Teaching...................................................6
Potential Implications of the Pillars ......................................................................................7
The Pillars Complement Past Models of Learning .............................................................13
The Pillars Enhance Explicit and Implicit Learning...........................................................14
How the Pillars Interact with Each Other ...........................................................................15
Adding Value to Existing Research on the Brain and Learning .........................................16
Chapter 2 Economizing the Effort Needed to Learn .................................................19
Overlapping Networks ........................................................................................................19
From Piaget to Neurons: Constructivism and Hierarchical Complexities..........................20
Neuroconstructivism.....................................................................................................................26
Radical Constructivism.................................................................................................................27
Radical Neuroconstructivism........................................................................................................ 28
Chapter 3 Radical Constructivism Meets Curriculum Design.................................30
The Structure of Teaching and Learning............................................................................31
Arguments in Favor of Dividing the Curriculum by Subjects ............................................31
Arguments in Favor of the Pillars: How to Avoid the Curriculum Reform Madness ........33
Chapter 4 Complexity via Simplicity: Examples of the Pillars in Math and
Language........................................................................................................................35
Chapter 5 Pillars that Lead to Enhanced Diagnosis Ability .....................................40
Chapter 6 New Learning Goals in the 21st
Century...................................................41
Chapter 7 Ages vs. Stages vs. Prior Experience: What determines learning
potential?........................................................................................................................44
Ages vs. Stages....................................................................................................................44
Prior Experience..................................................................................................................45
Chapter 8 Teacher Training: Past, Present, and Future...........................................48
Chapter 9 Conclusions..................................................................................................49
Summary ................................................................................................................................49
Potential Drawbacks to the Application of the Model........................................................50
Potential Benefits of Application of the Model ..................................................................50
Final Thoughts ....................................................................................................................51
References ......................................................................................................................53
APPENDIX A: The Connectome Project....................................................................59
The Connectome Project: New, But Still Inconclusive, Insights .................................................59
APPENDIX B: Examples of Original Research Aims and the Added Dimensions of
Pillars..............................................................................................................................60
Appendix C: . Subject areas covered in curriculum around the world ...................64

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Figures
Figure 1. The Five Pillar Model........................................................................................2
Figure 2. Pillars and Sub-Pillars........................................................................................7
Figure 3. Examples of Symbols ........................................................................................8
Figure 4. Examples of Patterns .........................................................................................9
Figure 5. Examples of Order...........................................................................................10
Figure 6. Examples of Categories ...................................................................................11
Figure 7. Examples of Relations .....................................................................................12
Figure 8. Interrelation of Pillars......................................................................................15
Figure 9. Basic Educational Constructivism...................................................................20
Figure 10. Author’s initial attempts to divide the hierarchy of learning in Math by the
five pillars, Jan 2015 ...............................................................................................22
Figure 11. Hierarchy of learning in Math 0-6 years using the five pillars, Author.........23
Figure 11 An Embellished Elaboration Theory of Instruction, Author. .........................24
Figure 12. Myelination....................................................................................................25
Figure 13. Rehearsal reinforces myelination sheath, Author..........................................25
Figure 14. The Three Legs of Learning, Author............ ¡Error! Marcador no definido.
Figure 15. Five Pillar Examples......................................................................................30
Figure 16. Example of Learning Hierarchy of Math Skills Areas by Level Rather than
by Grade..................................................................................................................38
Figure 17. Overlap mapping of pillars and subject areas................................................39
Figure 18. Author’s Vision of Bruner’s Spiral Review of Hierarchical Information
Integrated with 21st
Century Pedagogy...................................................................43
Figure 19. Constructivist Pillar Model for Mastery........................................................47
Figure 20. Schulman's Original Category Scheme compared to Ball, Thames & Phelps
.................................................................................................................................48

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Chapter 1 Elegant Complexity: The Five Pillars
Introduction
A few years back I was asked to do a study for a Central American
government that suspected that children’s lack of academic success in the early
years was due to a failure to strengthen certain brain networks during preschool
experiences (0-5 years-old). This intriguing hypothesis led to the documentation of
16 neural networks needed for pre-numeracy and pre-literacy preparedness, more
than half of which were not stimulated enough in the preschool settings we
observed in regular practice (Rivera, 2013; Tokuhama-Espinosa & Rivera, 2013). It
appeared that the hypothesis was correct: Early development of key neural
networks needed for reading and math were not rehearsed enough, which
probably contributes to school failure in the primary years. This finding was
important because it highlighted at least two aspects of the teaching-learning
process that have only just begun to be incorporated into modern teacher training
based on Mind, Brain, and Education science.
First, learning does not take place in single isolated spots in the brain nor
due to a singular type of experience, but rather through a series of connections
gleaned from a variety of moments that link areas and networks together to create
the potential to learn. These neural networks or basic brain circuitry are inherited
through our genes and strengthened through our daily life experience. Learning
can be improved depending on the type of stimuli a person receives in his or her
learning environments, including home, school, the wider community as well as
the surrounding culture. The exciting conclusion drawn from this new information
is that we teachers can improve student learning outcomes by taking advantage of
a better understanding of these neural networks followed by the use of
methodologies that correctly stimulate them in an orderly way. The
appropriateness of the methodologies depends on determining this “orderly way,”
however, which unfortunately, has yet to find full consensus in the world of
academia. However, we are getting closer, thanks to better documentation of
classroom practices and findings in neuroscience.
This leads to the second finding that reveals what appears to be a new
dimension to learning previously undocumented in the literature. When sorted, I
found that the 16 neural networks needed for pre-literacy and pre-numeracy skills
fell into just five distinct types of studies, shedding light on a different way to
structure teaching that may be more natural than our current curriculum divisions
by subject or domain areas. Upon review of nearly a thousand studies of the pre-
reading brain and the early forming math brain, it became apparent that all these
studies could be divided into just five “pillars” which were related to one another
in an iterative design and through a constructivist hierarchy.
This concept paper will first describe the five pillars, explain their
complementary nature to current models of learning and offers evidence for their
existence in distinct research domains. It ends with an invitation to examine the
potential implications of the pillars in educational practice.

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Evidence for the Existence of the Five Pillars
The neuroscientific studies I have reviewed from 1990 to the present about
the brain as it learns to read or as it learns to do math can be sorted into either (1)
symbols, (2) patterns, (3) order, (4) relations and/or (5) categories. I refer to
these groupings as “pillars” because each can be considered on its own and stand
firmly without external support, however, when combined, they can sustain even
larger structures, in this case, human learning.
In the literature there are hundreds of studies about how the brain encodes,
recalls, recognizes, shapes, and creates symbols such as letters and numbers (e.g.,
Smolensky, Goldrick & Mathis, 2014).
Similarly, there are a myriad of reviews of the brain’s pattern-seeking
mechanisms from those in nature, sentence structuring, analogies and behaviors
(e.g., Long, Li, Chen, Qiu, Chen, & Li, 2015).
Likewise, studies showing the brain as it struggles to structure its world as
it learns that “Tom likes Sally” is very different from “Sally likes Tom” shows that
true learning relies, at least in part, on order (e.g., Dunn, Greenhill, Levinson, &
Gray, 2011).
It is also apparent that relations are fundamental to learning concepts both
in and outside of school settings (e.g., Baumann, Chan & Mattingley, 2012).
Understanding magnitude, measures and proportions enable humans to connect
ideas and link their surroundings in ways that explain natural phenomenon as well
as the world of ideas.
Finally, there are numerous studies that explain what at first seems like the
brain’s ability, but later is clearly identified as the brain’s necessity, to create
categories in the world of physical things as well as ideas and intangible concepts
(e.g., Kourtzi & Connor, 2011). The seemingly intuitive manner in which semantic
memories are grouped along similar neural pathways, for example, make it clear
that the brain facilitates learning by economizing networks and expediting
retrieval by placing similar schematic representations together and/or by
grouping categorical knowledge along similar routes.
The Pillars versus Traditional Domain Areas of Teaching
My initial study focused on pre-literacy and early math skills in pre-school
children. I then expanded my review of the literature to include Math and Literacy
from primary through high school. When I found that these studies could also be
grouped into the pillar structure, I expanded my search to include other academic
fields. After researching nearly 4,000 different studies related to human teaching
and learning, it appears that just about anything that can be studied and learned
can fit into the five pillars. These five basic pillars of human learning -- symbols,
patterns, order, relations and categories— appear to be the foundations for all
subject area study as far as the brain is concerned, not only language and math but
every other domain area taught in school.
My review of the cognitive neuroscience literature from 2003 to 2015 on
learning found studies that considered the Arts (e.g., Mell, Howard, & Miller, 2003;
Segev, Martinez & Zatorre, 2014; Vessel, Star & Rubin, 2012; Zeki & Nash, 1999;),
History (e.g., Thomson, 2011; Kennerley & Kischka, 2013), Physical Activity (e.g.,

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Erickson, Hillman & Kramer, 2015; Hillma, 2012; Staiano & Calvert, 2011; Zatorre,
Fields, & Johansen-Berg, 2012), and Science (e.g., Gray, 2013; Lipko-Speed,
Dunlosky & Rawson, 2014; Wagenmakers, van der Maas, & Farrell, 2012), that
could all be documented showing symbols, patterns, order, relations and
categories; nothing fell outside of these five pillars. It appears that different types
of learning as documented by brain circuitry tend to be similarly aligned to take
advantage or economize the process of learning itself. I presume this cannot be
accidental; the brain is far too efficient for such a coincidence. Independent of
domain content information, similar types or modalities of learning travel similar
pathways in the brain.
After comparing academic fields typically found in K-12 education, I then
asked friends in Architecture, Gender Studies, Figure Design, Museology, Peace
Studies, Administration, Economics, International Trade, Communications,
Technology, Artificial Intelligence and Neuroscience if their fields could similarly
be divided into area knowledge using the five pillars and found initial puzzlement
and then amazement as we found that anything they considered field knowledge
could, indeed, fall under the same five pillars. I then asked gardeners, grocery store
owners, bank tellers, journalists and baby sitters the same question: Does what
you do fall neatly into the five pillars? If found that is appears that just about
everything humans can learn can fit into these five pillars, so long as the definition
of these groupings is agreed upon in a broad way. I suggest the following sub-pillar
categories:

Figure 2. Pillars and Sub-Pillars, Tokuhama-Espinosa, 2015
Potential Implications of the Pillars
Cumulatively speaking, I propose that it is possible to analyze all human
learning through Symbols (forms, shapes, representations), Patterns (series, rules,
regularity, chronology), Order (sequences, cycles, processes, operations, systems
thinking), Categories (qualities and equivalencies) and Relations (proportions,
correspondence, approximations, estimation, magnitude, measure, quantity, space
and context). I suggest that the pillars serve as a complementary system that can
accompany any existing curriculum structure, or teaching, evaluation or research
system. I hypothesize that learning outcomes can be improved by adding the
pillars dimension to teaching.

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Figure 3. Examples of Symbols

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Figure 4. Examples of Patterns

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Figure 5. Examples of Order

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Figure 6. Examples of Categories

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Figure 7. Examples of Relations

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The Pillars Complement Past Models of Learning
These two insights (neural networks develop as a consequence of
potentiating genetic composition and the existence of the pillars) complement
existing theories of learning. Happily, these five pillars do not contradict other
types of research sorting schemes or learning theories, but rather complement
them by adding a new dimension to their usefulness in academia.
The pillars explain the holistic functioning of the brain and learning. This
means that common practices of looking at learning from cognitive stages of
development, chronological and mental ages, or through physiology and neuro-
functions can be complemented by viewing the data through the pillars and can
change the way we approach teaching and learning processes. We can look at
learning through distinct methodological approaches, environments, techniques
and routines in a new way by applying the pillar dimensions to existing processes,
as is explained in Chapter x. The pillars also help bridge studies from neuroscience
to those in education by offering the commonality of symbols, patterns order,
relations and categories that are found in the classroom, the lab, and in society.
Learning can be difficult and often feel foreign, forced and unnatural. As I
wrote in Making Classrooms Better (2014), thankfully the brain is efficient in its
dealings with new information. The natural pathway of a stimulus makes its way
into the brain with first stops in memory centers to compare what it already
knows to the new information: All new learning passes through the filter of prior
experience (Tokuhama-Espinosa, 2008). When the brain is faced with something
with which it does not already have some kind of past experience, one of the best
ways to approach it is through analogies. Learning through the pillars is learning
through the analogical references of prior symbols, patterns, order, relations or
categories.
Kauchak and Eggan (1998) suggest that the introduction of new content
should always be done within a familiar frame of reference. When direct
links to past knowledge are not available, the use of analogies is key: “The
closer the fit of the analogy, the more learning is facilitated” (Kauchak &
Eggan, 1998, pp. 295–296). Ever since human communication has existed,
analogies have been used to help learners connect with unknown concepts
by offering “parallel” ideas (Harrison & Croll, 2007). Before the written word
existed, Aesop’s fables, Bible lessons, and almost all forms of teaching were
passed down through stories, a special type of analogy (see Hulshof &
Verloop, 2002, for concrete examples of analogy use in language teaching).
Being able to piece together knowledge from past experiences is a fundamental
aspect of all new learning and vitally important in developing thinking skills.
(Tokuhama-Espinosa, 2014, p.213)
In addition to remembering the role of analogies in new learning, it is also
important to remember that feedback and metacognition are intractably linked.
The brain can’t help but learn, but it does not reach levels of metacognition
without training and guidance. External feedback and explicit teaching help
develop habituated, intrinsic thinking patterns and improve the internal
metacognitive processes of learners. If we were to teach children to identify the
symbols, patterns, order, relations and categories around them in a routine fashion

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throughout their education, they would then naturally call upon this way of
thinking as they approached anything new throughout their lifetime. Guided
feedback from teachers improves metacognitive abilities in students -- how they
think about how they think. I suggest that if teachers were to regularly include the
pillars dimension to their classroom teaching they would deepen students’
understandings of new information because their prior knowledge would become
more visible thanks to analogical processing.
The Pillars Enhance Explicit and Implicit Learning
The five pillars have the additional benefit of taking advantage of both
implicit as well as explicit learning. The difference between implicit and explicit
forms of learning was first discussed in detail in the 1970s (e.g., Brooke & Miller,
1979; Reber & Lewis, 1977). Reber noted that implicit learning displays a lack of
consciousness of what and how something is learned (in DeKeyser, 2008), whereas
explicit learning moments include mnemonics and strategies as well as
representational systems (Reber, Kassin, Lewis & Cantor, 1980). An example of
implicit learning is the use of authentic, real-life contexts, such as when a child
learns to ride a bike, while explicit learning examples include classroom settings
with typical methodologies such as precise discussion strategies to highlight a
specific type of vocabulary in a foreign language class.
The understanding of symbols and the recognition of patterns are both
implicit and explicit depending on the methodology employed. This is also true of
order, relations, and categories. Whereas the understanding of patterns, for
example, is generally an implicit aspect of learning, the use of the pillars would
make it an explicit learning tool. The use of both implicit and explicit learning
enhances the probability of recall.
While implicit and explicit memory systems are distinct neural networks in
the brain (Dennis & Cabeza, 2011), there is speculation by Dew and Cabeza (2011)
that “under certain circumstances, there may be an important and influential
relationship between conscious and nonconscious expressions of memory (Dew &
Cabeza, 2011, p.174). This could imply that if the use of the pillars is habituated
over time that the interface between implicit and explicit learning can be
improved, leading to enhanced uptake and improved recall, though this is only
speculation as of the date of writing. What does seem likely, however, is that
content knowledge and non-domain specific knowledge will find greater overlaps
when the pillars are used.
Different types of learning (semantic recall [e.g., Flegal, Marín-Gutiérrez,
Ragland, & Ranganath, 2014], affective learning [e.g., Berridge & Kringelbach,
2013], implicit memory dependent learning [e.g., Curran & Schacter, 2013],
Bayesian learning [e.g., Gopnik & Wellman, 2012], symbolic and non-symbolic
representation learning [e.g., Gullick, Sprute & Temple, 2011], cooperative learning
[e.g., Fairhurst, Janata & Keller, 2013], auditory and visually stimulated learning
[e.g., Altieri, Stevenson, Wallace & Wenger, 2013]), among others, tend to follow
predisposed “logical” circuits similar in all humans, though individual variances
are notable. This, according to Sirois and colleagues (2008), is how
neuroconstructivism works: “Activity-dependence is one part of a feedback loop
with morphology, with each affecting the other” (Sirois et al., 2008, 321). While no

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two human beings appear to follow identical routes, similar neural pathways are
easily identified in large-scale studies that indicate general human tendencies.
Some impressive documentation of these networks can be found on the Human
Connectome Project webpage (http://www.humanconnectomeproject.org/) in which hundreds
of healthy adults have submitted themselves to brain scans while conducting the
same activities to document neural network use (see Appendix B). This means that
not only are the pillars a neat way of organizing curricula, they also appear to
mirror the way the brain aligns like-elements in neural networks.
How the Pillars Interact with Each Other
It is important to remember that the pillars are mutually interdependent
and are not necessarily regulated by a hierarchy themselves. Categories, for
example, are dependent on patterns; patterns in turn rely heavily on symbols;
order depends on relations, and so on. All of the pillars can proceed and succeed
one another.
In many cases it might seem logical to first consider symbols as conceptual
representations that usually precede patterns, order, categories and relations,
however this is not always true. For example, there are no symbols in some
patterns. For example, some patterns that occur in time and space -- such as
weather patterns, heart beats, sleep patterns, historical patterns, orbital patterns,
and so on -- do not necessarily depend on symbols. Similarly, while it might seem
predictable that relations and categories always occur together, this is not
necessarily true either.

Figure 8. Interrelation of Pillars
One way to envision the pillars in everyday life exchanges comes from a
memory I have of road trips. “20 questions” is a guessing game we used to play as
a family on long rides. My mother would always begin by asking if what I was
thinking was an “animal, vegetable or mineral?” This categorizing tool quickly
narrowed down the seemingly infinite number of options. She would then
inevitably ask if what I was thinking of was something we could see, or something
we had in our house, or something I liked. This was to determine the relationship
we had with the unknown object. Both the categorization question (“animal,
vegetable or mineral”) and the relationship questions were helpful in narrowing
down the choices, but they were not mutually dependent. This means the five

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pillars do not always exist together, but when they do, they are always
complementary.
Adding Value to Existing Research on the Brain and Learning
Researchers of teaching and learning processes find that studies in our field
are often grouped into journals to respond to specific stages of development (e.g.,
Child Development; Early Childhood Research Quarterly; Early Development and
Education; International Journal of Behavioral Development; Developmental Science;
Archives of Pediatrics & Adolescent Medicine; Studies in Higher Education;
Psychology and Aging), cognitive abilities or domain areas of study (e.g.,
Memory; Affect and Cognition; Creativity and Cognition; Intelligence; Learning and
Individual Differences; Mind and Language; Journal of Research in Mathematics
Education; Journal of Language and Social Psychology; Social Studies Curriculum;
Science Education; International Journal of Technology, Knowledge and Society),
problem areas or ranges in the human spectrum of intelligence (e.g., Gifted Child
Quarterly; Educational and Psychological Measurement; ADHD; Journal of Child
Neurology; International Journal of Language & Communication Disorders; Journal
of Learning Disabilities; European Journal of Special Needs Education; School
Psychology International; Journal of Child Neurology), explanations of the
physiology of learning (e.g., Cerebral Cortex; Genes, Brain and Behavior; Neuron;
Journal of Neuroscience; Journal of Cerebral Blood Flow & Metabolism; Behavioral
and Brain Sciences; Sleep; Memory; Journal of Neurophysiology; Brain Structure and
Function; Physiology and Behavior;), the teaching-learning process, teaching
techniques and best practice (American Educational Research Journal;
Educational Researcher; Review of Educational Research; Pedagogies, an
International Journal; Journal of the Scholarship of Teaching and Learning; Research
in Science and Technology Education; Perspectives in Pedagogy; International
Journal of Education and Research; Educational Studies), field tendencies (Trends
in Cognitive Science; Frontiers in Human Neuroscience; Frontiers in Education;
Research in Comparative and International Education; International Review of
Education; Nature Reviews Neuroscience; Frontiers in Integrative Neuroscience;
Cambridge Journal of Education; International Journal for Academic Development;
Mind, Brain and Education), and even research tools (Journal of Magnetic
Resonance; Brain Imaging and Behavior; NeuroImage; Brain Topography;
Qualitative Inquiry; Journal of Qualitative Studies in Education; Review of Research
in Education).
Such categorization does not lend itself to the intriguing potential of
elegantly separating these same studies into the ways that the brain itself might
actually sub-divide networks or webs of knowledge: symbols, patterns, order,
relations and categories. While the current research divisions are helpful and
necessary for publication processes, editorial division, grant recipients, and can aid
researchers in delving deeply into isolated areas of expertise in highly specific
aspects of the learning process, I argue that dividing information generated from
research into the five pillars better equips us to structure learning moments and
maximize the potential of children in our classrooms.
I do not advocate rejecting the existing division of research and teaching-
learning practices, but rather to their expanded use by adding the pillars to our

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thinking constructs. The pillars complement the characteristics of existing
research divisions by adding a new dimension to how they can be used. This
means we can read Patricia Kuhl’s Early Language Learning and Literacy:
Neuroscience Implications for Education (2011) with her original intent as a
comment on the importance of learning in social contexts and we can also review it
as a study related to “patterns” as part of her work considered infants’
computational abilities and the normal language processing (the regular patterns
of development) of monolingual and bilingual children. Similarly we can read
Rueda, Checa and Cómbita’s study on improved executive functions (EFs) in
children (Enhanced Efficiency of the Executive Function Attention Network After
Training in Preschool Children [2012]) as a confirmation that EFs can be enhanced
through training and additionally, as a study of how the brain manages
congruencies and incongruences through the pillars of “order” and “relations”.
This means that the rich body of literature already available that examines specific
aspects of the brain’s learning mechanisms can be extended in use by applying the
pillars dimension. Not only can neuroscientific articles be interpreted this way, but
articles in the field of education and psychology as well.
Examples from Education include Schleppegrell’s Content-based Language
Teaching with Functional Grammar in the Elementary School (2014), which
maintains its original purpose of teaching foreign languages through content areas,
but also can be viewed as a study on symbols (written expressions in different
languages), patterns (similarities between language systems), relations (how
content knowledge in one domain can be used to learn a new language), or
categories (grammatical rules; schematic understanding of content concepts).
In another example, Smolleck and Nordgren’s study on hands-on inquiry-
based learning in science (Transforming Standards-Based Teaching: Embracing the
Teaching and Learning of Science as Inquiry in Elementary Classrooms [2014]) can
also be viewed as a study of all five of the pillars, not just as best practice science
instruction. Scientific symbols, patterns of inquiry, the order of scientific
methodology, the relationships between observation and evidence, and categories
of hands-on experience that enhance scientific learning in middle school students
are all gleaned from this article as well.
The main idea is that all journal articles, independent of the field of study
can be interpreted through the additional lenses that the pillars provide. This does
not require any specialized knowledge of the field, but rather an openness of mind.
With a little imagination and a certain level of flexibility anyone can learn to think
through the lenses of symbols, patterns, order, relations and categories, and doing
so expands the utility of existing research by adding a new dimension of
interpretation.
Additionally, the pillars bridge education and neuroscience. Studies on
Executive Functions (EFs) training (e.g., Diamond, 2012) can retain their original
purpose of showing the benefits of training, but can also be viewed through the
pillars of order (motivationètime on taskèlearning) and relations (mutual
strengthening of working memory, cognitive flexibility and inhibitory control; the
relationship between EFs and decision-making). Yuan and Raz’s work (2014) on
structural neuroimaging of executive functions in adults can be seen as a general
meta-analysis of the “bigger is better” hypothesis of prefrontal cortex volume and

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thickness as it relates to EFs and it can be seen as a study of the relationship
between age and EFs, or the categories of tasks used to measure EFs. If viewed
through the pillars, we can analyze these two studies together to see whether the
types of studies that are used in the meta-analysis to measure EFs in adults
correlate with the types of real-world experiences children have in classes. This
means that existing studies will take on added value and can have extended
comparative use.
These different studies show that independent of what type or aspect of
learning is considered (domain area instruction, methodologies or activities,
neural correlates of learning, etc.), the pillars can serve as an additional lens
through which to view the data. Other examples of extended use of existing
research are found in Appendix C.

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Chapter 2 Economizing the Effort Needed to Learn
Overlapping Networks
By applying the five pillars to existing studies we can map out human
learning over a wide range of traditional school subject areas as well as consider
their overlap points, reducing the need for additional teaching time in those areas.
This exciting area of research related to “the economy of brain network
organization” (Bullmore & Sporn, 2012) has grown exponentially just over the last
few years thanks to the Connectome Project (www.humanconnectomeproject.org) and
better brain imagery which combines findings from a variety of imaging tools
(resting-state fMRI, task-evoked fMRI, diffusion imaging [dMRI], T1- and T2-
weighted MRI for structural and myelin mapping, plus combined
magnetoencephalography and electroencephalography [MEG/EEG]) and
behavioral and genetic data to render a more thorough understanding of learning.
The central idea of this Review is that the brain’s connectome is not
optimized either to minimize connection costs or to maximize advantageous
topological properties (such as efficiency or robustness). Instead, we argue
that brain network organization is the result of an economical trade-off
between the physical cost of the network and the adaptive value of its
topology. (Bullmore & Sporns, 2012, p.347; italics added by author)
This means that we as teachers have the potential of economizing student
learning as the same neural networks can often serve distinct academic goals. For
example, Stanislas Dehaene found that many of the neural mechanisms required
for reading preparation are similar to neural mechanisms needed for numeracy
skills (Dehaene, 2007; 2009). These overlapping areas provide great insight as to
how we should actually teach by emphasizing the similarities between language
and math rather than separating them and highlighting differences. Such an
approach would lead to a more efficient use of teaching time and strengthen both
language as well as math networks in the brain. Instead of teaching math symbols
alone, for example, teachers could complement math symbols (or patterns, order,
relations and categories) with symbols from language, (science, natural
surroundings, art, and so on), which may help some children relate to the symbols
better and/or remember math symbols better.
The fact that symbolic representations overlap leads to speculation that
other pillar networks could similarly overlap. The economizing of learning means
that core concepts in school may be mastered faster, providing more time to go
into depth in the subject areas. As all teachers know, time is of the essence in our
classrooms and many areas of the curriculum are short-changed in terms of
“coverage” due to the limited amount of time dedicated to each domain. The pillars
would allow for greater time in distinct domains by economizing areas of overlap.
It is thought-provoking to note that there are overlapping neural circuitry
for physical pain and social rejection (Eisenberger & Lieberman, 2004), visual
attention and eye movement (Striemer, Chouinard, Goodale & de Ribaupierre,
2015), social connection and physical warmth (Inagaki, 2014), self and other
perspective taking based on facial expressions (Lamm, Batson & Decety, 2007),

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and substantial literature over decades on the overlapping circuits of facial
expressions and emotions (e.g., Sprengelmeyer, Rausch, Eysel & Przuntek, 1998).
Many of these studies point to the importance of retraining teachers in their social
interaction with students as well as their delivery of classroom activities to
enhance learning outcomes. They also point to the likelihood of finding even
further documentation of overlap in pattern, order, relations and category
networks. The existence of overlapping neural mechanisms coupled with the
pillars points to the need for a dramatic restructuring of teacher training.
From Piaget to Neurons: Constructivism and Hierarchical Complexities
A few pages back I wrote, “The exciting conclusion is that we teachers can
improve student learning outcomes by taking advantage of an understanding of
these networks followed by the use of methodologies that correctly stimulate them
in an orderly way.” And then I lamented that the “orderly way” hadn’t yet been
found. This isn’t entirely true.

Figure 9. Basic Educational Constructivism, Tokuhama-Espinosa, 2015
Seeds were planted for better teaching and learning processes based on a
constructivist design using a hierarchical model as early as the early 1900s
starting with Dewey, Montessori and Piaget’s work (Ultanir, 2012). Constructivism
means that “base” elements are taught before “advanced” ones, and done so
through a hierarchy of skills revealed by stripping down subject areas into their
“lower” to “higher” elements. The results of introducing learning concepts this way
is improved positive transfer for each new higher-order learning stage as can be
seen in Figure 9.
Constructivism also explains why some learning goals are not met. For
example, a child cannot learn subtraction (learning goal) if he does not understand
addition (pre-requisite knowledge). To be successful, he will first need to
understand everything behind the concept of addition, and then make his way to
the higher-order skill of subtraction. If any one of the pre-requisite skills (laid out
in the hierarchy) is not developed properly, the child will have trouble mastering

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the new knowledge upon which it is based. Most neuroscientists know and almost
every parent can confirm that missing conceptual knowledge is the culprit of most
academic failure. For example, most of us have actually experienced how some
children will learn to mechanically identify the pattern of subtraction questions
and appear to dominate that skill, but in reality, they are simply using extended
working memory and an understanding of patterns to feign knowledge. This
permits the child to be moved through the school system because he displays the
mechanics of answering the subtraction question, despite not really understanding
what he is doing. True understanding means he can comprehend, identify, explain,
use and transfer knowledge as evidenced by creating his own problems in
subtraction correctly. These skills are rarely tested in a multiple-choice format,
and therefore rarely measured in current standardized testing.
In the 1930s and 1940s Luria and Vygotsky helped catalyze the debate on
constructivism through contributions on the learning mind (Luria & Vygotsky,
1930; Vygotsky, 1933, 1934), which set the stage for the most recognized leader of
constructivist design, Jean Piaget, who is well-known to educators and
psychologists alike for his careful observation and documentation of child learning
through constructivist stages (1954). The idea of mastery learning made popular
by Benjamin Bloom in 1956, means that the students should be helped to master
each learning unit before proceeding to a more advanced learning task (Bloom,
1985). Subsequently, Robert Gagné (former President of the American
Psychological Association’s Division 15) developed a “hierarchy of knowledge”
concept leading to specific curriculum recommendations of basic to advanced
learning tasks (Gagné, 1962, 1965, 1968, 1973). Harvard’s Jerome Bruner
contributed positively to this important discussion (1960) by complementing a
spiral review of hierarchically-presented information while preserving Bloom’s
mastery concept. Bruner declared that when learning was designed in an ever
iterative spiral upwards, “[t]he end stage of this process was eventual mastery of
the connexity [sic] and structure of a large body of knowledge,” (pp.3-4). That is,
the declared goal of education, as stated for the past several decades, is mastery
learning achieved through ever-more-complex thinking. Unfortunately, learning
goals and educational goals are not always the same, as can be seen by the current
educational model found in many countries around the world which are aimed at
standards or minimum acceptable levels in content knowledge rather than higher
order thinking skills or mastery.
In the 1970s many thinkers converged on the idea of hierarchical designs to
improve learning outcomes, however it wasn’t until the late 1970s and early 1980s
that real curriculum reform measures were launched that capitalized on the
concept. White (1973) joined Gagné and elevated the discussion (White & Gagné,
1974) about learning hierarchies while Phillips and Kelly (1975) summarized the
various hierarchical theories of development and educational instruction
propelling the concept of hierarchical complexities into the educational spotlight.
Jones and Russell (1979) helped subject-specific queries take hold by looking into
the specific hierarchical learning paradigm in science instruction.

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Figure 10. Tokuhama-Espinosa’s initial attempts to divide the hierarchy of learning in Math by the five
pillars, 2014

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The depth and complexity of hierarchical design in learning was also
improved upon by Harvard University’s Kurt Fischer (1980) who began some of
the first work stretching hierarchies to consider neural networks and the constant
change experienced by learners, rather than just discipline or domain area content.

Figure 11. Hierarchy of learning in Math 0-6 years using the five pillars, Tokuhama-Espinosa, 2013

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Fischer’s original theory of cognitive development related to “the control
and construction of hierarchies of skills” (1980) and has since grown into his
Dynamic System Theory (2001, 2008; Fischer & Yan, 2002; Rose & Fischer, 2009;
Fischer, Rose & Rose, 2007, 2009). Dynamic System Theory is rooted in two guiding
concepts: “(1) Multiple characteristics of person and context collaborate to
produce all aspects of behavior; and (2) variability in performance provides
important information for understanding behavior and development” (Rose &
Fischer, 2009, p.264). Fischer embellished the basic traits of hierarchical
complexity by returning to a more humanistic focus of learning design that
involves the messiness of individual change, independent of the content area of
learning. While others focused on structuring a hierarchical representation of
content information, Fischer and colleagues (2005) were concerned with how to
explain webs of knowledge and how thinking processes became more accurate,
efficient and elaborate over time and due to experience (including classroom
contexts).
A new model joining content-based hierarchies and thinking skills was
finally achieved in the late 1980s. In Commons and colleagues’ Hierarchical
Complexity of Tasks Shows the Existence of Developmental Stages (1988) the effort
to join the domain versus thinking hierarchies became a reality. Fischer and
Commons collaborated with other colleagues to unite their theories on the shape
of conceptual developmental throughout the lifespan based on complexity levels of
moral reasoning (Dawson-Tunik, Commons, Wilson & Fischer, 2005). This merging
of the minds expanded the developmental aspect of the constructivist and
hierarchical models to include life-long aspects of learning and the understanding
of human development in the process.
Reigeluth and colleagues’ summarized the body of work on hierarchy of
skills in The Elaboration Theory of Instruction (1980; 1983) in which they stated
what many excellent teachers already know is the art in the science of teaching:
the best learning moments are organized from (a) simple to complex, (b) general
to detailed and (c) intangible to concrete to abstract. Based on our slightly better
understanding of learning gleaned since the 1980s, we can add to these three core
hierarchical measures two bookends: pre-requisite knowledge the consolidation
the learning through transfer.

Figure 11 An Embellished Elaboration Theory of Instruction, Tokuhama-Espinosa, 2015.
Learning requires reinforcement. Few things are learned only after a single
exposure (and those are generally life-threatening situations); all academic
learning requires rehearsal. How much rehearsal depends on the learner’s past
Pre-requisite
Knowledge
(prior
knowledge)
Simple to
Complex
General to
Detailed
Intangible to
Concrete to
Abstract
Reinforcement,
Extension and
Transfer (fnew
experiences)

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experiences related to the new learning (greater prior experience, less rehearsal).
The speed of recall depends in part on the myelin sheath surrounding axonal
connections, which in turn depends of rehearsal.

Figure 12. Myelination (http://theteenbrain.bravehost.com/myelination.jpg)
If we combine Bruner’s spiral learning with Piaget’s constructivism and add
on knowledge about the way the brain’s speed of recall is influenced by rehearsal,
we have a model that might look something like the following:

Figure 13. Rehearsal reinforces myelination sheath, Author.
The more roles a piece of knowledge plays in an individual’s life, the faster
the recall. This is why something in math that is also learned as a pattern (or
symbol or order or relation or category) will be easier to recall than something in
math that is learned as a “cluster” (CCSS, 2011, p.5) or other intangible, unrelated
term. In other words, concepts learned in a vacuum with little context are not as
easily retrieved as concepts given multiple meanings through the pillars. This
explains why authentic learning contexts, in which the student easily relates new
learning to something he is already familiar with, are more memorable, and
therefore learned faster with better recall than information without context.
Constructivism (Piaget, 1954), hierarchies (Bloom, 1956; Commons et al.,
1988), spiral learning design (Bruner, 1960) and webs of knowledge (Fisher,

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2005) are different notions but coincide in the clear mapping of learning. In the
past these learning concepts were divided as domain areas (e.g., Math, Language,
etc.), and thinking skills (e.g., stages of cognition); the pillars elegantly mesh this
division.
Over the past 100 years of interest in the idea of complex hierarchies, there
has been growing precision in identifying the exact skills sets of domain areas and
neuroscience confirms observational accounts of cognition hierarchies
(Westermann, Mareschal, Johnson, Sirois, Spratling & Thomas, 2007). If one takes
apart textbooks based on official curriculum design, then one type of hierarchical
structure can be found. A publishing company typically has a “1st Grade Reader” a
“2nd Grader Reader,” a “3rd Grader Reader,” and so on, with content that builds
from one level to another. Similarly, curricula design (common Core, International
Baccalaureate, etc.) also has similar structures. If this is compared with studies in
neuroscience a slightly different hierarchy appears, which complements the first;
the more comparisons that are made, the greater the level of precision in the
hierarchy. The curriculum hierarchy can then be compared with subject area
specialists’ opinions to confirm order. For example, once Math hierarchies have
been mapped based on educational textbooks and neuroscientific studies, the
suggested hierarchy can be confirmed by math teachers who can use their real-life
student contact to add other factors into the successful learning model mix (see the
hierarchy example of Math concepts in Appendix A). The consensus from this
enquiry is probably the closest and most accurate hierarchy of learning
competencies we can achieve until neuroscience confirms the neuroconstructivist
design of each subject area.
Combined, the domain areas and thinking hierarchies provide a powerful
structure for organizing learning, one arguably superior to existing models. This
paper suggests that by adding a third leg to the hierarchies’ concept, the five
pillars, we might be able to make the structure stand more firmly.
Neuroconstructivism
Both the hierarchical model of learning and the idea of constructivism are
linked by the very important and relatively recent area of study of
neuroconstructivism (Ansari & Karmiloff-Smith, 2002; Dekker & Karmiloff-Smith,
2011; Karmiloff-Smith, 2006, 2009, 2012; Karmiloff-Smith & Farran, 2011;
Mareschal, 2011; Mareschal, Johnson, Sirois, Spratling, Thomas & Westermann,
2007; Mareschal, Sirois, Westermann & Johnson, 2007; Sirois, Spratling, Thomas,
Westermann, Mareschal & Johnson, 2008; Westermann, Thomas & Karmiloff-
Smith, 2010). Neuroconstructivism explores “the construction of representations in
the developing brain” based on “the experience-dependent development of neural
structures supporting mental representations” (Westermann, Mareschal, Johnson,
Sirois, Spratling & Thomas, 2007, p.75), or identifiable networks that are created
or strengthened through new experiences. Similar to the more familiar
“educational constructivism,” neuroconstructivism considers how new knowledge
in the brain is structured through networks in which simple circuits must be laid
down before more complex ones can take hold, a process which usually parallels
“typical” growth stages.

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Neuroconstructivism emphasizes the interrelation between brain
development and cognitive development. We see constructivist
development as a progressive increase in the complexity of representations,
with the consequence that new competences can develop based on earlier,
simpler ones. This increase in representational complexity is realized in the
brain by a progressive elaboration of cortical structures. (Sirois, 2008,
p.322)
Some of the most prolific authors in neuroconstructivism argue for
learning’s “middle ground” in which the basic architecture for learning is not
purely inborn as nativists would argue, nor it is completely externally and
experience-driven, a cognitivists would argue, but rather somewhere in the center
in which “cascades of interactions across multiple levels of causation from genes to
environments” influence learning outcomes (Karmiloff-Smith, 2009, p.99). This
can be seen as an argument in favor of the pillars. General neural networks for
learning are documented in neuroscience as having typical or atypical
development in all humans, but it is clear that individual experiences (including
classroom instruction) also alter these global configurations.
What is clear is that the brain’s efficiency groups similar types of learning
along predictable pathways. Whereas just a few years ago it was common to talk
about the possibility of each neuron connecting to millions or billions of other
neurons, it is now clear that there is a more organized and greatly reduced
possibility of connections.
Neuronal circuitry is often considered a clean slate that can be dynamically
and arbitrarily molded by experience. However, when we investigated
synaptic connectivity in groups of pyramidal neurons in the neocortex, we
found that both connectivity and synaptic weights were surprisingly
predictable.
Perin, Berger and Markram (2011) discovered that neuronal connections
were highly influenced by their neighbors and that “the neurons cluster into small
world networks” (p.5419) depending on what is happening close by. They
discovered “a simple clustering rule where connectivity is directly proportional to
the number of common neighbors, which accounts for these small world networks
and accurately predicts the connection probability between any two neurons”
(p.5419).
We speculate that these elementary neuronal groups are prescribed Lego-
like building blocks of perception and that acquired memory relies more on
combining these elementary assemblies into higher-order constructs.
This elegant finding explains why neuronal networks for specific skills
gather along similar tracks and are not randomly located throughout the brain in a
haphazard way.
Radical Constructivism
The concept of “radical constructivism” coined by Von Glasersfeld (1995)
extends regular or “trivial” constructivism by adding the element of subjectivity. In
radical constructivism an individual’s understanding and his actions are circularly

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conjoined; an individual’s subjective interpretation of his experience also
influences the learning cycle. This personalizes the idea of constructivism to
indicate that not only are the body of unique, individual experiences influential in
learning, but the interpretations of those experiences change learning outcomes as
well. This individualist radical view of constructivism gives weight to the idea that
while there are similar configurations for learning mechanisms and neural
pathways in the brain for similar experiences, there is also a heavy dose of
individual interpretation about that actual learning, meaning pathways will vary.
Radical Constructivism can serve as an explanation for Fischer’s Web of
Skills, which show pulsating advances in knowledge gains. They could either be, as
Fischer claims, natural highs and lows in the learning process. Or, alternatively,
they could be the brain’s needs to consolidate information over time, or they could
be due to the methodology used to teach, or to the lack of reinforcement, or they
could be due to the individual nature of the learner’s interpretation of his own
experiences (radical constructivism).
Radical Neuroconstructivism
Most teachers understand that there are no two identical brains because the
connections between synapses and the resulting neural pathways rely to an extent
on individual experiences (and no two individuals have the identical experiences).
This “uniqueness” is counter-balanced by the fact that there is a general design to
how the brain “typically” learns. That is, certain areas and networks within the
brain tend to function in similar ways in all humans, though there are, of course,
important exceptions as well as differences due to culture and/or atypical
development.
For example, most humans use pathways outlined by Dehaene and others to
learn to read (2009), but some people who have dyslexia are forced to use distinct
pathways because the normal channel is blocked, missing elements or inaccessible
(Shaywitz, Shaywitz, Pugh, Fulbright, Constable, Mencl,... & Gore, 1998). Others
who live in cultures with different conceptual schemata due to distinct cultural
artifacts for written language also vary in networks for reading (e.g., Tan, Spinks,
Gao, Liu, Perfetti, Xiong, ... & Fox, 2000). Neuroplasticity means that we can never
say “X” pathways or neural network is responsible for “Y” in all humans; there will
always be exceptions both due to the uniqueness of individual human experiences
as well as due to culture. This means that while there are typical pathways that can
be documented in studies with large numbers of participants to indicate a “norm,”
it will be impossible to prescribe teaching methodologies that will always work on
all subjects.
I believe that radical neuroconstructivism may point to the justification
needed to impulse change in current curriculum design. Whereas the division by
subject areas was recommended by academics to encourage ever-deeper
exploration in each of their domain areas, neuroconstructivists examine how the
brain creates and stores information based on a distinct logic for all learning,
which, I argue is more similar to the pillars than typical curriculum divisions in
existence today.
The final and perhaps most important question at this stage is whether or
not the hierarchy of complexities also parallel neuroconstritivism for all existing

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domain areas. Is the measure of increased white matter pathways in the brain
enough evidence to say that learning has occurred in a constructivist design? Is
there evidence of pillars at all levels of hierarchical conceptual development in all
domain areas, or is this just a good guess about how the brain processes memory?
And would the answer to this question change whether or not we adopt it?
At the least, these questions pose fertile soil for continued research
collaboration between neuroscience and education and in the best-case scenario, it
establishes justification for experimenting with a pillars constructivist hierarchy
model in education.

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Chapter 3 Radical Constructivism Meets Curriculum Design
The human brain is ominous and multifaceted and should be celebrated. It
is unfortunate that many teachers fall into the allure of simplistic approaches as to
its use and function rather than celebrating its complexity. The intricacy of how
humans learn causes interest and awe in the best of academic circles, but the
reality is that most research on the learning brain is delivered in the foreign
language of neuroscience, causing many teachers to retreat to unsophisticated
explanations and inadequate use of the potential of the information.
This paper suggests a new way to approach learning and the brain based on
Symbols (forms, shapes, representations), Patterns (series, rules, regularity,
chronology), Order (sequences, cycles, processes, operations, systems thinking),
Categories (qualities and equivalencies) and Relations (proportions,
correspondence, approximations, estimation, magnitude, measure, quantity, space
and context). I propose that if teaching and learning processes were approached
through these Five Pillars, there would be important improvements in teaching
and learning, curriculum design and diagnosis of learning difficulties.

Examples of
Symbols
Examples of
Patterns
Examples of
Order
Examples of
Relations
Examples of
Categories

Figure 15. Five Pillar Examples, Author
This chapter begins by considering how the Pillars can change current
curriculum design. This is followed by implications of the Pillars for improved
diagnosis of students’ levels of learning. Subsequently, we consider how the
Pillars can enhance the probability of successfully achieving 21st century deep
thinking skills. This will be followed by how the Five Pillars have significant
implications for changes in initial teacher formation and continual teacher
training. Finally, the Five Pillars create a solution to the dilemma caused by the
traditional separation of students in schools by their ages, stages of cognitive
development and/or prior experience. The paper concludes by identifying the
next steps necessary to apply the Pillars in actual school contexts and invites
readers for critical feedback and ideas.

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Advances in Teaching and Learning
There have been many keen insights by educators over recent years whose
work has helped us get to the heart of good teaching. Most of these efforts relate to
teaching methods, strategies, tools, activities, habits of mind (i.e., Costa & Kallick,
2009), best practices (i.e., Zemelman, Daniels, & Hyde, 2005), routines (i.e.,
Ritchhardt, Church & Morrison, 2011), mindsets (i.e., Dweck, 207), design (i.e.,
Wiggins & McTighe, 2005), attitudes (i.e., Esquith, 2007), techniques (i.e., Lemov,
2010), instruments (i.e., Feuerstein & Jensen, 1980), motivation (i.e., Cushman,
2012), teacher-student relationships (i.e., Fink, 2013); differentiation and potential
(i.e., Tomlinson, 2014), management (i.e., Marzano & Marzano, 2003), and/or
teaching to the whole child (i.e., Perkins, 2010). Most are these insights are applied
thorough a constructivist view of learning (i.e., Ultanir, 2012) and achieve
reasonably good results.
There have also been excellent front-line interventions by classrooms
teachers themselves who approach their daily work from imaginative
perspectives, such as Quinn’s pyramid model based on Reggio Emilio formats (i.e.,
Quinn, 2013) in San Francisco or the Wisconsin Innovative Schools network (Stout,
personal conversation 18 April 2015), which look to neuroeducation, creativity
and divergent thinking models for inspiration. If the pillars were to be adopted,
then the successful elements of these isolated efforts could be celebrated as there
are several crossover areas between these innovative efforts and the Pillars.
To the best of my knowledge, however, while there have been a number of
attempts at modifying the curriculum (Common Core; International Baccalaureate;
various State Standards) over the past 100 years, there have only been small dents
in its subject-oriented design. In international comparisons of school curriculum,
there is a surprising amount of similarity in content. All school systems around the
world teacher some form of language, math, social studies (history or civics), art,
science, physical education (health) and nearly all require a second language. Some
schools offer technology/computers, and moral or ethical studies. About half
surveyed teach work-related or vocational skills as well as the aforementioned
courses.
School curriculum has been and remains focused on the delivery of specific
academic subjects (domain areas of knowledge) such as math, language, science
and art. Deep content area knowledge is a welcome outcome of learning and there
are many paths towards this goal. I recommend considering the pillars dimension
to complement existing teaching methodologies and/or as a complement to
current curriculum design.
Arguments in Favor of Dividing the Curriculum by Subjects
Dividing curriculum by subjects appears outwardly logical because it
presumes we can then assign specialist teachers to classes, deepening the level of
content knowledge and therefore understanding by students. However, it was
found that having a Master’s degree in one’s domain area – a demonstration of
specialization -- had little effect on student learning outcomes (Hattie, 2009). A
teacher with a Master’s in biology was no better a teacher than a teacher with a
Bachelor’s degree in biology when it came to teaching high school biology,

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presumably because primary and secondary school classes rarely reach the depth
of content held by a Master’s level degree earner (Hattie, 2009). This means that
“going deeply into the subject” may not be as much of interest as knowing how to
help students “think like a biologist” which appears to depend more on
pedagogical knowledge than content knowledge. This means that a teacher’s
pedagogical content knowledge is more important than simple content knowledge
when it comes to learning.
It can also be argued that it is easier to divide physical spaces, teachers and
textbooks when they can be separated into subject areas. This is probably true and
it is definitely comfortable, after all “that’s the way we’ve always done it” as Ian
Jukes likes to say (2014). It is far easier for publishers to generate textbooks when
they deal with a single subject (“language arts”; “math”; “biology” etc.), organize
class schedules and physical rooms by subject blocks, and hire teachers by their
areas of content knowledge. Likewise, dividing by subjects is easier on the school
administrator, who can more simply schedule classes, buy textbooks and hire
teachers. But who benefits from this “easier” way of going about structuring our
schools? This is what I like to call the “delivery room” model – it makes sense for
the doctor to lie a woman on her back, but it goes against the very nature of
physiology and a woman’s best instincts when she’s ready to give birth.
Where did these types of curriculum subject divisions come from in the first
place? If we think back to the oldest “classrooms” in which Socrates seamlessly
integrated different domain areas under wider case studies, problem-based
learning or real-world dilemmas, it seems almost comic to imagine him dividing up
his day starting off with an hour of pure math (or language arts, or science). In was
common for Socrates to delve into a problem or case and illicit reflection from a
variety of disciplinary lenses to resolve it, while children in school today are asked
to study subjects such as chemistry in a vacuum, often far away from physics,
math, history and biology though each has multiple overlaps with the other.
Socrates is reputed to have employed inquiry-based learning, something highly
recommended in today’s schools (Campbell & Groundwater-Smith, 2013). When
education became free and obligatory for all at the end of the 19th century, more
children than even filled our schools, forcing us to “streamline” the educational
practice or divide our time between different subjects.
Decisions about area specialties, textbooks and classrooms divided by
subjects became the norm and few have questioned this for 125 years. This leads
us to the present in which the focus on subjects taught in silos divorces children’s
understanding of their real life contexts. One of the failures of the current school
structure is its distance from real world problems, which are rarely resolved with
information from a single domain area. While expertise is desirable, narrowing
down one’s approach to problem-solving to a single domain area limits the
potential answers we can offer. Pure subject area studies are rarely superior in
problem solving using trans-disciplinary approaches. Some enlightened schools
are moving away from subject-bound course design and broadening their
approach to be based on real-life problems that use subject area knowledge to
reach resolution (Søby, 2015) rather than as an end in itself. The textbook
dilemma, the physical space distribution question and teacher formation all hinge

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on the decision of whether or not to teach curriculum in subject matter divisions
or not.
Arguments in Favor of the Pillars
The five basic pillars of human learning took on a new importance for me as
I witnessed the never-ending discussions by schools, universities and entire
governments contemplating curricular reform. Should we give more hours to math
and less to foreign language? Should physical education even have a place in an
academic curriculum? How important are the arts versus the hard sciences? Then I
asked myself, could the curriculum debate about the different priorities in
education of different governments (STEM versus Core Curriculum versus “the
Basics,” versus the International Baccalaureate, and dozens of other options) at
different times in history based on different convictions become trivial if viewed
under the pillars? Can the curriculum debate be resolved by enhancing subject
area instruction with an interdisciplinary look at symbols, patterns, order,
relations and categories in a hierarchical or constructivist fashion?
My belief is that school curriculum can be redesigned around the pillars and
delivered in a constructivist way throughout formal schooling, though this is an as-
of-yet unproven hypothesis. A pillars design would introduce student to all current
subject areas simultaneously as well as to learning which currently has less
priority in the curriculum (foreign language, the arts, physical education), through
the lenses of symbols, patterns, order, relations and categories. Such a structure
would also create the space for subjects we consider important in 21st century
learning, but for which there is little time in the current school structure
(creativity, values, entrepreneurship). This would surely bring more dynamism to
school learning by making every lesson interdisciplinary and authentic, and
celebrate the way neuroscience shows us the brain categorizes and structures
networks to begin with.
A class in early years “Patterns” for example, would touch on math, art,
science, nature, language, physical education, nutrition, etc., through a
transdisciplinary understanding of sentence patterns, fractals, even numbers,
artistic genres, architecture, dietary needs, and so on. This would make all learning
naturally interdisciplinary and connected and therefore, authentic and more
interesting. Far too long have subjects fought for hierarchy in the class schedule
rather than being understood as complementary. A strong argument for enhanced
interdisciplinary teaching is that it is very hard, if not impossible, to think of any
real-life problem that can be resolved by only considering how a single discipline
(math alone, language alone, biology alone, etc.) might answer the query; most
real-world problems demand an interdisciplinary approach for full resolution.
If adopted, the pillars would be a paradigm shift. For example, this would
cause a huge riff in the publishing world. It is not uncommon to find that children’s
textbooks pose questions that appear single-subject-dependent, but real teachers
in real classrooms know that the solutions that students propose are almost
always more interdisciplinary because they are more in touch with considerations
we can now see in the five pillars.
For example, a 4th grader might be asked how much pizza each child gets
when it is divided evenly by four kids (25%; ¼; one-quarter). But almost any 4th

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grader will tell you a mathematical solution is not enough. Some kids are bullies
and will take more than their fair share (patterns of social dominance). Others
dislike the toppings and will take less (categories of likes and dislikes). Yet others
want hamburgers and hate pizza and will protest and take none (relationships of
cause and effect). Others have a parent who “shares” the piece with their child,
rendering a fraction (order of family structure). Depending on the size of the pizza,
a fourth might be too much for the average 4th grader to eat (relationship of size of
stomach to amount of food). And so on. There are multiple angles and
considerations in every real-world problem, and most children don’t let us forget
that as they try and answer the ridiculously simple pizza dilemma in their
textbooks. When students offer us all of these non-mathematical answers they are
teaching each other and us about different perspectives on the same problem. This
is a display of cognitive flexibility as they relate to real life anecdotes and
something we should celebrate in our classrooms.
The brain adapts to what it does most. If children are forced into “siloed”
thinking model to complete their workbooks on time, or asked to respond to the
pizza question from a purely mathematical angle, this means that when it comes
time to face the real world problems outside of their classrooms they will be at a
disadvantage. After years of habituating domain-specific responses it is ironic that
in the upper grades we spend a lot of time explicitly telling students they need to
think in more interdisciplinary ways. If children were asked to use the filters to
think of the pizza question in terms of symbols (“how many different symbols can
be used to express twenty-five percent”?), patterns (“what else looks and divides
like a pizza?—clocks? cakes?”), order (“how many different ways can we order this
problem?”), relations (“what is the relation of each piece of pizza to the whole?”),
and categories (“would one-forth be the same in a pizza as in a square?” “are
words, fraction, decimals and percentages the same or different?”), then we could
habituate better thinking practices over time.
My belief is that if children are taught in an interdisciplinary manner from
the start of their school life they would not have to learn how to think
interdisciplinarily in an explicit form later; rather this approach would be
habituated into their mindsets. Students educated to think through the pillars will
find it more natural to use a transdisciplinary approach to problem-solving. While
pillars can be used at any stage of education, an early start to their application
(pre-kindergarten onward), will create the possibility of incorporating them into
habituated thinking habits throughout the lifespan (Ramanathan, Luping, Jianming
& Chong, 2012). Habits formed early in life lead to automated responses, and
integrated transdisciplinary skills lead to better problem resolution.

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Chapter 4 Complexity via Simplicity: Examples of the Pillars in
Math and Language
The five pillars have the attraction of being simple to understand; any
kindergarten child can comprehend symbols, patterns, order, relations and
categories meaning this type of approach can be used in the earliest years of
education and throughout schooling. It is possible that the five pillars approach can
improve the use of neuroscientific information by teachers because it can celebrate
the complexity of the human brain in terminology immediately applicable to
classroom contexts. Similarly, neuroscientists will be able to understand
educational concepts easier if they, too, are expressed through the pillars. For that
matter, just about any field of study will be able to understand others because they
will share the “language” of the pillars.
In early childhood education we often seamlessly integrate the physical
sciences with art, language with math and history with our own neighborhoods in
an interdisciplinary way (for example, see Brooks-Gunn, Burchinal, Espinosa,
Gormley, Ludwig, Magnuson & Zaslow, 2013). This natural integration of
disciplines through the pillars facilitates student recall for concepts and better
reflects the child’s world, which will hopefully lead to greater interest in school-
taught content (Willigham, 2009). If all levels of education were approached
through symbols, patterns, order, relationships and categories as established
through neuroscientific evidence, then teachers would be able to benefit from
findings in the lab through already familiar entryways.
I suggest that each current subject area taught in schools be broken down
into a complex hierarchy in a constructivist way based on evidence from complex
hierarchy modeling and from neuroscience (see Paper 1 for a more detailed
justification of this approach).
Once placed in this hierarchy, the learning concepts can be divided into the
five pillars. For example, in Math can be mapped by pillar and constructivist level.
This can then be reorganized into a new division of learning concepts by
levels.

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Figure 16. Example of Learning Hierarchy of Math Skills Areas by Level Rather than by Grade
I imagine groups of students arranged by levels (rather than grades) with
flexible movement between them. In an ideal setting teachers would be trained to
understand each level and perhaps specialize in it. Having said that, too much
change too fast can lead to the rejection of the pillars. In the short term, we could
start by training traditional subject area teachers in how to use the pillars as an
additional dimension of teaching. That is, they could be trained in the hierarchy of
complexities in Math Level X (or Language, or Art, etc.) as represented by Level X’s
symbols, patterns, order, relations and categories. Eventually, after there is a
significant acceptance of the pillars, teachers could be encouraged to learn the
entire Level X content in all traditionally taught subject areas or the symbol,
patterns, order, relations and categories in math, language, social studies, art,
science and physical education.
I believe that once domain areas are plotted individually in a hierarchical
form by pillar, this alone will improve curriculum design by affirming a logical
order of competencies introduction. However, I recommend an addition step. Once
all domain areas have been plotted, they should be overlaid, one upon the
other. Once all subjects regularly taught in school have been plotted (math,
language, science, art, computer science, physical education, and social studies) in
a pillars-hierarchical-constructivist model, then a final curriculum design will
emerge that provides not only an orderly and efficient structure for school
study, but it will more importantly create more authentic learning for
students.

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Figure 17. Overlap mapping of pillars and subject areas

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Chapter 5 Pillars that Lead to Enhanced Diagnosis Ability
Another interesting benefit of pillar application relates to diagnosis.
The pillars create a type of safety net in their design in that their mapping
assures that if taught in the suggested constructivist order, it becomes very easy to
identify where children have gaps in knowledge. If symbols, patterns, order,
relations and categories are taught in a hierarchical way and in a constructivist
order, it will be easier to identify missing pre-requisite knowledge and accurately
pinpoint learning needs. Experienced teachers are aware that children can appear
to have math problems when they really have language problems. An additional
benefit of applying the pillars is that it would make the exact area of deficit more
transparent as distinct domains can be analyzed through the similar lens of a
single pillar (math and language through the pillar of symbols, for example). Once
the maps are overlapped, a teacher would then be able to see if the missing pre-
requisite knowledge was located in math or in language, and in doing so, be able to
provide more accurate remediation to fill that gap.
For example, if a child is successful in school up through the concepts of
multiplication but begins to show signs of weakness as he starts to divide, a
teacher can review the pre-requisite skills or area knowledge to better identify
how to fill in his gaps so he can continue to flourish in math. Is he lacking
reinforcement on the different types of symbols learned between multiplication
and division stages? Or has he misunderstood the order of operations? Or how the
relationship of numbers is changed in division when they are positive and
negative? Or does he simply misunderstand the written directions? By identifying
his precise “missing piece” of pre-requisite knowledge, teachers can better
diagnose the math problem and as a result, more easily correct for it. Hopefully, as
the child experiences multiple corrections of this sort he will also begin to become
more independent in identifying his own gap by interpreting the concept hierarchy
and grow into an independent learner.
Accurate diagnosis is half the solution
It is unfortunate that in current practice when a child begins to fail in math
we often globally recommend more rehearsal (additional worksheets). This lack of
diagnostic accuracy means that we often send the wrong type of remediating work,
which is a waste of time and can potentially exacerbate the problem as the child’s
frustration grows. Teachers do not yet have access to easy diagnostic tools that can
help accurately identify problem areas with such precision. Hopefully the new five
pillars constructivist hierarchy will change how classroom teachers can react and
treat gaps in knowledge.
I suggest that the precision with which we can identify and correct problem
areas increases by following the five pillar constructivist hierarchy. Teachers must
be trained to understand how overlapping neural circuitry can be used
advantageously. The use of pillars would break down the overlap information into
manageable and easily understood groupings, improving the probability of
application in real classrooms and enhanced diagnostic capability.

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Chapter 6 New Learning Goals in the 21st Century
The push for 21st century skills adds to the debates about content and
curriculum design. Modern educators are pushed to reach beyond simplistic
delivery of domain content information and to become more creative in how they
integrate life skills into the classroom. Society expects much more from schools
than they did just a generation ago because much more is readily available to
learners outside of school, making explicit classroom instruction unnecessary for
many topics that once took up a great part of our curriculum. Research such as
Sugatra Mitra’s Hole in the Wall experiment illustrates how small groups of self-
organizing children can teach themselves the content of the entire primary school
curriculum in a shorter time than normally achieved in formal school settings
(Dolan, Leat, Mazzoli Smith, Mitra, Todd & Wall, 2013; Mitra, 2003; Mitra &
Crawley, 2014). This means that it is no longer important for teachers to focus
solely on math formulas, for example, as the Internet can do that through free Apps
and usually in a shorter time frame than many classroom teachers, but rather on
the use of those formulas. We no longer need teachers who simply deliver content;
we need teachers who know how to explain how and why the content can be used
to resolve problems in the real world. Educators are now responsible for
developing learners who know how to communicate well, collaborate with one
another, use technology, and to solve problems in innovative and creative ways.
While teaching through content areas once seemed like the most efficient
way to learn the knowledge needed to resolve problems, in recent times learning
processes have been aided by technology to the extent that new learners are
permitted to go beyond simple content delivery of information in schools to newer
ways of creatively resolving real-life problems in more innovative ways through
technology. For example, if a teacher can send recorded explanations of how a
math formula is set up, then instead of using time in class to do this, she can step
up the level of inquiry by actually getting the kids to use the formula in class with
her. Deeper thinking and elevated learning goals are more achievable if students
can receive content information before class and then when in class, explore,
debate and use that information under the tutelage of their teachers. Flipping the
classroom in this way is one means of leveraging technology for better learning.
There is no shortage of knowledge these days as was once the challenge for
previous generations who had limited access to resources. The difficulty today is
that here is a serious deficit in good judgment about the quality of information and
an understanding of how to evaluate good versus bad sources. Teachers are the
new knowledge brokers whose job, in part, is to help students navigate the sea of
information that is at their fingertips. Any kid with a smart phone has access to a
world of data, what they need is to learn to judge its quality. Our jobs as teachers
have gone from information deliverer to guides in judging quality evidence for
specific purposes.
In addition to covering the general curriculum, (domain-focused or not),
there are high expectations that schools help form 21st century learners: good
communicators, collaborators, culturally sensitive individuals, community
contributors, personally responsible individuals who are creative and critical
thinkers who can work well in heterogeneous groups, use tools (including

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technology), and who are autonomous in their actions. This demand creates an
additional criticism of the way our schools design learning experiences through
domain-specific curriculum, rather than by skill sets. The goals of teaching have
changed, therefore the way we structure leaning must also change.
One can argue that the pillars are a rejection of subject area instruction; this
is not my intention. The pillars and subject or domain areas are highly
complementary forms of teaching. The pillars remind us that there are distinct
ways to divide curriculum instruction beyond just thematic, topical or
methodological lines (case studies, problem-based learning, Socratic instruction,
etc.), and invite a new way to conceptualize learning.
To appreciate the complexity of excellent teaching-learning processes we
need to think more holistically. We need to remember, as scholars such as David
Perkins remind us, that learning is a all-inclusive process and involves not only
what we teach (curriculum) and how (pedagogy), but also who is receiving
learning (developmentally speaking), when they do so (age), and with what
background knowledge (prior experience), including how their culture influences
learning outcomes. Once again, thankfully, the five pillars are complimentary to
any set of governmental curriculum priorities.

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Figure 18. Author’s Vision of Bruner’s Spiral Review of Hierarchical Information Integrated with 21st
Century Pedagogy

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Chapter 7 Ages vs. Stages vs. Prior Experience: What determines
learning potential?
Finally, the more I reviewed the neuroscience behind human learning, the
more the “ages vs. stages vs. past experiences” debate stood out.
Ages vs. Stages
We currently divide kids into age groups in our schools. We do this based
on a logistical need created by the implementation of universal education at the
end of the 19th century, which forced us to make a decision about how to divide
our overcrowding classrooms. While dividing children by their birthdate may
seem logical at first (after all, it’s the way we have always done it, right?), we often
forget that cognitive development is not always in parallel with chronological age.
In fact, there are numerous studies indicating that some key goals for school
success, such as reading, are normal if taught in schools anywhere between three
and nine years old (Tokuhama-Espinosa, 2008). This means that the creation of
standards may often spell failure for some who develop differently (those we call
“late bloomers”) if we ignore that “[b]oth age and education are associated with
hierarchical development” (Dawson-Tunik, Commons, Wilson & Fischer, 2005,
p.11).
If one reviews failure rates in schools, startling patterns emerge as to who it
is that usually miss the standardized test score minimums (see Lucio, Hunt &
Bornovalova, 2012; Oyserman, 2013). It is interesting how boys, who genetically
mature slightly slower than girls (see Marceau, Ram, Houts, Grimm & Susman,
2011), bilinguals, whose vocabulary evens out at a slightly slower rate in the
earlier years than monolinguals (but usually ends up being superior to
monolinguals) (see Poulin-Dubois, Bialystok, Blaye, Polonia, & Yott, 2013),
subsequent children as compared with first children (e.g., Berglund, Eriksson &
Westerlund, 2005), minorities (e.g., Appel & Kronberger, 2012) and children from
low SES groups (e.g., Currie & Thomas, 2012) are all naturally “slower” on the
comparative scale of things in the early years. Having said that, some of these
differences are merely developmental and go away on their own, leaving no
perceivable differences by mid-primary school. In other cases, it is impacting how
having great teachers can reduce the gap between these slow starters, sometimes
availing such extreme benefits as to reduce perceivable differences between these
groups after high quality intervention over just a few years (Stigler & Hiebert,
2009), for example.
Even if we accept that there is a natural evening-out of the playing field over
time for many children, it is often too late for many who are labeled slower, which
for a variety of reasons ends up becoming a self-fulfilling prophesy (Hattie, 2009).
Many children, labeled as slow too early in their academic careers are potentially
superior learners, but due to our zeal to “treat early” we mistakenly categorize
them, which can lead to a downward spiral in self-efficacy as well as academic
failure (Hattie, 2009; Hudak, 2014). Once a child has been labeled, he has to
struggle his way back up to even. Unfortunately, we sometimes limit their chances
to show us what they know because we pollute their self-perception as learners
with the suggestion that they are “behind” or are somehow less intelligent than

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their peers. As a student’s self-perception as a learner is the greatest influence on
student learning outcomes (Brophy, 2013; Hattie, 2013), it is sad to watch how
some children mistakenly negatively judge their own potential to learn because
they are slightly behind the developmental curve. Had we taught them better by
structuring their learning in a more personalized way, we would find less failure. I
propose that if students were allowed to advance through different levels of
mastery rather than be grouped by age there would be less school failure.
Prior Experience
The speed with which a person can recall information is directly related to
the level of repetition received for that information (Zatorre, Fields & Johansen-
Berg, 2012). The myelin sheath that insulates the axonal connections is
responsible for how quickly a person can “find” the right information in the brain
(Hartline, 2008). You have some habituated behaviors for example, that seem
ingrained in your intuitive behavior, but which have actually been cemented into
memory due to the high level of repetition (think of driving for example). A certain
amount of repetition is required for true learning to take place (Rock, 1957). We
know that different kids will enter our classes with different amounts of prior
experience and its related level of repetition due to the experiences in their lives.
This makes some kids seem exceptionally intelligent (or slow) when their
outcomes are primarily due to experience, not to intelligence.
The order in which skills are learned is more important than one’s age,
meaning that the alignment of cognitive development and past experience is most
indicative of a child’s potential to learn. For example, a child who has been read to
since birth will have more connections in place when it comes time to learn to read
in school than a child who has ever been read to before at home (Bus, Van
Ijzendoorn, & Pellegrini, 1995). As prior experiences create the building blocks
upon which new learning can occur, constructivism both as a pedagogical concept
as well as a neurological reality must be considered. Without proper prior
knowledge, new learning is slowed and often even inhibited. As we mentioned
earlier, a child who knows how to add will be able to learn how to subtract in a
relatively short amount of time compared with a child who does have sufficient
practice in addition. There are thousands of kids who fail in school not because
they lack the intelligence to succeed but rather because they don’t have the
necessary prior experiences upon which to learn quickly, (and usually not due to
any fault of their own).
If we restructure learning based on a pillars constructivist hierarchy design
for mastery, we would likely help many more students reach their full potential
because the hierarchical mapping of skills would be transparent, making learning
goals clearer to all involved and replace steps in learning with current judgment
calls on intelligence. If we used the pillar, teachers, students and their parents alike
would be able to see exactly which pieces of the puzzle were preventing new
learning from occurring. Once it is clear where the gaps are in a student’s
knowledge, the road to repair is paved (this would be true whether or not we use
the five pillars as a curriculum base). The added benefit to restructuring
curriculum design to include the pillars rather than solely by domain areas is the
natural transdisciplinary nature of learning. This, combined with more authentic

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problem-based learning pedagogy, would be a better path towards the final
objective of developing creative and critical thinkers.
If we were to develop curricula by levels, not by ages (starting at “0” for our
traditional Pre-K learners), we would be able to structure learning in a more
transparent way.

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Figure 19. Constructivist Pillar Model for Mastery

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Chapter 8 Teacher Training: Past, Present, and Future
Eisner (1979), pointed to the many ways that curricula could be structured and how
learning occurred in explicit (content area learning) and implicit ways (how we think
about what we are learning). Schulman was the first to disaggregate the many elements of
“Teacher Knowledge” into sub-areas of knowledge of the learner and his characteristics,
general pedagogical knowledge, knowledge of contexts, knowledge of educational
objectives, knowledge of curriculum, content knowledge and pedagogical content
knowledge (1986).

Figure 20. Schulman's Original Category Scheme compared to Ball, Thames & Phelps, 2008, p.5.

Ball and colleagues (2008) agree with Schulman’s general assertion that being
experts in teacher’s pedagogical content knowledge (TPCK) is what leads to greater
student success than the other elements. That is, TPCK is better than content alone or
pedagogy alone (Ball, Thames & Phelps, 2008). Knowledge of math does not make you a
good math teacher, nor does knowledge of teaching make you a good math teacher, but
rather knowledge of Math and knowledge of Teaching make you a good math teacher. In
their studies on math teacher formation, Ball and colleagues make it clear that “the
mathematical knowledge for teaching” that is needed to be a successful math teacher also
relates to the general hierarchy of math concepts, which no level of good pedagogy can
substitute.
Based on the fact that there are distinct neural networks related to basic numeracy,
for example, than for those related to affective aspects of learning, such as student-teacher
relationships, it is clear that teachers need to improve both their new content or domain
area knowledge, as well as improve their teaching skills. In the new five pillars
constructivist hierarchy this means that teachers would not only have to be trained in the
new pillars content, but also improve the methodologies with which they teach them. If
such a model were to be implemented, a strikingly new type of teacher formation would
occur in which the traditional TPCK would be supplemented with a disaggregation of
concepts as expressed through the five pillars constructivist hierarchy.

Five Pillars of Neuroconstructivism in the Brain by Tracey Tokuhama-Espinosa, Ph.D. March 2017

Five Pillars of Neuroconstructivism in the Brain by Tracey Tokuhama-Espinosa, Ph.D. March 2017

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Five Pillars of Neuroconstructivism in the Brain by Tracey Tokuhama-Espinosa, Ph.D. March 2017