On Piaget

2025-09-05

Rick Gilmore

Department of Psychology

Prelude

– Madonna (2017)

Today’s topics

  • Check-in on hierarchical task analyses (HTA)
  • Presentation schedule
  • Background ideas
  • Theoretical foundations: Piaget
    • General Readings: Siegler & Alibali (2021) Chapter 2; Piaget (1953); Newcombe (2013)

Check-in on HTA

  • Relevance?
  • Utility?
  • Do task demands/abilities change across development?
  • What are the tasks of the infant, toddler, pre-schooler, etc.?

Background ideas

Gilmore’s influences

Gilmore’s influences

Newcombe (2013) Table 1

On mechanism

On mechanism

Wikipedia contributors (2025a)

On mechanism

  • Is the human mind/brain/body a machine?
  • What are the parts?
  • How do they connect and interact?
  • What do they do?

Wikipedia contributors (2001)

On state spaces

…a mathematical model of a physical system that uses state variables to track how inputs shape system behavior over time.

…These state variables change based on their current values and inputs, while outputs depend on the states and sometimes the inputs too.

– Wikipedia contributors (2025g)

On state spaces

…The internal state variables are the smallest possible subset of system variables that can represent the entire state of the system at any given time…

Wikipedia contributors (2025g)

On state spaces

In computer science, a state space is a discrete space representing the set of all possible configurations of a system…State spaces are useful in computer science as a simple model of machines.

– Wikipedia contributors (2025h)

On state spaces

  • Representations \(\rightarrow\) states (\(s\))
  • Processes \(\rightarrow\) changes in state across time
    • \(s_{next}=s_{now}+\delta s\), where \(\delta s\) is a change in state.
  • Time scale of states, changes?
    • \(s(t+1)=F(s(t))\)

On state spaces

  • What is the state of the child’s mind/brain/body at time t?
  • How does that state change over some time interval?
    • Short term: behavior
    • Longer term: learning or adaptation or development
    • Really long term: evolution

On state spaces

flowchart LR
  A(Body) -->|Sensation| B(Nervous System)
  B -->|Response| A
Figure 1: A simple state space for the nervous system 
flowchart LR
  A(Body) -->|Sensation| B(Nervous System)
  B --> B
  B -->|Response| A
Figure 2: A slightly more complicated state space for the nervous system.

On state spaces

flowchart TD
  W(World) --> W
  W -->|Experience| B(Body)
  B -->|Behavior| W
  B --> B
  B -->|Sensation| N(Nervous system)
  N -->|Response| B
  N -->|Cognition| N
Figure 3: A more complete state space for the nervous system

On state spaces

Swanson (n.d.)

  • Separable but interacting neural pathways
  • Input (from world and body state)
  • Output (to body and world)

On reflexes

In biology, a reflex, or reflex action, is an involuntary, unplanned sequence or action and nearly instantaneous response to a stimulus…

A reflex occurs via neural pathways in the nervous system called reflex arcs…

– Wikipedia contributors (2025j)

On reflexes

These neural signals do not always travel to the brain, so many reflexes are an automatic response to a stimulus that does not receive or need conscious thought.

– Wikipedia contributors (2025j)

On reflexes

– RegisteredNurseRN (2020)

On reflexes

  • What is the input? What is the output?
  • What purpose(s) do reflexes serve?

The vestibulo-ocular reflex (VOR)

– Castilla (2007)

The vestibulo-ocular reflex (VOR)

Wikipedia contributors (2025i)

  • Stabilizes gaze in allocentric coordinates
  • Within ~10 ms

On reflexes

  • Sensations and responses temporally linked
    • Causally (mechanically) linked via
    • Specialized neural circuits
  • Sensation \(\rightarrow\) Response \(\rightarrow\) (New) Sensation
  • Imagine a mechanism that “records” these links
  • (Random) Response \(\rightarrow\) Sensation
    • Sensation \(\sim\) (Recorded prior) Sensation

Aside: Vestibulo-ocular reflex (VOR)

  • One of many behavior systems that reduce “noise”, improve reliability in input
  • Input “reliability” improves over long time span

Visual acuity in young children not adult-like

Gilmore, DiFulvio, Beamer, & Cruz (2025)

Background ideas: Summary

  • Mind/brain/body as a mechanism
  • State space formalism aids specifying states and transitions
  • Reflexes as simple, early emerging sensorimotor behaviors
  • Reflex arcs (Wikipedia contributors, 2025d) \(\rightarrow\) Piaget’s “circular reactions”
  • Perceiving “sameness” of sensations & actions critical

On Piaget

Jean Piaget from Wikipedia contributors (2025c)

Core ideas

  • Origins of knowledge (epistemology)
  • Categories of knowledge
    • Space, time, classes/categories, causality
  • Reflexes innate
  • Child as “scientist”, solving “problems”

Core ideas

  • Stages (and sub-stages)
    • Sensorimotor (0-24 mos)
    • Preoperational (2 - 6 or 7 years)
    • Concrete operations (6 or 7 - 11 or 12 years)
    • Formal operations (11 or 12 - 14 or 15 years)

Core ideas

…describes a pattern of thought or behavior that organizes categories of information and the relationships among them. It can also be described as a mental structure of preconceived ideas, a framework representing some aspect of the world, or a system of organizing and perceiving new information.

Core ideas

  • Assimilation

fitting new information into pre-existing cognitive schemas (Wikipedia contributors, 2025c)

  • Accommodation

taking new information in one’s environment and altering pre-existing schemas in order to fit in the new information (Wikipedia contributors, 2025c)

Core ideas

  • Equilibration

integrating individual pieces of knowledge into a unified whole. (Siegler & Alibali, 2021, p. 24)

Core ideas

  • Means (how to do/actions)
  • Ends (what to do/goals)
  • Means-ends analysis central to AI and the science of problem solving (Wikipedia contributors, 2023)

Core ideas

Core approach

Figure 2-1 from Siegler & Alibali (2021)

Core ideas

  • Detecting “sameness”

To be able to recognize the same thing again as it evidences itself to one’s senses in a multiplicity of ways, thus affording multiple opportunities to accumulate and apply information about it is, I believe, the most central challenge there is for cognition – Millikan (2017)

Core ideas

  • Tasks that require the detection of some sort of sameness
    • Object permanence
    • Conservation of number, solid & liquid quantity
    • Perspective taking
    • Number

Core approach

Questions

  • How does Piaget view the question of cognitive continuity vs. discontinuity?
  • Are the relations among sensations and actions described in Piaget (1953) clearly specified that you could write out the schema?
  • Gilmore’s attempt to unpack the causal relations at work in the situation of the infant in the bassinet
    • Do developmental scientists need to “complexify” our phenomena before we simplify them?

Notable comments

To assimilate a sensorial image or an object, whether through simple assimilation, recognition, or generalizing extension, is to insery it in a system of schemata, in other words, to give it a “meaning”.

– Piaget (1953), p. 189

Notable comments

Secondary circular reaction, in so far as it is a reproduction of an interesting result fortuitously obtained, is, effect, far from constituting a behavior pattern peculiar to the child. An adult, unacquainted with machinery, does not behave differently from the baby when, having by chance touched part of a motor, he does not understand the effect produced and repeats the action which set it in motion.

– Piaget (1953), p. 207

Evaluating Piaget

There are several problems with Piaget’s approach to cognitive development…the various capabilities did not cohere in the way that Piaget’s stage theory had envisioned…children frequently achieved competence in some of the stage-relevant tasks while lagging behind on other stage-relevant tasks…

– Newcombe (2013) p. 481

Evaluating Piaget

…Piaget seriously underestimated the cognitive competence of infants and young children…A large amount of research beginning in the 1970s and proceeding apace to this day has shown…that infants and young children have far more substantial abilities than Piaget had observed.

– Newcombe (2013) p. 481

Piaget

…Piaget talke in general terms about the process of developmental change as being the operation of equilibration…Many investigators argued that a more detailed specification of the mechanisms of change was needed.

– Newcombe (2013) p. 481

Evaluating Piaget

Piaget’s theory is…‘too monumental to embrace, and at the same time, too omnipresent to detect (Beilin, 1992)’

– Siegler & Alibali (2021) p. 48

Some of the reasons for its influence and its lasting appeal are the important acquisitions it describes, the large span of childhood it encompasses, and the reliability and charm of many of its observations.

– Siegler & Alibali (2021) p. 48

Evaluating Piaget

[Piaget’s] trait descriptions thus seem to be in the right ballpark, but to gloss over exceptions. More generally, Piaget’s theory continues to be of interest because it communicates a good feel for children’s thinking and it asks the right questions.

– Siegler & Alibali (2021) p. 49

Wrap-up

Next time…

  • Piaget: Deep dive
    • Student presentation A: How robust is the evidence for Piaget’s trajectories?
    • Student presentation B: When does object permanence emerge?
      • Skim: R. Baillargeon, Spelke, & Wasserman (1985); Renée Baillargeon (2008)

Resources

About

This talk was produced using Quarto, using the RStudio Integrated Development Environment (IDE), version 2025.5.1.513.

The source files are in R and R Markdown, then rendered to HTML using the revealJS framework. The HTML slides are hosted in a GitHub repo and served by GitHub pages: https://psu-psychology.github.io/psy-548-fall/

References

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