Computational Thinking (Wing, 2006)

Defining Computational Thinking for Math & Science Classrooms

A Pedagogical Taxonomy & Framework

David Weintrop et al. (2016)
Journal of Science Education and Technology, 25:127–147

The Core Educational Dilemma

• The Scientific Reality: Modern science and math are computational endeavors (bioinformatics, astrophysics, materials science).
• Policy Expectations:
  • NGSS Practice 5: Using Mathematics and Computational Thinking.
  • Common Core Math: Using technological tools to deepen concept acquisition.
• The Classroom Gap:
  • "Computational Thinking" (CT) remained ill-defined for STEM teachers.
  • Extant definitions drew almost exclusively from pure Computer Science (CS).

Why Situate CT in Math & Science?

• Reciprocal Learning Synergy:
  • Computation deepens math and science concept learning.
  • Authentic STEM investigations provide rich problem contexts for computing.
• Equity & Broad Reach:
  • Avoids self-selection biases found in elective CS courses.
  • Reaches all students across existing, compulsory STEM coursework.
• Epistemic Authenticity:
  • Reflects non-linear, stochastic, and complex system modeling in modern research.

Historical & Conceptual Foundations

"Computer presence could contribute to mental processes not only instrumentally but in more essential, conceptual ways, influencing how people think even when far removed from a computer."
— Seymour Papert (Mindstorms, 1980)

• Seymour Papert (1980, 1996): Computational representations for powerful ideas.
• Andrea diSessa (2000): Changing Minds — computation as a core literacy.
• Jeannette Wing (2006): CT as a universally applicable analytical skillset.
• The Authors' Shift: Grounding CT away from generic CS abstraction toward authentic STEM classroom practices.

Taxonomy Development Methodology

1. Literature Review: Analyzed NRC reports, CS Principles, and NAEP frameworks (identified 10 initial skills).
2. Curriculum Open-Coding: Analyzed 34 high school STEM lessons (physics, chem, bio, math) yielding 208 facets and 45 practices.
3. Internal Synthesis: Clustered practices into 27 codes across 5 categories.
4. Educator Review: Refined with 16 high school teachers and curriculum experts; shifted terminology from "skills" to "practices".
5. Expert Validation: Validated through 15 interviews with practicing scientists and mathematicians.

The Four Major CT-STEM Categories

• Data Practices: Collecting, creating, manipulating, analyzing, and visualizing scientific data.
• Modeling & Simulation Practices: Interacting with, assessing, designing, and constructing runnable representations.
• Computational Problem Solving Practices: Programming, modularity, algorithmic thinking, and debugging tailored to STEM.
• Systems Thinking Practices: Managing complexity, identifying dynamics, and analyzing emergent multi-level behaviors.

Category 1: Data Practices

"Data lie at the heart of scientific and mathematical pursuits... new technologies allow scientists to probe realms previously inaccessible." (p. 135)

• Present in 27 of the 34 classroom lessons analyzed.
• Modern STEM relies on massive, empirical, or simulated datasets.
• Shifts student inquiry from manual tables to computational data management.

Data Practices: The 5 Elements

1. Collecting Data: Designing automated data-gathering protocols; using digital probes, sensors, or video tracking.
2. Creating Data: Generating synthetic data via simulations when physical observation is impossible (e.g., galactic evolution).
3. Manipulating Data: Filtering, sorting, cleaning, and normalizing complex datasets.
4. Analyzing Data: Identifying trends, anomalies, and mathematical best fits.
5. Visualizing Data: Designing charts, plots, and dynamic displays to communicate patterns.

Category 2: Modeling & Simulation

"The sciences do not try to explain, they hardly even try to interpret, they mainly make models."
— John von Neumann (1955)

• Models are runnable, dynamic epistemic objects.
• Facilitate inquiry into phenomena that are dangerous, costly, or multi-generational.
• Guides students along a trajectory from model consumers to model builders.

Modeling & Simulation: The 5 Elements

1. Using Models to Understand a Concept: Exploring simulations to observe scientific phenomena.
2. Using Models to Find & Test Solutions: Exploring multi-dimensional parameter spaces to test engineering hypotheses.
3. Assessing Computational Models: Identifying assumptions, simplifications, and limits of validity (all models are wrong, some are useful).
4. Designing Computational Models: Defining rules, agents, and parameters conceptually before coding.
5. Constructing Computational Models: Authoring or modifying code/rules within modeling environments (e.g., NetLogo).

Category 3: Computational Problem Solving

"Applied computer science is now playing the role which mathematics did... providing an orderly, formal framework and exploratory apparatus."
— S. George Djorgovski (2005)

• Adapts computer science techniques directly to scientific problem solving.
• Focuses on code literacy, algorithmic pragmatism, and systematic troubleshooting.
• Prepares students to build reusable tools rather than one-off calculations.

Problem Solving: Practices (Part 1)

• Preparing Problems for Computational Solutions:
  Reframing and decomposing STEM problems so computational tools can solve them.
• Computer Programming:
  Writing, editing, and reading code (from short scripts to modular functions).
• Choosing Effective Computational Tools:
  Selecting appropriate programming languages, libraries, and environments for specific tasks.
• Assessing Different Approaches / Solutions:
  Evaluating solutions based on speed, memory, extensibility, and clarity.

Problem Solving: Practices (Part 2)

• Developing Modular Computational Solutions:
  Structuring scripts into discrete, reusable functions and modules.
• Creating Computational Abstractions:
  Isolating core mechanisms while backgrounding secondary details.
• Troubleshooting and Debugging:
  Isolating logical errors, running reproducible tests, and fixing code systematically.

Category 4: Systems Thinking Practices

"Instead of looking at one thing at a time... the sciences now look at a number of interacting things and note their behavior as a whole."
— Ervin Laszlo (1996)

• Addresses non-linear dynamics, feedback loops, and emergent behaviors.
• Provides alternatives to reductionist, single-variable approaches.
• Leverages computation to make aggregate systemic changes observable.

Systems Thinking: The 5 Elements

1. Investigating a Complex System as a Whole: Measuring system inputs/outputs while black-boxing internal details.
2. Understanding Relationships within a System: Identifying feedback loops, interdependencies, and interactions.
3. Thinking in Levels: Connecting micro-level interactions (agents/particles) to macro-level patterns (pressure, flocking).
4. Communicating System Information: Presenting structural systems data clearly to non-specialist audiences.
5. Defining Boundaries & Managing Complexity: Deciding what entities belong inside the system model vs. external environment.

Classroom Exemplar 1: Physics

Video Games: Physics Phact or Phiction?

• Context: High school mechanics (kinematics and energy).
• Task: Students capture gameplay videos (e.g., Angry Birds) to test virtual physics against reality.
• Practices Enacted:
  • Collecting & Visualizing Data: Video analysis via Tracker to plot trajectory curves.
  • Analyzing Data: Curve-fitting parabolas to determine game gravity.
  • Assessing Models: Identifying where game rules intentionally diverge from Newtonian laws to improve gameplay.

Classroom Exemplar 2: Biology

DNA Sequencing from the Ground Up

• Context: Genetics and molecular biology.
• Task: Students construct the algorithmic logic required to assemble sequenced DNA fragments.
• Practices Enacted:
  • Decomposition: Reassembling scrambled song lyrics alphanumeric passwords base pairs.
  • Computational Abstraction: Developing overlap-detection algorithms.
  • Programming: Authoring and testing pseudocode routines to evaluate scaling constraints.

Classroom Exemplar 3: Chemistry

Gas Laws & Emergent Microscopic Behaviors

• Context: Kinetic molecular theory and ideal gas laws.
• Task: Students use interactive simulations (PhET / GasLab) to observe gas behaviors.
• Practices Enacted:
  • Creating Data: Running simulation runs and recording metrics.
  • Thinking in Levels: Connecting particle wall collisions to macroscopic pressure.
  • Systems Thinking: Treating the container as an aggregate input-output system to derive .
  • Assessing Models: Evaluating assumptions like elastic collisions and zero intermolecular attraction.

Key Takeaways for STEM Educators

• Shift to Practices: Focus on what scientists actually do with computation, not just coding syntax.
• Low Floor, High Ceiling: Scaffold activities from using models to assessing, designing, and coding them.
• Explicit Naming: Explicitly label CT practices during lessons so students recognize the transferability of their skills.
• Shared Disciplinary Language: Bridges computational competencies consistently across biology, chemistry, physics, and mathematics departments.

Discussion & Curriculum Planning

• Which of the 4 taxonomy categories is already represented in your current curriculum?
• How can a standard cookbook verification lab be redesigned to include Assessing Computational Models or Thinking in Levels?
• Resource Portal: http://ct-stem.northwestern.edu