Foundational Thinking DPF Suite
7 publications. Open a title to read, or expand its contents below.
Read the Suite introduction — Foundational Thinking DPF Suite
Computational Thinking DPF
A pattern language for constructing, understanding, analyzing and transforming algorithms, including their interpretation and interaction.
Contents · 15 patterns in Computational Thinking DPF
- Table of Contents
Computational Thinking - Readme
Practical entries
- CP-INDEPENDENT-EXTENSIONS - A new data form and a new operation must work together
- CP-TRANSLATION-SCOPE - A translation works on test inputs; which executions does it preserve?
- CP-ANSWER-UNDER-LIMITS - Obtain the answer the work needs within available resources
- CP-RETRY-AND-RECOVER - Share calculations without merging requests or repeating their effects
Computational Thinking DPF Architectural Reference
- CMP.Reference:1 - Problem frame and the algorithmic difficulty
- CMP.Reference:2 - Forces that shape the construction
- CMP.Reference:4 - Worked connection - One best selection becomes every best selection
- CMP.Reference:5 - Use checks, assumptions and recurring failures
- CMP.Reference:6 - Consequences and Architectural Rationale
- CMP.Reference:7 - Shared sources, alternatives and relations
- CMP.Reference:End
Part A - Construct an algorithm
- CMP.1 - Solve One Problem through Another or Transfer a Limit (Computational Reduction)
- CMP.2 - Derive a Recursive Procedure from a Problem Decomposition
- CMP.3 - Share and Schedule Repeated Subcomputations
- CMP.4 - Construct Computational Search with Justified Exclusions
- CMP.5 - Bound an Optimum or Recover a Feasible Candidate through a Relaxed Problem
- CMP.6 - Derive an Iterative Computational Update from Local Information
- CMP.7 - Construct a Learner from Examples and Feedback
Mathematical Modeling DPF
Methods for constructing mathematical representations of a question, connecting unknown relations, observations and available actions, and revising the resulting models.
Contents · 17 patterns in Mathematical Modeling DPF
- Table of Contents
Mathematical Modeling DPF Architectural Reference
- MMP.Reference:1 - Problem frame - Make a mathematical question useful
- MMP.Reference:2 - Problem and forces - Choose what the model must retain
MMP.Reference:3 - Solution - Connect the contributions the question needs
- MMP.Reference:3.1 - Form the first account and recover its interpretation
- MMP.Reference:3.2 - Represent admissible objects and construct missing relations
- MMP.Reference:3.3 - Construct change and observation together when they interact
- MMP.Reference:3.4 - Turn uncertainty into a question about available action
- MMP.Reference:3.5 - Simplify, diagnose and revise for the required consequence
- MMP.Reference:3.6 - Use the model-forming result across the Suite
- MMP.Reference:3.7 - Constituent actions in ongoing work
- MMP.Reference:3.8 - Compare or construct the way work is performed
- MMP.Reference:5 - Conformance Checklist - Can the result do its intended work?
- MMP.Reference:6 - Common Anti-Patterns and How to Avoid Them
- MMP.Reference:7 - Consequences, biases and limits
- MMP.Reference:8 - Architectural Rationale - Organize by model-forming operations
- MMP.Reference:9 - Source use and currentness
- MMP.Reference:10 - Relations to continued inquiry and work
- MMP.Reference:End
B. Infer, distinguish and revise
- MMP.7 - Construct a Probability Model of the Recorded Data
- MMP.12 - Formulate an Inverse Problem and Choose Whether and How to Use Regularization
- MMP.13 - Infer Unknowns Statistically under a Stated Observation Model
- MMP.14 - Find and Repair a Mathematical Model’s Failed Predictions
- MMP.15 - Identify an Intervention Effect from Available Data
- MMP.19 - Construct and Bound a Mathematical Counterfactual Comparison under a Causal Model
- MMP.16 - Design Observations to Separate Mathematical Model Alternatives
Mathematical Thinking DPF
A pattern language for constructing mathematical objects, operations and arguments, using their results, and developing the next useful question.
Contents · 20 patterns in Mathematical Thinking DPF
- Table of Contents
Mathematical Thinking DPF Architectural Reference
- MATH.Reference:1 - Problem frame - Construct mathematics for the question
- MATH.Reference:2 - Problem and forces - Make a usable construction
MATH.Reference:3 - Solution - Connect constructions through what they supply
- MATH.Reference:3.1 - Form objects, operations and representations
- MATH.Reference:3.2 - Obtain an argument and the object it supports
- MATH.Reference:3.3 - Change a construction and develop its theory
- MATH.Reference:3.4 - Return a construction to further work
- MATH.Reference:3.5 - Use this contribution within the wider repertoire
- MATH.Reference:3.6 - Constituent actions in ongoing work
- MATH.Reference:4 - Worked use - Choose a representation after the question changes
- MATH.Reference:5 - Worked use - Construct a choice after finding an obstruction
- MATH.Reference:6 - Checks and common failures - Preserve what the next construction needs
- MATH.Reference:7 - Consequences, biases and limits
- MATH.Reference:8 - Architectural Rationale - Organize by reusable constructions
- MATH.Reference:9 - Source use and currentness
- MATH.Reference:10 - Relations to further reasoning and work
- MATH.Reference:End
Part A - Choose and relate constructions
- MATH.16 - Choose a Mathematical Construction from Its Required Maps (Universal Property)
- MATH.17 - Construct Mathematical Spaces of Operations and Operations on Them
- MATH.1 - Build a Mathematical Structure of Composable Paths
- MATH.2 - Treat Objects as the Same While Preserving Operations (Quotient)
- MATH.5 - Extend a Generator Assignment While Preserving Operations (Homomorphism)
- MATH.7 - Transport a Mathematical Structure Through a Bijection
- MATH.18 - Compare Mathematical Accounts through Interpretations
Part C - Change a construction and develop its theory
- MATH.11 - Construct an Invariant from Transformation Rules
- MATH.13 - Derive a Consequence from a Symmetry
- MATH.8 - Generate a Solution Family by Symmetry
- MATH.9 - Determine Whether and How a Choice Rule Can Respect Symmetry
- MATH.10 - Improve a Mathematical Candidate or Derive a Necessary Condition by Admissible Variation
- MATH.21 - Construct an Object through Convergent Approximations
- MATH.22 - Change Axioms and Trace Their Consequences
- MATH.23 - Develop a Conjecture by Changing a Construction
Notational Engineering DPF
A pattern language for designing expressions that people and computational agents can interpret, manipulate, translate and use together.
Contents · 8 patterns in Notational Engineering DPF
- Table of Contents
Notational Engineering DPF Architectural Reference
- NOT.Reference:1 - Problem frame and the work of designing a notation
- NOT.Reference:2 - Forces that shape the choice
- NOT.Reference:5 - Conditions of use, checks and recurring failures
- NOT.Reference:6 - Consequences and Architectural Rationale
- NOT.Reference:7 - Shared sources, alternatives and refresh
- NOT.Reference:8 - Relations to the rest of the Suite
- NOT.Reference:End
Physical Thinking DPF
A pattern language for forming physical accounts, deriving usable consequences, constructing observations and revising the physical assumptions.
Contents · 10 patterns in Physical Thinking DPF
- Table of Contents
Physical Thinking DPF Architectural Reference
- PHY.Reference:1 - Problem frame - Construct a physical account you can use and change
- PHY.Reference:2 - Problem and forces - Keep the physical question through the calculation
- PHY.Reference:4 - Worked connection - From an unknown resistance to a useful comparison
- PHY.Reference:5 - Bias, use checks and recurring failures
- PHY.Reference:6 - Consequences and Architectural Rationale
- PHY.Reference:7 - Shared sources, alternatives and relations
- PHY.Reference:End
Part A - Construct and constrain a physical account
- PHY.4 - Constrain an Unknown Physical Law by Transforming the Situation
- PHY.5 - Choose an Effective Physical Description by Scales and Couplings
- PHY.6 - Construct Physical Evolution from Balances and Response Laws
- PHY.7 - Obtain Motion from a Physical Variational Principle
- PHY.8 - Infer Macroscopic Physical Behavior from Microscopic Alternatives
Part B - Compare, observe and act
- PHY.1 - Construct Physical Similarity Across Changed Conditions
- PHY.2 - Construct a Physical Analogue from Interactions
- PHY.9 - Construct a Measuring Interaction for a Physical Distinction
- PHY.10 - Construct a Physical Test That Separates Rival Accounts
- PHY.3 - Derive a Physical Limit from Permitted Transformations
References and other texts
- Foundational Thinking DPF Suite Architectural Reference
Find the mathematical, physical, computational, modeling or notational contribution your question needs, and understand how the contributions work together.