The Research Foundation
The 11 invariants aren't opinions. They're derived from decades of peer-reviewed research in cognitive science and instructional design.
The Framework
The Invariant framework was synthesized by Carl Hendrick, drawing on foundational research in cognitive load theory, direct instruction, retrieval practice, and mastery learning.
Each invariant traces back to specific, replicable findings about how humans learn. This page documents those foundations.
Research Foundations
Why one concept per lesson?
Working memory has severe capacity limits. Introducing multiple new elements simultaneously causes interference and prevents transfer to long-term memory.
Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257-285.
Sweller, J., van Merriënboer, J., & Paas, F. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10(3), 251-296.
Why must the target process be the only path?
Faultless communication requires that the target skill be the sole path to correct responses. If students can succeed through shortcuts, the instruction has failed.
Engelmann, S. & Carnine, D. (1982). Theory of Instruction: Principles and Applications. Irvington Publishers.
Engelmann, S. (1980). Direct Instruction. Educational Technology Publications.
Why active production, not recognition?
Retrieval practice produces dramatically better retention than recognition tasks. The act of generating an answer strengthens memory in ways that selecting an answer does not.
Roediger, H. L. & Karpicke, J. D. (2006). Test-enhanced learning: Taking memory tests improves long-term retention. Psychological Science, 17(3), 249-255.
Roediger, H. L. & Butler, A. C. (2011). The critical role of retrieval practice in long-term retention. Trends in Cognitive Sciences, 15(1), 20-27.
Why binary mastery checks?
Percentage scores hide specific weaknesses behind averages. Mastery learning requires clear pass/fail thresholds on specific skills, with targeted remediation for gaps.
Bloom, B. S. (1968). Learning for Mastery. Evaluation Comment, 1(2), 1-12.
Bloom, B. S. (1984). The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Tutoring. Educational Researcher, 13(6), 4-16.
Why must errors trigger corrective loops?
Errors that go uncorrected become encoded. The specific sequence matters: immediate interruption, modeling, guided replay, and required retry.
Metcalfe, J. (2017). Learning from Errors. Annual Review of Psychology, 68, 465-489.
Why atomize instruction into knowledge components?
Learning is more effective when instruction is broken into the smallest teachable units. This allows precise diagnosis and targeted remediation.
Koedinger, K. R., Corbett, A. T., & Perfetti, C. (2012). The Knowledge-Learning-Instruction Framework: Bridging the Science-Practice Chasm. Cognitive Science, 36(5), 757-798.
Full Bibliography
Cognitive Load Theory
- Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257–285.
- Sweller, J., van Merriënboer, J., & Paas, F. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10(3), 251–296.
Direct Instruction
- Engelmann, S. & Carnine, D. (1982). Theory of Instruction: Principles and Applications. Irvington Publishers.
- Engelmann, S. (1980). Direct Instruction. Educational Technology Publications.
Retrieval Practice
- Roediger, H. L. & Karpicke, J. D. (2006). Test-enhanced learning: Taking memory tests improves long-term retention. Psychological Science, 17(3), 249–255.
- Roediger, H. L. & Butler, A. C. (2011). The critical role of retrieval practice in long-term retention. Trends in Cognitive Sciences, 15(1), 20–27.
Mastery Learning
- Bloom, B. S. (1968). Learning for Mastery. Evaluation Comment, 1(2), 1–12.
- Bloom, B. S. (1984). The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Tutoring. Educational Researcher, 13(6), 4–16.
Knowledge Components
- Koedinger, K. R., Corbett, A. T., & Perfetti, C. (2012). The Knowledge-Learning-Instruction Framework: Bridging the Science-Practice Chasm. Cognitive Science, 36(5), 757–798.
Error Correction
- Metcalfe, J. (2017). Learning from Errors. Annual Review of Psychology, 68, 465–489.
See these principles applied.
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