Field Notes
White papers, research summaries, thought leadership, and tools at the boundary of psychometrics, learning science, and instructional practice.
Featured
White Paper
The gap between a well-intentioned exit slip and a defensible diagnostic instrument is wider than most districts realize. This paper introduces the cognitive architecture framework and misconception taxonomy that close it — and describes what happens to instructional decision-making when the gap is closed.
Read the paper →Diagnostic value by instrument type
"A diagnostic instrument is not a test. It is a theory about how students fail."
Research Summary
A synthesis of the cognitive research on how students build — and misbuild — mathematical understanding. Covers Vergnaud's multiplicative conceptual fields, Fischbein's intuitive models, and what they imply for diagnostic design.
Thought Leadership
High-quality instructional materials are necessary but insufficient. The missing piece is measurement infrastructure that travels with the curriculum — and the research tells us exactly what it needs to look like.
White Paper
An honest look at what it takes to produce classroom-level assessment data that meets even minimal psychometric standards — and what the field would need to invest to make that happen routinely.
Research Summary
Item response theory is a powerful lens for understanding how students perform on assessments — but only if items are designed to generate interpretable response patterns. Most aren't. Here's the gap and how to close it.
Thought Leadership
Not all misconceptions are created equal. Gateway misconceptions reframe everything downstream — and if you don't screen for them first, your diagnostic data will be systematically misleading. Here's why and what to do about it.
Research Summary
The transition from additive to multiplicative reasoning is one of the most studied and most consequential developments in K–12 mathematics learning. This summary synthesizes what the research tells us and what it means for instruction and assessment.
Tools & Templates
A structured template for building a misconception taxonomy for any mathematics standard. Includes the five-column format (Code, Name, Observable Behavior, Failure Step, Key Implication) with worked examples.
↓ Download (.docx)A 20-point quality checklist for evaluating diagnostic exit tickets. Covers stem completeness, distractor integrity, local independence, coverage, and the constructed-response test.
↓ Download (.pdf)A blank framework for mapping the cognitive steps required to demonstrate understanding of any standard, with the potential failure points that generate assessment distractors.
↓ Download (.docx)A structured template for building a response pattern guide for a diagnostic block — mapping response profiles across items to diagnoses and instructional implications.
↓ Download (.xlsx)A protocol for auditing standards-to-instruction-to-assessment coherence in an HQIM lesson or unit, with a rubric for rating alignment quality and documenting gaps.
↓ Download (.pdf)A structured worksheet for generating expert-based b, a, and c parameter priors using cognitive demand analysis and distractor design quality — with a worked example from a 6th grade ratio standard.
↓ Download (.xlsx)