For Every Classroom
Concept maps · Critical thinking · Collaboration · Assessment — a formative model of mastery learning where everyone in the class can master the content and earn an "A."
What is 3CA?
3CA is a model of mastery learning: if you complete all the assignments in a responsible way, you will achieve mastery and an "A." In most classes there are those who are successful and those who are not — in this class, all can be successful with the necessary effort.
The model teaches the skills of concept mapping, critical thinking, prioritization, social and cognitive synthesis, group evaluation, and the creation of multiple-reasoning items. Every step toward mastery is observable, transparent, and open to public view by the students.
It takes about two sessions to get used to the procedures. Students in previous semesters have found them difficult at the beginning — and super easy after a few sessions.
The 3CA Model
3CA makes critical thinking teachable and mastery reachable. By having students build concept maps, apply Aristotle's WH questions, collaborate, and write the very items used to assess them, every step toward understanding becomes observable, transparent, and fair — so that everyone in the class can succeed.
3CA is where the Meta-Self Learning Model becomes classroom practice. It primarily cultivates the cognitive and meta-cognitive domains — but through collaboration it also develops the sociocultural domain, and through self-assessment and reflection it strengthens the conative and affective domains. Critical thinking here is a path toward the Meta-Self.
For multilingual learners, the WH questions are also language — the grammar of inquiry. Building maps, discussing them in pairs, and writing questions gives students authentic reasons to read, speak, negotiate meaning, and write. Thinking and language grow together, which is exactly how the EZ Model teaches English.
The Toolkit
Aristotle's critical-thinking questions, used at every step of the model.
Targets a single event — understanding the thing itself, the focus of inquiry and the nature of being.
What is the relation between two events? The familiar question of causal relations — central to scientific research and deductive reasoning.
What is the relation between a series of events? An exercise in inductive reasoning — the hallmark of procedural knowledge and goal-directed action.
Events as periods in time. Historians and storytellers ask when — and using what + when together deepens our understanding of events.
Human beings and human perspectives — explaining the actions of I, you, he, she, we, and they that lead to an event.
Deceptively complex, because context includes all the others. A picture of the context is a picture of the whole — the background for judgment and action.
Phase One · At Home
Completed each week before class — this preparation makes the collaborative phase possible.
Step 1
Identify the key concepts of the week's chapter — at least 20 key terms plus five of your own choosing — and build a digital map (e.g., at mindmup.com).
Step 2
Label every arrow connecting your concepts with one of the six questions — why, when, what, where, how, who. Which question fits is a matter of your own thinking.
Step 3
Order the concept–critical-thinking items from most to least important — this list feeds the next step.
Step 4
Write the questions that will become the basis of your own assessment.
Step 5
Submit the concept map, critical-thinking connections, prioritized list, and questions as one package to the course platform.
Phase Two · In Class
The same steps — now synthesized with your partners. Groups of six, working in three pairs, with a rotating leader.
Step 1
Find your group, choose the session's leader, pair up — a different partner each session, so communication skills keep growing. All of you have different talents; let's learn from each other.
Step 2
Exchange maps. Give feedback, agree, disagree, and discover the gaps in each other's thinking — then combine the individual maps into a new collaborative map.
Step 3
Rank the collaborative map's concepts, then write and critique multiple-reasoning questions in pairs — including one compound and one "what-if" question per group.
Step 4
The whole group reviews all 18 items, critiques and revises them, and chooses the best 9 — the very questions used on the mid-term and final exams. The leader posts them for the whole class to see.
Times New Roman · 12 pt · double-spaced · capital-letter alternatives, answer after the choices:
A child typically has a vocabulary of about 50 words at which of the following ages?
A. 6 months B. 12 months C. 18 months D. 24 months
Answer: C
The Research Behind the Model
The 3CA / 3CAM model was developed and tested through peer-reviewed research and a doctoral dissertation. Each paper is free to read or download.
Journal article · 2019
Elham Zandvakili, Ernest Washington, Edmund W. Gordon, Craig Wells & Mzamo Mangaliso
SAGE Open
A research report of teaching patterns of critical thinking using the competency-based 3CA model (Concept maps, Critical thinking, Collaboration, and Assessment) to change the grammar of schooling. Critical thinking is defined as the Aristotelian "WH questions" — what, when, where, how, who, and why — threaded through concept maps, collaboration, and assessment. Individual groups used more "what" questions; collaborative groups used more "why" and "how" questions.
PhD dissertation · 2019
Elham Zandvakili
Doctoral Dissertation, University of Massachusetts Amherst
The full doctoral dissertation developing the 3CAM model — a formative, skill-based model of mastery learning and assessment built on the Language Games of Critical Thinking (LGCT). Drawing on Bloom's mastery learning, Wittgenstein's language games, Chomsky's syntax, and Gordon's assessment theory, it shows how every step toward mastery can be made observable, transparent, and open to public view by students.
Journal article · 2018
Elham Zandvakili, Ernest Washington, Edmund Gordon & Craig Wells
Journal of Education and Learning, 7(6)
M3CA is a formative model of skill-based mastery learning developed in a college classroom. Mastery is built on students' own concept maps and the skills of critical thinking, prioritization, individual and group synthesis, and writing multiple-choice items to assess the knowledge embedded in their maps — giving students ownership, fairness, and a transparent picture of their own thinking.
Conference proceedings · 2018
Elham Zandvakili & Ernest Washington
NERA Conference Proceedings
A review of the literature underpinning each component of the 3CAM model — mastery learning, concept maps, critical thinking, collaboration, and assessment — starting from the theoretical framework of the Language Games of Critical Thinking and culminating in a complete picture of the model.
And Finally
"Take good care of yourself (1000000000000000000000000000000000010000000000000000 min)" — yes, that is really in the manual.