Cognitively Guided Instruction¶

Strategy · All strategies
Evidence · 1 claim (1 for) · 3 studies (2 causal, 1 quant-synthesis), q3 · 1 of 3 report an effect size

Description¶

Cognitively Guided Instruction (CGI) is a professional development program and instructional stance in which teachers learn the research-based taxonomy of children's mathematical problem-solving strategies (direct modeling, counting strategies, derived facts, recall) and the classification of problem types (e.g., join, separate, part-part-whole, compare), then use that knowledge to listen to and build instruction on students' own informal strategies. Rather than teaching a prescribed procedure first, teachers pose problems, elicit multiple solution strategies, and sequence problems to support students' progression toward more efficient reasoning.

Design Implications¶

CGI rests on the constructivist premise that learners arrive with informal, meaningful strategies that instruction should build upon rather than replace Activation of prior knowledge improves learning outcomes. [+M]. Its distinctive move is making the teacher's knowledge the target of intervention: CGI professional development does not script lessons but deepens teachers' models of student thinking, on the theory that teachers who understand the developmental trajectory will make better moment-to-moment instructional decisions than any curriculum script could [~S]. Longitudinal studies show CGI-trained teachers gain greater knowledge of student thinking, spend more time on problem solving, and their students show stronger problem-solving and number-sense outcomes with no loss in computational skill [+S].

Context¶

Requirements¶

• Teachers trained in the taxonomy of problem types (additive structures, then multiplication/division structures) and the developmental sequence of solution strategies
• A classroom culture where students explain their reasoning aloud and strategies are publicly compared
• Rich, contextualized word problems rather than bare computation exercises
• Time for students to solve problems in their own way before formal procedures are introduced

Constraints¶

• Effectiveness depends on teacher uptake: teachers who adopt the vocabulary but not the underlying attention to student thinking show little classroom change [-S]
• Requires substantial professional development time; one-shot workshops do not produce durable changes in practice [-M]
• Can be misread as "never teach procedures," leaving students without efficient strategies; CGI research supports building toward fluency, not stopping at informal methods [-M]
• Less directly applicable outside well-structured domains like early number and arithmetic, where the strategy taxonomy is well mapped [~W]

Implementation Variability¶

• Whole-class problem solving with strategy sharing, small-group work, or one-on-one conferences
• Integrated with curriculum materials (posing CGI-style problems within an adopted textbook) or as a standalone problem-solving routine
• Extended versions (e.g., "CGI fraction" work) apply the same stance to later-grade topics

Target Learners¶

• Elementary students, especially K–3, developing number sense and additive/multiplicative reasoning [+S]
• Lower-achieving students benefit particularly, because their informal strategies are honored rather than bypassed [+M]
• Teachers as the primary learners: the professional development targets teachers' knowledge of student thinking

Target Learning Goals¶

• Conceptual understanding of number operations and problem structure
• Problem-solving flexibility: selecting and inventing strategies suited to a problem
• Procedural fluency built on understanding rather than rote recall [~S]

Instructions¶

1. Learn the problem-type taxonomy (join, separate, part-part-whole, compare; later multiplication/division structures) and the developmental sequence of children's strategies.
2. Pose a contextual word problem without demonstrating a procedure first, allowing activation of students' informal knowledge.
3. Circulate and observe, using the taxonomy to interpret each student's approach (direct modeling → counting → derived facts → recall).
4. Facilitate a strategy-sharing discussion in which students explain their methods; sequence sharing from concrete to efficient.
5. Pose follow-up problems chosen to nudge students toward the next strategy in the progression — the teacher's knowledge of student thinking drives problem selection, not a fixed script.

Related Strategies¶

• Problem-Based Learning — shares the structure of learning driven by problems rather than by prior explanation
• Activating Prior Knowledge — CGI institutionalizes this by treating informal strategies as the entry point
• Formative Assessment — interpreting student strategies against a developmental trajectory is a form of embedded assessment
• Encourage children to model and discuss multiple solution strategies for number problems instead of hunting for clue words

Patterns That Use This Strategy¶

• CGI for Math — the pattern-level articulation of this strategy in the mathematics classroom

Examples¶

• CGI professional development program (Carpenter, Fennema, and colleagues, University of Wisconsin–Madison) — summer workshops plus yearlong support in which teachers analyze videos of children solving problems and plan instruction from student work.
• Children's Mathematics: Cognitively Guided Instruction (Carpenter, Fennema, Franke, Levi, & Empson, Heinemann) — the practitioner book and accompanying classroom video cases used widely in district CGI implementations.
• A first-grade CGI classroom solving "There were 8 birds on a branch; 3 flew away; how many are left?" — some students model with cubes, some count back, some recall the fact — followed by sharing that surfaces the counting-back strategy for peers still using direct modeling.

Key Sources¶

• Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C.-P., & Loef, M. (1989). Using knowledge of children's mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531. doi:10.3102/00028312026004499
• Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use children's thinking in mathematics instruction. Journal for Research in Mathematics Education, 27(4), 403–434. doi:10.2307/749875
• Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2015). Children's mathematics: Cognitively guided instruction (2nd ed.). Heinemann.
• Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers' generative change: A follow-up study of professional development in mathematics. American Educational Research Journal, 38(3), 653–689. doi:10.3102/00028312038003653