Technical mathematics course structure combining expert modeling lectures with collaborative workshop sessions

Design · All designs
Evidence · 2 claims (2 mixed) · 1 study (1 causal), q2 · 0 of 1 report an effect size · 2 claims rest on one study

Description

This pattern describes the structure of the experimental technical mathematics classes tested in the study. "During the formal instruction, the teacher modeled problem solving sixty percent of the time and used the whole class for group problem solving," while "Collaborative small group problem solving was then done by the students forty percent of the time," with the teacher acting as a coach. Three of five weekly periods were allocated to teacher modeling of solutions using feasible heuristics and describing expert thought processes; the remaining two periods placed students in teacher-assigned groups working on more difficult, application-oriented problems, with the teacher roaming, questioning, scaffolding, and fading assistance as students became more proficient.

Design Implications

Context

Requirements

• Problems must be selected so they can be solved with an appropriate strategy and contain mathematical concepts relevant to the course material
• Teachers must roam among groups, ask students what they are doing and why they selected a method, and provide scaffolding when knowledge is lacking

Constraints

• The study took place during ten weeks of a fifteen-week semester in community college technical mathematics classes; the authors recommend more time be allotted for lab sessions in future implementations

Target Learners

• community college vocational students in industrial technology programs

Target Goals

• problem-solving skill in technical mathematics
• ability to talk through and defend mathematical solutions

Claims

• Cognitive Apprenticeship Hybrid Model Six Strategies [+M]
• Cognitive apprenticeship instruction produced no significant differences from traditional instruction on post-treatment problem-solving, final, and standardized mathematics exams in community college technical mathematics [~W]
• Cognitive apprenticeship students became more anxious about mathematics but reported gains in self-confidence, rapport, and enjoyment [~W]

Related Patterns

• Workshop Model
• Traditional Lecture / Reading / Midterm / Final Assessment

Examples

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Key Sources

• Johnson, Scott D.; Fischbach, Rita McDonough. (1992). Teaching Problem Solving and Technical Mathematics Through Cognitive Apprenticeship at the Community College Level. National Center for Research in Vocational Education. https://eric.ed.gov/?id=ED352455

Page metadata

Field	Value
type	design
id	modeling-lectures-plus-collaborative-workshop-sessions
title	Technical mathematics course structure combining expert modeling lectures with collaborative workshop sessions
description	This pattern describes the structure of the experimental technical mathematics classes tested in the study.
status	review
generated	by process:wiki-ingest on 2026-10-02
trust	unverified — no one has confirmed this page's content
sources	1 — johnson-1992

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