Full and completion worked examples for simultaneous-equation algebra

Element · All elements
Evidence · 7 claims (6 for, 1 mixed) · 7 studies (5 causal, 1 review, 1 theoretical), q2–q3 · 0 of 7 report an effect size · 5 claims rest on one study

Description

Two versions of the same worked algebra problems used in the study. "The full- worked examples provided complete solution steps at every level; the completion -worked examples provided partial solution steps by withholding information in the problem solving process". The 12 problems were adapted from a middle school algebra textbook on systems of equations and studied on a computer before practice in a booklet.

Design Implications

Context

Requirements

• Problems are built as a pair: one version showing every solution step, one with answers blanked out at each step (Table 1).
• Materials were reviewed by content experts and university faculty and piloted before use.

Constraints

• The study measured only immediate effects; long-term retention and transfer were not examined.

Target Learners

• Non-science major college students at a Research I university in the western United States

Target Learning Goals

• Solving simultaneous equation (systems of equations) algebra problems

Affordances

• Expertise Reversal Effect
• Cognitive Load Theory

Claims

• Lower-prior-knowledge learners scored higher on an algebra posttest after full-worked than completion-worked examples, while higher-prior-knowledge learners' non-significant advantage ran the other way [+W]
• Prior knowledge, worked-example type (full vs completion) and task difficulty show a significant three-way interaction on an algebra posttest, but not on self-reported cognitive load [+W]
• Prior knowledge and worked-example type (full vs completion) interact significantly on self-reported germane cognitive load, but not on intrinsic or extraneous load [+W]
• Studying worked examples improves novices' algebra performance on problems with the same structure as the examples [+M]
• The learning benefit of the worked-example textbook was greater for students with lower pretest proportional reasoning skills [~W]

The evidence by question

• For whom: how does the benefit change with prior knowledge? Worked-example guidance becomes less effective as learner expertise increases. [+S]
• How should learners move from studying examples to solving problems alone? Successively fading out worked solution steps is effective for facilitating the transition from learning from worked examples to problem solving, compared to example-problem pairs [+M]

Related Elements

• Worked Examples
• Completion Problems
• Faded Worked Examples
• Worked_Examples_Types

Examples

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Key Sources

• Gupta, U., & Zheng, R. Z. (2020). Cognitive Load in Solving Mathematics Problems: Validating the Role of Motivation and the Interaction Among Prior Knowledge, Worked Examples, and Task Difficulty. European Journal of STEM Education, 5(1), 05. https://doi.org/10.20897/ejsteme/9252

Page metadata

Field	Value
type	element
id	full-and-completion-worked-examples-for-simultaneous-equations
title	Full and completion worked examples for simultaneous-equation algebra
description	Two versions of the same worked algebra problems used in the study.
status	review
canonical	True
generated	by claude/unspecified on 2026-09-24
trust	unverified — no one has confirmed this page's content
sources	1 — gupta-2020

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