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Potential Research Questions

Example-based Learning in University-Level Mathematics
by

Danae Romrell

on 21 February 2014

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Transcript of Potential Research Questions

Example-Based Learning in University Level Mathematics:
Research Question Proposal

Danae Romrell
Idaho State University
February 20, 2014

Cognitive Load Theory
e-Learning
Mathematics Education
Searching the Literature
Cognitive Load Theory:
A Theoretical Perspective
Mathematics Education: The Learning Context

Database Searches
e-Learning:
Providing Instruction via Technology
Worked Examples:
Reducing Cognitive Load for Mathematics Instruction
Gaps in the Literature:
Future Research
Cognitive Load Theory (CLT)
CLT is a theory of learning that is "based on a model of human cognitive architecture" (Ayres & Van Gog, 2009, p. 253).
Types of Cognitive Load
Germane
Intrinsic
Extraneous
(Hollender et al., 2010, Vogul-Walcutt et al., 2011)
"An appropriate instructional design should reduce the extraneous cognitive load while inducing the germane cognitive load within working memory capacity" (Lee & Anderson, 2013, p. 457).
Worked Examples
(Based on Driscoll, 2005)
Gender Differences in e-Learning
Females exhibit more anxiety than males when using wikis, blogs, online games, and immersive virtual environments (Huang, Hood, Yoo, 2013)
Technology Use
Males and females use their time on the internet differently (Lai & Gwung, 2013)
Learner are often uncomfortable with or anxious about new technology.

Learner's often don't know how to use technology effectively and efficiently without instruction.
Choice
Control
Adaptation
Using multimedia or e-Learning applications can help increase student motivation (Huang, Hood, & Yoo, 2013; Thompson, 2013), especially in mathematics (Loong & Herbert, 2012, Davidson & Elliot, 2007).
Gender Differences in Multimedia Worked Examples?
Females are more anxious than males about using multimedia tools (Huang, Hood, & Yoo, 2013)
Males and females spend time differently when using the internet (Lai & Gwung, 2013)
Worked Examples in Calculus and beyond?
1 - Pre-algebra (Kay, 2012a)

6 - Algebra I (Ayres, 2013; Newton et al., 2010; Sweller, 1985; Booth, 2013; Reed et al., 2012, Scheiter et al., 2009)

2 - Geometry (Schwonke et al., 2009; Schwonke et al., 2011)

2 - Algebra skills for Chemistry students (Ngu, 2012; Ngu, 2013)

1 - Precalculus (Kay, 2012b)

1 - Technical Calculus (Miller, 2010)

1 - Linear Algebra (Corbalan, 2010)


15 studies
Not multimedia
Study was really about feedback
Ill-defined problems in Mathematics?
Fish Identification (Jarodzka et al., 2013)

Law Education (Nievelstein et al., 2013)

Electrical Circuits
(Richey & Nokes-Malach, 2013)

Design and Architecture (Rourke & Sweller, 2009)
Researched Domains
Student Behavior While Viewing Worked Examples?
Kay (2012) suggested that more research was needed on how student viewing behavior impacted learning outcomes
Jenkinson (2009) calls for research on educational technology that goes beyond comparing learning gains among two different methods.
Learner Control While Viewing Worked Examples?
Provide Instruction on New Technology
Sweller (1985) noted that, to a certain extent, mathematical teaching is stereotyped. There are usually three steps:
Information is introduced to students
A small number of example problems and solutions are studied
A large number of problems are presented to students to solve.
Augmented Reality and Mental Models
Web-based homework, cognitive tutors
Video Examples
e-Learning or Multimedia Learning
(Bujak et al., 2013; Gogus, 2013)
(Bukova-Güzel & Cantürk-Günhan, 2011; Craig et al., 2013; Tariq & Jackson, 2008; Taylor, Pountney, & Baskett, 2008)
(Kay & Edwards, 2012; Kay & Kletskin, 2012; Kay, 2012; Moreno & Valdez, 2007)
(Andrade-Aréchiga, López, & López-Morteo, 2012; Crowe & Zand, 2000a, 2000b; Loong & Herbert, 2012)
Metacognition, self-regulation, motivation
(Kim, 2012; Schwonke et al., 2013; Zhou, 2013)
Procedural Knowledge
Conceptual Knowledge
vs.
Flexibility
(Newton & Lynch, 2010)
“A worked example is a step-by-step demonstration of how to perform a task or solve a problem” (Clark & Mayer, 2011, p. 224).
Defining Worked Examples
Fade from worked examples to problems
Promote self-explanations
Include instructional explanations
Apply the multimedia principles to examples
Support learning transfer
Self-Explanations
Expertise Reversal Effect
Correct vs. Incorrect Examples
Example/Practice vs. Practice/Example pairs
Worked Examples in
Less-Structured Domains
(van Gog, 2011)
(Booth et al., 2013)
(Boekhout et al., 2010)
(Kay 2012a, 2012b; Kay & Kletskin, 2012; Reed et al., 2012; Scheiter et al., 2009; Wong et al., 2012)
Paas (1992) - Mental effort scale (e.g. Boekhout et al, 2010, Nievelstein et al., 2013, Van Gog et al., 2011).

Measuring different types of cognitive load is difficult (Ayres & van Gog, 2009; Kalyuga, 2009; Kirschner et al., 2011; Van Gog et al., 2009)
The expertise reversal effect indicates that "worked examples are more favorable in earlier stages of learning, while problem solving could be more effective in later stages" (Salden et al., 2009, p. 290).
Fading
Adaptive Fading
(Kalyuga, 2007)
(Salden et al., 2009)
Guided practice along with worked examples led to better conceptual knowledge that worked examples alone (Booth et al., 2013).
Using self-explanations can lead to higher germane cognitive load (Hilbert & Renkl, 2009)
InstructionalExplanations
Based on a meta-analysis of worked example research, Wittwer and Renkl (2010) found that using instructional explanations is not more effective than using self-explanations.
Fish Identification (Jarodzka et al., 2013)
Law Education (Nievelstein et al., 2013)
Electrical Circuits (Richey & Nokes-Malach, 2013)
Design and Architecture (Rourke & Sweller, 2009)
Research on worked examples in less-structured (ill-defined) domains has found that worked examples are effective for reducing cognitive load and for learning. There is also less of an expertise reversal effect.
Expert vs. Novice Models
Type of Example
More research is need on how best to provide learner control. Allowing learner control increases student motivation, but it also increases cognitive load (Ayres & Van Gog, 2009; Kirschner, Ayres, & Chandler, 2011)
Allowing learner control increases student motivation, but it also increases cognitive load (Ayres & Van Gog, 2009; Kirschner, Ayres, & Chandler, 2011)
References:
(Thompson, 2013; Huang, Hood, & Yoo, 2013; Bukova-Guzel, Canturk-Gunhan, 2011)
A few key research results.....
Potential Research Questions
Population:
Students in a university-level "flipped" calculus course.
Flipped Course:
Students view worked-examples prior to class as a replacement for some of the traditional lecture/homework.
Worked Examples:
The examples are multimedia worked examples that use fading, self-explanations prompts, and follow good multimedia design principles.
Qualitative Questions
Quantitative Questions
Research Question #1
What are the common behaviors among students using worked examples to provide instruction in a university-level calculus course?
Research Question #2
What are student attitudes regarding using example-based homework to provide instruction in a university-level calculus course? How is student motivation affected?
Research Question #3
How deeply do the students engage with the content when using a worked example? Do they use the self-explanation prompts effectively in a way that increases the germane cognitive load?
Research Question #6
How effective are the worked examples at helping students gain conceptual knowledge? Procedural knowledge? Flexibility? Problem-solving skills?
Research Question #5
Are there any gender differences in learning gains for students who use worked examples prior to class to replace traditional lecture/homework and students who complete traditional homework in a university-level calculus course.
Research Question #4
Is there a significant difference in the learning gains for students who use worked examples prior to class to replace traditional lecture/homework and students who complete traditional homework in a university-level calculus course.
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