Vol 13 No 1 - August 2015

International Journal
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Vol.13 No.1

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VOLUME 13 NUMBER 1 August 2015
Table of Contents
Influence of Mathematical Representation and Mathematics Self-Efficacy on the Learning Effectiveness of Fifth
Graders in Pattern Reasoning ...............................................................................................................................................1
Ming-Jang Chen, Chun-Yi Lee and Wei-Chih Hsu
Mentors in an Undergraduate Psychology Course: A Comparison of Student Experience and Engagement......... 17
Jill A. Singleton-Jackson, Marc Frey, Martene Clayton Sementilli and Tyler Pickel
On the Nature of Experience in the Education of Prospective Teachers: A Philosophical Problem.......................... 29
Christi Edge, Ph.D
Learning as you Teach ......................................................................................................................................................... 42
Dr Abha Singh and Dr Megan Lyons
Analysis of Fragmented Learning Features under the New Media Environment ...................................................... 55
Peng Wenxiu
Skill Education in Pre-service Teacher Education for Elementary School Teacher ..................................................... 64
Ikuko Ogawa
Plagiarism Education: Strategies for Instructors .............................................................................................................. 76
Julia Colella-Sandercock and Hanin Alahmadi
Introducing Pre-Service Teachers to Programming Concepts with Game Creation Approach.................................85
Chiung-Fang Chiu
Validity of Post-Unified Tertiary Matriculation Examination (POST-UTME) as Screening Instrument for Selecting
Candidates into Degree Programmes in Nigerian Universities .................................................................................... 94
James Ayodele OLUWATAYO Ph.D. and Olufunke Olutoyin FAJOBI (M.Ed.)

1
© 2015 The authors and IJLTER.ORG. All rights reserved.
International Journal of Learning, Teaching and Educational Research
Vol. 13, No. 1, pp. 1-16, August 2015
Influence of Mathematical Representation and
Mathematics Self-Efficacy on the Learning
Effectiveness of Fifth Graders in Pattern Reasoning
Ming-Jang Chen
National Chiao Tung University
No. 1001, University Rd. Hsinchu 30010, Taiwan (R.O.C)
Chun-Yi Lee
National Taipei University
No.151, University Rd., San-Shia Dist., New Taipei City 23741, Taiwan (R.O.C.)
Wei-Chih Hsu
Mai-Liao Elementary School
No. 260, Zhongshan Road, Mailiao, Yunlin County, Taiwan (R. O. C.)
Abstract. The aim of this study was to examine the influence of
mathematics self-efficacy and diverse mathematical representations in
learning materials on the performance and learning attitude of
elementary school learners with regard to pattern reasoning. The
research samples comprised one hundred and fifty fifth-grade students
from an elementary school in Central Taiwan. We adopted a two-factor
quasi-experimental design with mathematical representation and
mathematics self-efficacy as the independent variables. Digital learning
materials were graphical or numerical and the learners designated as
having high or low mathematics self-efficacy. The dependent variables
included performance of pattern reasoning and attitudes towards
learning mathematics. The former was divided into number sequence
reasoning and graphic sequence reasoning, whereas the latter included
learning enjoyment, motivation, and anxiety. The research findings
indicate that (1) using graphical learning materials enhances
performance in pattern reasoning; (2) using digital learning materials in
teaching can improve attitudes towards learning mathematics; (3)
learners with high mathematics self-efficacy display more positive views
towards learning mathematics.
Keywords: pattern reasoning; representation; mathematics teaching;
digital learning materials; mathematics self-efficacy
1. Introduction
In mathematics, pattern reasoning is generally a difficult topic for elementary
school learners. Learners often fail to perceive pattern relationships and
internalize them into personal knowledge and understanding, which then leads

2
to inflexibility in their approach to mathematical problems (Lee, Chen & Chang,
2014). As the thinking patterns of elementary school learners are still in the
concrete operational stage, they require manipulable objects, the enactive and
iconic representation of which helps learners make connections with previously-
acquired knowledge. Providing learners with concrete representations on
interactive digital platforms can thus assist them in translating concrete into
abstract thinking.
The learning of pattern reasoning generally begins with inductive reasoning
related to quantitative relationships before progressing on to deductive
reasoning. These higher levels of logical thinking often involve abstract
concepts, which learners must represent with concrete objects or appropriate
symbols. Lewis and Mayer (1987) indicated that most difficulties in problem-
solving occur in the representation stage. As a result, the process of translating
problems into internal representations is the key to whether learners can
successfully solve a problem. If learners can understand different forms of
conversion processes for mathematical representation, they will be able to grasp
the mathematical concepts involved.
The self-efficacy of learners is also a factor of learning effectiveness, and
mathematics is no exception. Learners with greater mathematics self-efficacy
have more confidence and better learning effectiveness in mathematics as well as
less mathematics anxiety (Lee & Chen, 2015; Hackett & Betz, 1989; Schunk,
2007). The means of enhancing the mathematics self-efficacy of learners is thus
an issue worth investigating. We used digital learning materials designed for
diverse mathematical representation with the objectives of improving the
performance of fifth graders in pattern reasoning and their attitudes toward
learning mathematics. During this process, we examined the influence of various
mathematical representations and degrees of mathematics self-efficacy on the
performance of learners in pattern reasoning and their attitude towards learning
mathematics and determined whether interaction effects exist between
mathematics self-efficacy and mathematical representations.
2. Literature Review
We investigated the influence of different mathematical representations and
degrees of mathematics self-efficacy on the performance of learners in pattern
reasoning and their attitude towards learning mathematics from the perspective
of mathematics teaching and the incorporation of information technology into
teaching. We thus collated relevant literature associated with pattern reasoning,
mathematical representations, and mathematics self-efficacy.
2.1 Pattern reasoning
The essence of mathematics is seeking patterns and relationships among them
(Lee & Chen, 2009). With the experience accumulated from pattern reasoning,
one can learn the means of perceiving and generalizing quantitative patterns in
objects and matters to set up and solve mathematical problems. Blanton and
Kaput (2002) stated that behind any special phenomenon lies the basis and
pattern of its occurrence.

3
Pattern reasoning activities not only emphasize inductive reasoning beginning
from quantitative patterns but also extend to deductive reasoning activities
(Fernandez & Anhalt, 2001). This means that learners identify and confirm
patterns before further generalizing the patterns for problem solving. Owen
(1995) divided mathematics patterns into three types: repeating patterns,
structural patterns, and growing patterns, all of which are present in the
elementary school mathematics curriculum in Taiwan.
2.1.1 Repeating patterns
As the name suggests, repeating patterns evidence cycles or repetition (Owen,
1995) of specific characteristics such as colors, shapes, directions, sizes, sounds,
or numbers, for example, “yellow, green, red, yellow, green, red,” and “□, ○,
△, □, ○, △”.
2.1.2 Structural patterns
Structural patterns imply the presence of certain characteristics within a group,
for example, compositions of 5 (4 + 1, 3 +2, 2 +3, and 1 + 4). In elementary school
mathematics, the commutative laws, the associative laws and the distributive
laws of multiplication and addition are all topics involving structural patterns.
For example, 3×5=15 and 5×3=15, or 8×4=(5+3)×4=(5×4)+(3×4).
2.1.3 Growing patterns
Growing patterns involve changing the form of a number through predictive
methods. Owen (1995) categorized the contents of growing patterns as
sequences, which are lists of non-repetitive numbers that expand according to a
single rule. In formal curriculum activities, number sequences are the most
typical type of sequences, encompassing arithmetic sequences, geometric
sequences, and Pascal’s triangle. For instance, the sequence 5, 10, 15, 20…
increases by 5 with every term.
2.2 Mathematical representation
Mathematical representations are defined as the different forms of
representations that learners use to interpret a problem (Ainworth, 2006). The
National Council of Teachers of Mathematics (NCTM) (2000) identified
mathematical representations as depictions of mathematical concepts formed by
learners, indicating their understanding and application of said concepts.
Mathematical representations therefore play an important role in the formation
of mathematical concepts. Through different representations, learners learn
mathematics and gain knowledge. Bruner (1966) claimed that the process of
conceptual development is the formation of a system of representations; he
divided learning into three development processes involving enactive, iconic,
and symbolic representations. Heddens (1984) divided learning stages into
concrete, semi-concrete, semi-abstract, and abstract representations and stated
that learners must first be able to internalize new knowledge in the concrete
stage before systematically assigning abstract representations to the new
knowledge. By creating sound connections between the real world and the
abstract world, they build solid foundations for mathematical thinking.
Kaput (1987) sought to explain the link between mathematical representation
and mathematics learning, proposing four categories of the former: cognitive
and perceptual representation, explanatory representation, representation

4
within mathematics, and external symbolic representation. Janvier (1987)
showed that external symbolic representations influence as well as reflect the
internal representations of the mathematical knowledge possessed by learners.
Based on the perspective of communication, Lesh, Post, and Behr (1987)
classified five different types of representations: real script, manipulative models,
static pictures, spoken language, and written symbols. They stressed the
importance of conversions between representations, which means that learners
of mathematics must be able to understand diverse forms of representation,
move easily between forms of representations, and select the most appropriate
and convenient method of representation to explain and solve problems.
Willis and Fuson (1988) found the use of pictorial representations in teaching
second graders to solve word problems in addition and subtraction to be
effective. Tchoshanov (1997) carried out a pilot experiment on trigonometric
problem solving and proof for high school students in Russia. The analytic
group was taught by a traditional algebraic approach. The visual group was
taught by a visual approach using enactive (i.e., geoboard as manipulative aid)
and iconic (pictorial) representations. The representational group was taught by
a combination of analytic and visual means. The results showed that the
representational group had a better learning performance than the visual and
analytic groups. Therefore, we understood that any intensive use of only one
specfic mode of representation does not enhance students' conceptual
understanding and representational thinking.
2.3 Mathematics self-efficacy
Self-efficacy is a determinant influencing the learningeffects in mathematics and
can be used to accurately predict learning achievements in mathematics. Hackett
and Betz (1989) established significant and positive correlations among learning
effectiveness, self-efficacy, and learning attitudes in mathematics. Anjum (2006)
further indicated a positive correlation between self-efficacy and mathematics
achievements on every grade level of elementary school, the degree of which
increased with the grade. Skaalvik and Skaalvik’s (2006) found that middle
school and high school mathematics students showed self-efficacy predicted
subsequent learning performance more accurately than prior achievement. They
found that self-efficacy mediated academic achievement. Mathematics
achievement is influenced significantly by student’s attitudes and self-efficacy.
Lee and Cheng (2012) also found that students with high mathematics self-
efficacy have better learning outcomes and attitudes toward mathematics than
those with low mathematics self-efficacy when learning equivalent fractions.
Therefore, enhancing the mathematics self-efficacy of learners can benefit their
effectiveness in learning mathematics.
3. Methodology
3.1 Research Participants
In this study, we targeted fifth-grade elementary learners. The research samples
comprised four fifth-grade classes from an elementary school in Central Taiwan.
Before conducting the experiment, the participants were randomly assigned to

5
two groups: one using graphical learning materials and the other using
numerical learning materials. A mathematics self-efficacy scale was used to
assign the top 45 % and the bottom 45 % of the learners as those with high and
low mathematics self-efficacy, respectively. We derived a total of 121 valid
samples.
3.2 Research Instruments
3.2.1 Mathematics self-efficacy scale
The purpose of applying a mathematics self-efficacy scale was to assess whether
the learners had the confidence to effectively execute mathematical learning
activities. We adopted the mathematics self-efficacy scale revised by Lee and
Cheng (2012) from the General Self-efficacy subscale developed by Sherer and
Maddux (1982). The scale comprises three constructs: initiation, persistence, and
self-confidence. Initiation involves the degree of confidence that a learner has to
initiate learning when encountering a new mathematical learning activity or a
more difficult mathematical task; persistence indicates the degree of confidence
that a learner has to persist in learning when experiencing setbacks; and self-
confidence refers to the degree of confidence that a learner has in completing
tasks. Each construct contained 6 question items, accounting for a total of 18
question items in the scale. We adopted a five-point Likert scale, ranging from
strongly disagree (1) to strongly agree (5). Higher scores represented greater
mathematics self-efficacy, meaning that learners had greater confidence in their
ability to effectively execute mathematical learning activities. An internal
consistency test on the reliability of the scale presented an overall Cronbach’ s α
of 0. 95 – an ideal internal consistency coefficient.
3.2.2 Pattern reasoning materials
AMA (Activate Mind Attention) is a widely known software program in Taiwan
that utilizes PowerPoint as a platform for the design and presentation of media
for mathematical instruction (Lee &Chen, in press). It is available free of charge
from http://ama.nctu.edu.tw/index.php, and its core functions include the
structural cloning method (SCM) and trigger-based animation (TA). SCM uses
the concepts of structure and cloning to interpret shapes. Its original purpose
was to resolve positioning issues in the design of teaching materials, but its
ability to imitate paintings of natural landscapes, and create complex
symmetrical compositions and spot series ensure a wide range of potential
applications. In TA, certain objects serve as buttons that control series of
animations. TA can assist users in displaying digital content to attract the
attention of the audience, guide cognition, and reduce cognitive load.
For the contents of the learning materials used in this study, we referred to the
curriculum regarding number sequences and graphic sequences in mathematics
textbooks published by Kang Hsuan Educational Publishing Group. We used
AMA to design the digital materials, which were then reviewed and revised by
elementary school teachers and experts who are professional at this topic. The
primary learning objective in this topic is to perceive simple quantity patterns
and solve problems through concrete observation and exploration, and make
connections with three other learning areas in mathematics: numbers and
quantities, elementary algebra, and connection. The materials presented four
teaching foci in a progressive manner: sequences of odd numbers and even

6
numbers, triangular numbers, square numbers, and Fibonacci numbers. We
created materials and worksheets to act as step-by-step guides to exploration of
pattern reasoning. Learning objectives were set for each focus based on the
curriculum, and the learning achievements based on these objectives were
explained in detail. The designs of the digital materials in the numerical learning
materials group and the graphical learning materials group were different only
in the manner of mathematical representation; the remainder of the contents was
the same.
Numerical learning materials
These materials used numerical representations. Aided by worksheets, the
teacher presented the foci of the learning materials one by one. Figure 1 shows
an example with the square number sequence 1, 4, 9, 16, …. The learners are
asked to identify the seventh item and find the pattern. With the interactive
buttons in the digital materials, the teacher guided the learners’ exploration of
the relationship among the numbers, identifying the next item first before
finding the seventh with the perceived pattern and recording the ideas on the
worksheet.
Figure 1: Interactive materials showing the pattern of a square number sequence
Graphical learning materials
These materials used graphical representations. Aided by worksheets, the
teacher presented the foci of the learning materials one by one. Figure 2 displays
the graphical example of square numbers, also asking the learners to identify the
seventh item and find the pattern. With the interactive buttons in the digital
materials, the teacher presented the graphical changes and guided the learners’
exploration of the relationship among the graphs, identifying the graph of the
next item first before finding the seventh with the perceived pattern and
recording the ideas on the worksheet.

7
Figure 2: Solving the square number pattern with graphics
3.2.3 Pattern reasoning achievement test
The aim of the pattern reasoning achievement test was to assess the performance
of the learners in pattern reasoning after the teaching experiment using digital
materials with different mathematical representations. Based on the teaching
contents and the studies conducted by Rivera and Becker (2008), the test was
divided into two portions: number sequences and graphic sequences. Each
portion contained five problems with 1 point for each problem, resulting in a
total score of 10 points.
Number sequence reasoning was assessed by evaluating the learners’ ability to
seek patterns among numbers and solve number sequence problems. The
problems involved (1) arithmetic sequences and (2) second-order arithmetic
sequences, both of which were presented with number sequences. Graphic
sequence reasoning was assessed by evaluating learners’ ability to seek patterns
among graphs and solve graphic sequence problems. The problems involved (1)
arithmetic sequences and (2) second-order arithmetic sequences, both of which
were presented with graphic sequences.
An internal consistency test on the reliability of the pattern reasoning
achievement test yielded a Cronbach’s α of 0.71 in the number sequence
reasoning portion, a Cronbach’s α of 0.73 in the graphic sequence reasoning
portion, and a Cronbach’s α of 0.83 for the entire test, indicating acceptable
internal consistency. The difficulty indexes of the problems ranged between 0.30
and 0.86, whereas the discrimination indexes of the problems ranged between
0.35 and 0.95. On the whole, the difficulty index and discrimination index in the
pattern reasoning achievement test were appropriate.
3.2.4 Attitudes towards learning mathematics questionnaire
A questionnaire was used to understand the feelings of the learners as they
learned the concepts of number and graphic sequences using different
mathematical representations. We adopted the questionnaire created by Lee and
Cheng (2012), which is divided into three aspects: enjoyment of and motivation
and anxiety toward learning. Each aspect contains 5 question items, accounting
for a total of 15 question items. We utilized a five-point Likert scale, ranging
from strongly disagree (1) to strongly agree (5). Questions related to enjoyment
and motivation were positive, whereas those regarding learning anxiety were
negative. In the positive items, the subjects choosing 1 were given 1 point, those

8
choosing 2 were given 2 points, and so on. In the negative items, the scores were
the opposite. Higher total scores indicated more positive attitudes towards
learning mathematics. The Cronbach’s α of the entire questionnaire was 0. 74,
representing acceptable internal consistency.
4. Results and Discussion
4.1 Analysis of learning performance in pattern reasoning
We analyzed the performances of learners in both number sequence reasoning
and graphic sequence reasoning. The means and standard deviations of the two
sets of scores are showed in Table 1. The performance of the students in the
graphical learning materials group was better than that of the students in the
numerical learning materials group. Also, students with high mathematics self-
efficacy displayed better performance in pattern reasoning than those with low
mathematics self-efficacy.
Table 1: Summary of learning performance results
Pattern reasoning
construct
Group Mean
Standard
deviation
Number
of subjects
Number sequence
reasoning
Numerical learning
materials
2.86 1.212 56
Graphical learning
materials
3.29 1.027 65
High mathematics self-
efficacy
3.12 1.195 60
Low mathematics self-
efficacy
3.07 1.078 61
Graphic sequence
reasoning
Numerical learning
materials
2.48 1.375 56
Graphical learning
materials
3.02 1.192 65
efficacy
2.93 1.313 60
efficacy
2.61 1.282 61
4.1.1 Analysis of performance in reasoning with number sequences
Table 2 displays a summary of the ANOVA regarding number sequence
reasoning. The interaction effect between mathematical representation and
mathematics self-efficacy did not reach the significance (F(1, 117)= 0.159, p=
0.908). The main effect of mathematical representation was significant (F(1, 117)
= 4. 439, p = 0.037), whereas the main effect of mathematics self-efficacy was not
(F(1,117) = 0.018, p = 0.894). The mean score in number sequence reasoning
shows that the students were more receptive to the graphical learning materials
(mean= 3.29) than they were to the numerical learning materials (mean= 2.86). In
addition, the students with high mathematics self-efficacy exhibited no
differences in number sequence reasoning from those with low mathematics
self-efficacy.
Table 2 Summary of ANOVA for number sequence reasoning
Source of variance
SS
(Type-III
sum of
squares)
Df
(Degree
of
freedom)
MS
(Sum of
squares)
F
(F test)
Sig.
(Significance)

9
Mathematical
representation
5.626 1 5.626 4.439* .037
Mathematics self-efficacy .023 1 .023 .018 .894
Mathematical
representationMathematics
self-efficacy
.017 1 .017 .013 .908
Error 148.266 117 1.267
4.1.2 Analysis of performance in reasoning with graphic sequences
Table 3 displays a summary of the ANOVA for graphic sequence reasoning. The
interaction effect between mathematical representation and mathematics self-
efficacy did not reach the significance (F(1, 117)= 0.226, p= 0.635). The main
effect of mathematical representation was significant (F(1, 117) = 4. 896, p =
0.029), whereas the main effect of mathematics self-efficacy was not (F(1,117) =
1.517, p = 0.221). These results reveal that the students that had used graphical
learning materials (mean= 3.02) performed better in graphic sequence reasoning
than those that had used numerical learning materials (mean= 2.48).
Furthermore, subjects with high and low mathematics self-efficacy delivered the
same level of performance.
The analysis results regarding pattern reasoning performance show that the
mathematical representation used in the learning materials had significant
influence on the learning performances in number sequence reasoning and
graphic sequence reasoning, whereas mathematics self-efficacy did not have
significant influence.
The research results demonstrate that the performance displayed by learners
learning with graphical materials in pattern reasoning was superior to that
displayed by learners learning with numerical materials. One possible
explanation was that the graphical materials provided the environment so that
the students had more opportunities to have a connection between numerical
and graphic representations. This ability to adapt multiple representations to the
problem at hand reflects one’s grasp of mathematical concepts (Brenner, et al.,
1999; Cai, 2001). Therefore, making conversions between different representation
systems can assist learners in interpreting problems, enhance their
understanding of mathematical concepts, and enable them to make connections
with related concepts, all of which make learning mathematics more meaningful.
With regard to mathematics self-efficacy, we discovered no significant
differences between learners with high and low mathematics self-efficacy in
pattern reasoning. One possible reason was that both groups used dynamic
interactive digital learning materials, and both groups were able to observe
patterns in numerical and graphic representations to the same extent. Therefore,
the digital materials were helpful to learners with either high or low
mathematics self-efficacy.
Table 3 Summary of ANOVA for graphic sequence reasoning
Source of variance
SS
(Type-III
sum of
Df
(Degree
of
MS
(Sum of
squares)
F
(F test)
Sig.
(Significance)

10
squares) freedom)
Mathematical
representation
8.033 1 8.033 4.896* .029
Mathematics self-efficacy 2.489 1 2.489 1.517 .221
Mathematical
self-efficacy
.371 1 .371 .266 .635
Error 191.944 117 1.641
4.2 Analysis of attitudes towards learning mathematics
The means and standard deviations of the scores resulting from the mathematics
self-efficacy questionnaire are presented in Table 4. A score of 3 indicates a
neutral position, and higher scores mean more positive attitudes, which
implicate greater enjoyment in and motivation toward learning mathematics as
well as less anxiety. The mean scores show that the students displayed positive
learning attitudes towards the integration of different mathematical
representations in the materials. The graphical learning materials group
displayed attitudes that were slightly more positive than the numerical learning
materials group. The students also displayed positive learning attitudes
regardless of their degree of mathematics self-efficacy, but students possessing
high mathematics self-efficacy presented with higher scores than those
possessing low mathematics self-efficacy in all three aspects.
Table 4 Summary of results with regard to attitudes towards learning mathematics
Aspect of attitudes
towards learning
mathematics
Group Mean
Standard
deviation
Number
of
subjects
Enjoyment in learning
Numerical learning materials 3.400 1.086 56
Graphical learning materials 3.516 0.985 65
efficacy
3.806 1.001 60
efficacy
3.124 0.905 61
Motivation toward
learning
efficacy
3.966 0.958 60
efficacy
3.102 0.980 61
Anxiety toward
learning
efficacy
3.714 0.929 60
efficacy
3.168 0.946 61
Table 5 summarizes the ANOVA for attitudes towards learning mathematics. In
the enjoyment of and motivation toward learning, the two-dimensional
interaction effects between mathematical representation and mathematics self-
efficacy reached the level of significance (F(1,117) = 6.831, p= 0.010; F(1,117) =
5.400, p= 0.022). This shows that mathematical representation and mathematics
self-efficacy exert varying degrees of influence on the enjoyment and motivation

11
of learners in different groups. We then analyzed the simple main effects of
mathematical representation and mathematics self-efficacy on the two variables.
Table 5 Summary of ANOVA for attitudes towards learning mathematics
Source of variance
Dependent
variable
SS
(Type-
III sum
of
squares)
Df
(Degree
of
freedom)
MS
(Sum
of
squares)
F
(F
test)
Sig.
(Significance)
Mathematical
representation
Learning
enjoyment
5.399 1 8.033 .236 .628
Learning
motivation
8.484 1 8.484 .373 .543
Learning
anxiety
27.670 1 27.670 1.342 .249
Mathematics self-efficacy Learning
enjoyment
309.737 1 309.737 13.564* .000
Learning
motivation
514.294 1 514.294 22.610* .000
Learning
anxiety
223.604 1 223.604 10.845* .001
Mathematical
self-efficacy
Learning
enjoyment
155.995 1 155.995 6.831* .010
Learning
motivation
122.839 1 122.839 5.400* .022
Learning
anxiety
16.374 1 16.374 .794 .375
Error Learning
enjoyment
2671.813 117 22.836
Learning
motivation
2661.322 117 22.746
Learning
anxiety
2412.309 117 20.618
Figure 3 displays the interaction effects between mathematical representation
and mathematics self-efficacy with regard to learning enjoyment. Different
mathematical representations caused learners with high mathematics self-
efficacy to display significant differences in this variable (F(1,59) = 4.567, p=
0.037); that is, they had significantly more fun learning with graphical learning
materials than with numerical learning materials. In contrast, learners with low
mathematics self-efficacy did not display differences in learning enjoyment with
regard to mathematical representation (F(1,60) = 2.383, p= 0.128). Furthermore,
in the numerical learning materials group, learners with high mathematics self-
efficacy showed no differences from those with low mathematics self-efficacy in
this variable (F(1,54) = 0.407, p= 0.526); however, in the graphical learning
materials group, learners with high mathematics self-efficacy had significantly
more fun than those with low mathematics self-efficacy (F(1,63) =29.060, p< 0.05).
The simple main effects analysis of learning enjoyment thus demonstrates that
learners with high mathematics self-efficacy have significantly more fun
learning mathematics with graphical learning materials than learners using
numerical learning materials and learners with low mathematics self-efficacy.

12
Fig. 3 Interaction effects between mathematical representation and mathematics self-
efficacy in learning enjoyment
Figure 4 exhibits the interaction effects between mathematical representation
and mathematics self-efficacy with regard to learning motivation. Learners with
high mathematics self-efficacy presented significant differences in learning
motivation with regard to mathematical representation (F(1,59) = 4.447, p=
0.039); those learning with graphical learning materials were more motivated
than those learning with numerical learning materials. In contrast, learners with
low mathematics self-efficacy showed no differences in learning motivation with
regard to mathematical representation (F(1,60) = 1.426; p= 0.237). The degree of
mathematics self-efficacy did not have significant influence on students’
motivation in the numerical learning materials group (F(1,54) =1.962, p= 0.167);
however, it did have significant influence on learning motivation in the
graphical learning materials group (F(1,63) = 41.275, p< 0.05): learners with high
mathematics self-efficacy were significantly more motivated than those with low
mathematics self-efficacy. The simple main effects analysis of learning
motivation thus reveals that learners with high mathematics self-efficacy are
significantly more motivated when learning mathematics with graphical
learning materials than learners using numerical learning materials and learners
with low mathematics self-efficacy.
4.042
3.314
2.942
3.500
0
1
2
3
4
5
Numerical learning
materials
Graphical learning
materials
Learners with high mathematics self-efficacy
Learners with low mathematics self-efficacy
Averagescore

13
Fig. 4 Interaction effects between mathematical representation and mathematics self-
efficacy in learning motivation
In learning anxiety, the main effect of mathematics self-efficacy reached the level
of significance (F(1,117) = 10.845, p= 0.001). The main effect of mathematics self-
efficacy and the mean scores of learning anxiety indicate that learners with high
mathematics self-efficacy experience less anxiety in learning mathematics than
learners with low mathematics self-efficacy. In other words, learners with low
mathematics self-efficacy feel more anxious about the learning activities in
pattern reasoning.
The analysis results concerning the attitudes towards learning mathematics
indicate that when learning with graphical learning materials, learners with high
mathematics self-efficacy experience a greater degree of enjoyment and
motivation than learners with low mathematics self-efficacy. However, when
learning with numerical learning materials, the learners displayed no significant
differences in learning enjoyment and motivation related to the degree of
mathematics self-efficacy. We speculate that this is because the wealth of
information that graphical learning materials provide give learners with high
mathematics self-efficacy the confidence to solve the problems without
assistance, and they will therefore set more challenging objectives for themselves
and work harder in the face of setbacks. As a result, they will have more fun and
be more motivated to learn than learners with low mathematics self-efficacy.
Numerical representations in learning materials are monotonous and lack the
excitement of graphics. For this reason, the students with high mathematics self-
efficacy learning with these materials presented no significant differences from
those with low mathematics self-efficacy in learning enjoyment or motivation.
Learners with high mathematics self-efficacy feel relatively less anxiety with
regard to mathematics than do learners with low mathematics self-efficacy. The
students in the numerical and graphical learning groups showed no significant
differences in learning anxiety. We conjecture that learners with low
4.188
3.254 2.954
3.676
0
1
2
3
4
5
Numerical learning
materials
Graphical learning
materials
Learners with high mathematics self-efficacy
Learners with low mathematics self-efficacy
Averagescore

14
mathematics self-efficacy generally believe that their tasks are harder than they
really are, that any amount of effort cannot change an established fact, and that
their ability to solve problems is insufficient. Such beliefs weaken self-confidence
and evoke negative emotional reactions such as anxiety, tension, stress, and
depression (Bandura, 1986), all of which cause learners with low mathematics
self-efficacy to have greater anxiety in learning mathematics.
The variability and interactivity of the digital learning materials provided in this
study make manifest abstract concepts. In addition, as this was the first time the
students had used such materials in math class, they were a novelty. As a result,
the learners expressed positive feelings regardless of the type of learning
material and presented no significant differences in learning anxiety.
5. Conclusions and Suggestions
5.1 Using graphical learning materials can improve the performance of
learners in pattern reasoning
In the analysis of performance in number sequence reasoning, the results
indicate that learners that had used graphical learning materials obtained better
scores than those that had used numerical learning materials. Similar results
occurred for graphic sequence reasoning, and both presented significant
differences. Therefore, integrating graphical learning materials into teaching can
improve the performance of learners in pattern reasoning.
The dynamic and static pictures presented in the graphical learning materials
enabled the learners to make connections with previously-acquired knowledge
and practice converting from one mathematical representation to another. This
kind of flexible use of representation systems is an essential feature of
mathematical ability (Dreyfus & Eisinberg, 1996). The answers to the pattern
reasoning achievement test also revealed that learners in the graphical learning
materials group were more able to describe the patterns that they perceived. In
other words, diverse representation during the learning process enhances the
understanding of concepts and induces better learning effectiveness in pattern
reasoning.
When learners encounter difficulties in mathematics, it is often due to the
inability make flexible use of mathematical representations to solve problems.
Therefore, teachers should make use of diverse mathematical representations,
such as manipulative models, graphs, and abstract symbols, in order to promote
independent thinking and holistic understanding rather than the mere use of
formulas and algorithms for by-rote problem solving.
5.2 Providing appropriate strategies to enhance mathematics self-efficacy can
improve attitudes towards learning mathematics
When learning with graphical learning materials, learners with high
mathematics self-efficacy had more fun and were more motivated than those
learning with numerical learning materials. Moreover, learners with high
mathematics self-efficacy experienced less anxiety with regard to mathematics.
Therefore, the provision of appropriate strategies to enhance mathematics self-
efficacy will help learners improve their attitudes towards learning mathematics.

15
We suggest that teachers use strategies such as teacher feedback, goal setting,
and make use of interactive models to help learners increase their mathematics
self-efficacy (Siegle & McCoach, 2007).
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192-201.

17
©2015 The authors and IJLTER.ORG. All rights reserved.
Vol. 13, No. 1, pp. 17-28, August 2015
Mentors in an Undergraduate Psychology
Course: A Comparison of Student Experience
and Engagement
Jill A. Singleton-Jackson, Marc Frey,
Martene Clayton Sementilli & Tyler Pickel
University of Windsor
Windsor, Ontario, Canada
Abstract. Curricular peer mentoring is a specific course-based form of
peer mentoring that is intended as academic support for students
(Smith, 2013, Chapter 1). This study focussed on a curricular peer
mentoring program being used specifically in an undergraduate child
psychology course. This study aimed to discover differences in student
experience, engagement, and achievement in three courses as impacted
by having mentors or not having mentors. Students from all three
sections of the course participated in the study. It was found that those
in the mentored group (M = 7.73 ±2.45) reported significantly higher
levels of Group Engagement as compared to those in the non-mentored
groups (M = 5.83 ±1.93), yielding t(120) = 3.88, p < 0.001, Cohen’s d =
0.71. Similarly, those in the mentored group (M = 9.02 ±2.20) reported
significantly higher levels of Social Engagement as compared to those
in the non-mentored groups (M = 7.55 ±2.56), yielding t(120) = 3.31, p <
0.001, Cohen’s d= 0.60. Further, with regard to achievement There were
significant main effects found for evaluation type and group
membership; however, these differences were qualified by an
interaction between evaluation type (midterm, final) and mentorship
group (non-mentored-2011, non-mentored-2013, mentored-2012),
yielding F2, 500 = 52.85, p < 0.001, η 2 = 0.18. Further investigation of the
interaction using contrasts demonstrated that there were no differences
between the mentorship groups on average midterm grades (F1, 500 = 6.64,
ns) but that the grades on the cumulative final exam were significantly
better in the mentored group when compared to the non-mentored groups
(F1, 500=42.33, p<.001, η 2=.08).
Keywords: education; higher education; mentoring; curricular peer
mentoring

18
Introduction
Mentors lead us along the journey of our lives. We trust them because they have
been there before. They embody our hopes, cast light on the way ahead,
interpret arcane signs, warn of us lurking dangers and point out unexpected
delights along the way. (Daloz, 1986, p.17)
While mentors and mentoring have gained momentum in many arenas since its
emergence into the vernacular of business and education in the 1970s, it is not a
new concept – it predates the 70s by several 1000 years (Lahman, 1999). While
mentoring now is associated with broad personal and social development, the
original “mentor” is referred to in Homer’s Odyssey. Mentor was the trusted
advisor of Odysseus. When Odysseus leaves to fight in the Trojan War, he
entrusts his household and his son, Telemachus, to Mentor (Campbell,Smith,
Dugan, & Kornives, 2012; Gannon and Maher, 2011; Lahman, 1999). While
based in this historical atmosphere of guidance, mentoring today is a very
relevant and multi-faceted “modern” concept, especially in the context of higher
education. As institutions of higher education face ever-growing challenges
ranging from economic to enrollment, the role of mentoring has gained
increasing significance. Mentoring at all levels frequently comes into play as
colleges and universities strive to make progress toward institutional goals of
increasing both the quality of education and the undergraduate experience
(Murray and Summerlee, 2007).
Mentoring
Various researchers have, over the years, posited many descriptions and
definitions of mentoring. The key elements that appear in these definitions
include opportunities for growth and individual development; a relationship
between more experienced (mentor) and less experienced individuals (mentee);
positive outcomes for the mentor and the mentee; and focused goal attainment
(Fleck and Mullins, 2012; Kram & Bragar, 1992; Kram and Ragins, 2007;
Tremblay & Rodger, 2014). While mentors have typically been thought of as
senior professionals who are in the role of “”elder” professional overseeing the
development of a protégé or junior member of an institution, this definition can
be expanded. “…a mentor can also be a peer who is close to the protégé in age
and position” (Holland, Major, & Orvis, 2001, p. 343). One advantage to having
mentor and mentee be closer in age comes from the mentor being able to draw
on more recent experiences when aiding in the mentee’s transition and adoption
of a new role (e.g., university student). The smaller age gap between a mentee
and mentor who is more peer-like also results in mentees sometimes being more
comfortable approaching the mentor for guidance (Parker, Hall, & Kram, 2008).
The key to the mentor/mentee relationship is that the mentor provides
guidance, encouragement, and support. The overarching conclusion drawn by
researchers and practitioners is that mentoring is a powerful tool for
influencing the personal development, empowerment, success, and goal
attainment of those who are mentored. According to Kram (1985), these
changes are brought about as a result of the relationship between mentor and
mentee as the more experienced mentor guides the mentee by providing

19
“guidance, role modeling, and acceptance for the mentee (as cited in Campbell
et al., 2012).
Mentoring Theory
The emergence of mentoring in the 1970s was supported theoretically by the
examination of young men’s lives as detailed by Levinson, Darrow, Levinson,
and McKee’s (1978) study in which they “found mentorship to be the single
more important relationship in they psychosocial development process,
influencing both commitment and self concept” (Campbell, et. al p. 4). Further
current explorations of the theoretical underpinnings of mentoring include
Tremblay and Rodger’s (2014) summation of the potential for positive outcomes
as a result of mentoring. They have concluded, based on the findings of a
number of studies, that this positive outcome is based in social, cognitive, and
motivation theory (Allen, McManus, & Russell, 1999; Bank, Slavings, & Biddle,
1990; Fantuzzo, Riggion, Connelly, & Dimeff, 1989; Hayes, 1999; Karabenick &
Knapp, 1999; Selbert, 1999). More specific to educational mentoring, Tremblay
and Rodger (2014) have discussed the impact of these three factors. The social
perspective revolves around the idea of persistence, or not dropping out, as a
result of peer influence; this persistence being the result of a feeling of
belongingness resulting from the mentee having positive relationships with the
members of the “organization,” in this context the university or the course. The
cognitive theoretical component of successful mentoring deals with cognitive
skill development that results from the interaction of mentor and mentee. For
example, this might include tutoring or study skill development. If approaching
the mentor impact with a view toward the motivational component, the qualities
of self-efficacy and help-seeking come into play. It is suggested that students
who are involved in a mentor-mentee relationship will be more motivated to
seek-help as well as feel more capable, thus increasing their chances of success
and satisfaction with the educational experience.
The mentoring program discussed in the current study has used this theoretical
explanation as a basis for the program. More specifically, the current study
explores the impact of a curricular peer mentoring program in an undergraduate
psychology course. While peer mentoring is a widely used term that can refer to a
variety of learning activities and programs, curricular peer mentoring is more
specific as it is a course-based form of peer mentoring that is intended as
academic support for students (Smith, 2013, Chapter 1). Curricular peer
mentoring has become more widely used in higher education in the last decade.
Other Studies
A number of researchers have explored peer mentoring in the educational
setting from a variety of perspectives and with varying approaches and
emphases. The studies cited here have in common the recognition that
mentoring programs are used to overcome numerous challenges in the
classroom, the university, and the larger social environment. Universities face
challenges both economic and societal. As budgets shrink and the value of
education comes into question, institutions of higher education find the need to
be creative as they attempt to overcome many of these challenges. The state of

20
the economy affects enrollments which affect operating budgets and
opportunity for growth. Student success, reputation, retention, graduation rates,
and the provision of undergraduate experiences beyond just coursework are
some of the things that can be enhanced by implementing mentoring programs
and providing students with the opportunity to engage in developmental
relationships (Gannon & Maher, 2012; Larose, Cyrenne, Garceau, Brodeur,
Tarabulsy, 2010; Lahman, 1999; Noonan, Ballinger, & Black, 2007; Shojai, Davis,
& Root, 2014). These studies, while taking different approaches and with
different specific goals ranging from retention to academic success to human
progress all have in common the acknowledgment of the changing face of
education and how mentoring programs can address many of the challenges
faced on the personal, pedagogical, societal, economic, and macro levels.
Along with these factors, one that might be considered the core issue in many
mentoring programs is the idea of growth for the mentee, and, though
sometimes overlooked, also growth in leadership skills for the mentors. As a
result of growth and the resulting academic personal success experienced by
mentees, retention rates are positively affected. Fleck and Mullins (2014) report
that “California University of Pennsylvania found that 10% more
undergraduate students were likely to stay the following school years when
participating in the university’s peer mentoring program” (p.272). This increase
in retention as a result of a mentoring program follows from the support
mentored students receive with regard to planning their future, studying,
psychosocial development, and identification with the community of scholars
(Fleck & Mullins, 2012). Gannon and Maher (2012) have likewise explored the
components most critical for mentoring programs to be successful in socializing
mentees into new environments and roles. This identification and socialization
results in growth, satisfaction, and persistence in the goal of the mentee. In short,
retention. The university where this study was conducted has been
implementing mentoring programs in the faculty of arts and social sciences since
2004. These programs have taken various forms and there have been multiple
iterations. In a current study evaluating the effects of mentoring programs for
arts and social sciences students, Pugliese et. al (2015) found positive effects for
both the students and the mentors in these programs. Namely, the students
experienced increased retention between first and second year as well as
academic and social benefits. For the mentors, Pugliese et. al (2015) noted
increased personal growth for the mentors in a number of areas including
leadership, presentation, and organizational skills. Also noted were increases in
self-esteem and self-confidence for the mentors.
An additional example of the use of mentoring undergraduate education comes
from Holland et al.’s investigation of the “role of peer mentoring and voluntary
self-development activities (i.e., capitalization) in anchoring science, technology,
engineering, and mathematics students to their college majors” (2012, p.343). In
this study, the investigators found a positive relationship between mentoring
and capitalization as well as discovering that capitalization and mentoring both
positively impacted students’ “satisfaction with one’s major, involvement in
one’s major, and willingness to be a mentor (Holland et al., p. 343).

21
Further, mentoring programs can be used in any discipline or major and at any
level of education to increase retention, achievement, degree completion and to
enhance student experience. A high quality program, undergraduate or
graduate, includes a variety of educational experiences that reach past the
coursework. While the content of coursework at all levels is critical for mastery
of the field of study, there is more to be gained in the educational setting with
regard to socialization and leadership (Noonan et al., 2007). With this in mind,
mentoring has been used to enhance the curricular and extracurricular content
of students in graduate programs as well as undergraduate programs. For
example, while widely established as a means of enhancing undergraduate
education, mentoring has also been used in graduate level programs to
“motivate and retain doctoral students, provide them with necessary
experiences associated with future job responsibilities, or socialize them into
their new leadership positions” (Noonan et al., 2007, pg. 251). Other findings
with regard to graduate student specific mentoring programs indicate that
participant reported outcomes include “psychosocial assistance, networking
help, and relational outcomes….” (Fleck & Mullins, 2012, p.271).
The Current Study
This study was conducted as a formative and exploratory investigation of a
mentoring program that was used in a 200 level (second year) undergraduate
child psychology course. This study was an attempt to take the things known
historically and through current research regarding mentoring and investigate a
current application of the established theories and principles. The purpose of the
study was to gain information from mentored students about the nature of their
experiences of being mentored and how this impacted engagement, experience,
and achievement in the course for them.
The mentors in this program took a prescriptive approach to mentoring in of
that they engaged in their relationship with the mentees with the goal of helping
the mentees increase academic performance, engage with their classmates, and
have an enhanced experience both in the class, the department, and in the
university environment as a whole. One of the driving forces behind the
prescriptive nature of the mentoring program described in this study is the
phenomenon wherein large courses in which the main teaching method is
lecture can lead to student passivity with students being oriented toward marks
as opposed to learning. Canaleta, Vernet, Vicent, and Montero (2014) have
discussed the use of active learning strategies to combat this passivity that leads
to a performance orientation as opposed to a learning orientation. The mentors
in this study approached their goals of increasing achievement, experience, and
engagement by taking an active learning approach with their mentees.
Specifically, for the mentored section of the course, mentors were assigned small
groups (10-12) students at the onset of the course. The groups and mentors
stayed the same for the duration of the course. For the majority of the course
meetings, mentors were given 20-30 minutes in each 80 minute lecture block to
work with their mentees in small breakout groups. The breakout sessions were
designed by the mentors and coordinated, for the most part, with the lecture

22
topic(s) for that day’s class meeting. The goal was to increase engagement with
fellow students and with the material. Breakout sessions did, on other occasions,
cover more general “survival” skills (e.g, time management, study skills, exam
taking techniques). For the non-mentored courses, the students did a
comparable amount of small group covering the same material, but they worked
independently and did not have facilitation by a mentor. For this study, we
specifically set out to discover if there existed differences in student experience,
engagement, and achievement in a course with mentors as compared to
alternative sections of the same course that did not have mentors.
Method
Participants and Procedure
Students who had completed an undergraduate child psychology course at the
University of Windsor in the fall semester of 2011, fall semester of 2012, or
winter semester of 2013 were invited to participate in an online survey about
their experience in the course. Students in these three semesters took the same
course taught by the same professor, with the exception being the inclusion of a
peer mentorship program in the fall 2012 semester. All students were invited to
participate after their grades were finalized, and participants were reminded
that their involvement had no repercussions for their grade in the course. Of
these students, 123 opted to complete the survey. Of the 123 participants (92%)
were female, and nine were male (0.08%). One student identified as transgender.
A total of 97 of the students surveyed identified as Caucasian/White, accounting
for 79% of participants. Of the 123 participants, 72 were students from either the
fall 2011 or winter 2013 semesters, which featured no peer mentorship
component. The remaining 51 participants had been enrolled in the fall 2012
version of the course featuring peer mentorship.
Measures
All the participants were given a link to access an online survey comprised of a
number of measures. The measures included the following: general
demographics; Motivated Strategies for Learning Questionnaire (MSLQ);
Student Attitudes toward Group Environments (SAGE); and a modified version
of the National Survey of Student Engagement (NSSE). The NSSE was
abbreviated in order to reduce the length of the survey and to narrow the items
down to those most relevant to the goals of this study. This was done with the
permission of the NSSE office at Indiana University Center for Postsecondary
Research. Additionally, participants from fall 2012 were given survey questions
relating specifically to their experience with being in a course with mentors in
their course.
Results
Data Analysis
This study relied on both qualitative and quantitative data analysis approaches.
First, participants provided open-ended information about their class
experience. A content analysis was conducted, which resulted in the more
specific quantitative items mentioned above that were given to the mentored
students. These data were analyzed at the item level using descriptive statistics.

23
Group comparisons were made using t-tests for follow-up questionnaires
specific to student engagement. The corresponding assumptions were assessed
and found to be tenable prior to analyzing these data.
In addition, midterm and final examination grades were analyzed across the 3
mentorship comparison groups (non-mentored-2011, non-mentored-2013,
mentored-2012). This resulted in a 3 (non-mentored-2011, non-mentored-2013,
mentored-2012) by 2 (midterm, final) mixed by repeated measures ANOVA
design. These data were assessed for the assumptions of ANOVA; 4 outliers (SD
> 3.0; 0.79%) were removed from the analysis resulting in a final sample size of
503. With these outliers removed the assumptions were found to be tenable. All
analyses were conducted using an alpha of 0.05.
Exploratory Findings
Participants from the mentorship group (2012) were provided an opportunity to
voice their opinions of the class and the following themes came to the forefront:
breakout sessions benefited students’ peer integrations, the classroom
community, and the work environment. Table 1 includes items that were asked
about breakout session efficacy as part of the quantitative follow-up regarding
these themes. In general, the students from the mentorship group agreed that
breakout sessions assisted in peer learning, perspective taking, and fostering a
positive work environment.
Student Engagement
Those in the mentored group (M = 7.73 ±2.45) reported significantly higher levels
of Group Engagement as compared to those in the non-mentored groups (M = 5.83
±1.93), yielding t(120) = 3.88, p < 0.001, Cohen’s d = 0.71. Similarly, those in the
mentored group (M = 9.02 ±2.20) reported significantly higher levels of Social
Engagement as compared to those in the non-mentored groups (M = 7.55 ±2.56),
yielding t(120) = 3.31, p < 0.001, Cohen’s d= 0.60. It it important to note here that
as described above, all students, mentored and non-mentored did engage in
group work.
Student Achievement
There were significant main effects found for evaluation type and group
membership; however, these differences were qualified by an interaction
between evaluation type (midterm, final) and mentorship group (non-mentored-
2011, non-menotred-2013, mentored-2012), yielding F2, 500 = 52.85, p < 0.001, η 2 =
0.18. All means and standard deviations for the interaction can be found in Table
2 and a visual representation of the interaction can be found in Figure 1. Further
investigation of the interaction using contrasts demonstrated that there were no
differences between the mentorship groups on average midterm grades (F1, 500 =
6.64, ns) but that the grades on the cumulative final exam were significantly
better in the mentored group when compared to the non-mentored groups (F1,
500=42.33, p<.001, η 2=.08). These findings suggest that the mentorship program
resulted in greater academic performance on the final cumulative evaluation,
while at the first evaluation (midterm) the groups were statistically equivalent in
terms of academic performance.

24
Table 1. Follow-up Breakout Sessions Responses Based on Qualitative Themes.
Items Agree Disagree Undecided
Breakout sessions allowed me to learn from
my peers.
76% 18% 6%
Breakout sessions helped me better consider
the views of others.
82% 14% 4%
Breakout sessions allowed me to share ideas. 74% 12% 14%
Breakout sessions created a positive work
environment.
74% 8% 18%
Note: Questions were provided to those from the mentorship group, those who
responded completed all of the questions, N = 51.
Table 2. Grade Means and Standard Deviations for Mentorship Groups by Evaluation
Type
Mentorship Group Mean SD N
Midterm Non-mentored
2011
68.28 13.99 183
Non-mentored
2013
68.94 12.88 135
Mentored 2012 68.37 14.25 185
Midterm Total 68.49 13.77 503
Final Non-mentored
2011
64.38 13.17 183
Non-mentored
2013
61.80 13.42 135
Mentored 2012 70.66 11.05 185
Final Total 65.99 13.02 503
Note: Mean represents average scores as a percentage on midterm and final
evaluations.

25
Figure 1. Mentorship Group by Evaluation Type on Academic Performance
Note: Mean represents average scores as a percentage on midterm and final
evaluations.
Discussion
Based on our qualitative investigation, the students who were in the mentored
classroom experience expressed that the class format allowed them
opportunities to learn from their peers, consider the views of others, and share
their own ideas, culminating in a positive classroom work environment and
achieve a higher final exam and final course grade. The mentorship model
appears to provide an opportunity for students to connect with their peers by
offering them an outlet through which they can share ideas and raise questions
about course content and general academic concerns. Further, mentored
students report that their interactions within their groups offered them
opportunities to learn from the perspectives of a diverse peer group. Such
perspective taking is a valuable skill in the classroom, workplace, and
interpersonal relations, however it is typically absent in the traditional lecture
style learning environment. As similarly found by Smith and Cardaciotta (2011)
in their study of the effects of active learning approaches, in terms of student
engagement, we found that students in the mentored class environment
reported that they had higher levels of Group Engagement and Social
Engagement, suggesting that students in the mentored environment were more
engaged in the social components of the learning experience. Students in the
mentored class expressed that being a part of a small group gave them a sense of
accountability which motivated them to complete readings and assignments in
order to contribute to the group activities and discussions. This aligns with the
findings of Teng (2006) who reported that students in her study experienced
several positive academic and interpersonal effects as a result of collaborative
work. This format of using mentors allowed for more active and collaborative
learning, which can help overcome some of the downfalls of large lecture-based
classes. Moreover, this sense of accountability serves to challenge the
anonymity that is often associated with the lecture format. The intimate group
56
58
60
62
64
66
68
70
72
Midterm Final
AxisTitle
Accademic Performance
2011
2013
2012 (Mentor)

26
structure may provide students with a peer-support network and keep them
engaged in their studies and academic community. By bringing students
together, this model seems to offer students support and recognition amongst
their peers, and may keep them socially and academically engaged, both factors
that have been established as important in retention (Pugliese et al., 2015).
Regarding academic performance, we found that at the initial evaluation
(midterm) mentored and non-mentored students performed at the same level;
however, in the cumulative final assessment students in the mentored classroom
experience outperformed those in the non-mentored classes. Given that the
students had approximately equivalent performance early in the class
(midterm), this would provide additional evidence that the process of the
mentored class experience contributed to the success of the students over the
course of the semester. Because academic improvement was not realized until
the final cumulative exam, it is possible that students required some time to
acclimate to the new model of learning; however, the significant improvement in
exam performance suggests that a mentorship model leads to substantial
benefits when sustained over time.
The current study was exploratory in nature and had its limitations. Most
significantly, all responses required students to reflect on past experiences, thus
leaving the data vulnerable to inaccurate recall. Further, without longitudinal
data, it is impossible to determine if the benefits reported were sustained over
time. Future research should explore the long term effects of participating in a
mentorship program and to determine if the benefits outlast the novelty of the
new experience. It is also suggested that the efficacy of such programs be
explored when provided by different instructors across multiple subject areas.
Finally, all data were collected from students who attended the University of
Windsor and were enrolled in Developmental Psychology: The Child. As all
respondents shared multiple experiences (city, university, and course selection,
and instructor), we cannot rule out the influence of common factors. This model
should be explored across numerous disciplines and schools to explore the
generalizability of our findings.
Based on the results of our investigation, it is reasonable to conclude that
participation in the mentorship experience contributed to an enhanced learning
experience and increased engagement. Our data indicates that those who
participated in the mentored class experienced greater social and academic
engagement resulting in overall higher satisfaction with the course and higher
grades upon conclusion of the program. The mentorship model is a diverse
pedagogical method with potential for adaptability to other programs and
classroom environments and is deserving of continued study in higher
education.

27
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29
©2015 The author and IJLTER.ORG. All rights reserved.
Vol. 13, No. 1, pp. 29-41, August 2015
On the Nature of Experience in the Education of
Prospective Teachers: A Philosophical Problem
Christi Edge, Ph.D.
Northern Michigan University
Marquette, Michigan, United States of America
Abstract. In this exploratory paper, the author argues that a core,
ontological assumption—the nature of experiece—could be a part of the
enduring problem in preparing prospective teachers. The paper begins
by identifying contrasting perspectives of teaching as simple versus
teaching as complex in order to illuminate how perspectives relate to a
construction of reality. Positioning this literature review as creative
inquiry, the author first identifies seventeen assumptions related to the
preparation of teachers in the United States and analyzes the constructs
of place, purposes, practice, and the nature of field experiences. Finally,
the author asserts that the foundation for the purposes and practices of
experience in preparing teachers resides on a problematic assumption
about the nature of reality as “out there” in the field or in the future. An
examination of this problem in light of extant literature calls attention to
the need for teacher educators to attend to ontological assumptions
rooted in experience.
Keywords: Field Experiences; Teacher Education; Prospective Teachers;
Experience
Introduction
Public mythos that “anyone can teach” (National Commission of
Teaching and America‟s Future, 1996, p. 51) impugns the pedagogical
perspective of teaching—however easy it might appear (Labaree, 2000)—as a
complex (Hammerness, Darling-Hammond, Bransford, Berliner, Cochran-Smith,
Macdonald, and Zeichner, 2005; Jackson, 1974) and difficult (Labaree, 2000)
enactment (Kennedy, 1999; Simon, 1980) of pedagogical content knowledge
(Shulman, 1987) and “pedagogical reasoning” (Wilson, Shulman, & Richert,
1987, p. 118) that requires “adaptive expertise” (Hammerness et al., 2005). These
contending views of teaching as simple or easy and teaching as complex and
challenging represent different ways of knowing and different constructions of
reality for different educational constituents. After all, the United States public
comprises, for the most part, people who have been students, and from the

30
vantage point of the student desk, the commonplace task of teaching may
indeed seem easy (Hammerness et al., 2005; Labaree 2000; Lortie, 1975). Even to
prospective teachers in a college of education, it is possible that the act of
teaching appears easier than it is (Edge, 2009; Edge, 2011). Bransford, Darling-
Hammond, and LePage (2005) liken classroom teaching to a concert
performance. In this scenario, the public perspective is likened to that of
audience member‟s and the prospective student‟s view is likened to that of a
musician‟s. From these vantage points, the conductor‟s role could appear easy.
However, the concert-goer‟s as well as the musician‟s perspective of the
conductor‟s reality is limited:
Hidden from the audience—especially from the musical novice—are the
conductor‟s abilities to read and interpret all of the parts at once, to play
several instruments and understand the capacities of many more, to
organize and coordinate the disparate parts, to motivate and
communicate with all of the orchestra members. In the same way that
conducting looks like hand-waving to the uninitiated, teaching looks
simple from the perspective of students who see a person talking and
listening, handing out papers, and giving assignments. Unseen in both of
these performances are the many kinds of knowledge, unseen plans, and
backstage moves…that allow a teacher to purposefully move a group of
students from one set of understandings and skills to quite another over
the space of many months. (p. 1)
Like the music lover enjoying a concert or the musician concentrating on playing
her instrument well, the general public and the student both view the experience
of education from a different perspective, from a different reality than the
teacher. This perspective is a physical/temporal reality, and it is “an enacted or
constructed reality, composed of the interpretive, meaning-making, sense-
ascribing, holism-producing, role-assuming activities which produce
meaningfulness and order in human life. These two worlds—or realities—exist
in parallel and alongside one another, interacting and influencing each other”
(Lincoln, 2005, p. 61). Like the musical novice who cannot understand all that a
conductor knows and does from her or his limited physical and enacted reality,
the student of education constructs a different sense-making reality from a
physical and temporal, often biographical (Britzman, 2003; Kelchtermans, 1993;
Lortie, 1975), reality.
Paul (2005) has demonstrated how perspectivism, “the idea that truth is
embedded within a particular perspective” (Paul, 2005, p. 43), is useful for
broadly thinking about and interpreting scholarship. He offers the philosophical
topics of ontology, epistemology, methodology, and values (or axiology) for
considering how perspectives are framed. It will be argued here, that a core,
ontological assumption—the assumption of reality—could be a part of the
enduring problem in preparing prospective teachers to be, first “students of
teaching” (Dewey; Cruickshank, 1996 ), and ultimately, to be “adaptive experts”
(Hammerness et al., 2005) of teaching and learning (Westheimer, 2008).
Like all scholarship, this review of the literature and its analysis is
framed by ontological, epistemological, methodological, and axiological

31
assumptions. Although a systematic description of these is beyond the
immediate scope of this paper, I make conscious attempts to use language that
alludes to the philosophical paradigms in which this review is couched
(Creswell, 2013). By no means “exhaustive,” I would characterize my attempt to
problematize philosophical assumptions of experience in teacher education as
exploratory: a first step toward a new notion of knowing in a quest for
meaningful understanding in light of extant literature. In his article “Literature
Review as Creative Inquiry: Reframing Scholarship as a Creative Process”
(2005), Montuori argues that a literature review need not be merely the mealy
regurgitation of who said what and when; it is also an opportunity for the kind
of critical and creative thinking that delves “deeply into the relationship
between knowledge, self, and world” (Montuori, 2005, p. 375). A literature
review is a survey of the field, and is the reviewer‟s interpretation of that field
(p. 376). Accordingly,
[a] literature review can be framed as a creative process, one in which the
knower is an active participant constructing an interpretation of the
community and its discourse, rather than a mere bystander who attempts
to reproduce, as best she or he can, the relevant authors and works.
Creative inquiry also challenges the (largely implicit) epistemological
assumption that it is actually possible to present a list of relevant authors
and ideas without in some way leaving the reviewer‟s imprint on that
project. It views the literature review as a construction and a creation that
emerges out of the dialogue between the reviewer and the field.
(Montuori, 2005, p. 375)
It is with this intention—to discover, to think about, to critically examine, and to
ultimately share my interpretation of the problems in preparing teachers in
general, and the problems, assumptions, and peculiarities of the place of
experience within that preparation, specifically—that I reviewed the literature
on field experiences. Initially, my review led me to generate a list of seventeen
assumptions related to the education of prospective teachers—those who are
enrolled in a university program or alternative certification program as a
pathway to initial teacher certification in the United States.
Assumption #1: Experience is necessary and vital.
Assumption #2: Prospective teachers know how to learn from field
experiences.
Assumption #3: Because practicing teachers have classroom experience,
they can teach prospective teachers who do not.
Assumption #4: Teacher educators, prospective teachers, and
mentor/cooperating teachers share a common language for talking about
education.
Assumption #5 (an offshoot of #4): When we do use the same language
to communicate “teaching,” we mean the same things.

32
Assumption #5: Field experiences help prospective teachers to develop
into professional educators.
Assumption #6: Prospective teachers know how to learn from “less than
ideal” or non-examples in the field.
Assumption #7: Prospective Teachers know how to use/apply what they
have learned during their education coursework to teaching situations in
classroom environments.
Assumption #8: Prospective teachers have constructed a cognitive map
for teaching and know how to navigate that map in various contexts.
Assumption #9: Enactment—prospective Teachers can do what they
know they should. (That they know what and why but also when and
how to do.)
Assumption #10: Prospective teachers know how to learn from their
successes and their struggles during field experiences.
Assumption #11: Prospective teachers (a) evoke their prior knowledge
during practice teaching scenarios; (b) they know how to use that
knowledge when they do; and that (c) the prior knowledge they recall is
in fact, from their study of education and not solely from their personal
experience as a student.
Assumption #12: Reflections help prospective teachers to think through
their experiences in practicum field experiences. (The assigned task of
“reflection” does not necessarily mean that there is much more than
recall or hypothetical thinking going on.)
Assumption #13: Prospective teachers know how to think through their
experiences in ways that help them to analyze, deconstruct, reconstruct,
make connections, and grow. (It is possible that Prospective Teachers go
through these motions discretely, never linking the pieces together.)
Assumption #14: Prospective teachers know when they are learning,
how they learned, and why they learned, and are able to think about
learning beyond their own experiences for purposes of helping
individual students.
Assumption #15: Prospective teachers either already know how to or will
come to see students as individuals rather than a group or class.
Assumption #16: Prospective teachers will develop the ability to consider
learning beyond self (student)-centered experiences.
Assumption #17: That the perceived and documented problems in field
experiences are “experience” problems.

33
Further consideration of these assumptions led me to consider the philosophical
assumptions of the place, purposes, practice, and nature of experience in teacher
preparation.
The Place of Experience in the Education of Prospective Teachers
Experience in education is a topic of perennial interest. Students of
education often view field experiences as the most valuable, critical, and
personal component of their education (Cherian, 2003; Cruickshank & Armaline,
1986; Cruickshank, Bainer, Cruz, Giebelhaus, McCullough, Metcalf, & Reynolds
1996; Lortie, 1975). Teacher educators, the general public, even critics of teacher
education also “agree that whatever else might be dispensable, practice teaching
is not” (Silberman, 1971 as cited in Cruickshank & Armaline, 1986; p. 35). Field
experience emerges from the literature as a critical component in the education
of teachers (Conant, 1963; Cruickshank & Armaline, 1986; Cruickshank et al.,
1996; Zeichner, 1980). The notion or place of experience in education is not, then,
a point of disagreement; discrepancy, rather, hinges on what is meant by
“experience.”
The Purposes and Practice of Experience in the Education of
Prospective Teachers
Nolan‟s (1982) historical inquiry into the purpose and nature of field
experience in teacher education begins with Dewey‟s (1904) “The Relation of
Theory to Practice in Education” as an inaugural treatise to address the purpose
of field experiences. In it, Dewey delineates between apprenticeship and
laboratory models of learning to teach. He advocates for reflective criticism
through laboratory experiences as a way to bridge the historical, psychological,
and sociological theories of education with the practice of teaching. Since 1904,
the purposes of experience in education seem to swing along a pendulum,
arching from the Deweyian notion of intellectual inquiry, experimentation, and
critical reflection to the more technical teaching skills designed to induct novices
into the profession (Nolan, 1982). Current research indicates that the pendulum
of purpose is returning to a point which values the kind of educative experiences
John Dewey introduced in 1904 and advocated for in Experience and
Education(1938).
In the first edition of the Handbook of Research on Teacher Education (1990),
Guyton and McIntyre‟s review of the literature on field experiences noted the
missing theoretical basis for the purpose and design of filed experiences in
education. In a second edition to the handbook, McIntyre, Byrd, and Foxx (1996)
review an emerging constructivist theoretical framework for teacher education
and the constructivist framework‟s emphasis on “the growth of the prospective
teacher through experiences, reflection, and self-examination” (p. 172). McIntyre
and associates (1996) refer to Bullough (1989) who “asserts that the first priority
in developing a reflective teacher education program is to restructure all field

34
experiences so students can engage in reflective decision making and can act on
their decisions in the spirit of praxis” (p. 172). A critical and reflective field
experience program which guides prospective teachers in becoming active
decision-makers is the beginning of students‟ being able to see from the teacher‟s
perspective.
In light of a constructivist theoretical framework for teacher education,
field experiences have the potential to bridge theory and practice; however, too
frequently, field experiences “widen the gap between the two” (McIntyre et al.,
1996, p. 172). To modify the conditions of student teaching to meet constructivist
methods and values, McIntyre et al. cite McCaleb, Borko, and Arends (1992) who
suggest that "student teaching placements must no longer be viewed as the „real
world‟ and instead should be viewed as learning laboratories or studios where
student teachers experience both the university and the school as „the real world‟
(McIntyre et al., 1996, p. 172). Such a program would be characterized by the
continuing inquiry of the student teacher, the cooperating classroom teacher,
and their students.
McCaleb, Borko, and Arends‟ (1992) ontological assertion—that “the real
world” for students of teaching consists of the physical/temporal place of both
the university and the community—was timely. Literature from the 1980‟s and
early 1990‟s was saturated by language which designated “the real world” to be
the schools which students of teaching would eventually teach (e.g. Cruickshank
& Armaline, 1986; Cruickshank et al., 1996; Nolan, 1982). For example,
Cruickshank and Armaline‟s (1986) frequently cited article on field experiences
in teacher education, situates practice teaching as an “unabated” commitment to
“learning by doing” since the “dawn of formal teacher training in America” (p.
34). They offer a detailed, five-point taxonomy of teaching experiences. This
taxonomy addresses the following characteristics: settings; degree of directness
and concreteness; purposes; duration; and placement or sequence in the
education program. The nature of field experiences is discussed in terms of
whether the experience is direct or indirect, concrete or abstract. This portion of
Cruickshank and Armeline‟s taxonomy reads as follows:
Directness and Concreteness
a. Direct experiences with reality. You are the teacher teaching real
learners in a real classroom.
b. Direct experiences using a model of reality. You are the teacher
teaching in a contrived setting.
c. Indirect experiences with reality. You are “observing” real teaching.
d. Indirect experiences using a model of reality. You are “observing”
simulated teaching. (p. 35)
Subtle in the language is the ontological declaration that the real world is “out
there” apart from the daily life of the student of teaching in the teacher
preparation program. Are the experiences in a university classroom where
students teach their peers not reality? Is this not a real classroom with real
learners?

35
Literature since the 2000‟s (e.g. Bransford et al., 2005; Bransford, Derry,
Berliner, Hammerness, & Beckett, 2005; Darling-Hammond, 2006; Edge, 2011;
Hammerness et al., 2005; Roasaen & Florio-Ruane, 2008; Rodgers & Scott, 2008;
Strom, 2015; Westheimer, 2008; Zeichner, 2012) indicates that education has
moved and continues to move toward constructivist theories of teaching and
learning. Bransford, Derry, Berliner, Hammerness, and Beckett (2005) state that a
constructivist theory of teaching and learning is a theory of knowing not
teaching. Lincoln (2005) operationalizes the definition of constructivism to mean
“an interpretive stance which attends to the meaning-making activities of active
agents and cognizing human beings” (p. 60). She outlines constructivism as a
theoretical and interpretive perspective that comprises ontology, epistemology, a
methodology or methodologies, and axiology. Ontology asks, “What is
reality?”; epistemology asks, “What and when is knowledge?”; methodology
asks, “How do we know or acquire knowledge?”; and axiology asks, “What
contributions do our values and beliefs make toward our judgments of what is
true?” (Lincoln, 2005; Paul, 2005). In a constructivist paradigm, researchers think
about how learners construct knowledge in relationship to their contexts
(Westheimer, 2008). Students of teaching are considered active problem solvers
who make sense of their experiential worlds and who influence and are
influenced by their contexts.
The Nature of Experience in the Education of Prospective Teachers
The foundation of the purposes and practices of experience in preparing
teachers is predicated upon an assumption or presumption of the nature of
reality. It will be argued here that this presumption is problematic. It will be
hypothesized that this problem is a foundational problem which could
potentially create a fissure in the whole “house” of teacher preparation.
First, a reality which bifurcates teaching from learning is a flawed and
potentially fatal assumption. As Westheimer (2008) notes, “[i]n both Norwegian
and Hebrew, the verbs „to teach‟ and „to learn‟ are etymologically inseparable.
Teaching and learning…are two sides of the same pedagogical coin” (p. 756).
When teacher education programs implicitly separate learning—as something
you do here (e.g., in a college of education; in a university classroom; as a
“student”)—from teaching--something you do there (in P-12 schools as a
professional)—then the concept of practice teaching removes the act of
constructing reality from the context in which it occurs, causing fragmented
ways of knowing and being for students of teaching. Conversely, in
constructivist ontology, the reality of teaching and learning are continuous; they
happen both here and there, both as a teacher and as a student, for they are
transactionally connected by an individual learner‟s experiences in her or his
environment (Dewey, 1938).
When teaching and learning are separated, teacher educators should not
be surprised to discover beginning teachers “reverting” to teach in the manner
that they learned—and consequently perpetuating the separation of teaching
and learning for their own students (Lortie, 1975). What they‟ve come to know

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