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The Effects of Instructional Strategies on Preservice Teachers’ Math Anxiety and Achievement

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The results reported herein represent the quantitative portion of a mixed method investigation that employed a non-equivalent control group design conducted to determine the effects of teaching methods on math anxiety and achievement among preservice elementary teachers enrolled in a mathematics course. Two teaching methods, inquiry-based learning (IBL) and direct instruction (DI), were compared. These results indicated that math anxiety decreased significantly for the IBL group while increasing for the DI group over the course of an academic semester. There was no difference in measured learning outcomes between the two groups. A significant negative correlation between math anxiety and student achievement, however, was found. Qualitative results, discussed in a companion article, contextualize these findings and reveal that the participants attributed varying levels of math anxiety to several factors including course content, teaching methods, assessments, and student behaviors.
JOURNAL OF RESEARCH IN SCIENCE, MATHEMATICS AND TECHNOLOGY EDUCATION
DOI: 10.31756/jrsmte.425
The Effects of Instructional Strategies on Preservice Teachers’ Math Anxiety
and Achievement
Janelle K. Lorenzen
Southeastern Louisiana University, USA
Thomas J. Lipscomb
The University of Southern Mississippi, USA
Introduction
Theoretical Framework
Traditional teaching methods, such as direct
instruction (DI), have been used in mathematics
instruction for decades. These methods, commonly
used in elementary, secondary, and post-secondary
math instruction, typically involve demonstration and
have theoretical foundations in social learning theory
(Bandura, 1977). In classrooms in which DI is
employed, it is typical for teachers to guide students
through mathematical concepts by lecturing while
students passively take notes. Following lectures,
students may engage in problem-solving activities
related to the content just presented (Ardeleanu, 2019).
Emphasis is often placed on procedural fluency of
mathematical algorithms through repeated practice
(Brahier, 2013). This is the type of teaching that many
preservice teachers experienced in their elementary
mathematics coursework, and thus influenced their
beliefs that DI constitutes effective mathematics
teaching (Althauser, 2018). This orientation is in
contradistinction to recommendations of the National
Council of Teachers of Mathematics (NCTM), an
organization which has been advocating for
mathematics teaching reform for decades (NCTM,
1991).
Another teaching method sometimes utilized in
mathematics instruction is inquiry-based learning
(IBL), a student-centered, active-learning approach
based on the constructivist perspective (Prince &
Felder, 2006). IBL encourages active participation on
the part of the learner, geared toward the discovery of
new knowledge (de Jong & van Joolingen, 1998). In
an IBL classroom, the instructor acts as a facilitator by
actively engaging students in the problem-solving
Abstract: The results reported herein represent the quantitative portion of a mixed method investigation that
employed a non-equivalent control group design conducted to determine the effects of teaching methods on math
anxiety and achievement among preservice elementary teachers enrolled in a mathematics course. Two teaching
methods, inquiry-based learning (IBL) and direct instruction (DI), were compared. These results indicated that math
anxiety decreased significantly for the IBL group while increasing for the DI group over the course of an academic
semester. There was no difference in measured learning outcomes between the two groups. A significant negative
correlation between math anxiety and student achievement, however, was found. Qualitative results, discussed in a
companion article, contextualize these findings and reveal that the participants attributed varying levels of math
anxiety to several factors including course content, teaching methods, assessments, and student behaviors.
Keywords: Math anxiety; Achievement; Preservice teachers; Inquiry-based learning, Direct instruction;
Mathematics Education
134 | L O R E N Z E N & L I P S C O M B
process. While characteristics of IBL classrooms
vary, features often found include self-discovery of
mathematical content, minimal lectures if any at all,
emphasis on communication among students and the
instructor, alternative assessments, and students’
presentations of problems (Schinck, 2014). As
Freeman et al. (2014) put it, such an active learning
approach “engages students in the process of learning
through activities and/or discussion in class, as
opposed to passively listening to an expert. It
emphasizes higher-order thinking and often involves
group work” (p. 8413-8414).
Teaching Methods
Even though traditional teaching methods are
commonplace in mathematics classrooms, these
methods may result in students who seldom inquire in
the classroom, engage in reasoning or sense-making,
or think of themselves as problem solvers (Boaler,
2008). On the other hand, teaching methods
promoting active learning may facilitate student
success by reducing the number of students who fail
or withdraw from a course; result in higher learning
gains, particularly for low-achieving students; and
improve students’ understanding of and self-
confidence in doing mathematics (Freeman et al.,
2014; Kogan & Laursen, 2013; Laursen & Hassi,
2012; Smith et al., 2009). Benefits of IBL teaching
methods with pre-service elementary education
students include significant gains in students’
mathematical knowledge specific to teaching, deeper
understanding of mathematical concepts, and
increased self-confidence in teaching ability (Laursen
& Hassi, 2012; Smith et al., 2009).
The Association of Mathematics Teacher Educators
(AMTE) and the Conference Board of Mathematical
Sciences (CBMS) recommend a student-centered
approach to content courses for preservice teachers. In
Standards for Preparing Teachers of Mathematics,
AMTE clearly states that quality instruction includes
conceptual emphasis on relevant school mathematics,
process standards, productive dispositions, and the
“instructor use of active-learning and inquiry-based
strategies” (AMTE, 2017, p. 154). The CBMS
suggests that courses should encourage preservice
teachers to develop the habits of mathematical
thinking and problem solving, such as reasoning
quantitatively and abstractly, explaining and modeling
mathematics, being precise in their computations, and
constructing valid arguments. The teaching style
should be flexible, nurturing, and interactive with
plenty of opportunities for preservice teachers to feel
successful in solving challenging problems (CBMS,
2012). Features of mathematics content courses that
promote high-quality instruction include having
preservice teachers reflect upon their own learning as
students, providing opportunities for students to use
mathematics in a variety of contexts, emphasizing
conceptual understanding and reasoning, encouraging
students to work collaboratively, and making
connections between mathematical content knowledge
and pedagogical content knowledge (Lubinski & Otto,
2004; Mestre & Cocking, 2002; Thanheiser et al.,
2010).
Mathematics Anxiety
The experience of anxiety is well-known to be
counterproductive to content mastery. Further, there is
evidence to suggest that preservice elementary
teachers may experience the highest level of
mathematics anxiety of any college major and female
students with low mathematics self-efficacy typically
have high levels of mathematics anxiety (Hembree,
J. of Res. in Sci. Math. and Tech. Edu. | 135
1990; Rozgonjuk, D. et al., 2020). Mathematics
anxiety can be defined as a state of discomfort that one
experiences when involved in situations requiring the
use of mathematics and can affect people of all ages -
from elementary school children to adults (Ashcraft,
1995; Cemen, 1987; Wu et al., 2014). Many who
suffer from mathematics anxiety perceive
mathematical tasks as being threatening to their self-
esteem and may experience concomitant physical
changes such as tension, sweaty palms, difficulty
breathing, and inability to concentrate (Burns,1998;
Bursal & Paznokas, 2006; Dutton & Dutton, 1991;
Hembree, 1990; Trujillo & Hadfield, 1999).
Mathematics anxiety can also negatively impact a
student’s ability to reason flexibly and creatively about
mathematical algorithms and strategies (Fetterly,
2020; Ronghuan et al., 2021).
Preservice elementary teachers have reported that their
mathematics anxiety was caused by several factors
including having to complete timed tests, mathematics
classes being boring, course material being taught too
quickly, and a heavy emphasis placed on obtaining the
correct answer. All of these are characteristics often
found in classes focused on utilizing traditional
teaching methods (Harper & Daane, 1998). Other
factors influencing the mathematics anxiety level of
college students can be attributed to course instructors
not explaining the material well, a heavy reliance on
worksheets, and negative teacher dispositions
(Rhoads, 2020). It might be hypothesized, therefore,
that learner-centered teaching methods that avoided
these anxiety triggers might be most beneficial in
reducing anxiety experienced and increasing student
learning outcomes.
It is possible then that preservice teachers who
experience high levels of anxiety are prone to become
schoolteachers who continue to experience some level
of mathematics anxiety. Students with mathematics-
anxious teachers are likely to experience relatively
poor mathematics instruction that focuses on
algorithmic procedures, insufficient time spent on
mathematics in the classroom, and the development of
math anxiety themselves (Buhlman & Young, 1982;
Karp, 1988, 1991; Middleton & Spanias, 1999;
Scholfield, 1981). Furthermore, higher mathematics
anxiety levels in teachers result in lower mathematics
achievement in elementary students (Ramirez, 2018;
Szczygiel, 2020). Perhaps if mathematics content
courses for preservice teachers emphasized conceptual
understanding and inquiry, the cycle of math anxiety
being passed from teacher to student could be broken
as teaching candidates strengthen their conceptual
mathematical understanding.
Research Design
Although previous research has demonstrated that an
active learning approach can be more effective than
traditional teaching methods, no study to date has
directly compared the efficacy of IBL and DI
instruction on either content mastery or mathematics-
related anxiety within the preservice mathematics
classroom. Such were the purposes of the present
study. This study specifically addressed how these
differing teaching methods might directly affect
preservice elementary teachers’ levels of mathematics
anxiety and achievement in a mathematics content
course and provided context by including descriptions
of their experiences in the course in relation to their
mathematics anxiety and achievement. The general
goal of this project was to determine if teaching
methods that employ IBL are more effective than DI
136 | L O R E N Z E N & L I P S C O M B
at reducing preservice elementary teachers’ levels of
math anxiety while increasing their achievement.
In their seminal treatise, Campbell and Stanley (1963)
and later, Campbell and Cook (1979) and Shadish,
Cook, and Campbell (2002) advocated the use of what
they labeled quasi-experimental designs in situations
in which complete pre-experimental equivalence
between groups could not be accomplished through
randomization. One specific design that results in
studies high in internal validity is the non-equivalent
control group design in which there are pre-tests and
post-tests assessing the dependent variable(s) in two or
more groups. This design was chosen for the present
study. A convergent mixed methods design was used
in which both quantitative and qualitative data were
collected before, during, and after the intervention
(Creswell & Creswell, 2018). The quantitative results
will be presented in this paper while qualitative results
that contextualize these findings reported here will be
presented in a companion manuscript. The
independent variable was the type of teaching method
employed by the course instructor - DI or IBL. The
dependent variables were the students’ math anxiety
level as measured by the Mathematics Anxiety Rating
Scale Short Version (MARS-S), their self-reported
mathematics anxiety from journal entries, their
achievement as measured by a test of their
mathematics content knowledge, and their self-
reported level of understanding from journal entries.
Research Questions
1. What effect do different teaching methods have on
preservice teachers’ levels of mathematics anxiety?
2. What effect do different teaching methods have on
preservice teachers’ mathematics achievement?
Methods
Participants
Participants (n = 103) were undergraduate students
majoring in education enrolled in one of four sections
of a mathematics content course for preservice
teachers at a midsize, state-supported university in the
Southeast United States. The course covers content
relating to fractions, decimals, probability, and data
analysis and is the second course in a three-course
sequence. Approximately 96% of the participants
were female, 2% freshmen, 36% sophomores, 53%
juniors, and 9% seniors. The large percentage of
female participants can be attributed to the
disproportionate amount of female elementary
education majors (95%) at the university. Each of the
participants was majoring in elementary education
with a concentration in grades PK-3, grades 1-5, or
grades 4-8. To preserve their anonymity throughout
the study, all participants identified themselves with a
randomly-generated 6-digit course ID number that
they used on all instruments in place of their name.
Data Collection Instruments
Mathematics Anxiety: In all classes, the participants
completed an initial demographic questionnaire.
Participants’ levels of mathematics anxiety were
assessed using the Math Anxiety Rating Scale Short
Version (MARS-S) pre- and post-intervention as well
as through self-reports in journal entries throughout
the semester. The MARS-S is a 30-item self-rating
scale created by Richard Suinn (2003) that uses a 5-
point rating scale for each of the 30 items with a score
of 1 indicating that the respondent is not at all
frightened by that situation and a score of 5 indicating
that the respondent is very much frightened by that
situation. Overall anxiety scores are determined by
J. of Res. in Sci. Math. and Tech. Edu. | 137
adding the respondents’ raw scores on each item with
higher total scores indicating relatively higher levels
of anxiety. According to Suinn (2003), the MARS-S
has a test-retest reliability coefficient of 0.90 (p < .001)
at one-week intervals. In addition, Cronbach’s alpha
was found to be .96, which confirms the instrument
has high internal reliability indicating that the items
are considered to be measuring the different
dimensions of the same construct, mathematics
anxiety. The MARS-S also has demonstrated
construct and content validity. Specifically,
correlations between the MARS-S and the longer 98-
item MARS were found to be r = .92 (p < .001) and r
= .94 (p < .001) when the instruments were
administered one week apart to the same sample.
Furthermore, Suinn (1993) found MARS-S scores to
be negatively correlated with mathematics grades r =
-.41 (p < .001), which is not surprising because
mathematics anxiety is known to be negatively
associated with mathematics performance.
Exploratory factor analysis of MARS-S data indicated
that there are two primary factors: (a) learning
mathematics anxiety and (b) mathematics evaluation
anxiety (Suinn, 2003).
Content Knowledge: To assess participants’ content
knowledge and measure their achievement over the
course of the semester, the participants completed a
20-question multiple-choice content knowledge
assessment at two points in the semester. The
participants completed the assessment during the first
week of classes and then again at the end of the
semester. Because the content knowledge assessment
was administered at the end of the semester, the
researcher opted to have it be a component of the final
exam. This course, along with the other two courses
in the sequence, have a common, departmental final
exam that all enrolled students complete. The format
of these exams is the same for the three courses and
includes a multiple-choice component and a
constructed-response component. The assessment
was designed to align with course content while
assessing students on both conceptual understanding
and procedural fluency of selected course topics. Two
mathematics instructors at the university who
regularly taught the course reviewed the assessment
and confirmed that the content was valid for the
course.
Journal Entries: Teacher candidates at the
university are assessed on their professional
dispositions several times throughout their
program. One disposition on which they are
evaluated is their ability to be a self-reflective
practitioner. Thus, participants completed five
journal entries over the course of the semester in which
they reflected upon their experiences, understanding
of course material, and anxieties. In each journal
entry, participants rated their understanding of course
material and level of math anxiety each on a scale from
1 to 10. A score of one indicated a low level of
understanding (or math anxiety), whereas a score of 10
indicated a high level of understanding (or
mathematics anxiety). They also detailed reasons for
each self-assessed rating and documented any course
content with which they needed additional practice.
Course Format
Sections: There were four sections of the class offered
with enrollment totals in each class of 30, 28, 32, and
13 students. Two of the four sections were taught
using DI, and the other two sections were taught using
IBL. The sections were all taught by the same course
138 | L O R E N Z E N & L I P S C O M B
instructor, who also happened to be the lead researcher
in this study. The instructor previously taught this
course for several years in addition to having
experience using both IBL and DI teaching methods in
a variety of mathematics courses.
IBL: The format of the IBL classes consisted of
students’ collaborating with each other and presenting
their solutions to problems from the course problem
set. Small group work and communication with peers
were emphasized during this time. Because the focus
in the IBL classes was for the students to develop deep
conceptual understanding as well as effective
classroom communication and problem-solving skills,
the instructor did not conduct any lectures. This was
to minimize the likelihood of students’ modeling the
instructor’s work, thus promoting independence in the
students’ thinking. A typical class meeting consisted
of students’ presenting their work from the previous
class and participating in student-led discussions
facilitated by the instructor regarding relevant course
content, transitioning into small-group work on the
next section of course material.
DI: The classes that were taught using DI were
teacher-centered classes with the majority of class
time spent on the instructor’s lectures. Homework
problems were briefly reviewed at the beginning of
each class, and there was little time allocated for
independent problem solving and communication
among the students. The basis of the instructor’s
lectures and the assigned homework problems were
from the same course problem set. Thus, the students
in the IBL and DI classes completed the same
problems over the course of the semester although the
manner in which those problems were presented
differed.
Results
Demographics
Demographic data included the participants’ GPAs,
college majors, grades in the previous mathematics
course, and whether they had previously taken any
IBL classes. It is noted that there were differences in
GPA between the IBL and DI groups; however, there
were no statistically significant differences in terms of
scores on the pretest. Table 1 summarizes the
demographic data.
MARS-S
A 2 (Teaching Method: IBL and DI) x 2 (Time: Initial
and Final) mixed ANOVA revealed a statistically
significant interaction between the teaching method
and time on the MARS-S scores, F(1, 95) = 11.91, p =
.001, partial = .111. To test for simple effect of
teaching method, independent samples t-tests were run
to determine if there were differences in the initial and
final MARS-S scores of the students in the IBL and DI
classes. Initial MARS-S scores for the IBL students
(M = 85.00, SD = 17.71) were significantly higher than
the scores for the DI students (M = 76.17, SD = 21.19),
t(99) = 2.22, p = .029, d = 0.45. However, the MARS-
S scores of the IBL students decreased while the
MARS-S scores of the DI student increased over the
course of the semester such that on the final MARS-S
measure, there was not a statistically significant
difference between the IBL (M = 79.84, SD = 18.50)
and DI students (M = 81.95, SD = 18.67), t(97) = .56,
p = .577, d = 0.11. Figure 1 displays the interaction.
2
J. of Res. in Sci. Math. and Tech. Edu. | 139
Table 1
Demographic Data
Characteristic
IBL
DI
Percentage
Frequency
Percentage
Major
Grades PreK-3
34.1%
16
28.0%
Grades 1-5
47.7%
34
59.6%
Grades 4-8
18.2%
7
12.3%
GPA
≥ 2.00
4.5%
1
1.7%
2.01 3.00
59.1%
25
43.1%
3.01 4.00
36.4%
32
55.2%
Previous Course Grade
A
11.4%
22
38.6%
B
68.2%
21
36.8%
C
20.5%
14
24.6%
Previous IBL Classes
Yes
34.1%
32
56.1%
No
65.9%
25
43.9%
Figure 1
Mean MARS-S scores for the IBL and DI groups at the beginning and end of the semester.
140 | L O R E N Z E N & L I P S C O M B
Paired samples t-tests were run to test for the simple
effect of time. The IBL classes showed a statistically
significant difference in initial and final MARS-S
scores with final MARS-S scores (M = 80.00, SD =
18.90) being lower than initial MARS-S scores (M =
86.24, SD = 17.18), t(40) = 2.41, p = .021, d = 0.38.
The DI classes also had a statistically significant
difference in initial and final MARS-S scores.
However, in this case, final MARS-S scores (M =
81.95, SD = 18.67) were higher than initial MARS-S
scores (M = 76.59, SD = 21.19), t(55) = 2.48, p =
.016, d = 0.33. Table 2 summarizes descriptive
statistics related to these measures.
Table 2
Initial and Final MARS-S Scores for Paired Samples t-Test
MARS-S Scores
IBL
DI
n
Mean
SD
n
Mean
SD
Initial
41
86.24
17.18
56
76.59
21.19
Final
41
80.00
18.90
56
81.95
18.67
Note. indicates a statistically significant difference within teaching methods.
Self-reported Mathematics Anxiety
A 2 (Teaching Method: IBL and DI) x 5 (Time:
Journal 1, Journal 2, Journal 3 Journal 4, Journal 5)
mixed ANOVA showed that there was a statistically
significant interaction between the teaching method
and self-reported mathematics anxiety scores over the
course of the semester on the, F(4, 328) = 7.57, p <
.001, partial = .085. (See Figure 2).
When testing for the simple effect of time within each
teaching method, Mauchly’s test of sphericity
indicated that the assumption of sphericity had been
violated, 2(9) = 19.33, p = .023. Therefore, degrees
of freedom were corrected using Greenhouse-Geisser
estimates of sphericity ( = .78). Statistically
significant differences in self-reported mathematics
anxiety for the IBL classes over the course of the
semester were found, F(3.12,118.49) = 6.14, p = .001,
partial = .139. Pairwise comparisons showed that
self-reported math anxiety was significantly reduced
between journal entry 1 (M = 7.00, SD = 2.44) and
journal entry 5 (M = 5.59, SD = 2.51), 95% CI [0.018,
2.803], p = .045. Significant differences in the self-
reported math anxiety for the IBL group also existed
between journal entry 2 (M = 7.31, SD = 1.98) and
journal entry 5 (M = 5.59, SD = 2.51), 95% CI [0.451,
2.985], p = .003. There were also statistically
significant differences in self-reported mathematics
anxiety for the DI classes, F(4,176) = 3.47, p = .009,
partial = .073. Pairwise comparisons for the DI
classes indicated that self-reported mathematics
anxiety increased to a statistically significant extent
between journal entry 1 (M = 5.42, SD = 2.55) and
journal entry 5 (M = 6.78, SD = 2.72), 95% CI [
2.616, 0.095], p = .027. There was also a
significant increase between journal entry 3 (M = 5.62,
SD = 2.41) and journal entry 5 (M = 6.78, SD = 2.72),
95% CI [ 2.167, 0.144], p = .015. A significant
increase also existed between journal entry 4 (M =
5.58, SD = 2.65) and journal entry 5 (M = 6.78, SD =
2.72), 95% CI [ 2.298, 0.102], p = .023.
2
2
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J. of Res. in Sci. Math. and Tech. Edu. | 141
Figure 2
Mean self-reported math anxiety levels for the IBL and DI groups throughout the semester based on student journal
entries.
To test for the simple effect of teaching method on
self-reported mathematics anxiety, independent
samples t-tests were conducted for each time period.
Significant differences were found between the classes
for journal entry 1, t(94) = 3.03, p = .003, d = 0.62;
journal entry 2, t(96) = 2.44, p = .017, d = 0.51; and
journal entry 5, t(96) = 2.33, p = .022, d = 0.47.
Corroborating the results of the MARS-S, the means
for self-reported mathematics anxiety scores were
higher for the IBL classes than the DI classes for
journal entries 1 and 2 at the beginning of the semester
but were lower for journal entry 5, which was
submitted during the last week of classes. However,
when applying the Bonferroni correction to control the
family-wise error rate, the only remaining significant
difference between the IBL and DI groups was for
Journal 1. Descriptive statistics related to these
measures are depicted in Table 3.
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Table 3
Self-reported Math Anxiety (MA) for Independent Samples t-Test
MA Journal
IBL
DI
n
Mean
SD
n
Mean
SD
Journal 1*
43
6.93
2.40
53
5.38
2.57
Journal 2*
42
7.12
2.05
56
5.91
2.68
Journal 3
44
6.39
2.21
56
5.86
2.40
Journal 4
44
6.20
2.46
54
5.65
2.45
Journal 5*
44
5.73
2.46
54
6.93
2.60
Note. * indicates a statistically significant difference between teaching methods.
Content Knowledge Assessment
A 2 (Teaching Method: IBL and DI) x 2 (Time: Initial
and Final) mixed ANOVA revealed that there was not
a statistically significant interaction between the
teaching method employed and measures of content
mastery over the course of the semester on the content
knowledge scores, F(1, 99) = 0.75, p = .389, partial
= .008. However, there was a statistically
significant main effect of teaching method between the
pre-test and post-test scores on the content knowledge
assessment, F(1, 99) = 212.92, p < .001, partial =
.683. Based on the results of paired samples t-tests,
there were statistically significant differences between
the initial and final scores for the IBL classes, M =
4.41, 95% CI [5.28, 3.54], t(43) = 10.24, p <
.001, d = 1.54, as well as for the traditional classes, M
= 4.97, 95% CI [5.88, 4.05], t(56) = 10.89, p <
.001, d = 1.44. Thus, both teaching methods resulted
in statistically significant increases in content mastery
over the course of the semester with no statistically
significant difference between the two. Figure 3
displays the mean content knowledge scores.
Self-reported Understanding
A two-way 2 (Teaching Method: IBL and DI) x 4
(Time: Journal 2, Journal 3, Journal 4, Journal 5)
mixed ANOVA showed that there was not a
statistically significant interaction between the
teaching method and the time elapsed over the course
of the semester on the self-reported level of
understanding, F(3, 222) = 1.07, p = .363, partial
= .014. However, there was a statistically significant
main effect of teaching method between the journal
entries, F(3, 222) = 3.87, p = .010, partial = .050.
There was a statistically significant increase in self-
reported understanding from journal 2 (M = 5.62, SD
= 2.23) to journal 3 (M = 6.54, SD = 2.08), 95% CI
[1.52,0.34], p = .002. A significant increase was
also found between journal 2 (M = 5.62, SD = 2.23)
and journal 4 (M = 6.21, SD = 1.96), 95% CI
[1.24,0.03], p = .040. There was a statistically
significant increase in self-reported understanding
from journal 2 (M = 5.62, SD = 2.23) to journal 5 (M
= 6.22, SD = 2.30), 95% CI [1.24,0.14], p = .014.
Figure 4 displays the mean self-reported levels of
understanding. Because journal entry 1 was collected
on the second day of class, students were not asked to
discuss their level of understanding of course material
in their journal entries, only their mathematics anxiety.
2
2
2
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J. of Res. in Sci. Math. and Tech. Edu. | 143
Figure 3
Mean content knowledge scores for the IBL and DI groups on pre- and post-assessments.
Figure 4
Mean self-reported levels of understanding for IBL and DI groups throughout the semester based on student journal
entries.
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Correlational Analysis
Pearson’s correlation coefficient was computed
between students’ self-reported levels of mathematics
anxiety and understanding, as well as initial and final
MARS-S and content knowledge scores. Notable
correlations include the statistically significant
negative relationship between each self-reported level
of mathematics anxiety with its corresponding self-
reported level of understanding, indicating that as
mathematics anxiety scores increased, students’ levels
of understanding decreased (journal entry 2: r(93) =
.52, p < .01; journal entry 3: r(92) = .40, p < .01;
journal entry 4: r(86) = .56, p < .01; journal entry 5:
r(89) = .37, p < .01). There was also a strong
positive correlation between students’ initial and final
MARS-S scores, r(95) = .61, p < .01, whereas a weak
negative correlation existed between students’ final
MARS-S scores and final content knowledge scores,
r(97) = .28, p < .01. A significant strong positive
correlation existed between students’ initial MARS-S
scores and their self-reported level of mathematics
anxiety at the beginning of the semester on journal
entry 1, r(92) = .65, p < .01. Final MARS-S scores
and the students’ self-reported level of mathematics
anxiety at the end of the semester on journal entry 5
were moderately positively correlated, r(94) = .49, p <
.01. The results are summarized in Table 4. The
interpretations of these correlations were based on
benchmarks provided by Cohen (1988).
Table 4
Correlations
Measure
1
2
3
4
5
6
7
8
9
10
11
12
1. IN.MARS
2. FI.MARS
.61**
3. IN.CK
.14
.26**
4. FI.CK
.25*
.28**
.24*
5. J1MA
.65**
.33**
.11
.18
6. J2MA
.50**
.41**
.13
.29**
.49**
7. J3MA
.42**
.43**
−.25*
.40**
.45**
.34**
8. J4MA
.49**
.48**
.29**
.49**
.45**
.43**
.58**
9. J5MA
.19
.49**
.25*
.42**
.28**
.32**
.56**
.57**
10. J2UN
.24*
.34**
.08
.33**
.16
.52**
.20
.17
.25*
11. J3UN
.33**
−.43**
.14
.24*
.19
.14
.40**
.28**
.33**
.32**
12. J4UN
.37**
.46**
.37**
.40**
.25*
.16
.38**
.56**
.48**
.26*
.51**
13. J5UN
.10
.21
.02
.21
.08
.18
.15
.21*
.37**
.41**
.32**
.30**
Note. IN.MARS = initial MARS-S score, FI.MARS = final MARS-S score, IN.CK = initial content knowledge score,
FI.CK = final content knowledge score, J1MA = journal 1 mathematics anxiety level, J2MA = journal 2
mathematics anxiety level, J3MA = journal 3 mathematics anxiety level, J4MA = journal 4 mathematics anxiety
level, J5MA = journal 5 mathematics anxiety level, J2UN = journal 2 understanding level, J3UN = journal 3
understanding level, J4UN = journal 4 understanding level, J5UN = journal 5 understanding level. *p < .05. **p <
.01
J. of Res. in Sci. Math. and Tech. Edu. | 145
Discussion
Although previous research has demonstrated that the
implementation of inquiry-based Learning (IBL) in
college-level STEM courses successfully promotes
content mastery (e.g. Freeman et al., 2014; Kogan &
Laursen, 2013; Laursen & Hassi, 2012; Smith et al.,
2009), no study had previously included a direct
comparison of IBL methods with more traditional
pedagogical practices. This is the first known study to
use a quasi-experimental design, the non-equivalent
control group design, as part of a mixed methods
investigation to assess the direct effects of teaching
method on preservice students’ math anxiety and
achievement. The primary advantage of the use of this
design feature is that it provides a high degree of
internal validity thereby allowing for a high degree of
confidence in the inference of cause-effect
relationships not possible with other types of
methodologies (Campbell & Stanley, 1963; Cook &
Campbell; 1979; Shadish, et al., 2002).
The results of the present study show statistically
significant gains in content knowledge from pretest to
posttest over the course of the semester for both groups
with no statistically significant differences between
these two different teaching methods. These results
differ from those reported in the meta-analysis
performed by Freeman et al. (2014), which indicated
that students enrolled in active-learning classes in
STEM disciplines experienced higher achievement
scores than those enrolled in traditional classes.
Perhaps, as this study indicates, student achievement
may be affected by other variables, such as the course
instructor or course materials, rather than the teaching
methods employed by the instructor. It is worth noting
that while both groups demonstrated improved content
knowledge, the degree to which they did is somewhat
disappointing. On the 20-question assessment, both
groups improved their average number correct from
approximately 7 questions at the beginning of the
semester to approximately 12 questions at the end of
the semester. While this result may be statistically
significant in terms of achievement, it does indicate an
overall lack of sufficient content knowledge related to
the course content that warrants further investigation.
Because of the quasi-experimental design of the study,
the findings strongly suggest that trajectories of
anxiety over the course of the semester are causally
related to the teaching method used in the course.
Analyses revealed a significant difference between the
IBL and DI groups in their initial mathematics anxiety
based on both the MARS-S scores and self-reported
levels of mathematics anxiety from the students’
journal entries. At the beginning of the semester, the
IBL group reported significantly higher mathematics
anxiety than did the DI group on both measures. As
the semester progressed, the trajectory of mathematics
anxiety for both groups flowed in different directions.
By the end of the semester, mathematics anxiety had
significantly decreased for the IBL group on both
measures. In contrast, however, mathematics anxiety
significantly increased for the DI group on both
measures. It is important to note that on the MARS-S,
the final mathematics anxiety levels between the IBL
and DI groups were not significantly different from
each other, whereas the self-reported mathematics
anxiety levels of the IBL group were significantly
lower than the DI group on the final journal entries.
These results differ from those of Alsup (2004) who
found that students enrolled in a DI, lecture-style
course showed a larger decline in mathematics anxiety
as compared to those in a constructivist, active-
learning course. On the other hand, the results are
146 | L O R E N Z E N & L I P S C O M B
consistent with those of Pan and Tang (2005), Harper
and Daane (1998) and Sloan (2010) who found that
features of IBL classes, such as emphasis on problem
solving, small group work, peer teaching, and actively
participating in class, are helpful in reducing
mathematics anxiety.
The results on the students’ self-reported mathematics
anxiety are not at all surprising. For approximately
two-thirds of the IBL participants, this was their first
time in an IBL class. Being told on the first day of
class that there would be no class lectures and that the
students would do the majority of the work on the
boards could have come as a shock to many of the
students and could have been a contributing factor to
their heightened anxiety levels. Furthermore, both
groups demonstrated increased anxiety levels between
the first and second journals; however, this can
possibly be attributed to several factors. These include
the first unit in the course focusing on fractions (a topic
that is historically challenging for the teacher
candidates), the first test in the class being
administered near the time Journal 2 was submitted,
and in the case of the IBL students, becoming
accustomed to the new course format. However, once
the IBL students had sufficient time in the course to
become familiar with the format, their anxiety began
to decrease and continued to do so for the remainder
of the semester, even as the final exam approached.
The same cannot be said for the DI students. Whereas
their anxiety levels remained fairly constant and lower
than the IBL students throughout the majority of the
semester, their anxiety peaked and surpassed that of
the IBL students before the final exam.
Mathematics anxiety is well-known to have a
detrimental effect on student learning outcomes (e.g.
Hembree, 1990). Consistent with previous findings,
significant negative correlations between mathematics
anxiety and content knowledge were found, implying
that as students’ math anxiety increased, their
achievement decreased. Indeed, and not
unexpectedly, there were several converging lines of
evidence in the data for an inverse relationship
between mathematics anxiety and mathematics
achievement. Overall and irrespective of teaching
method, correlational analysis yielded significant
negative relationships between participants’ self-
reported levels of mathematics anxiety and self-
reported levels of understanding as indicated in the
journal entries. For those participants whose self-
reported level of anxiety increased over the course of
the semester, self-reported levels of understanding
decreased while for those for whom anxiety levels
decreased, their self-reported levels of content mastery
increased. Corroborating these findings in the present
study was the presence of a weak negative correlation
between participants’ final MARS-S scores and final
content knowledge scores at the end of the semester.
These results are consistent with the results of prior
studies including those of Hembree’s (1990) meta-
analysis of data from 225 research studies, which
indicated a significant negative correlation between
mathematics anxiety and achievement as well as those
of Ashcraft and Kirk (2001).
Conclusion
The preservice teachers who were enrolled in the
courses with IBL as the teaching method experienced
a significant decrease in their levels of mathematics
anxiety over the course of the semester as compared to
the preservice teachers who were enrolled in the
courses with DI as the teaching method as evinced by
both the MARS-S scores and participants’ self-
reported mathematics anxiety levels. However, while
J. of Res. in Sci. Math. and Tech. Edu. | 147
each group of participants experienced significant
increases in achievement based on the results of
content-specific pre- and post-test gains, there was not
a statistically significant difference in achievement
between the IBL and DI participants. Finally,
corroborating previous research, the present study
found a negative relationship between mathematics
anxiety and student learning outcomes.
Limitations
The study was limited to only preservice elementary
school teachers who self-enrolled in the researcher’s
mathematics content course based on their scheduling
needs. Student assignments to class sections were not
random. The results of the study may not generalize
to students with other college majors or those enrolled
in other mathematics courses. The study was also
limited to primarily female students. Approximately
96% of the participants were female, so the results of
the study may not generalize to classes in which the
majority of the students are not female. Additionally,
the study was limited by its short time frame as it was
conducted over a single semester, and the course in
which the participants were enrolled is the second
course in a three-course sequence. Lastly, the study
was limited by the honesty and clarity of the
participants’ responses on questionnaires and journal
entries.
Impact at Institution
The results of this study have already made a direct
impact on the design of mathematics coursework
required for teacher certification at the institution at
which it was conducted. New courses for pre-service
teachers have been designed to accommodate updated
state guidelines, and the course materials that have
been recently adopted promote discovery learning and
collaboration among students. Furthermore,
instructors of these courses now incorporate inquiry,
problem solving, and reflection regularly during class
meetings.
Recommendations for Practice
Based on the results of this study, it is recommended
that instructors of mathematics content courses for
preservice elementary teachers strongly consider
adopting student-centered, IBL techniques in their
classrooms. Furthermore, it is recommended that they
familiarize themselves with current standards,
including Common Core Standards for Mathematical
Practice, NCTM Effective Teaching Practices, and
AMTE Standards for Preparing Teachers of
Mathematics. Participating in professional
development opportunities focused on student-
centered learning and conceptual understanding of
mathematics could also prove to be helpful.
Recommendations for Future Research
Further research is needed to determine if the results
from this study would generalize to students with
different college majors or to those enrolled in general
education mathematics courses. Also, a longitudinal
study following a cohort of preservice elementary
teachers through the entire elementary education
sequence of mathematics content courses taught using
IBL methods could offer invaluable insight into their
experiences and the impact of those experiences on
their own teaching methods.
148 | L O R E N Z E N & L I P S C O M B
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Corresponding Author Contact Information:
Author name: Janelle K. Lorenzen, Ph.D.
Department: Department of Mathematics
University, Country: Southeastern Louisiana University, Hammond, LA, USA
Email: Janelle.lorenzen@southeastern.edu
Please Cite: Lorenzen, J., K., & Lipscomb, T., J. (2021). The Effects of Instructional Strategies on Preservice
Teachers’ Math Anxiety and Achievement. Journal of Research in Science, Mathematics and Technology
Education, 4(2), 133-151. DOI: https://doi.org/10.31756/jrsmte.425
Copyright: © 2021 JRSMTE. This is an open-access article distributed under the terms of the Creative Commons
Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the
original author and source are credited.
Received: January 06, 2021 ▪ Accepted: May 09, 2021
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Elementary school teachers’ math anxiety has been found to play a role in their students’ math achievement. The current study addresses the role of teacher math anxiety on ninth-grade students’ math achievement and the mediating factors underlying this relationship. Using data from the National Mindset Study, we find that higher teacher math anxiety is associated with lower math achievement. This relationship is partially mediated by the students’ perception that their teacher believes not everyone can be good at math and is not explainable by teachers’ usable knowledge to teach mathematics. In subsequent analyses, we find that higher teacher math anxiety relates to a reduction in process-oriented (as opposed to ability-oriented) teaching practices, which in turn predict students’ perception of teacher mindset. We argue that math anxious teachers and their use of particular teaching strategies have the potential to shape students’ math achievement and their perceptions of what their teacher believes about math.
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Using a Mixed Methods approach, this study investigated changes in levels of self-efficacy among elementary preservice teachers following a semester course on teaching elementary students’ mathematics. Participants in this study included 347 preservice elementary teachers at a mid-size regional university who had just completed an elementary mathematics methods course. The data were collected from several semester groups. The instruments used were the Mathematics Teaching Efficacy Beliefs Instrument, interview data, and observation data collected during the clinical experience. The focus of this study was to compare the changes in teacher self-efficacy following a methods course that emphasized hands-on mathematics instruction with manipulatives by means of the 5E instructional format. The results of the paired-samples t-test indicated that there was a significant difference in the preservice elementary teachers’ self-efficacy for teaching mathematics after engaging in the elementary methods course. Preservice teachers reported that their understanding of various instructional practices changed significantly from a “tell, show, and do” model to an approach utilizing interactive and engaging activities. They also reported that their attitude toward mathematics had improved significantly and that there had been a direct impact on their confidence for teaching mathematics as a result of the structure of the elementary math methods course.