Using Alternative Assessment Methods to Alleviate Math Test Anxiety
A Capstone Project
Submitted in Partial Fulfillment of
the Requirements for the Degree of
Master of Arts in Teaching: Mathematics
Bradley Lloyd Dennis
Department of Mathematics and Computer Science
College of Arts and Sciences
Graduate School
Minot State University
Minot, North Dakota
Summer 2012
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This capstone project was submitted by
Bradley Lloyd Dennis
Graduate Committee:
Dr. Kodwo Annan, Chairperson
Dr. Laurie Geller
Dr. Ryan Winburn
Dean of Graduate School
Dr. Linda Cresap
Date of defense: July 5, 2012
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Abstract
Math test anxiety causes a gap between a student’s understanding and test achievement. This was
a concern for me as a classroom teacher as it decreased the validity of my tests as assessment
tools, and worse, it created contempt toward math. If I could alleviate some of this anxiety
toward math tests I could consequently produce more accurate test scores and better student
sentiment. After researching different methods of reducing test anxiety, I used cheat sheets and
the allowance of hints on tests as alternative assessment techniques in my classroom. These
assessment techniques gave students a safety net should they freeze up from test anxiety and also
gave me additional assessment tools as a math teacher.
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Acknowledgements
First, I would like to thank my mom and dad for instilling in me the values of hard work
and perseverance, along with many others. These qualities have molded me into the person I am
today. Thank you for being such outstanding parents.
Thank you to the staff at Minot State University, especially Dr. Kodwo Annan for his
diligence as my Capstone advisor, and Dr. Laurie Geller for her extensive help throughout my
time at MSU. Your knowledge and insight were essential in the completion of this project.
Thanks to my friends and colleagues Sue Forster and Steve Schultz for being my
sounding boards. I admire you both on personal and professional levels. Sue, it has been a
pleasure and an honor having the room next to yours for the last five years; you are the
measuring stick by which I compare all high school math teachers.
Finally, I would like to thank those students at Bismarck High School who were my
inspiration for this project. Your dedication to learning and persistence when faced with
difficulty inspired me to be a better teacher. On the occasions I see these individuals after
graduation, I am never surprised these aforementioned qualities have led to your success.
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Table of Contents
Page
Abstract .......................................................................................................................................... iii
Acknowledgements ........................................................................................................................ iv
List of Tables ............................................................................................................................... viii
List of Figures ................................................................................................................................ ix
Chapter One: Introduction ...............................................................................................................1
Motivation for the Project ....................................................................................................2
Background on the Problem.................................................................................................2
Statement of the Problem .....................................................................................................3
Statement of Purpose ...........................................................................................................4
Research Questions/Hypotheses ..........................................................................................4
Summary ..............................................................................................................................4
Chapter Two: Review of Literature .................................................................................................5
Teacher/Classroom ..............................................................................................................6
Student’s Lack of Test Preparation Strategies .....................................................................7
Student’s Worry ...................................................................................................................8
Fear Appeals ........................................................................................................................9
Distractions ..........................................................................................................................9
Traditional vs. Dynamic Testing........................................................................................10
Collaborative Assessment ..................................................................................................10
Cheat Sheets .......................................................................................................................11
Distraction Avoidance .......................................................................................................12
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Summary ............................................................................................................................12
Chapter Three: Research Design and Method ...............................................................................14
Setting ................................................................................................................................14
Intervention/Innovation......................................................................................................14
Design ................................................................................................................................15
Description of Methods......................................................................................................16
Expected Results ................................................................................................................18
Timeline for the Study .......................................................................................................18
Summary ............................................................................................................................18
Chapter Four: Data Analysis and Interpretation of Results ...........................................................20
Data Analysis .....................................................................................................................20
Interpretation of Results .....................................................................................................30
Summary ............................................................................................................................31
Chapter Five: Conclusions, Action Plan, Reflections, and Recommendations .............................32
Conclusions ........................................................................................................................32
Action Plan.........................................................................................................................33
Reflections and Recommendations for Other Teachers.....................................................33
Summary ............................................................................................................................35
References ......................................................................................................................................37
Appendices .....................................................................................................................................40
Appendix A: Cheat Sheet Requirements ...........................................................................41
Appendix B: Geometry Preliminary Survey ......................................................................42
Appendix C: Geometry Post Test Survey: Cheat Sheets ...................................................43
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Appendix D: Geometry Post Test Survey: Hints ...............................................................44
Appendix E: IRB Approval Form ......................................................................................45
Appendix F: Principal Consent Form ................................................................................46
Appendix G: Research Participant Assent Form ...............................................................47
Appendix H: Parent/Guardian Research Consent Form ....................................................49
Appendix I: Chapter Seven Test ........................................................................................51
Appendix J: Chapter Eight Test .........................................................................................55
Appendix K: Chapter Nine Test ........................................................................................59
Appendix L: Chapter Ten Test ..........................................................................................64
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List of Tables
Table
Page
1.
Preliminary Survey Results................................................................................................21
2.
Chapter 7 Survey Results After Using Cheat Sheets .........................................................23
3.
Chapter 8 Survey Results After Using Cheat Sheets .........................................................25
4.
Chapter 9 Survey Results After Using Hints .....................................................................27
5.
Chapter 10 Survey Results After Using Hints ...................................................................28
6.
Comparison of Student Sentiment for Each Survey ..........................................................30
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List of Figures
Figure
Page
1.
Student response to a question on the preliminary survey. ................................................22
2.
Student response to a question on the chapter seven post-test survey after
using cheat sheets. ..............................................................................................................24
3.
Student response to a question on the chapter eight post-test survey after
using cheat sheets. ..............................................................................................................26
4.
Student response to a question on the chapter nine tests survey using hints. ....................27
5.
Student response to a question on the chapter ten post-test survey using hints. ................29
Chapter One
Introduction
I have been a math teacher for seven years, during which time I have administered and
corrected hundreds of tests and quizzes. As simplistic as it may be, the majority of my students
who prepared themselves appropriately for tests performed well and those who did not
performed poorly. While I have had those gifted few students who seem to effortlessly ace every
exam with little thought to preparation, most students needed several hours of practice,
questioning, and studying to perform well on a math test. I enjoyed helping students individually
to understand concepts taught in class and with their test preparations as it gave me feedback on
their triumphs and struggles in learning the material.
While much of this interaction was during class, there were many other chances for
student contact. During tutoring there were far fewer students, an environment that gave shy
students less apprehension in asking questions. Before and after football and wrestling practice,
along with bus rides and hotel stays, there was an opportunity to help my athletes and
statisticians when they needed it. Sometimes the only time needed was in the hall between
classes. All of these different relations allowed me to better understand my students, and I
believe they better understood me as well.
After these interactions I would form an idea of how well I thought these students should
do on my test. While my impressions of answered questions and completed homework indicated
those students understood the concepts, this was not a true assumption. The day of the test would
arrive and without fail I would have tests that would have me at a loss. “Suzy” left questions
blank she had answered without pause just the day before. “Jordan” averaged an A on his
homework for the chapter but got a C on the test. I couldn’t understand why this happened.
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Not only was it disheartening for students who worked so hard when they received their
tests back, it was discomforting for me as well. What was causing this difference between my
perception of student ability and their actual test score? I would wait for a personal opportunity
to ask them what they thought was going on; thinking there had to be something I was missing.
While their demeanor ranged from mad to embarrassed (which was hard for me to witness),
when I asked them what had happened, the answer usually boiled down to one basic thing… they
failed to recall what they knew just the day before. Many of these students blamed anxieties for
their troubles as well.
Motivation for the Project
This presented me with a problem. As a classroom teacher, I expect my students to learn
math and be ready for the next level of math, be it high school, college, or the job market.
Testing is the primary tool I use when determining whether a student has mastered concepts or
not. Intuitively, performing well on a test demonstrates student understanding, while poor
performance implies insufficient knowledge of the content. This black and white view does not
tell the whole story however if a student’s test anxiety impedes their ability to process and recall
information for a test. Alarmed with this inconsistency, I wanted to change it: this became the
goal of my research project. I was also interested in determining if those students who showed a
lack of motivation had similar anxieties of testing poorly.
Background on the Problem
It has been my observation that many people have no problem expressing they are bad at
math. In the classroom, the students often give the excuse “I hate math” or “I am just not good at
math.” At parent teacher conferences, it is often the case where the parents insist they are of no
help to their student when it comes to math. Both parents and students often give the excuse, “I
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hate math” or “I am/was not good at math.” Chinn (2009) stated, “It appears to be socially
acceptable to admit to having low abilities with numbers, a situation that lowers anxiety in
adults” (p. 61). On the flip side of the coin, I have never overheard anyone saying, “It’s no big
deal that ‘Little Johnny’ isn’t doing well in English, I can’t read either.” I wondered if this
dislike of mathematics arose not from their inability to use math, but from their anxiety and/or
poor performance on math tests.
Walker (1975) defined anxiety as a reaction people have to a situation where they believe
their well-being is endangered or threatened in some way. Anxiety related to mathematics is not
uncommon. The combination of having only one correct answer often combined with the added
stress of time constraints also leads to a negative outlook on mathematics (Chinn, 2009). It
makes sense that a student who gave an honest effort to prepare but came up short will be
anxious about performing poorly on the next test. The problem for me then became finding a
way to make the student sufficiently comfortable in what has become an uncomfortable situation.
The benefits of success here were twofold: students would feel less stress during the test and the
test would produce a more accurate depiction of student knowledge. After researching possible
many possible avenues, I decided to examine the alternative assessment methods of using cheat
sheets and hints in my classroom. Hints are a type of dynamic assessment method that allows
students to ask a hint on a question in exchange for losing a point, while cheat sheets are a
limited set of self-prepared notes the students may use during the exam. It was my hope that
these methods would reduce math test anxiety in my students.
Statement of the Problem
Testing is needed to assess students and will inevitably cause some stress in my students.
Conversely, testing a student who is overloaded with anxiety levels causing their minds to be
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overridden by worry is counterproductive. If teachers are to help anxious students successfully
take math tests, it is important to seek a remedy to reduce their anxiety.
Statement of Purpose
The purpose of my action research project was to implement and compare the
effectiveness of hints and cheat sheets at reducing test anxiety in my geometry students.
Different approaches were needed in an attempt to assist a range of students and their levels of
anxiety. In doing so, I hoped my tests would produce more accurate assessments results of
student performance.
Research Questions/Hypotheses
Do cheat sheets and hints reduce math test anxiety in my geometry students? If so, to
what degree are these interventions effective and which method do students prefer? Will test
scores improve through the use of these methods?
Summary
This chapter addressed my initial concerns with math test anxiety. Math test anxiety can
result in inaccurate test scores due to students’ inability to recall what they have learned. A
combination of discomfort with mathematics and apprehension when taking tests can lead to an
uncomfortable situation in a math classroom. The intent of my action research project was to
determine if I could reduce the amount of anxiety my students experienced through alternative
assessment techniques. In Chapter Two, research pertaining to test anxiety in mathematics is
discussed.
Chapter Two
Review of Literature
The implications of test anxiety are far-reaching when considering how frequently tests
are administered throughout primary, secondary, and post-secondary settings. A student’s
educational career is determined in large part by his or her performance on tests. Therefore,
when an individual experiences test anxiety, the results can be dramatic.
The purpose of my project was to implement and compare the effectiveness of hints and
cheat sheets at reducing test anxiety in my geometry students. Many ways to alleviate test
anxiety through use of different testing strategies exist, along with research on elements that
contribute to test anxiety. Much of the research was related to unique test anxieties associated
with mathematics, as this was my discipline of expertise as well as the environment in which
strategies were put into practice.
Wigfield and Meece (1988) studied math test anxiety on students from elementary to
secondary schools and observed that test anxiety was highest in ninth grade and lowest among
sixth graders. They concluded that strategies to build anxious students’ confidence in their math
ability are necessary to improve test scores. They also suggested that math anxious students may
need trainings in order to reduce their fear and dread in math tests.
Numerous factors interacted when determining if a student has experienced anxiety on
tests or in mathematics (Brady & Bowd, 2005; Putwain, 2007; Woodard, 2004). It was nearly
impossible for one to consider all environmental, dispositional, and situational factors (Baloglu
& Kocak, 2006) attributed to every student in a single classroom. While studies indicated that
many factors contribute to math test anxiety, they frequently mentioned the effect of teacher’s
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role, tests associated with the classroom setting, students as individuals, and types of tests as
significant.
Teacher/Classroom
The traditional mathematics classroom has created feelings of discomfort for many
students (Baloglu & Kocak, 2006; Brady & Bowd, 2005; Woodard, 2004). Thoughts of
memorizing formulas and algorithms, rigorous proofs, the “kill and drill” approach to learning
math facts, and other less than favorable factors may have contributed to anxiety (Brady & Boyd,
2005). Often times a math teacher has been thought of as a hostile, or at best insensitive,
individual (Brady & Boyd, 2005) whose attitude creates anxiety in itself (Baloglu & Kocak,
2006). Much of this perception probably has stemmed from the habitual pursuit of a singular
correct answer in the primary grades (Brady & Boyd, 2005). Poor teaching strategies have
developed negative feelings toward mathematics when a student is repeatedly told they are
incorrect in their calculations. The combination of these factors compounds the problem, which
made math class feel more like entering a dragon’s lair even if their perceptions were more
imagined than real.
As with any curricular area, ineffective teaching methods in the mathematics classroom
have led to student anxieties (Baloglu & Kocak, 2006; Woodard, 2004). These anxieties start at a
young age for several reasons. Brady and Boyd (2005) found instructors at the elementary level
who had elevated measures of anxiety “spend less time planning mathematics lessons and using
mathematics instruction time for non-mathematics related activities more often than their less
math-anxious colleagues” (p. 39). Unfortunately, the instructor’s anxieties often translated to
anxieties for their students (Vinson, 2001). These problems were not confined to just the
elementary level, as both elementary and secondary teachers of mathematics may have relatively
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weak academic backgrounds (Brady & Bowd, 2005).
Recognizing poor mathematics instruction as detrimental and contributing to
mathematics anxiety (Brady & Bowd, 2005) has improved methods of instruction by alleviating
the causes of math anxiety. Rachal, Daigle, and Rachal (2007) found “many students do not
develop effective learning strategies unless they receive explicit instruction and the opportunity
to apply these skills” (p. 191). Without the “know how” students struggled when attempting to
study for tests. Alerting students to these methods may have helped reduce their anxieties.
Math instructors could have developed helpful pedagogic strategies; these included
communicating passion in their subject area, conveying clear objectives, and giving feedback
(Woodard, 2004). Childs (2009) found teachers who encouraged a positive attitude in regards to
testing itself and who viewed exam days as celebratory dates recorded positive results in their
classroom. According to Woodward (2004), teachers reduced stress when awarding credit for
procedure when grading instead of focusing only on the answer. Alternative assessment
techniques such as “oral questioning, observation, demonstration, discussion, journal writing and
retesting” (Woodard, 2004, Recommendations section, para. 1) may have produced a more
accurate picture of student knowledge.
Student’s Lack of Test Preparation Strategies
According to Covington and Omelich (as cited in Veenman, Kerseboom, & Imthorn,
2000), “Learning must be present in order to be interfered with” (p. 392). While one may have
been quick to dismiss the student who was not taking notes in class or otherwise had not
appeared to be making use of their time as lazy, there were reasons for inattentiveness. This
apparent negligence was often because students had not developed good learning strategies, not
only in mathematics but throughout the curriculum. The assumption is that students were
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developing cognitive and behavioral skills on their own at some time in their academic career
(Rachal et al., 2007). These skills include the metacognitive skills of “task orientation, planning,
monitoring, checking, and recapitulation” that were considered prerequisites to effective learning
(Veenman et al., 2000). Many students have been found to be deficient in these areas of
cognition, which can be attributed to two factors. In the first case, they lacked the self-knowledge
of their own learning strategies. In other words, these students did not figure out how best they
learn as individuals. Consequently, those students who had poor study skills often experienced
failure and as a result developed test anxieties (Veenman et al., 2000).
According to Doron, Stephan, Boiche, and Le Scanff (2009), individuals who viewed
ability as stable or constant often displayed behavioral disengagement. These students considered
ability to be predetermined and fixed, and thus felt they had no control over their performance on
exams. These beliefs were reinforced by students experiencing repeated failures in the past. Not
surprisingly, the study found those individuals with a belief in ability to change (improve)
accurately predicted the use of positive strategies for learning to adapt to examination demands.
Student’s Worry
Despite their efforts, some students with good study skills suffer from math test anxiety.
These are students who performed well when given an informal assessment the day before a test,
but froze up when the test was placed in front of them. According to Rodger, Murray, and
Cummings (2007), “Proneness for high-anxious people leaves them susceptible to tension and
nervous reaction in a wide range of evaluative situations, including a test or exam” (p. 92).
Individuals who had task irrelevant negative self-thoughts experienced a component of anxiety
referred to as “worry” (Chinn, 2009; Doron et al., 2009; Miejer, 2001; Putwain, 2007; Putwain &
Symes, 2011; Veenman et al., 2000). Not only were these thoughts distracting, they worsened
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the confidence level of the student taking the test, which inhibited their test taking ability. Poor
performance on previous tests was an example of these thoughts (Putwain, 2007). Feelings about
previous experiences distracted from the test being taken. Failure to answer questions invoked
more anxiety as the test taker’s threat perception increased (Rodger et al., 2007). In essence,
when worry goes unchecked it can have a compounding affect.
In contrast, students who had a positive attitude toward mathematics were found to have
less anxiety on math tests (Dodeen & Darabi, 2009). As mentioned previously, students did
better when teachers showed tests in a positive light (Childs, 2009). Recent research has shown
mathematics anxiety can be forecasted by a student’s predisposition toward test anxiety (Cates &
Rhymer, 2003; Kesici & Erdogan, 2009). Observing a student’s learning strategies and
motivational beliefs predicted success or failure in mathematics.
Fear Appeals
It has been a commonly used practice for teachers to motivate students by putting added
stress on the importance of a test and the implications of performing well on it (Putwain &
Symes, 2011). While fear-based emphasis may be beneficial in other areas, it is better left out of
the test setting. As discussed by Putwain and Symes (2011), these fear appeals can actually be
detrimental to student learning. Some students perceive fear appeals as threatening, producing
worry and apprehension that invokes poor test performance (Putwain & Roberts, 2009).
Repeated use can result in a test taker disregarding importance of the exam entirely, something
similar to “the teacher who cried wolf.”
Distractions
Working memory is an integral part of taking mathematics tests (Beilock & Carr, 2005).
As previously discussed, test anxiety contributes to distractibility in testing situations which
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exhausts a portion of working memory during a test. Therefore outside distractions are especially
detrimental to students experiencing anxiety as compared to those who are not highly anxious
(Parks-Stamm, Gollwitzer, & Oettingen, 2010). While temptation-inhibiting strategies are
discussed later, it can be stated here that any efforts to eliminate distractions from the test taking
environment would appear beneficial.
Traditional vs. Dynamic Testing
Traditional testing techniques do not allow an individual to draw conclusions based on
their mistakes, unlike many typical day-to-day situations (Miejer, 2001). For example, when one
is trained in on a job, in many instances an individual is supervised in training before being left
alone to do a task independently. In contrast, students in most math classes take an entire test
independent of outside influences before they hand in the test and are later given feedback.
Miejer (2001) stated these “static” testing conditions are associated with higher levels of test
anxiety.
In Miejer’s (2001) article, “Learning Potential and Anxious Tendency,” he described a
dynamic testing method, in which students were allowed hints and were graded in response to
the number of hints needed to attain the correct answer. In this alternative assessment method,
some credibility was given to the hypothesis that conventional testing techniques are biased
against those experiencing anxious tendencies. This bias can be lessened, to an extent, by
offering help to students during a test while maintaining the validity of the test itself. While this
strategy may have its merits, difficulties may arise for a teacher trying to attempt this in a large
classroom. Miejer’s (2001) study utilized computers to alleviate this problem.
Collaborative Assessment
Many studies have shown collaborative assessment to decrease the level of test anxiety
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experienced by students (Ioannou & Artino, 2010). Ioannaou and Artino (2010) found
collaborative assessment was “more enjoyable and generally less stressful than a regular test,”
(p. 195) supported by the fact several of the students in the study admitted to having studied less
than usual. Individuals whose anxieties make it difficult to retrieve learned information may find
it easier to recall when they can discuss questions and answers with others (Breedlove, Burkett &
Winfield, 2004). In addition, it should be noted this study found no significant difference in
scores between students taking a test collaboratively and those testing individually.
Cheat Sheets
Erbe (2007) discussed how using cheat sheets can reduce test anxiety in students. Most
people know cheat sheets as a piece of paper on which notes, examples, formulas, definitions,
etc. are written to use on a test. Without the use of a cheat sheet, this material must be
memorized.
Memorization of one form or another has been previously mentioned as source of anxiety
on math tests (Brady & Boyd, 2005). However, Bloom and Krathwohl (1956) found recall is a
low level skill in the cognitive domain, which presents a paradox of sorts; aspects students
stressed over most are the least important in regards to learning. Erbe (2007) added these facts
and formulas are the easiest to find in a “real life problem-solving situation” (p. 96); meaning,
the failure to remember formulas did not prevent the attainment of an answer for a resourceful
individual. Teachers, and thus students, focused studying on higher level problems instead of
memorizing facts and formulas.
Cheat sheets included other benefits; they have been shown to increase test scores
(Skidmore & Aagaard, 2004) and facilitate deeper learning. As with many classroom teachers,
Erbe (2007) found, “Students loved …cheat sheets. They found, however, that they rarely
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needed them” (p. 97). This implies sufficient learning took place from the preparation of the
cheat sheet.
Distraction Avoidance
Parks-Stamm et al. (2010) stressed developing a strategy to maintain focus on the test.
The goal was to maintain focus without creating distracting thoughts of test stress. Of the two
strategies tested, the technique of “temptation-inhibiting implementation intentions” (p. 30) was
found most effective as test anxiety increased. Instead of trying to maintain focus on the task
(test) when presented with a distraction, the method focused attention away from the task. This
technique dismissed the distraction (e.g. “If my neighbors are distracting, I will not pay attention
to them”). Subjects in the same study who attempted to avoid distraction by focusing harder on a
task (e.g. “If my neighbor is distracting, I will focus harder on my test”) were less effective when
experiencing high levels of test anxiety. In other words, it was better to recognize a distraction
and dismiss it, rather than project the anxious energy back into the test.
Summary
Test anxiety and math anxiety were prevalent and had numerous causes. Poor
pedagogical practices on the part of the instructor have led to students who are turned off from
mathematics, situations, or both. Failure on the students’ part to adequately prepare for a test or
lack of test preparation strategies put them at a disadvantage, creating anxieties during the test.
Highly anxious students had distracting thoughts about their impending failure and were more
easily distracted by their environment, thus depleting working memory needed in testing
situations. Traditional testing practices do not model real world situations, where collaboration,
learning, and problem solving are stressed.
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There have been several attempts to look at new methods of testing more beneficial and
less stressful than those used by mainstream teachers. These tests more closely model real world
situations where adaptability, resourcefulness, and collaboration are as important as knowledge
and memory. In the next chapter, I discussed how I incorporated a few of these ideas into
practice, attempting to alleviate test anxiety and obtain a better picture of student knowledge
from assessment.
Chapter Three
Research Design and Method
The focus of this project was to implement and compare the effectiveness of hints and
cheat sheets at reducing test anxiety in my geometry students. A cheat sheet is a hand written set
of notes a student creates as an aid in remembering information from the instructional unit being
assessed. Hints are used to prompt a student that is stuck on a problem in hopes that the student
will then be able to complete the problem. This chapter explains who was part of the study, how
I incorporated each intervention, and the strategy used to analyze the data.
Setting
At the time of this study, I taught high school mathematics in a Midwestern state. The
population of the high school was about 1,400 students in grades 10-12. The school was one of
two public high schools in the city, along with an alternative high school and two private high
schools that also existed. I taught two sections of Geometry, which I used to conduct my
research. The initial sample size for each class was 17 and 13 students, which was average for
the school but slightly less in comparison to previous years. The two geometry classes consisted
of 9 females, 8 males and 8 females, 5 males, respectively. Two students were dropped during
the project; one because of a change in schedule and the other for lack of attendance.
Intervention/Innovation
I required students to use cheat sheets on Geometry tests for the first two tests of the
semester. My primary goal was to alleviate test anxiety, but I also hoped to improve the test
preparation strategies of my students. The requirements of the cheat sheet (see Appendix A)
were distributed more than one week before the first test of the third quarter. I required each
student produce a cheat sheet at the beginning of class the day before the test. A prior
15
arrangement with another teacher allowed me to make copies of the sheets and return them to the
students before the end of the class. The original cheat sheets were also collected when the test
was handed in to compare with the copied versions of the cheat sheets. This was used to
determine how much was added to each cheat sheet the night before test. Students were awarded
points for completion based on the copied version, and the original was used to award bonus
points. The purpose of awarding bonus points in this manner was to encourage students to start
preparing for the test days in advance instead of the night before test.
I used hints to alleviate anxiety on the third and fourth tests of the semester. Hints allow
students to ask for help to assist them in solving a problem. The purpose of my hint was to jump
start a student who drew a blank when starting a question, as is common with test anxiety. If a
student asked for a hint, it was noted on the test and one point was subtracted from the score of
the test for each hint given. Students were allowed to ask for help on any number of questions,
but were limited to one hint per question. This process required me to have point totals for each
question displayed on the test and also necessitated my complete attention to the class for the
duration of the test.
Design
This action research project used a mixed methods approach. Statistical analysis using
mean, median, mode and standard deviation was done on all assessments where cheat sheets or
hints were used. When I analyzed tests allowing hints, I noted the number of hints given.
Surveys were given to all participating students in both classes to analyze the perceived
effectiveness of cheat sheets and hints in reducing test anxiety. A preliminary survey (see
Appendix B) was given to get a baseline for student sentiment toward tests and mathematics.
Surveys were also given after the tests are handed back to the students. Post-test cheat sheet
16
surveys (see Appendix C) included questions about using the cheat sheets along with general
questions about tests and math. Post-test surveys after tests that allowed hints (see Appendix D)
included questions about hints together with general questions about tests and math.
Qualitative analysis was done in two ways. A free response comment section was
included on all surveys to try to uncover advantages or disadvantages I had overlooked during
my teaching. I also kept a journal to document general observations of anxiety in my students.
For tests involving cheat sheets, journal entries were made describing the differences in the
amounts of information on the cheat sheets between the two days. On days I allowed hints on
tests I noted in my journal the effects on student anxiety as well as any advantages or
disadvantages to the teacher.
Description of Methods
The Minot State University Institutional Review Board (IRB) needed to provide written
approval before my study (see Appendix E). Written approval was also requested from the
school principal to allow the study to take place in my classroom (Appendix F). All participants
in the study were informed of the study by a letter preapproved by the Minot State University
Institutional Review Board (Appendix G) and signed an attached consent form stating they
agreed to participate. Every student’s parent/guardian in this study signed a consent form stating
they agreed to their child’s participation in the study a week in advance of the first test
(Appendix H). All information presented in this project was presented only in aggregate form so
the confidentiality of all participants was maintained.
My study took place in the second semester of the 2011-2012 school year. The first and
second tests of the semester required the students to create a cheat sheet for use on the test.
Students were given instructions for the cheat sheets at least one week before the first test. In this
17
way they were given the opportunity to start making their cheat sheets several days before the
test.
The day before the test, students were required to turn in their cheat sheets for a
completion grade. I arranged to have another teacher make copies of the cheat sheets during the
class period so that students would have them back before the end of the period. The students
also turned in their original cheat sheets with the test. In my journal I noted observations on the
apparent effectiveness of the cheat sheets in reducing test anxiety during the test. Reductions in
test anxiety were also indicated by the students’ responses on the survey given after the test was
returned.
The third and fourth tests of the semester involved using hints. Students were informed
how to ask for hints verbally before they were used. When correcting the tests using hints, I kept
track of the number of times each student asked for a hint. I tallied the number of correct answers
in instances where a hint was given, which helped demonstrate how effective this type of
dynamic assessment was. Students who answered the question correctly after a hint tended to
indicate they drew a blank due to anxiety, where students who could not complete the problem
despite getting a hint indicated they were not prepared for the test question. It seemed unlikely a
student could answer a free response question correctly if he or she had little understanding of
the test question, even after receiving a hint.
After a test was given back to the student, a survey was given to determine students’
experience using hints. This gave students time to reflect on the assessment and comment. It was
not given directly after the test, as test takers who used most of the period might have been
rushed to finish the survey. I returned the assessments within one or two school days so the
assessment experience was fresh in their minds.
18
Expected Results
As a result of my study, I expected my Geometry students to have more completed
problems, more correct answers, and less anxiety during both types of tests. It was anticipated
that their grades would improve slightly, but I did not predict a dramatic change. I hoped that
some or all students realized they were not referring to their cheat sheets during the test as often
as they expected. This would demonstrate the use of cheat sheets was a good study technique
even when they were not allowed on tests.
After using cheat sheets to reduce anxiety and illustrate a study technique, I expected
using hints would reduce anxiety for those students who prepared themselves for the test.
Students who studied less thinking hints would get them through the test, may have found they
were wrong. Thorough knowledge of the content was still required to answer a question
correctly.
I anticipated some awkwardness when first using hints for the students and me. It was
expected that students would want more of a hint than what I gave them, especially if they were
underprepared. I predicted that I would need to adjust how much or what kind of hint I gave
students on the questions for the second test using hints.
Timeline for the Study
My study began and ended during the second semester of the 2011-2012 school year.
Therefore, all tests and quizzes in this study were given between the dates of January 16, 2012
and April 14, 2012 to allow for sufficient time to study the use of hints and cheat sheets. Data
was analyzed and interpreted before the end of the school year.
Summary
In this chapter I have established where, when, and how I used cheat sheets and hints to
19
study if either alleviated math test anxiety. Both qualitative and quantitative methods of data
collection were used to collect data during the study. Student anxiety was expected to decrease
from both methods of alternative assessment. Chapter Four describes the data collected from the
aforementioned methods and the interpretation of that data.
Chapter Four
Data Analysis and Interpretation of Results
The purpose of this project was to determine if hints and cheat sheets reduced test anxiety
in my Geometry students. In this chapter I described how data were collected in the classroom.
The collected data from surveys and tests were analyzed, along with my own observations, to
determine if they were effective. The combination of analysis, observations, and participant’s
grades were used to determine if cheat sheets and/or the use of hints were effective in reducing
anxiety.
Data Analysis
Preliminary surveys were given to my Geometry students to get a baseline of their
sentiment toward math and test anxiety, as well as several other questions concerning math tests.
The same four questions were asked on surveys given after the tests were returned to the students
to see if their sentiment toward math and test anxiety had changed after the use of cheat sheets
and hints. Additional questions on cheat sheets and hints were asked on those corresponding
surveys. These surveys can be seen in Appendices B, C and D.
To evaluate the reactions to each Likert-like survey question with an odd number of
responses, a number value ranging from 1 (Strongly Disagree) to 5 (Strongly Agree) was
assigned, with a value of 3 given to those who chose to give no opinion on the question. These
numbers were then averaged for each statement to see if the collective sentiment of the class was
in agreement or disagreement. A score higher than 3 corresponds with agreement, while the
opposite is true for numbers less than 3.
Table 1 showed the cumulative results of the preliminary survey. There were several
indicators that seemed to show cheat sheets and the use of hints would be successful. Student
21
sentiment was the greatest toward the statement “I feel I could do better on math tests if I had
something to jog my memory” as shown in Figure 1. This result predicted cheat sheets and hints
would indeed be beneficial to students on tests, which could in turn lessen student anxiety.
Another indication the project would be beneficial was that over half of the students agreed they
struggled memorizing information. Secondarily, I was not surprised by how many students
admitted to not knowing how to study for math tests, but it was my hope that they would see how
memory was improved by making a cheat sheet and develop student confidence in their ability to
do well on tests.
Table 1
Preliminary Survey Results (n = 28)
Item
I draw a blank on questions during math
tests.
SD
D
N
A SA
4% 29% 14% 29% 25%
M
3.43
SD
1.26
4% 11%
7% 32% 46%
4.07
1.15
I struggle trying to memorize information
needed on math tests (formulas, definitions,
etc.)
11% 14% 21% 36% 18%
3.36
1.25
I know how to study for math tests.
11% 50% 18% 14%
7%
2.57
1.10
4% 32% 25% 29% 11%
3.11
1.10
I feel I could do better on math tests if I had
something to jog my memory.
I study enough to achieve the grade I want
on math tests.
Note. SD = Strongly Disagree, D = Disagree, N = No Opinion, A = Agree, SA = Strongly Agree, M = Mean, SD =
Standard Deviation
Students were informed before the chapter started that they would be allowed cheat
sheets on the chapter seven test (see Appendix I). I collected all of the cheat sheets the day
before the test and had a fellow teacher make copies of them. The cheat sheets were returned to
the students before the end of class. Students were awarded ten points for turning in a cheat sheet
the day of the test and two bonus points if they had not changed their cheat sheet from the day
22
before. The bonus points were used to encourage students not to cram by making the cheat sheet
the night before the test, and having copies from the day before allowed me to see their progress.
I feel I could do better on math tests if I had
something to jog my memory.
Strongly Disagree
Disagree
No Opinion
Agree
Strongly Agree
Figure 1. Student response to a question on the preliminary survey indicating cheat sheets and
hints would be helpful in reducing math test anxiety.
While most took full advantage of using cheat sheets, two of the students in the survey
chose not to use cheat sheets. There were also others I had observed quickly write down
formulas at the last second to get the ten points for handing in the cheat sheets. Seventeen of the
twenty-nine students surveyed received the two points for having their cheat sheets completed
the day before the test.
Looking at Table 2, it was evident that more students felt stress relief when using cheat
sheets than not. About two-thirds of the students responded they could concentrate more on
concepts without having to memorize formulas (see Figure 2). Only five students of the twentynine surveyed felt that making a cheat sheet was more work than it was worth. These findings
23
voted positively for the use of cheat sheets. This was reinforced by several comments on surveys,
such as “Cheat sheets for all tests” and “The cheat sheet was excellent help.”
Table 2
Chapter 7 Survey Results After Using Cheat Sheets (n = 29)
Item
SD
D
N
A SA
I felt less stressed before this test because I
10% 10% 31% 31% 17%
knew I could use the cheat sheet.
M
3.34
SD
1.20
I felt less stressed during the test because of
the cheat sheet.
17% 14% 10% 48% 10%
3.21
1.32
I did better on the test than if I had not used
a cheat sheet.
10% 14% 41% 24% 10%
3.10
1.11
I could concentrate more on understanding
concepts because I didn’t worry about
memorizing.
3% 21% 10% 41% 24%
3.62
1.18
2.59
1.09
7%
2.41
1.18
I did not need to use the cheat sheet as much 17% 28% 17% 21% 17%
as I thought I would.
2.93
1.39
I studied enough to achieve the grade I
wanted on this test.
10% 45% 31%
3% 10%
Making a cheat sheet was more work than it
was worth.
24% 34% 24% 10%
Note. SD = Strongly Disagree, D = Disagree, N = No Opinion, A = Agree, SA = Strongly Agree, M = Mean, SD =
Standard Deviation
The average score on the chapter seven test was 76.7% with a standard deviation of
17.9%. Unfortunately, eight students failed the test even with the use of cheat sheets which
accounted for the large standard deviation. The median score on the test was 81.1% with modes
of 75.7%, 86.5%, and 92.6%. Analysis of these students’ cheat sheets showed most had a
complete sheet of formulas. This led me to believe the students genuinely struggled with the
concepts, although it was questionable if those students did all they could to prepare for the test.
I state this because of the difficulties I had in getting several students to complete their
homework assignments.
24
I could concentrate more on understanding
concepts because I didn't worry about
memorizing.
Strongly Disagree
Disagree
No Opinion
Agree
Strongly Agree
Figure 2. Student response to a question on the chapter seven post-test survey indicating cheat
sheets proved useful in allowing students to focus more on understanding than memorizing.
For the chapter eight test (see Appendix J), I decided to help the students with the
creation of their cheat sheets. This was in contrast to chapter seven where the students were
responsible for what they produced, although I had hinted to important formulas and concepts
along the way. Several factors resulted in 100% of the students using cheat sheets on this test.
These factors include my input about what to put on the cheat sheets, class time to complete
them, and familiarity with cheat sheets from the previous test. Most students had a complete
page covered with notes which were also organized as to be easy to use. Some even added notes
from the previous chapter.
Table 3 contains the results of the surveys given after the chapter eight test using cheat
sheets. This survey indicated many students experienced less stress and felt they achieved higher
scores than if they had not been able to use cheat sheets. Although all stress before the test was
25
not eliminated, over half of my student felt less stressed before and during the test. A full third of
students strongly agreed they could concentrate more on understanding concepts without
worrying about memorizing. In fact, there was only one student who disagreed with this
statement. This reduced anxiety seems to relate to the 82.2% mean on the chapter eight tests,
which was by far the best average grade of all the tests. The median of the test was 83.5% and
the standard deviation was 11.4%, with modes of 87.5% and 89.7%.
Table 3
Chapter 8 Survey Results After Using Cheat Sheets (n = 27)
Item
SD
D
N
A
I felt less stressed before this test because I
7% 7% 22% 56%
knew I could use the cheat sheet.
SA
7%
M
3.48
SD
1.01
I felt less stressed during the test because of
the cheat sheet.
11% 15% 15% 41% 19%
3.41
1.28
I did better on the test than if I had not used
a cheat sheet.
7% 15% 15% 30% 33%
3.67
1.30
I could concentrate more on understanding
concepts because I didn’t worry about
memorizing.
0%
3.96
0.90
I studied enough to achieve the grade I
wanted on this test.
4% 26% 37% 26%
7%
3.07
1.00
7%
4%
2.15
1.03
4% 26% 33% 30%
7%
3.11
1.01
Making a cheat sheet was more work than it
was worth.
I did not need to use the cheat sheet as much
as I thought I would.
4% 30% 33% 33%
26% 48% 15%
Note. SD = Strongly Disagree, D = Disagree, N = No Opinion, A = Agree, SA = Strongly Agree, M = Mean, SD =
Standard Deviation
26
I felt less stressed during the test because of
the cheat sheet.
Strongly Disagree
Disagree
No Opinion
Agree
Strongly Agree
Figure 3. Student response to a question on the chapter eight post-test survey after using cheat
sheets for a second time. This chart indicates over half of the students experienced less stress as a
result of using cheat sheets.
Chapter nine was the first chapter in which I gave hints on the test in order to assist
students that became stuck on a problem. The cost for receiving a hint was one point. Each
question on the test had a designated point value on the test so the students could weigh the cost
of the hint in comparison to the value of the question.
The results of the surveys given after the chapter nine tests (see Appendix K) are in Table
4. While the results of this data were spread out more than previous surveys, the responses to two
of the statements indicated that hints were not as affective in relieving stress as cheat sheets. As
seen in Figure 4, almost two-thirds of the students disagreed with the statement “I felt less
stressed because I could ask for a hint on the test.” This seems to be related to how many
students responded they were reluctant to ask for hints for fear of losing points.
27
Table 4
Chapter 9 Survey Results After Using Hints (n = 27)
Item
SD
D
N
A
If felt less stressed because I could ask for a 26% 37% 22% 11%
hint on the test.
SA
4%
M
2.30
SD
1.10
I studied less because I knew I could ask for
hints on the test.
15% 30% 33% 15%
7%
2.70
1.14
I felt comfortable asking for a hint on the
test.
11% 15% 41% 22% 11%
3.07
1.14
7% 19% 48% 11% 15%
3.07
1.11
11% 15% 19% 41% 15%
3.33
1.24
0% 26% 52% 11% 11%
3.07
0.92
I used less hints than I should have.
I was reluctant to ask for a hint because I
did not want to lose any points on the test.
I studied enough to do well on this test.
Note. SD = Strongly Disagree, D = Disagree, N = No Opinion, A = Agree, SA = Strongly Agree, M = Mean, SD =
Standard Deviation
If felt less stressed because I could ask for a
hint on the test.
Strongly Disagree
Disagree
No Opinion
Agree
Strongly Agree
Figure 4. Student response to a question on the chapter nine tests survey using hints. Hints seem
to be unsuccessful in alleviating stress for most of the students.
28
Only thirteen hints were asked for out of twenty-eight tests, each with eighteen questions.
A large percentage of the hints requested during the test were used to ask for formulas needed to
complete the question, which probably would have been at their disposal on their cheat sheet for
the previous test. The mean score on the chapter nine tests was 78.6% with a standard deviation
of 15.1%. The median for the test was 82.1% and the mode was 83.9%.
The chapter ten test (see Appendix L) was the second chapter test on which I allowed
hints. It was my hope that students would be more comfortable with asking questions this time
around. Again, I observed the biggest reason for requesting a hint was to ask for a formula. The
amount of hints asked increased to twenty-one, but this still seemed low in comparison to how
many students struggled on the test.
Table 5
Chapter 10 Survey Results After Using Hints (n = 27)
Item
SD
D
N
A
If felt less stressed because I could ask for a 11% 26% 37% 26%
hint on the test.
SA
0%
M
2.78
SD
0.97
15% 33% 30% 15%
7%
2.67
1.14
I felt comfortable asking for a hint on the
test.
7% 22% 30% 33%
4%
3.04
1.04
I used less hints than I should have.
7% 22% 33% 26% 11%
3.11
1.12
I was reluctant to ask for a hint because I
did not want to lose any points on the test.
4% 22% 15% 37% 19%
3.46
1.17
2.66
1.08
I studied less because I knew I could ask for
hints on the test.
I studied enough to do well on this test.
15% 33% 41% 11%
7%
Note. SD = Strongly Disagree, D = Disagree, N = No Opinion, A = Agree, SA = Strongly Agree, M = Mean, SD =
Standard Deviation
While this survey indicated the chapter ten test caused less stress than the previous test
(see Table 5), it still did not have the desired effect of reducing stress for many students. As
29
Figure 5 demonstrates, it was also evident that several students were still reluctant to give up
points in exchange for hints on this test. The mean score for the chapter ten tests was 71.7%,
which was by far the lowest average of all the test scores. The median was even lower at 71.5%.
The standard deviation was 13.2% and modes for the test were 56.1% and 78.9%. I observed as
an instructor that the students had less background in the content of chapter ten than other
chapters. This hurdle along with the ineffectiveness of the hints explains in part the lower test
scores for this chapter.
I was reluctant to ask for a hint because I
did not want to lose any points on the test.
Strongly Disagree
Disagree
No Opinion
Agree
Strongly Agree
Figure 5. Student response to a question on the chapter ten post-test survey using hints. Even
after on the second test using hints, over half of my students did not want to trade the cost of a
single point for a hint on the test. This was a major problem in using this type of alternative
assessment technique.
Table 6 shows the results of the first four questions that were kept consistent on each
survey. I asked these questions to determine if using cheat sheets and hints would change student
30
sentiment toward math and testing as the project went along. Students were given only four
possible answers to these questions so they had to make a decision one way or the other.
Table 6
Comparison of Student Sentiment for each Survey
Chapter
8
(Cheat
Sheets)
2.48
Chapter
9
Chapter
10
PreSurvey
2.61
Chapter
7
(Cheat
Sheets)
2.24
(Hints)
2.19
(Hints)
2.37
I like math class.
2.68
2.31
2.78
2.63
2.48
I worry before taking all tests.
2.39
2.34
2.44
2.52
2.41
I worry before taking math tests.
2.68
2.62
2.81
2.74
2.70
Number of students questioned:
28.00
29.00
27.00
27.00
27.00
76.7%
82.2%
78.6%
71.7%
Item
I like math.
Average test grade:
Note. 1 = Strongly Disagree, 2 = Disagree, 3 = Agree, 4 = Strongly Agree
As can be expected, the students liked math more when their grades were better. What
did not correlate was how much worry students experienced in comparison to their average
scores. Student worry decreased from chapter eight to chapter ten, even though their grades were
getting worse. An explanation for this may be that as students worried less about their tests their
performance decreased as a result.
Interpretation of Results
The results of my project indicate there was a connection between using cheat sheets and
a reduction in anxiety on math tests. Not only were they an excellent study tool, but they
provided a safety net to those students who had difficulty remember formulas.
It could be argued that cheat sheets decrease the rigor of tests in the classroom, but I also
found that students could concentrate more on understanding the concepts in the chapter. This
means more rigorous, high level problems can be asked of students on tests, instead of asking
questions that are sheer feats of memory.
31
Hints were shown to be ineffective in reducing anxiety. It was my hope that the use of
cheat sheets in previous chapters would lead students to this technique of studying, and I could
fill in the gaps with the use of hints. My idea was the combination of the two would lead to even
less anxiety. To the contrary, hints did little to reduce test anxiety according to the results of the
surveys.
Unfortunately, by aiding the students in making cheat sheets during class, I think the
students learned they did not need to study on their own as much. The studying done by making
the cheat sheets in class was gone on the next test, but the students did not take up the slack by
studying on their own time. The students who needed to study, but lacked the motivation to do so
on their own, struggled on the tests using hints. When it came time to take the test the students
were anxious, and now it was going to cost them a point to get a hint, whereas previously they
could refer back to their cheat sheet without penalty. Some or all of these factors could have
contributed to the lack of success with hints. Without a control group, it is difficult to say if the
tests using hints caused more or less anxiety than tests using no hints at all.
Summary
Cheat sheets were successful in reducing anxiety for many of my Geometry students as
indicated by the results of the surveys and student comments. Hints were much less successful. It
is uncertain if the success of the first affected the lack of success in the second directly, but it is a
possibility. In the next chapter, I conclude my project and proceed to make suggestions and
recommendations from my observations.
Chapter Five
Conclusions, Action Plan, Reflections, and Recommendations
Conclusions
The two methods of alleviating math test anxiety used in my study had very different
outcomes. Using cheat sheets did seem to lessen anxieties in my students during those tests.
They were especially effective when the students were given some direction on the creation of
their cheat sheets. Giving hints in exchange for a one point deduction did not seem to lessen
anxiety in most of my students. This finding was reflected in both the survey results and
collective sentiment of the comments given by the students on the surveys.
It seems clear that cheat sheets lessened the worry of forgetting test materials for my
students. This was shown by the results of the surveys as well as the less anxious demeanor of
the students I observed before and during the test. While the cheat sheets reduced worry, I do not
think cheat sheets made it easier for the students. Cheat sheets do not take the place of homework
and studying, which was evident when eight of the twenty-nine students in the study failed the
chapter seven test, an abnormally large percentage for my Geometry students.
Secondarily, I think it was evident that many Geometry students lack the know-how to
study for math tests properly, and cheat sheets are one way of teaching this skill. This idea was
reinforced by responses to the surveys. One student comment from the chapter eight surveys hit
it on the head: “What really helped was making the cheat sheet, because writing it down so many
times was like studying.”
Hints proved unsuccessful in alleviating test anxiety in my Geometry students. I do think
with some practice and refinement this method could be an effective way of giving a “jump
start” to those students that draw a blank due to anxiety. This conclusion comes from the fact that
33
more than half of those who asked for a hint got the question correct after getting the hint. Many
of the hints involved giving a formula needed to answer the question. The students still needed to
know how to use the formula to get the correct answer. On the other hand, hints were not helpful
to those students who had no conceptual understanding of the problem, and so they still got the
question wrong. In conclusion, the rigor of a question is maintained as long as the hint given aids
the student only in one specific part of the problem.
Action Plan
In the future, I do plan on using cheat sheets again, especially when the emphasis of the
test is more on problem solving skills and less on the memorization of formulas. When I do, I
will definitely assist my students in the design of the cheat sheet on the first assessment or two to
help students get an idea of the types and amount of information to put on the cheat sheet.
Eventually I will hand the creation of the cheat sheets over entirely to the students when I use
them, as this will allow them to be creative and give them the responsibility of making their own
sheet.
I will continue to use hints selectively as well. They will be useful as an aid for those
students who have trouble starting a problem. Hints may be especially effective in upper level
high school math classes, where a question worth ten points can make or break a test grade. A
simple hint that allows the student to find the correct solution for most of the ten points is a more
accurate assessment of the student’s ability than if they lose all of those points because they
forgot one formula. As stated before, if they did not understand the concept, hints did not help.
Reflections and Recommendations for Teachers
Overall I think the study was a positive experience; I took several good things from it. I
will continue to refine and use these practices in the future. I would modify a few parts of the
34
study if given the chance to do so. First and foremost, I would give my students instructions on
creating cheat sheets the first time I used them in class. This guidance gives the students a feel
for what they need to put on a cheat sheet. It also gives the students some formal instruction in
taking notes, which is a skill in which many of my students were lacking. I found that even
students that previously would not bother to take out a pencil for notes made a cheat sheet when
given some class time, instructions, and a few points for their work. While some will argue these
tasks should be left to the student, I feel this approach was more productive for a difficult student
than staring blindly into space.
An issue I would warn against is using cheat sheets and hints together. This problem was
evident immediately; after earning points for creating a cheat sheet on the first two tests, I then
allowed them no sheet on the second two tests and told them it would cost them a point for a
hint. My intention was for hints to ease the transition out of using cheat sheets, but instead it was
like yanking the rug out from under their feet. This was definitely a case where principle and
practice did not align.
Ultimately, I found cheat sheets and hints are two different ways to lessen the impact of
anxiety on test scores. Cheat sheets help students study for a test and give them something to fall
back on should they get anxious. Hints do little to lessen the anxiety before and during a test, but
they allow a lifeline should their memory fail them due to worry or other distraction. A hint is
like helping place one key piece of a puzzle that leads to the eventual completion of the entire
picture. Both methods have their merits and pitfalls that must be addressed.
While the methods described and implemented in this project may be used in other
disciplines as well as mathematics, there are some obvious places cheat sheets and hints would
not work. Any assessment on terms, definitions, formulas, etc. that the student could simply copy
35
from a cheat sheet to the test would defeat the purpose of that examination. I think the same
could be said for giving hints during this type of assessment. There are instances when reciting
from memory is very important and no aid should be given. For example, if the purpose of an
exam in an Anatomy class is to assess the identification and naming of all 206 bones in the adult
human body, cheat sheets and hints will not work. This would be equivalent to my orthopedic
surgeon constantly looking at a chart to tell me the names of the muscles, bones, and tendons on
which he is going to operate, and I would prefer he did not have this preoccupation.
I believe tests allowing a cheat sheet more realistically reflect problem solving in real
world situations. If one is posed with a problem in a profession, it is often a person’s
resourcefulness in conjunction with their knowledge of content that leads to a solution. For
example, a licensed automotive mechanic can use references for parts and specifications of every
type of vehicle they encounter to supplement their understanding of how automobiles work.
Reference material is used because there is so much to memorize otherwise, and this
memorization is unnecessary. Even engineers taking the professional engineering exam are
allowed to bring in books and notes to use on the test. Tests that require students to perform
strictly from memory in many cases do not model tasks outside of school.
Summary
In closing, I have learned much about the use of alternative assessment techniques and
test anxiety. Cheat sheets and hints can be valuable tools for the classroom teacher, but they take
work to perfect and modification to specific teaching and testing styles. When used properly,
they both allow more accurate assessment of higher order thinking skills for those students who
experience anxiety on math tests. Cheat sheets can also be used to teach note taking skills and
stimulate the under motivated student who may be otherwise indifferent to properly preparing for
36
a test. While there are some instances where they are not appropriate, both cheat sheets and hints
can be useful tools to improve student success.
37
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Ioannou, A., & Artino, J. R. (2010). Learn more, stress less: Exploring the benefits of
collaborative assessment. College Student Journal, 44(1), 189-199.
Kesici, S., & Erdogan, A. (2009). Predicting college students’ mathematics anxiety by
motivational beliefs and self-regulated learning strategies. College Student Journal,
43(2), 631-642.
Miejer, J. (2001). Learning potential and anxious tendency: Test anxiety as a bias factor in
educational testing. Anxiety, Stress & Coping, 14(3), 337.
Parks-Stamm, E. J., Gollwitzer, P. M., & Oettingen, G. (2010). Implementation intentions and
test anxiety: Shielding academic performance from distraction. Learning & Individual
Differences, 20(1), 30-33. doi:10.1016/j.lindif.2009.09.001
Putwain, D. W. (2007). Test anxiety in UK schoolchildren: Prevalence and demographic
patterns. British Journal of Educational Psychology, 77(3), 579-593.
doi:10.1348/000709906X161704
Putwain, D. W., & Roberts, C. M. (2009). The development of an instrument to measure
teachers’ use of fear appeals in the GCSE classroom. British Journal of Educational
Psychology, 79(4), 643-661.
39
Putwain, D., & Symes, W. (2011). Perceived fear appeals and examination performance:
Facilitating or debilitating outcomes? Learning & Individual Differences, 21(2), 227-232.
doi:10.1016/j.lindif.2010.11.022
Rachal, K., Daigle, S., & Rachal, W. (2007). Learning problems reported by college students:
Are they using learning strategies? Journal of Instructional Psychology, 34(4), 191-199.
Rodger, S., Murray, H. G., & Cummings, A. L. (2007). Effects of teacher clarity and student
anxiety on student outcomes. Teaching in Higher Education, 12(1), 91-104.
doi:10.1080/13562510601102255
Skidmore, R. L., & Aagaard, L. (2004). The relationship between testing condition and student
test scores. Journal of Instructional Psychology, 31(4), 304-313.
Veenman, M. J., Kerseboom, L., & Imthorn, C. (2000). Test anxiety and metacongitive
skillfulness: Availability versus production deficiencies. Anxiety, Stress & Coping, 13(4),
391.
Vinson, B. (2001). A comparison of preservice teachers’ mathematics anxiety before and after a
methods class emphasizing manipulatives. Early Childhood Education Journal, 29(2),
89-94.
Walker, C. E. (1975). Learn to relax. Englewood Cliffs, NJ: Prentice-Hall.
Woodard, T. (2004). The effects of math anxiety on post-secondary developmental students as
related to achievement, gender, and age. Inquiry, 9(1). Retrieved from
http://www.eric.ed.gov/PDFS/EJ876845.pdf
Wigfield, A., & Meece, J. (1988). Math anxiety in elementary and secondary school students.
Journal of Educational Psychology, 80(2), 210-216.
Appendices
41
Appendix A
Cheat Sheet Requirements
Geometry
Mr. Dennis
Cheat Sheet Requirements
Students:
For the next two tests, you will be required to make a cheat sheet to use during the test.
The requirements for the cheat sheet will be:
1) The cheat sheet will be of paper with maximum dimensions of 8.5 by 11 inches. One or
both of the dimensions may be smaller.
2) You many only use one side of the sheet. The other side of the sheet must only have your
name on it.
3) The cheat sheet must be hand written. Use of a straightedge, protractor, compass, etc.
may be used for hand drawn illustrations, but no pictures or computer graphics are
allowed.
4) A completion grade of ten homework points will be awarded for making the cheat sheet,
which must be produced at the beginning of class the day before the test. The sheets will
then be copied and returned to you before the end of class.
5) Should a cheat sheet be deemed unacceptable by violating any of rules 1-3 when
collected the day before the test, you will be allow to fix it. If the cheat sheet still in
violation the day of the test, it cannot be used for the test.
6) The original cheat sheet will be handed in along with the test. Your grade will be out of
ten completion points based on the copied version.
7) You are allowed to add to your cheat sheet after it has been copied. If nothing new has
been added to your crib sheet, you will be awarded two bonus points which will be added
to your completion grade.
42
Appendix B
Geometry Preliminary Survey
Geometry Preliminary Survey
Name________________________
Please circle the number that best represents your response to each question.
Question:
Strongly
Disagree Disagree
Agree
Strongly
Agree
1. I like math.
1
2
3
4
2. I like math class.
1
2
3
4
3. I worry before taking all tests.
1
2
3
4
4. I worry before taking math tests.
1
2
3
4
Question:
Strongly
Disagree
No
Opinion
Strongly
Agree
5. I draw a blank on questions during
math tests.
1
2
3
4
5
6. I feel I could do better on math
tests if I had something to jog
my memory.
1
2
3
4
5
7. I struggle trying to memorize
information needed for math
tests (formulas, definitions, etc.)
1
2
3
4
5
8. I know how to study for math
tests.
1
2
3
4
5
9. I study enough to do achieve
the grade I want on math tests.
1
2
3
4
5
43
Appendix C
Geometry Post Test Survey: Cheat Sheets
Geometry Post Test Survey (after using cheat sheets)
Name_________________________
After reflecting on the test, please circle the number that best represents your response to each question.
Strongly
Disagree
Disagree
Agree
Strongly
Agree
10. I like math.
1
2
3
4
11. I like math class.
1
2
3
4
12. I worry before taking all tests.
1
2
3
4
13. I worry before taking math tests.
1
2
3
4
Question:
Question:
Strongly
Disagree
No
Opinion
Strongly
Agree
14. I felt less stressed before this test
because I knew I could use the
cheat sheet.
1
2
3
4
5
15. I felt less stressed during the test
because of the cheat sheet.
1
2
3
4
5
16. I did better on the test than if I
had not used a cheat sheet.
1
2
3
4
5
17. I could concentrate more on
understanding concepts because
I didn’t worry about memorizing.
1
2
3
4
5
18. I studied enough to do achieve
the grade I wanted on this test.
1
2
3
4
5
19. Making a cheat sheet was more
work than it was worth.
1
2
3
4
5
20. I did not need to use the cheat
sheet as much as I thought I
would.
1
2
3
4
5
Additional comments/ideas:
44
Appendix D
Geometry Post Test Survey: Hints
Geometry Post Test Survey (after using hints)
Name________________________
After reflecting on the test, please circle the number that best represents your response to each
question.
Question:
Strongly
Disagree Disagree
Agree
Strongly
Agree
1. I like math.
1
2
3
4
2. I like math class.
1
2
3
4
3. I worry before taking all tests.
1
2
3
4
4. I worry before taking math tests.
1
2
3
4
Question:
Strongly
Disagree
No
Opinion
Strongly
Agree
5. I felt less stressed because I
could ask for a hint on the test.
1
2
3
4
5
6. I studied less because I knew
I could ask for hints on the test.
1
2
3
4
5
7. I felt comfortable asking for a
hint on the test.
1
2
3
4
5
8. I used less hints than I should
have.
1
2
3
4
5
9. I was reluctant to ask for a hint
because I did not want to lose
any points on the test.
1
2
3
4
5
10. I studied enough to do well
on this test.
1
2
3
4
5
Additional comments:
45
Appendix E
IRB Approval Form
46
Appendix F
Principal Consent Form
I. Research Background (to be completed by researcher)
Title of the Study: Using Alternative Assessment Methods to Alleviate Math Test Anxiety
Name of Researcher: Bradley Dennis
Street address: 644 Meadow Lane
Phone: (701) 290-1288
City: Bismarck, North Dakota Zip: 58504
E-mail: brad_dennis@bismarckschools.org
II. Description of Research Proposal
The purpose of this action research project is to determine if using cheat sheets and hints will
decrease test anxiety on math tests. Cheat sheets will be used for the first two Geometry tests of
the semester, while hints will be used on the third and fourth Geometry tests of the semester.
Surveys will be given after each test is returned to the students to obtain student sentiment for
each type of alternative assessment.
III. Agreement (to be completed by principal)
I, ___________________________, principal of ____________________school, understand





the study and what it requires of the staff, students, and/or parents in my school,
that the privacy and confidentiality of any staff or student will be protected,
that I have the right to allow or reject this research study to take place at my school,
that I have the right to terminate the research study at any time,
that I have the right to review all consent forms and research documents at any time during
the study until project is completed and defended.
 I grant permission to the researcher to conduct the above named research in my school as
described in the proposal.
 I DO NOT grant permission to the researcher to conduct the above named research in my
school as described in the proposal.
 I understand that data should be released only by the departments that own them. My staff
and I shall not release data to the researcher without approval from the IRB.
Signature of Principal: _______________________________________
Ken Erickson, Principal, Bismarck High School
Date: _________________
47
Appendix G
Research Participant Assent Form
Invitation to Participate
You are invited to participate in a classroom study! The purpose of this study is to determine if changing how I
administer tests will decrease test anxiety. I, Bradley Dennis, will be conducting this study in all of my Geometry
classes at Bismarck High School. Mr. Ken Erickson, principal of Bismarck High School, has approved this research
study.
Basis for Selection
You have been selected because you are a Geometry student in one of my classes. In using students from both
classes, I hope to collect enough data to come to a conclusion on the effects of using cheat sheets and hints to reduce
math test anxiety. Cheat sheets and hints are described later in this document.
Purpose of the Research
The purpose of this research is to help determine if changing how I administer tests will decrease test anxiety for my
students. My main goal is to more accurately assess students’ knowledge without the distractions of heightened
anxiety. My findings may be beneficial for myself and other mathematics teachers. This study is one of the final
steps toward the completion of my Masters of Arts in Teaching: Mathematics degree through Minot State
University.
Explanation of Procedures
If you decide to participate, you will be asked to do the following:
1.
2.
3.
4.
Participate in a preliminary survey asking you general questions about taking tests and math.
You will be required to create a cheat sheet to use on the first two Geometry tests of the second semester of
the 2011-2012 school year.
You will take tests using hints for the third and fourth tests of the semester.
After each of these tests is returned to you, you will be asked to take another survey reflecting on your
feelings about the test.
Additionally, the researcher will be keeping a journal to document observed anxieties in the classroom.
The identity of all participants will remain confidential. Students will not be identified in the research report. All
research and observations will be done in the classroom.
Duration of Participation
You will participate in approximately a twelve week collection of test and survey data. I will record scores and other
data from student tests. I will collect data from each survey to find out if either cheat sheets or using hints have an
effect on test anxiety.
Benefits to the Individual
Cheat sheets allow students to write down material that normally must be committed to memory. Not only does this
help students study for a test, it allows more efficient use of time and brain power to concentrate more on learning
higher order skills, such as understanding concepts and problem solving. Such abilities reflect a higher level of
learning than memorization.
48
Hints are a type of dynamic assessment designed to help students who forget on tests due to test anxiety. If
prompted, I plan on giving you a predetermined hint to the troubling question during the test. This hint will give you
a better chance of finding the correct answer, in exchange for losing one point. This allows you, the student, a better
chance of answering questions correctly and therefore a chance for a better grade. It also reduces the anxiety
associated by students with the tendency to freeze up during test. It is your right to ask for as many hints as you
would like during the test, or ask for no hints at all.
Another potential benefit for both of these assessment techniques is increased test scores. Studies have shown there
is more working memory available to use during a test if test anxiety is diminished. More working memory will
hopefully allow you, the test taker, to think clearer and be better able to answer questions on the test.
Alternatives to Participation/Withdrawal from Study
If you decide not to participate, you will still take all of the tests. Your participation in this study is voluntary, and
choosing not to participate in this study will not affect your grade in any way. You will not complete any surveys,
and you will take all tests as they are normally administered. Cheat sheets using the same criteria as the participants
will be allowed for nonparticipants to maintain fairness in grading. The grades of students who choose not to
participate will not be used in the research. If you decide to participate in this study, you may withdraw at any time
during the study by contacting me.
Assurance of Confidentiality
All data will be treated confidentially by the researcher. Names of participants and their data sets will be kept in a
locked file cabinet in the researcher’s office and on a password-protected computer and will be destroyed once the
paper has been defended and approved. The researcher agrees to maintain strict confidentiality which means your
name will not be discussed or divulged with anyone outside of this research project. The researcher will also make
sure confidential information will not be discussed in an area that can be overheard that would allow an
unauthorized person to associate or identify the student with such information.
Offer to Answer Questions
If you have any questions or concerns during the study, feel free to contact me at 701-323-4800 ext. 6112 or email
me at brad_dennis@bismarckschools.org. If you have questions about the right of research subjects, contact the
Chairperson of the MSU Institutional Review Board (IRB), Dr. Vicki Michels at 701-858-3594 or
Vicki.Michels@minotstatu.edu.
Thank you for your consideration.
Participant Assent:
You are voluntarily making a decision whether or not to participate. You signature indicates that, having
read and understood the information provided above, you have decided to participate. You will be given a
copy of this assent form to keep.
 Yes, I approve.
No, I do not approve.
__________________________________________
Participant (Please Print Your Name above)
___________________________________________Date________________
Signature of Participant
___________________________________________Date________________
Signature of Researcher
49
Appendix H
Parent/Guardian Research Consent Form
Invitation to Participate
Your child is invited to participate in a study to determine if changing how I administer tests will decrease test
anxiety. I, Bradley Dennis, will be conducting this study in all of my Geometry classes at Bismarck High School.
Mr. Ken Erickson, principal of Bismarck High School, has approved of this research study.
Basis for Selection
Your child has been selected because he/she is a Geometry student in my class. In using students from both classes,
I hope to collect enough data to come to a conclusion on the effects of using cheat sheets and hints to reduce math
test anxiety. Cheat sheets and hints are described later in this document.
Purpose of the Research
The purpose of this research is to help determine if changing how I administer tests will decrease test anxiety for my
students. My main goal is to more accurately assess students’ knowledge without the distractions of heightened
anxiety. My findings may be beneficial for myself and other teachers. This study is one of the final steps toward the
completion of my Masters of Arts in Teaching: Mathematics degree through Minot State University.
Explanation of Procedures
If you decide to allow your child to participate, your child will be asked to do the following:
1.
2.
3.
4.
Participate in a preliminary survey asking you general questions about taking tests and math.
Your child will be required to create a cheat sheet to use on the first two Geometry tests of the second
semester of the 2011-2012 school year.
Your child will take tests using hints for the third and fourth tests of the semester.
After each of these tests is returned to your child, they will take another survey reflecting on their feelings
about the test.
Additionally, the researcher will be keeping a journal to document observed anxieties in the classroom.
The identity of all participants will remain confidential. Students will not be identified in the research report. All
research and observations will be done in the classroom.
Duration of Participation
Your child will participate in approximately a twelve week collection of test and survey data. I will record scores
and other data from student tests. I will collect data from each survey to find out if either cheat sheets or hints have
an effect on test anxiety.
Benefits to the Individual
Cheat sheets allow students to write down material that normally must be committed to memory. Not only does this
help students study for a test, it allows more efficient use of time and brain power to concentrate more on learning
and understanding concepts. This reflects a higher level of learning than memorization.
Hints are a type of dynamic assessment designed to help students who forget on tests due to test anxiety. When
prompted, I plan on giving predetermined hints during the test. In exchange for losing one point, students will
receive a hint that gives them a better chance of finding the correct answer. This allows the student a better chance
50
of answering questions correctly. It also reduces the anxiety associated by students with the tendency to freeze up
during test.
Another potential benefit for both of these assessment techniques is increased test scores. Studies have shown there
is more working memory available to use during a test if test anxiety is diminished. More working memory will
hopefully allow your child, the test taker, to think clearer and be better able to answer questions on the test.
Alternatives to Participation/Withdrawal from Study
If you decide to not allow your child to participate, he/she will still take all of the tests. Your child’s participation in
this study is voluntary, and choosing not to participate in this study will not affect his/her grade in any way. They
will not complete any surveys, and they will take all tests as they are normally administered. Cheat sheets using the
same criteria as the participants will be allowed for nonparticipants to maintain fairness in grading. The grades of
students who choose not to participate will not be used in the research. If you decide to allow the participation of
your child in this study, you may withdraw at any time during the study by contacting me at 701-322-4800 ext. 6112
or at brad_dennis@bismarckschools.org.
Assurance of Confidentiality
All data will be treated confidentially by the researcher. Names of participants and their data sets will be kept in a
locked file cabinet in the researcher’s office and on a password-protected computer and will be destroyed once the
paper has been defended and approved. The researcher agrees to maintain strict confidentiality which means your
student’s name will not be discussed or divulged with anyone outside of this research project. The researcher will
also make sure confidential information will not be discussed in an area that can be overheard that would allow an
unauthorized person to associate or identify the student with such information.
Offer to Answer Questions
If you have any questions or concerns during the study, feel free to contact me at 701-323-4800 ext. 6112 or email
me at brad_dennis@bismarckschools.org. If you have questions about the right of research subjects, contact the
Chairperson of the MSU Institutional Review Board (IRB), Dr. Vicki Michels at 701-858-3594 or
Vicki.Michels@minotstatu.edu.
Thank you for your consideration.
Guardian Consent
You are voluntarily making a decision whether or not to allow your child or legal ward to participate. You
signature indicates that, having read and understood the information provided above, you have decided to
permit your child or legal ward to participate. You will be given a copy of this consent form to keep.
 Yes, I approve.
No, I do not approve.
__________________________________________
Participant (please print student name)
___________________________________________Date________________
Signature of Parent or Guardian
___________________________________________Date________________
Signature of Researcher
51
Appendix I
Chapter Seven Test
52
53
54
55
Appendix J
Chapter Eight Test
56
57
58
59
Appendix K
Chapter Nine Test
60
61
62
63
64
Appendix L
Chapter Ten Test
65
66
67