Countdown to Math Anxiety
Scott
Bradley Gerhardt
Oregon
State University
Author Note
Scott Bradley Gerhardt, Department of Psychology, Oregon State
University
Correspondence to this article should be
sent to Scott Gerhardt, Department of Psychology, Oregon State University,
Corvallis, Oregon, 97331. E-mail: gerhards@onid.orst.edu
Abstract
There
exist multi-national concerns about levels of competency in mathematical knowledge gained by pupils in schools; inevitably the spotlight has fallen on
teachers, yet some children react as if wired by nature against mathematics and
for math anxiety (Ashcraft, 2002). This
research investigated the potential relationship (based on behavioral
psychology’s principles of operant conditioning (Skinner, 1938; 1953),
conditioned responses (Pavlov, 1927), and stimulus generalization (Watson,
1920)) between math anxiety and those whose parents issued a countdown
procedure to extinguish unwanted behavior.
The sample population included 49 male respondents, 45 female
respondents, and one participant who did not respond at all. The average age
was 29.8. The hypothesis tested was that
a parental countdown procedure primed and conditioned people for math
anxiety. Of the 52 people who did report
receiving a countdown procedure as a behavior extinguishment technique, 29, or
55.8%, also reported math anxiety. Of
the 43 people who did not report receiving a countdown procedure as a behavior
extinguishment technique two, or 4.65%, also reported math anxiety. The self report inventories were distributed
via the internet’s multiplicity of channels that is online links.
Countdown to Math Anxiety
Many economic, sociological,
cultural, and psychological theories have been postulated to try and assist
educators in motivating, empowering, and emboldening students, and advancing
pedagogy (Freire, 1968). Theories of classical (Pavlov, 1927), operant
(Skinner, 1953), and respondent (Pear & Eldridge, 1984) conditioning are
not new ideas; the three ideas evolved through psychological behavioral science
in that order. STEM, Science Technology Engineering and Mathematics, are
abstractions that share many commonalities, mathematics being one of the core
issues restraining many otherwise intelligent people from meeting their life
goals. At first the connection between
behaviorism and mathematics is not clear, until teaching and learning are added
to the paradigm of their relationship.
Mathematics and intelligence are helpful
and necessary in logic, reasoning, problem-solving, and computation inherent in
modern scientific endeavors. Fear and
anxiety responses tend to mask and inhibit implementation of metacognitive
processes necessary to elucidate solutions (Legg & Locke, 2009). Anxiety is
a common experience and a reaction to a stimulus. From Pavlov’s dogs (1927), to
Watson’s Little Albert, to Skinner’s operant conditioning (1938; 1953), thru
respondent conditioning (Pear & Eldridge, 1984), the dynamic mechanical
nature of behaviorism is a clear causational function deterministically fusing
stimuli and response forward through time; uniquely similar to reciprocal
determinism (Bandura, 1986).
Anxiety is a common experience and can be a reaction to a stimulus. From Pavlov’s dogs to Watson’s Little Albert
to Skinner’s operant conditioning to respondent conditioning the dynamic
mechanical nature of behaviorism is a clear causational function
deterministically fusing stimuli and response through time forward. The experiment examined the practical applications
of conditioning by exploring if any correlation exists between categorical
variables defined as individuals who self report math anxiety and as
individuals having experienced counting as an extinction technique implemented
by an authority figure as a child.
Behaviorism
The terms classical conditioning termed by Nobel Prize winning scientist Ivan Pavlov (1927) who happened upon
conditioning quite by accident while studying salivary glands and their role in
breaking down food via digestion for absorption into the blood. Pavlov (1927) began by observing: “I started
to record all the eternal stimuli falling on the animal at the time its reflex
reaction was manifested… at the same time recording all changes in the reaction
of the animal.” At first, the only reaction was the ordinary salivary reflex.
When an experimenter put food into a dog’s mouth, it salivated. But after a while, the animal would salivate
before receiving food. By observing the
“external stimuli falling on the animal,” Pavlov was able to see what triggered
these secretions. Pavlov noticed that
the smell or sight of food elicited secretions. Pavlov (1927) concluded two distinct reflexes:
the inborn, unconditional reflexes and the acquired conditional reflex. This is important in defining the variable of
a countdown procedure, and its recalled presence.
The Little Albert case study experiment (Watson, 1920) illustrated the
empirical evidence of classical conditioning in humans. The same study proved to be exemplary for
stimulus generalization. John B. Watson
(1920), after observing kids at play, was prompted to investigate the
relationship of loud noises and fear. He
set out to prove that classical conditioning could condition a human child to
respond with anxiety and fear to an otherwise benign stimulus. The study proved successful much to Albert’s
loss. This research endeavors to examine
a similar relationship between a “countdown” trigger presented to children as a
way to elicit extinction of an undesirable behavior by authority that later
manifests as ‘math anxiety’. The generalization of the countdown stimulus
can be different for each and every individual participant. If behaviorism is the path, (for the
hypothesis investigated) the beginning is the countdown and the destination is
the math anxiety. The paths are
different for everyone as they chose their response, which in turn determines
the next stimuli. This research did not
investigate individual pathways; rather it searched for those who had completed
a journey.
The term operant conditioning was termed by
B.F. Skinner. Skinner (1938; 1953) identified four operant procedures,
two that strengthen behavior, (positive and negative reinforcement) and two
that weaken behavior, (positive and negative punishment) juxtaposed and
orthogonally arranged in a 2X2 matrix just like the data in table 1 collected
from this research.
Punishment, the
procedure of providing consequences for a behavior that reduces the frequency
of that behavior (Skinner, 1953). Applying
behaviorism to pedagogy Catania (1998) proved a procedure must have three
characteristics to qualify as punishment, the procedure must have a
consequence, a decrease in strength (occur less often) and the latter must be a
function of the prior; which is to say it is iterative. The punishment and its consequences are often
referred to as punishers. Catania's fourth edition
of Learning (1998) is a comprehensive and authoritative account of
learning from a behavioral perspective. Bridging the separate literatures on
animal learning and basic behavioral processes with research on human language,
cognition, and memory, Catania
employs an internally consistent approach to reasoning that convincingly
illustrates that even the most complex types of human learning can be addressed
from a radical behavioral approach. Relevant topics include equivalence classes
for responses and stimuli, conditioned reinforcement, relational frame theory
(the emergence of higher order, generalized classes of symbolic behavior),
remembering early childhood events, applications of differential reinforcement,
and selection of the capacity to learn. This
applies to the ‘countdown’ as negative reinforcement of the anxiety felt while
experiencing the disapproval of authority, and its latter association with math
anxiety. Reinforcement is the procedure
of providing consequences for a behavior that increase or maintains the rate of
afore mentioned behavior. The positive
reinforcement is the response followed by the appearance of, or an increase in
the intensity of, a stimulus. This
stimulus, called a positive reinforcer, is ordinarily something the organism
seeks. Skinner (1953) later noted “the
only defining characteristic of a reinforcing stimulus is that it reinforces”. This is to say, a reinforcer is defined by its
effect on the behavior it follows. With negative reinforcement, a response is
strengthened by the removal of, or a decrease in the intensity of, a
stimulus. This stimulus, called a
negative reinforcer, is generally that which an organism is averse to; similar
to punishment, yet different. This
continued elucidation of possible pathways does not delineate individual pathways;
it merely aims to determine if further investigation is warranted.
Conditioned
reinforcers, or secondary reinforcers, are those who acquire their power by
having been paired with other reinforcers (Skinner, 1953). An example is provided by Zimmerman (1957),
who sounded a buzzer for two seconds before giving thirsty rats water. After the buzzer and water had been paired in
this way several times, Zimmerman put a lever into the rat’s chamber. Each time the rat pressed the lever, the
buzzer sounded. The rat soon learned to
press the lever, even when lever pressing never produced water as the buzzer
had become a conditioned reinforcer. A secondary reinforcer, punishment, or
conditioned reflex is those reinforcers that are dependent on their association
with other reinforcers or punishments (Zimmerman, 1957). This research aims to explore the possibility
that an acquired conditional reflex exists as a “countdown” stimulus first
presented in youth as a behavior extinguishment technique implemented by
authority that leads to math anxiety later in life. Specifically this would occur in a natural
treatment throughout the lifespan of the participant through various
institutional settings, following and temporally coinciding with the countdown
administration in youth.
Reciprocal
Determinism is the idea that
behavior is determined and/or controlled by individual cognitive processes, and
by environment through external social stimulus events. Its basis transforms individual behavior by
allowing subjective thought processes transparency as contrasted with
cognitive, environmental and external social stimulus events similar to experiencing
a countdown procedure to extinguish unwanted behavior. The specific instance manifests the
transformation in individuals as math anxiety, hardly a desired effect. The theory set forth by Albert Bandura
postulates that individual behavior can be conditioned through awareness of
consequences, which impact the environment to impact ego and the recursive
stimulus response chain containing the ego, within the environment and external
social stimulus. Such that a person’s
behavior, once influenced, continues to be self-reinforced by behavior that
both influences and is influenced by personal factors, relational frame theory,
and the social environment. This is also
evident in Catania’s
selection of the capacity to learn as individuals pursue passions, not what
individuals have been aversively conditioned against. Actions do not have direction as affected by
repercussions; rather behavior is complicated and cannot be limited to
environmental and individual means. This
behavioral phenomenon consists of environmental and individual elements woven
together in function and to function; exemplified in this research as the
different and varied cognitive behavioral paths that gathered people with math
anxiety in one place, and people without math anxiety in another.
The
present study was conducted to examine the relationship between the use of a
countdown procedure in childhood, as a way to decrease undesirable behavior,
and math anxiety. The hypothesis for
this study was developed based on the theories of conditioning (classical,
operant and operant-respondent), stimulus generalization (Watson, 1920), and
reciprocal determinism (Bandura, 1986).
Hypothesis 1: If a participant self reports on the inventory that they
remember an authority figure using a countdown procedure to extinguish
undesirable behaviors in their childhood; they will be more likely to also self
report having math anxiety than those participants that do not self report
remembering the use of a countdown procedure in childhood. The research’s initial premise was based on
behavioral psychologies principles of operant conditioning and stimulus
generalization; operant conditioning was measured as and represented by a
higher incidence of math anxiety in the population of people who had been exposed
to a generalize-able stimulus identified as a parental or authoritative issued
countdown procedure implemented to extinguish unwanted behavior during the
individuals in the sample population’s youth, as self reported by the
individual participants of the study.
Method
This experiment examined
practical applications of conditioning via exploration of relationships that
exist between categorical variables defined as individuals who self report math
anxiety and as individuals having experienced mathematically related extinction
techniques implemented by an authority figure as a child. The study included what
has classically been referred to as deception by misleading with relationships
of world view, life experience, and upbringing. This was done to mitigate false
memories prompted by the self inventory due to negative or positive
consequences inherent in the recall algorithm of replying to the self report by
balancing negative, neutral and positive stimuli of the inventory, thereby
burying the true goal/data within neutral and random yet relative concepts. There was deception present in the
informed consent and dissemination material so as to avoid any internal and
external validity issues that may arise. Studies on how negative emotion cause
false memories were used to account for memory processes that are measured in
the conjoint recognition paradigm (Brainerd, Stein, Silveria, Rohenkohl, &
Reyna, 2008). False memory was
operationalized as recollection rejection, phantom recollection, false acceptance
of similarity judgment and response bias.
While true memory was recognized by identity judgment, correct
similarity judgment, and response bias acceptance was used for verbatim, gist,
and verbatim plus gist questions (which were not explicitly listed in the
article). There were four findings about how valence affects false memory, true
memory and response bias; all were applied to the research conducted concerning
math anxiety and any conditioning that may exist in perpetuating it.
Participants
Of the 95 participants 94 self reported, that there were 49 male
respondents, 45 female respondents, and one participant who did not respond; an
average age of 29.8. The Population was
a slightly left shifted Gaussian distribution.
The race/ethnicity portion of the questionnaire was left blank and
without instruction, there were six people who left this space blank. 79 people self-reported Caucasian or White;
two people self reported Middle-Eastern decent, one Native American, one Creole
and another Cajun; and five from Eastern Asian: Japanese, Korean, Chinese, Singapore, and Thai. Participants were all able to read, write and
respond in English, were willing volunteers, and were limited to the population
with internet access. An overwhelming
majority would be demographically categorized as white college students and
white Midwestern WASP’s.
Materials
Informed consent, demographic information gathering, and a series of
three self report inventories, and debrief were conceived of, generated, and
loaded into and onto the survey monkey software as a service (SaaS)
website. The informed consent deceived
participants into thinking and believing the three self report inventories were
gathering information concerning worldview, life experience, and
upbringing. A tabulation of the
materials used, arranged in a matrix organization, are displayed in appendices
A, B, & C. The survey is located at
this link: http://www.surveymonkey.com/s/LWDRPLB.
Procedure
The study was conducted via Survey Monkey as a self report
inventory. The Inventories were
distributed via an online link to Survey Monkey and were made available on the Facebook,
twitter, tumblr, blogspot, read write web, and wordpress of the
researcher. The survey link was also
disseminated by an email sent out to the fall 2011CEM 342 Estimating II class
and to the fall 2011 PSY 301 section eleven class both through blackboard
website of Oregon State University Corvallis Campus in Oregon and through the email of Nyla
Gerhardt, the researcher’s mother; the email forward is still accumulating
data. Participants were initially
informed that it was a survey exploring relationships of world view,
perception, and upbringing. This was
done to mitigate false memories, negative, or positive consequences inherent in
filling out the self report inventory by balancing negative neutral and
positive stimuli and burying the true data in with related ideas.
For procedural,
visuospatial, timing and other possible references the survey is located at: http://www.surveymonkey.com/s/LWDRPLB. Participants clicked on the link to open it
in their web browser and follow the instructions presented as they are
presented until the time they chose not to.
The initial informed consent is part of the deception and frame of
reference manipulation as shown first on the first screen. The second screen is for the data entry of
self reported demographic information.
The next three screens were matrix self report inventories balanced
across positive, negative, and neutral salience and valence (Brainerd, 2008),
to ensure valid and reliable data recall.
The third screen
begins and consists of what is counted as the sixth ‘question’ formed as a fill
in the blank framed as “I am” followed by a matrix inventory of nine items on
the Y-axis: listening, math, job, public speaking, writing, school, being
myself, reading, getting lost; the participant self identifies weather they are
good, acceptable, or bad at these items along the X-axis, or a combination such
that the three choices can generate eight different codings and six different
scorings. The specific scoring and
coding instructions are listed in the coding and scoring instructions. For this round of this research the third
screen and sixth question is present primarily to neutralize priming effects or
false memory while staying consistent with the overall deception explained in
the informed consent, no variables are currently operationalized from this
screen of the survey.
The fourth screen
and seventh question posed as a fill in the blank of “I feel” is another matrix
inventory of eleven different participant feelings along the Y-axis and two
responses on the X-axis either positive or negative for the presence of the
feeling investigated. Each variable was
chosen contingent on its positive, negative, or neutral valence (Brainerd,
2008) in order to balance them; with context identified as part of the
condition and emotional response presented with two choices that can be scored
four different ways. For this round of
this research the majority of the information on the fourth screen and
contained in the seventh question is present primarily to neutralize priming
effects or false memory while staying consistent with the overall deception
explained in the informed consent. The
only variable operationalized was the fifth line on this screen where
participants could self-report their feelings of math anxiety, contained in
question seven of the survey for this round of this research.
Screen five is the
last matrix inventory framed by the fill in the blank question of “I remember”
with eleven different memories along the Y-axis that again have two choices on
the X-axis either remember or remember not, four possible codings, and four
possible scorings. The memories vary in intensity, context, situation, and
other forms of variance. The specific
scoring and coding instructions are listed in the coding and scoring
instructions. For this round of this
research the fifth screen and eighth question is present primarily to
neutralize priming effects or false memory while staying consistent with the
overall deception explained in the informed consent. The only variable operationalized was the
eighth line on this screen contained in question eight of the survey for this
round of this research. Multiple
variables were presented to increase the probability that the two variables the
research pursues were valid, reliable, and did not suffer from random sampling
error by dividing it among and across variables that were not operationalized,
this time. Using multiple variables was
also advantageous and congruent with the balancing of saliency and valence
(Brainerd, 2008).
The final screen
is the debriefing form. The debriefing
form was used to inform the participants of the true nature of the research,
inventories, and demographic information.
Then volunteers are done, and free to leave the terminal, if they
haven’t already.
Results
From the 95 participants,
94 reported their sex on the inventory.
The sample consisted of 49 male participants, 45 female participants, and
one participant whom abstained from answering; there was no unusual distribution
across the data set. The sample population
had a mean age of 29.8 years old. The population was a slightly left shifted
Gaussian distribution. The
race/ethnicity portion of the questionnaire was left blank and without
instruction, there were six people who left this space blank. Seventy-nine people self-reported being Caucasian
or White; two people self reported being of Middle-Eastern decent, one Native
American, one Creole and another one Cajun; and five from Eastern Asian:
Japanese, Korean, Chinese, Singapore,
and Thai. The Null hypothesis was that math anxiety is
socio economic, cultural, linguistic, biological, or of other non- cognitive
behavioral nature. Contrasted with the
hypothesis to be tested was that parental countdown procedure primed and
condition people for math anxiety. Of
the 52 people who reported receiving a countdown procedure as a behavior
extinguishment technique, 29, or 55.8%, also reported math anxiety (Table 1). Of the 43 people who did not report receiving
a countdown as a behavior extinguishment technique, 2, or 4.65% also reported
math anxiety (Table 1). This is more
than a tenfold differential multiplier. The Null hypothesis was rejected twice;
once by the CHI-square test of c2
(1, N = 95), p < 0.001; providing
grounds for further research (see Figure 1). And the null hypothesis was checked with a
two tailed T-test conducted using the rates of 4.65% and 55.8% from between the
two groups who did not receive the countdown, and those who did receive the
countdown. This reduced the possibility
of type I or Type II errors by increasing the degrees of freedom resulting in t(93) = 3.43, p < 0.01.
Discussion
None of the
demographic information collected was relevant in terms of deviating from what
may be considered a null hypothesis, although it could be noted that the
population is overwhelmingly Caucasian.
The hypothesis that there was a correlation and causation, is and
was supported dually through the research conducted investigating the
correlation of self reported math anxiety and the self reported presence of an
authoritative countdown procedure in youth by the CHI squared test results from
table 1 and figure 1. A two tailed
T-test was also conducted using the rates of the two groups reduce the
possibility of type I or Type II errors by increasing the degrees of freedom and
comparing the rate of incidence of math anxiety as displayed in table 2 and
figure 2. Using the two tailed T-test
essentially reduces the 2x2 factorial design to a 1x2 matrix in order to
compare the incidence rates. The other
supporting column of the overarching research is built upon the foundations of
behaviorism as a pathway.
This experiment examined practical
applications of conditioning via exploration of relationships that exist
between categorical variables defined as individuals who self report math
anxiety and as individuals having experienced mathematically related extinction
techniques implemented by an authority figure as a child. The study included what
has classically been referred to as deception by misleading with relationships
of world view, life experience, and upbringing. This was done to mitigate false
memories prompted by the self inventory due to negative or positive
consequences inherent in the recall algorithm of replying to the self report by
balancing negative, neutral and positive stimuli of the inventory, thereby
burying the true goal/data within neutral and random yet relative concepts;
based upon valence research (Brainerd, 2008).
Respondent
behaviors are those that are reflexive and occur automatically to previous
stimuli and are generally and typically referred to as involuntary (Pear, 1984). Who can salivate, blush, laugh or cry on
command. Some method actors and improvisationalists may appear to do so after
they have learned how or expressed the ability.
Operant behavior (Skinner, 1953) is controlled by consequences and is
sometimes referred to as voluntary. When
asked to do so some can readily sit, stand, walk, and talk, whisper, and so
on. This is in contrast to conditioned reflexive
responses which can involve smooth muscles and glands that are important to the
functioning of internal bodily processes such as relaxation prior to sleep or
arousal to a threatening situation; like a math test. Respondent and operant conditioning
procedures appear to influence two different kinds of behaviors (Pear &
Eldridge, 1984).
The Little Albert case study experiment (Watson, 1920), illustrated the
empirical evidence of classical conditioning in humans. The same study proved to be exemplary for
stimulus generalization. Stimulus
generalization refers to the natural procedure of reinforcing responses in the
presence of a stimulus or situation and the effect of the response becoming
more probable in the presence of another stimulus or situation (Watson, 1920).
This specific research investigated the possibility of generalization of
numbers, mathematics, and related ideas.
And this grouping of ideas as possible stimulus generalizations from
initial classical and operant conditioning presented in the countdown procedure
as not only a source of priming, but also as the frame for the introduction of
a new idea on a piece of the mind otherwise known as the impressionable tabula
rasa; the portion of the mind apart from nature where nurture is to be placed
in a child’s mind.
Valence was balanced in the self report inventories based on two
experiments. Valence had a simple
directional effect on false memory in both experiments. Participants displayed more false memory for
negative critical distracters than for neutral ones, and more false memory for
neutral critical distracters than for positive ones (Brainerd, et al, 2008).
Averaging over the experiments, the false memory increased from positive to
negative valence was 1.38 standard deviations.
Secondly valence had the same directional effect on true memory with
false memory increasing from positive to neutral to negative targets, although
the effect was smaller at just .73 standard deviations. Thirdly valence produced a qualitative shift
in the net accuracy of memory as indexed by the difference between false memory
values for targets versus critical distracters.
True memory exceeded false memory for items with positive and neutral
valence, but not for items with negative valence. Lastly, both the memory and the bias
parameters in the signal detection analysis showed a coherent picture of
valence effects. Negative valence
relative to positive or neutral valence elevated both true and false memory,
while lowering response bias (Brainerd, et al, 2008). Considering the negative salience of Math
Anxiety and childhood punishment it was important to account for confounding
factors prior to research to maintain internal validity of the self report inventories
necessary to conduct the research efficiently.
What has traditionally been known as the quasiexperimental design was not
used in this research; rather it was a natural treatment as quasi independent
variables of countdown and math anxiety.
It is also a before and after design in that the memory of the countdown
occurred temporally prior to the current frame of feeling math anxiety on math
tests. To some degree this nuance may
cater to a younger population with higher memory function, limiting the sample
population as the university sampling procedures did; also increasing validity
of recall. Before and after designs are
very similar in their analysis before and after a treatment. The treatment in this case was the
administration of the countdown procedure to reduce and eliminate undesired
behavior. The reliability of this
information is then called into question.
The answer is that it was accounted for to some degree in the balancing,
modeling, and focus of the self report inventory administered. This form of before and after design is the
interrupted-time-series design often used to examine observations before and
after a naturally occurring treatment. A
fact which has never been more true; given that it occurred before the
experiment was conceived of in some cases.
The intriguing aspect of this distinction is that a truly natural
treatment is only possible in a quasi-experimental design. This quasi-experimental approach is very
different from similarly structured simple two dimensional factorial experiment
considerations in which variables are defined conceptually, operationally, and
existentially a priori with groups formed by random assignment; as opposed to
self organizing systems, networks, and convergent realities assessed by quasi-experiments
and their truly infinite variability of contributing independent
variables.
At some point all the individuals in the study had a choice, as they
still now have, to either accept or reject the frame imposed, the choice given,
or decision of what to do in response to a stimulus. From deciding what to do about the familiar
frame obligated choice, and direction every single living person progresses
through life, building their life by and in the moment. Constructivist theories
acknowledge this experience of cultural exploration, of cultural differences;
accordingly this research would be negligent to not note Hong et al. (2000) who
framed quasi-experimental research in what has now been named constructivist
theory. Constructivist theory conceptualizes
culture as the infinite blend of techniques, symbols, images, metaphors,
procedures, practices, language and language use applied in, to, from, and for
human life prevailing in a given group, civilization, community, niche, or
society. Constructivism is active in all
participants as the pathway they chose in their response to their stimuli
defines the path they take in behaviorism and fuses with the person to define
the culture they identify with and eventually gravitate to. People with math anxiety tend not to choose
cultures, careers, or work where the typical response is that of anxiety.
Many threats exist to the countdown to math anxiety study conducted on
the external level; specifically the innumerable confounding variables that may
have conflicted, contradicted, or contributed to the measure of math anxiety,
including the cultural influences of the parent or authoritarian principle
caregiver. A poor teacher, community, or
period in an individual’s life coupled with bad timing could nullify all results;
as could a culturally confined and biased sample that is 80% Caucasian. Further constraining and possibly mitigating
factors include over half of the survey responses came from one email forward
via Nyla Gerhardt that may or may not be composed of overwhelmingly white
Anglo-Saxon Protestant Midwestern plains dwellers; an email forward that is
still gaining in terms of information and momentum. The self report inventories gave no explicit
or implicit direction, for it was assumed that previous experience would guide
individual intuition. At this time there
is no meta-behavioral method to ensure validity or reliability of intuition,
only distantly related meta-cognitive methodologies. A longitudinal design would be better suited
to assigned causalities although the research conducted provides grounds for
the continued investigation of external factors, longitudinal, temporal, cross
sequential, multi cultural, environmental, or otherwise. The self report survey marketed as a survey
was also limited to the people who would respond to such an inquiry via the
internet.
Internal threats also exist, especially if the balancing or ordering of
the extraneous variables used to balance salience is not actually as balanced
as it may seem. This could be especially
true for suggestive participants or because of the motives of an adept
researcher. The instructions were not
clear, or even present as recognized, until they were. The use of technically transcendental writing
similar to that of the American transcendental movement was also
implemented. Distributing the survey to
a population of consisting half of college students towards the end of an
Indian summer could affect data results; as could the economic tone or any
number of factors.
The self report
survey disseminated through survey monkey was written in the first person to
elicit introspection as opposed to the projection that maybe present in the use
of second person pronouns, like ‘you’. False
acceptance of similarity may have affected the data based upon the arrangement,
linguistics, and individual differences perceived from the self report
inventory. First Person was used in the
form of the pronoun frame implemented as “I”.
Historically surveys, questionnaires, and data collection were limited
to paper transactions where people would interact. This existential frame of didactics,
interaction, dualistic partnerships, multiple people, or other arrangements and
dynamics led to the primary use of second person pronoun implementation on self
report inventories and data gathering as framed by “you” and other consistent
pronouns. Whereas this inventory was to
be sent out to individuals interfacing with a machine, a computer, in some form
of human factor interaction; this opportunity was taken in an attempt to
inspire introspection of being alone and framing in the first person in a self
report inventory as opposed to didactic and reciprocal sharing that occurs in
human interaction artifacts from past research in second person framing.
The initial deception was not so much deception as it was frame
manipulation. Upbringing, life
experience, and world view are a large set.
Contained within that set are the identified variables of countdown
procedure, as a form of upbringing, and math anxiety, as a form of life
experience or worldview. The first self
report inventory located in Appendix A was the contained the most brevity. Simplification allows the participant to
grasp the initially sophisticated matrix design. The first self report inventory’s initial frame
is only three letters “I am”, displayed
in the upper left hand corner as is common practice for you and other readers
and writers of English. The next step in
the mad libs matrix self report inventory was choosing “good”, “acceptable”, or
“bad” at a noun that was displayed down the left justified y axis of the
page. “Good”, “acceptable”, or “bad”
were presented orthogonally across the page below the initial frame. Below this were the afore mentioned “at a
noun’s” displayed down the side of the left justified y-axis of the page. Participants were limited to people with
internet access, which could read, and think through a matrix self report
inventory similar to others they may have seen in the past. Six surveys were not completed and were
thrown out, participants may not have understood, some may have been voyeurs,
or something else. Regardless confusion
and misunderstanding can be conflagrating variables in any study. Participants essentially created nine structurally
consistent and introspectively framed “I statements” as a self report. On the next self report, presented in
Appendix B, the frame was expanded and complexity was added throughout the
balanced word salad selections. The material was presented in the same format
although the initial frame on that page is “I feel” and it was not formatted to
build a sentence as the previous self report inventory had been. Feelings may be more complex so they were
added as a way to build on the priming and learning from the first self report
inventory, but was kept simple to make the tasks fast for the participants in
order to diminish distractions or thoughts that could interfere with data
collection that takes too much time.
This could also be a source of confusion for participants. Once the participants mind was sufficiently
primed for introspection by the format of the first two self report inventories
the third and most complex sentence structures were presented in the third self
report inventory. The third self report inventory is initially framed as “I
remember” the format displayed in Appendix C does not contain consistent or
similar sentence structure throughout the eleven sentence endings following
either “Do remember” or “Do not remember”.
The difference is that the initial frame of “I remember” is disjuncted
on the third self report inventory and is not used in the sentence as was the
case with the first self report inventory.
This was done because the cognition framed by the language required a
person to remember in the past and report in the present, for participants who
noticed this difference this inventory may have been confusing. In future studies a debrief that gathers data
about the topic of disjuncted and separate yet consistent frames within the
matrix structure of the self report inventory may prove insightful. Especially given that participants may notice
the differences between the different inventories, another potential
distractions and source of variance in the data collection process. Disjuncted was used to describe and reference
cognition’s response to the written language perceived as an almost musical
nature in thought, adverbially, colloquially, and as well as in terms of
logic.
Once mitigating factors such as false memory were neutralized the simple
investigation of a 2x2 factorial design concerning math anxiety becomes much
easier. Conditioning was measured as
what was presented and represented by a larger score for the operationalized
independent variable presented at line eight of question eight “I remember…” my
parents issuing a countdown when I was naughty” represented as and measured as
a response of the stimulus for conditioning being scored and coded as listed
previously in the scoring coding instructions.
The conditioned response represented by a larger score for the
operationalized dependent variable presented at line five of question seven “I
feel math anxiety on math tests” represented as and measured as a condition of
the response from conditioning. All
other materials are present primarily to neutralize sources of error variance
specific to this study such as priming, false memory, and participant
manipulation, while increasing internal and external validity.
Backward chaining (Myerson, 1997) is a commonly used technique both in
the rearing of children, the education of mathematics, and game theory. Backward chaining is a method for
establishing a chain, (a behavioral chain in this instance) in which the last
step of the chain is taught or modeled first.
Then the nest available step is linked to the last and previous step,
and so on until the chain is learned. In
both mathematics and behaviorism the goal behavior and necessary solution are
synonymous as the starting point for backward chaining. The unfortunate coincidence found in this
study elucidated the confounding nature present in the harmonics of sociocultural
phenomenon; where different behavioral paths (individuals given momentum by the
countdown eliciting the self reported state of math anxiety) delivered
unwitting individuals to where they now stand.
References
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R.B. (1997) Game Theory: Analysis of
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Table 1
Numerical Measurement
of Responses
Raw data
|
math
anxiety
|
no
math anxiety
|
countdown
|
29
|
23
|
no
countdown
|
2
|
41
|
total
|
31
|
64
|
scored data
|
math
anxiety
|
no
math anxiety
|
countdown
|
261
|
69
|
no
countdown
|
6
|
41
|
total
|
267
|
110
|
Table 2
Percentage of positive math anxiety presence
from affirmative and negative presence of countdown procedure, or rate of
incidence of math anxiety between groups
Countdown
|
No Countdown
|
|
Math Anxiety
|
4.65%
|
55.8%
|
Figure 1
Figure 1. Numerical Results of Self report
Inventory (In number of responses per condition) The Null hypothesis was
rejected by the CHI-square test of c2
(1, N=95), p<0.001; providing
grounds for further research.
Figure 2
Figure 2.
Incidence of Math Anxiety between countdown condition groups in percentage of
sample population. Null hypothesis
was reject by T-test of t(93)
= 3.43, p < 0.01.
Appendix A
Appendix A
I am…
|
|||
Good
|
Acceptable
|
Bad
|
|
At listening
|
|||
At math
|
|||
At my job
|
|||
At public speaking
|
|||
At writing
|
|||
At school
|
|||
At being myself
|
|||
At reading
|
|||
At getting lost
|
Appendix B
I
feel…
|
||
Agree
|
Disagree
|
|
Apathetic
towards punishment
|
||
Nervous
before public speaking
|
||
Like
dancing when I hear music
|
||
Lost
when looking at maps
|
||
Math
anxiety on math tests
|
||
Like
getting married someday?
|
||
Happy
when I’m winning!
|
||
Average,
sometimes
|
||
Afraid
of being alone
|
||
Blessed
|
Appendix C
I
remember…
|
||
Do
remember
|
Do
not remember
|
|
Going
on fishing trips as a family
|
||
Getting
in trouble at school
|
||
Daydreaming
|
||
Waiting
in lines with people
|
||
Getting
hurt: pulled muscles, broken bones, cut, physical pain of some sort
|
||
Feeling
loved
|
||
Learning
from mistakes others have made or I witnessed
|
||
My
parents issuing a countdown when I was in trouble
|
||
My
parents rewarding me when I did something good
|
||
Wanting
to run away, or actually running away
|
||
Sunrises
and Sunsets
|
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