Research on the Psychological Interpretation

The report shows an experiment based on Computer-based mathematical expression and visual interpretations with the response of samples or participants in the experiment. This research is based on the object-oriented attribute, syntax knowledge on algebraic equivalence and colour verification with the references of several independent and dependent variables.

Running head: RESEARCH ON THE PSYCHOLOGICAL INTERPRETATION
RESEARCH ON THE PSYCHOLOGICAL INTERPRETATION
Name of the Student
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1RESEARCH ON THE PSYCHOLOGICAL INTERPRETATION
Table of Contents
Introduction................................................................................................................................2
Method.......................................................................................................................................2
Results........................................................................................................................................4
Strength..................................................................................................................................8
Limitation...............................................................................................................................9
Future scopes..........................................................................................................................9
Conclusion..............................................................................................................................9
References................................................................................................................................11

2RESEARCH ON THE PSYCHOLOGICAL INTERPRETATION
Introduction
The report shows an experiment based on Computer-based mathematical expression
and visual interpretations with the response of samples or participants in the experiment. This
research is based on the object-oriented attribute, syntax knowledge on algebraic equivalence
and colour verification with the references of several independent and dependent variables.
Eye-movement for symbolic and non-symbolic format helps people in understanding the
critical mathematical interpretation or expression. The independent variables varied by three
random allocated conditions, which are based on the spacing of the sub-expressions of
mathematical syntax. The three types of spacing conditions are neutral, consistent and
inconsistent and the spacing is dependent on the of two syntax grouping argument (within “x”
vs between “+”) (Tunmer & Hoover, 2017). Visual perceptions are also examined in this
study as the computer-based experiment includes the concept of eye movement patterns for
different symbolic and non-symbolic mathematical elements with the relation of calculation.
Object oriented attention is based on the expertise of each individual in hierarchical
syntax and algebraic expressions and visual retraining processes with the evaluation of
mathematical structure (Richter, Lins & Schöner, 2017). The cognitive abilities and
interpretations of samples or the people included in the experiment are the fundamental
principles of this study. This experiment emphasis on application of mathematical and
embodied for symbolic reasoning and visual perceptions regarding mathematical
interpretation. The three main hypotheses for the experiment are neutral, consistent and
inconsistent spacing with respect to knowledge of the syntax knowers and non-knowers. The
cognitive theory of the non-formal mechanisms in mathematics has described some concepts
regarding syntactic parsing, opportunistic selection of algebraic expression and errors
regarding the mathematical expressions (Braithwaite et al.,2016).

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The participants can detect formal syntactic expressions, and they solve the problems
with visual perceptions. According to Marghetis, Landy and Goldstone, (2016), the syntax
knowers are better in understanding the algebraic expression of hierarchical structures. The
study shows that technical teaching on syntax learning can help the knowers among the
participants have a better sense of reasoning and RUPAS system helps them to solve
hierarchical algebra.
This experiment is to connect the relevance of proximity in arithmetic for the
cognitive effect of the participants with the reference of algebraic retrains in the hierarchical
equation.
The research question for the experiment is to identify whether more appropriate
syntax knowledge is replicated by the findings of Marghetis, Landy, & Goldstone (2016)
The experiment has three main hypotheses depending upon the research question. The
purpose of the research question is to find out whether the findings of Marghetis, Landy, &
Goldstone (2016) repeat during more difficult syntax knowledge is considered. The three
main hypotheses are:
1. The syntax knower can better understand the colour changes among the algebraic sub-
expression groupings such as within ‘+’ and between ‘x’ than the non-knowers.
2. This effect of mathematical syntax knowledge will be constant when syntax
consistent spacing supports these sub-expression groupings.
3. Syntax inconsistent spacing disrupts the algebraic sub-expression groupings; as a
result, the mathematical syntax knowledge is eliminated.

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Method
The objective of the experiment is to analyse the importance of visual perception or
the eye movement for analysing mathematical equations. The participants are categorised as
syntax-knower and non-knower groups. Each participant is given only 10 seconds to answer
each question, and they are classified depending upon their prompt answers. The trials
depend upon the symbol spacing, algebraic equivalence and colour judgement of the
mathematical expressions.
Primarily the sample size was 642, and the final sample size was 450. This experiment
involves primary data and cross-sectional approach of data collections. Samples of
respondents were taken randomly, and each spacing condition included 150 participants.
Among those final 450 samples, every 150 groups had half syntax knower and half of the
non-knowers.
Respondents were asked some demographical questions regarding their age and
gender. These questions help to evaluate the gender percentage of female respondents, which
is 74% of total respondents. The total respondents are 450 and 330 among them were female,
and the range of ages in between 17-62 yrs.
Independent variables depend on the three conditions of the spacing of the symbols,
which are the primary conditions of the arrangement of spaces, and the dependent variables
are syntax grouping index, which includes within and between attributes. Computer-based
mathematical expressions were performed in the PsyToolkit software (Stoet, 2010). This
toolkit is to identify valid questions of the experiment by highly efficient C programming.
The questionnaires were answered by the respondents, and the analysis of those questions
was done by the same software (Stoet, 2017). The tool is to identify the psychometric
efficiency of the participants and the grouping effect of the syntax. The validated questions

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are to find colour recognition and to test algebraic equivalences among the participants. The
validations are syntax identification based on the arguments within vs. between syntax
groupings. The main questions are to identify the similarity between two letters and the
algebraic equivalence of them in the syntax. The study design is based on analysis of
grouping effect and syntax identification by the participants to detect the difference between
the knower and non-knower people.
The participants were asked some demographical questions about their sex and ages
to understand the frequencies and range of age. Participants used the software and analysed
the algebraic expressions in terms of colour and equivalence of the equations. The
participants, who scored 85% or higher for 25 questions, called syntax knower. The syntax
non- knower, were considered as they scored lower than 85% or could answer less than 21
questions. Each question required not more than 10 seconds, and if the participant was unable
to answer in the given time, they were marked as “too slow”.
The instructions appeared to the blank window, and the equivalence and the colour
recognitions measured in each trial. They were asked to press “p key” for the same answer
and “q key” for the different solution for both colour recognition and equivalence check. As
per the instruction, they had to press “p” when both colours are the same, and expressions are
equivalent and vice-versa. The participants were instructed to press the “Space” bar to
continue.

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Results
The computer-based study collects information about the syntax spacing and the
colour detection methods however; there were some demographics questions which detect
some statistics about the participants. The statistics shows that total number of observation in
final stage was 450 where mean value of age is 20.7 and standard deviation 5.71 was found in
the range of age 17 to 62yrs. Frequency of male and female were 101 and 333 whereas there
were another two categories such as 10 and 6. The percentage of females was the highest one
with 74% among the participants .
Hypothesis 1: The syntax knower can have well understanding with the comparison of non-
knowers in colour variations among the algebraic sub expression groupings for two different
arguments such as, within ‘+’ and between ‘x’.
Hypothesis 2: This result of mathematical syntax knowledge will be persistent while syntax
consistent spacing supports these sub-expression groupings.
Hypothesis 3: Syntax inconsistent spacing interrupts the algebraic sub-expression groupings
as an outcome the mathematical syntax knowledge is rejected
This experiment is analysed by the two-tailed t-test as the primary variables
considered by the knowledge of syntax .The experiment shows the primary criteria based on
the spacing conditions of the syntax. The three primary conditions are neutral, consistent and
inconsistent spacing conditions. The significance level is considered as 0.5. The experiment
includes three hypothesis based on the comparison of three types of syntax spacing groups
among the syntax knowers and syntax non-knowers. Each hypotheses has two types of
samples such as syntax knower and non-knower, which are taken under consideration with

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equal variances, which are standard error, t values, degree of freedom, and p values. There
are certain conditions to satisfy or check whether null hypothesis accepted or rejected based
on the difference of mean t values. The hypothesis are accepted if the p value of the test is
similar to the difference of the mean values.
Syntax Knower Syntax Non-knower
Mean
value
Standard
deviation
Mean
value
Standard
deviation
t value Degree of
freedom
p value
Neutral
spacing
condition
3.02667 .2245904 0.36 1.99079 8.2976 148 p<0.0001
Less than
0.0001 or
negligible
Consistent
spacing
condition
4.466667 1.810878 -.28 2.663872 12.7619 148 p<0.0001
Less than
0.0001 or
negligible
Inconsistent
spacing
-.346666 2.133981 -.54666 2.20131 0.5649 148 0.572997

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condition 7 67
The experiment for Hypothesis 1 shows that the p value is less than 0.0001 which
represents that null hypothesis is accepted and the alternative hypothesis is rejected which is
not statistically significant . It can be said that syntax knower are better in understanding of
the colour changes with the comparison of two algebraic sub expressions: within ‘x’ and
between ‘+’.
P value for the experiment of Hypothesis 2 is also less than 0.0001, which shows that
null hypothesis is accepted and alternative hypothesis is rejected. This proves that knowledge
of mathematical syntax supports the sub-expression groupings with the reference of
consistent symbol spacing. The rejection of the alternative hypothesis shows statistical
insignificance.
Third hypothesis is rejected, as the p value for the experiment is greater than 0.2865
and the alternative hypothesis are accepted. The p value for the third hypothesis is 0.572997,
which is statistically significant. As a result, it can be said that mathematical syntax
knowledge cannot be eliminated during the disruption of the sub expression groups when the
spacing is inconsistent.
Discussion
The experiment is based on the three hypotheses based on visual perception with
colour recognition and knowledge of syntax. The hypothesis is also depended on the various
spacing of syntax recognition, which is related to the findings of Marghetis, Landy, &
Goldstone (2016). The experiment result supports the first hypothesis, which represents

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between the two groups; syntax knower can detect the colour changes of sub-expression
groupings. The second hypothesis is also supported by the experimental values, which
indicates that the syntax consistent spacing will remain constant, as algebraic sub-expressions
are the main supporting factor for these. The third hypothesis is rejected; as a result, it does
not support the concept that disruption of sub-expression by inconsistent symbol spacing
eliminates the mathematical syntax knowledge.

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The first hypothesis says that the syntax knowers are more efficient in detecting
colour changes with the algebraic expression as they have object-based attention and better
visual perception. The symbolic mathematical elements are easier for the syntax knower as
they are technically trained . The interpretations are more relevant as the algebraic reasoning
and RUPAS are also included in the retrain methods. The visual property verification is one
of the specific systems, which can differentiate the same and different objects in the sub-
expressions in the colour verification trials. Possibilities of swapping the objects and
comparing the variables with respect to the presence of symbols can be adapted by the
perceptual discrimination in object-based attention. The object attention of the variables is
observed better among the trained people due to their improvement in embodied cognition.
Differentiating the algebraic expression prefers the colour verification or change in colour of
the objects. According to a study, the syntax knowers are performed better when the detection
of the colour change in continuous algebraic expressions has to be performed.
The second hypothesis also supports substantial evidence of the experiment. The
experiment shows that the persistent grouping effect is highly significant for the arithmetic
expression. The visual perception also depends on the spacing between the variables and
mental arithmetic influences the productivity of it. The Gestalt grouping effects is one of the
vital concepts in the implementation of the operator –operand function. The consistent gap
between the operation variables is sufficient for syntactic parsing and the accuracy of the
outcome. Foil error can be avoided in the calculation or the detection of algebraic expression
by consistent spacing in random equation (Landy & Goldstone, 2007).

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The third hypothesis is not supported by the experiment outcomes and signifies that
the disruption of inconsistent spacing cannot eliminate the mathematical effect of syntax
knowledge. The significance of the statement proves the mental mathematical analysis ,
verbal interpretation of data cannot be depended on the spacing between the values. The
knowers acquire the efficiency of syntax knowledge through technical teachings and better
perceptual mechanisms. The perceptual strategies enhance the cognitive ability of the human
brain and help to adapt verbal or databased arithmetic. This statement can be supported as
during a study in China; it was shown that the single variable and low-level algebraic
expression could easily interpret by the participants. This study neither support the statement
nor deny it, as there is no substantial evidence of relation of spacing with data interpretation.
White space in the code helps in the easy calculation and avoids data which can make
difficulties for the analysis of data (Landy, Allen & Zednik , 2014).
Strength
Object-based attention is one of the primary element of the colour recognition of the
experiment, which enhances the adaptability of the human brain. The participant’s
interpretation is depended on the embodied recognition, which is related to mental
mathematics and efficiency (Marghetis, Landy, & Goldstone, 2016). Mathematical expertise
is not related to the spacing for the syntax knower as they acquire the knowledge from the
technical method. Perceptual grouping effect is a constant factor for the participant of the
research experiments, and this has been proven in the various condition of the research
method (Overvliet& Sayim, 2016). Mental arithmetic with visual representation is also
discussed in the research, which helps in colour change and the differentiation of the
variables (Rivera, & Garrigan, 2016). Colour recognition is one of the central aspects of this
research as it determines the promptness of participants. Alphabetic proximity is one of the
critical components of the operator and operand relation. The proximity determines the

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accuracy of mental maths with respect to the spacing between the variables. Symbolic
reasoning is associated with human cognition and enhances neural stimulus and the
adaptation of visual perception (Goldstone, 2017).
Limitation
There are certain limitations of the study, as the research does not include the
importance of eye movement in symbolic or non-symbolic mechanisms properly (Pettersson
et al.,2018). The physical transformation of the notation part and foil errors are not clearly
described or related to the research. This research has not discussed visual masking and
verbal representation for symbol spacing for the algebraic expressions (Price, Wilkey&
Yeo ,2017). Visual proof of algebraic representation has not been analysed in the research as
the geometrical graphs and category theory are not highlighted in that study.
Future scopes
The research revolves around the perceptual interpretation of mathematical
expressions in the form of algebraic syntax among the participants. The PsyToolkit software
is used for the colour verification and recognition of the symbolic expression. The signal
detection theory can be explored in a vast range after the outcome of the research. This
experiment can give scope for better interpretation of the algebraic expression as the
promptness has been considered in the research. The ability of mental understanding and
appropriate proximity are taken under consideration of the research. The study can help in
acknowledging the syntactic parsing with visual attentional factor within a different period.
Conclusion
The hypothesis of the replication theory proposed by Marghetis, Landy, & Goldstone
(2016) was argued in the research question to understand the competence of syntax knower

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with comparison to the non-knowers. The research proves that the syntax knowledge is more
effective when data has to be interpreted by means of colour change and the symbolic
representation. The research clarifies that syntax knowledge is significant for mathematical
analysis and efficiency of syntax cannot be deprived due to inconsistent spacing of symbols.
However, the issue of the symbolic proximity and relation of promptness is not discussed.
The eye movement and the verbal perception for data interpretation have also remained
ambiguous after the experiment.

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References
Braithwaite, D. W., Goldstone, R. L., van der Maas, H. L., & Landy, D. H. (2016). Non-
formal mechanisms in mathematical cognitive development: The case of
arithmetic. Cognition, 149, 40-55.
Goldstone, R. L., Marghetis, T., Weitnauer, E., Ottmar, E. R., & Landy, D. (2017). Adapting
perception, action, and technology for mathematical reasoning. Current Directions in
Psychological Science, 26(5), 434-441.
Landy, D., & Goldstone, R. L. (2007). How abstract is symbolic thought?. Journal of
Experimental Psychology: Learning, Memory, and Cognition, 33(4), 720.
Marghetis, T., Landy, D., & Goldstone, R. L. (2016). Mastering algebra retrains the visual
system to perceive hierarchical structure in equations. Cognitive research: principles
and implications, 1(1), 25.
Overvliet, K. E., & Sayim, B. (2016). Perceptual grouping determines haptic contextual
modulation. Vision research, 126, 52-58.
Pettersson, J., Albo, A., Eriksson, J., Larsson, P., Falkman, K. W., & Falkman, P. (2018,
June). Cognitive ability evaluation using virtual reality and eye tracking. In 2018
IEEE International Conference on Computational Intelligence and Virtual
Environments for Measurement Systems and Applications (CIVEMSA) (pp. 1-6).
IEEE.

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Price, G. R., Wilkey, E. D., & Yeo, D. J. (2017). Eye-movement patterns during nonsymbolic
and symbolic numerical magnitude comparison and their relation to math calculation
skills. Acta psychologica, 176, 47-57.
Richter, M., Lins, J., & Schöner, G. (2017). A Neural Dynamic Model Generates
Descriptions of Object‐Oriented Actions. Topics in cognitive science, 9(1), 35-47.
Rivera, J., & Garrigan, P. (2016). Persistent perceptual grouping effects in the evaluation of
simple arithmetic expressions. Memory & cognition, 44(5), 750-761.
Stoet, G. (2010). PsyToolkit - A software package for programming psychological
experiments using Linux. Behavior Research Methods, 42(4), 1096-1104.
Stoet, G. (2017). PsyToolkit: A novel web-based method for running online questionnaires
and reaction-time experiments. Teaching of Psychology, 44(1), 24-31
Tunmer, W. E., & Hoover, W. A. (2017). Cognitive and linguistic factors in learning to read.
In Reading acquisition(pp. 175-214). Routledge.