Mastering mathematics improve how one sees mathematical equations Research Project 2022

Running head: IMPROVING VISUAL FOR MATHEMATICAL EQUATIONS 1
Mastering mathematics improve how one sees mathematical equations
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IMPROVING VISUAL FOR MATHEMATICS EQUATIONS 2
Does Mastering mathematics improve how one sees mathematical equations?
Introduction
Mathematics is more of a practical thing and in theory, change in the font; color or even spacing
on a mathematical equation or problem does not change the meaning and the solution of the
mathematical problem. Traditionally it was believed that mathematics is separated from one's
perception reasoning and actions. The primary objective of this research project is to evaluate if
mathematical reasoning is separated from one's perception and actions when solving a
mathematical problem. There is enormous evidence that suggests mathematical reasoning rely on
one's retained experience to relate and comprehend mathematical logic (Stoet, 2017). In practice,
mathematics involves solving of equations, geometric work, and also studying and the
interpretation of graphs; hence, the use of visual aid is core to mastering mathematical concepts.
Significance of the study
The significance of the study is to establish if there is a statistical association between mastering
mathematics logics and visual improvements in seeing mathematical equations. The study is
concerned in determining if the change in color and spacing for mathematical equations
influences the accuracy of the equation solution. The final objective of the study is to explore the
difference for accuracy levels for students who have mastered mathematical concepts (math’s
oriented students) and students with low skills in mathematics. Unlike other research projects on
the same , this project focuses only on the effect of changing the syntax spacing on the
performance for both research groups math’s oriented students and students with less
mathematical understanding.

IMPROVING VISUAL FOR MATHEMATICS EQUATIONS 3
Methods
Participants
642 participants constitute the entire study population; however, only 450 participants were
drawn to be in the sample size. Selection for sample size respondents was through the random
process, and the respondents grouped into three grouping conditions, namely neutral, consistent,
and inconsistent. 22.44% of the total respondents in the survey were male, while 74% of the total
participants in the study were female. 2.22% of the participants were reported to belong to other
gender categories, while 1.33% of the respondents choose not to give their gender identification.
Materials
The study experiment contains 25 mathematical equations to be completed by the respondents.
The participants are divided into two treatment groups' students who understand and perform
well in mathematics coded as syntax knowers and students who normally do not do well in
mathematics coded as syntax non-knowers. The two groups are categorized using the 25
equations test, for students who achieve <22/25 questions the respondents is grouped as syntax
knowers while respondents with <22/25 are grouped as syntax non-knowers. Solutions for the 25
equations were recorded for each respondent and marked appropriately to obtain the syntax
accuracy score for each response.
Procedure
The study comprises of two treatment groups participants who know syntax and participants who
do not know the syntax. All the participants in the sample size were randomly assigned to 1 of 3
treatment conditions, i.e., condition 1: neutral spacing, condition 2: syntax consistent spacing and

IMPROVING VISUAL FOR MATHEMATICS EQUATIONS 4
condition 3: inconsistent syntax spacing. All three conditions had the same set of rules and
instructions (Stoet, 2010). The test study also constituted color judgment tasks, where the
respondents were asked to detect the difference in color patterns. The tests tasked for each
iteration in the study is approximately 10 seconds in which the respondents have to give a
response and move to the next test for both color judgment tests and algebraic equivalence tests.
Analysis and Results
Descriptive Statistics
Descriptive statistics normally consists of measures of central tendency and measures of
variation. The demographic variable age is distributed as (M = 20.7, SD = 5.71) for all the 450
participants in the survey. The least age recorded for respondents in the survey is 17 years, while
the highest age recorded for the respondents is 62 years.
Hypothesis testing
The entire study focuses on three sets of hypothesis to achieve the set goal for the study. The
hypothesis is categorized into the three testing conditions; neutral, consistent, and inconsistent.
The hypothesis was tested using the two-sample t-test statistics at 0.05 level of significance.
The first hypothesis is carried out at the control level where the condition is set as neutral syntax
spacing. In support for the evidence for hypothesis 1, the syntax knowers group has higher
accuracy average (M= 3.0267, SD= 1.95), while the accuracy average for syntax non-know (M=
0.36, SD= 1.99). In support of analysis for hypothesis 1, there is a statistical difference in seeing
mathematical equations for syntax knowers in mathematical concepts and syntax non-knowers of
mathematical concepts for neutral syntax spacing condition is given by the t(148) = 8.2976, p <

IMPROVING VISUAL FOR MATHEMATICS EQUATIONS 5
0.001. For hypothesis 2 the test was carried out at a different treatment condition consistent
syntax spacing, in this test syntax knowers had an accuracy average (M=4.467, SD= 1.811),
while the accuracy average for syntax non-know (M= - 0.28, SD= 2.664). In support for the
analysis for hypothesis 2, there is a statistical difference between the seeing ability of
mathematical equations for syntax knowers and syntax non-know groups inconsistent syntax
spacing as indicated by t (148) = 12.7619, p < 0.001 (Kulkin, 2016). In the analysis of hypothesis
which was carried out at inconsistent treatment condition, syntax knowers have a higher
accuracy average (M= -0.347, SD= 2.134), while the accuracy average for syntax non-know is
given as (M = -0.547, SD= 2.201). In support for the significance for hypothesis 1, the test
showed there is no statistical difference in seeing mathematical equations for syntax knowers and
syntax non-know under inconsistent syntax spacing formats as given by t(148) = 0.5649, p =
0.5730 > 0.05.
Discussion
In the valuation of the analysis presented in the study, there is sufficient evidence to suggest that
both groups’ syntax knowers and syntax non-know have different seeing capabilities for
mathematical equations. In the analysis, the control condition where all presentations were
neutral. The results presented show that syntax non-know even under neutral presentations
scored an accuracy average of almost zero while syntax knowers have an accuracy average ten
times the average score for syntax non-know. The conditions for the second test was consistent
presentations of mathematical equations. The results thus indicate that under neutral conditions,
mastering mathematics improve the seeing ability of mathematical equations and the solution
presented to the equation (Borgonovi & Pokropek, 2019). From the results obtained, syntax
knowers registered a higher accuracy score compared to the average accuracy score for syntax

IMPROVING VISUAL FOR MATHEMATICS EQUATIONS 6
non-know group. The results suggest that there is a statistical difference in the average accuracy
scores for the two groups hence suggesting that the seeing capabilities for mathematical
equations are enhanced by the knowledge and understanding of mathematical concepts. Thus
indicating that under consistent presentation of mathematical equations, mastering mathematics
can improve the seeing ability of mathematical equations hence also affecting the solution
presented.
The final test was carried out under inconsistent syntax spacing of mathematical equations. From
the results given by the two-sample t-testt, the syntax knowers group registered a higher
accuracy mean score compared to the syntax non-know group, hence indicating that knowers
have a better visual of mathematical equations under inconsistent syntax spacing as compared to
syntax non-know group. Further analysis shows that both the treatment group’s syntax knowers
and syntax non-know registered the least average scores were obtained when the test was under
inconsistent syntax spacing condition. This suggests that inconsistency in mathematical
representations of the equations lower the accuracy of the solutions (Bernard & Chotimah,
2018). However, the study has also shown there is no statistical difference in scores for syntax
knowers and syntax non-know for mathematical scores for under inconsistent syntax spacing of
mathematical equations. It, therefore, means that mastering mathematics does not improve the
seeing and comprehension of mathematical equations under inconsistency syntax spacing of
mathematical equations. The general indication of the test is that seeing and comprehension of
mathematical equations is dependent on mastering and understanding of mathematical concepts
if the equations have an inconsistent syntax spacing.
Graphical representation for the accuracy levels for the two groups’ syntax knowers and syntax
non-know for presentations under the three spacing conditions indicate a higher accuracy

IMPROVING VISUAL FOR MATHEMATICS EQUATIONS 7
average for syntax knowers as compared to syntax non-know in all cases. This shows that
mastering mathematics have a significant influence on seeing mathematical equations, which
also increases the accuracy of the solution for the equations. Mastering of mathematical concepts
positively influence the seeing capabilities of mathematical equations, hence indicating that an
increase in comprehension of mathematical concepts improves the visibility strength of seeing
mathematical equations.
Conclusions
According to the results obtained from the report, the conclusion that there is a statistical
association between mastering mathematics and seeing of mathematical equations is valid. The
report has shown that students who have mastered mathematical concepts obtained better
mathematical accuracy in the tests compared to students who have not mastered mathematical
concepts. However, under inconsistent presentation condition, both groups failed there accuracy
levels, but students who mastered mathematical concepts had a better accuracy rate hence
supporting the latter statement. The report also concludes that mastering of mathematical
concepts may improve the seeing and comprehension of mathematical equations; however, the
change of syntax spacing will significantly reduce the accuracy level for the solutions. The test
was significant and provided sufficient evidence that comprehension and mastering of
mathematical concepts improve the seeing of mathematical equations under neutral spacing,
consistent spacing, and inconsistent spacing. Inconsistent syntax spacing makes it difficult to
give the correct solution; however, students with more mathematical knowledge have better
seeing and comprehension capabilities in given the correct solution.

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References
Bernard, M., & Chotimah, S. (2018, September). Improve student mathematical reasoning ability
with open-ended approach using VBA for PowerPoint. In AIP Conference Proceedings
(Vol. 2014, No. 1, p. 020013). AIP Publishing.
Borgonovi, F., & Pokropek, A. (2019). Seeing believes: Task-exposure specificity and the
development of mathematics self-efficacy evaluations. Journal of Educational
Psychology, 111(2), 268.
Kulkin, M. (2016). Math Is Like a Scary Movie. Helping Young People Overcome Math
Anxiety. Afterschool Matters, 23, 28-32.
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.