How Teaching Methods Affect Children's Mathematical Responses

This document presents a PhD research proposal focused on how different teaching methods affect children's incorrect responses to mathematical tasks, specifically in geometry. It aims to understand the cognitive processes behind these errors, including the role of memory and knowledge retrieval. The proposal includes research questions addressing the impact of teaching styles, the diversity of learners, and the contribution of memory to mathematical knowledge recall. The methodology involves a case study design with grade 5-7 students, employing tests, interviews, and data analysis using both qualitative (expert opinions) and quantitative (parametric tests like t-tests and ANOVA) methods. Ethical considerations are addressed to ensure participant rights and confidentiality. The research seeks to improve teaching practices by understanding the factors contributing to mathematical errors in children.

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Running head: How distinct types of teaching affect children wrong response to mathematical
task
How distinct types of teaching affect children wrong response to
mathematical task
Student Name
Institution Name

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How distinct types of teaching affect children wrong response to mathematical task
Introduction
With the technological advancements going on around the globe, the teaching of
mathematics has evolved to include different methods which were previously not in place. A
method of teaching is simply how the contents are relayed to the students. This covers the
style of instruction as well as materials applied in the teaching process (Katz and Parshall,
2014). Below are some methods popularly used in teaching maths.
One is the use of visuals. This involves using graphics in addition to giving
explanations during teaching, another technique is making connections; the brain is a major
player when it comes to learning. The long-term memory is composed of a web of neurons
which help students in developing connections (Lampert and Ball, 1998). This is what assists
the students understand the concepts. So, the teaching method in this case entails connecting
the taught concepts with the students’ worlds or other previously taught concepts and paying
close attention to the students’ reaction to the connections. Another style is the use of
assessments, in this the teacher use tests frequently to gauge areas understood by the students.
The tests are normally in form of formative tests which are not designed for the purpose of
grading. Lastly, focusing on strategies is another style. This entails modelling several models
of strategies to be used in problem-solving while at the same time encouraging students to
apply the taught skills in solving the existing problems (Carpenter, et al., 1997).
Statement of the problem
As per the above-mentioned explanations there are a number of techniques which are
applicable in teaching mathematics. These methods may occasionally raise wrong responses
by the students when thinking mathematically. The wrong response in this scenario is the
failure by the students to interpret the maths concepts appropriately. This may trigger
application of the concept is a wrongful manner by the student when trying to think
mathematically. The problem to be answered by this research is how different methods used
in teaching mathematics may be responsible for the children’s wrong response to
mathematical tasks.
Purpose of the study
The purpose of this study is to evaluate how distinct types of teaching affect children
wrong response to mathematical task. The teaching of mathematics is a very vital area in
children’s education. Mathematics is one of the subjects that enhance problem-solving skills

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How distinct types of teaching affect children wrong response to mathematical task
a factor which is very helpful for human existence. The unit of analysis in this study will be
the students of age group 10-11 years. The set will form the basis through which information
will be collected, data analysed, and generalisation made.
Research Questions
Regarding this study the below-listed questions will be addressed
The primary question is;
How distinct types of teaching affect children wrong response to mathematical task
The secondary questions are;
a. How do pupils retrieve mathematical answers from there memory?
b. How do distinct types of teaching impacts on recalling information from the memory?
c. Do diverse types of learners require diverse types of teaching methods?
d. How does memory contribute to recalling mathematical knowledge taught?
The research questions are the basis from which the hypothesis was computed. Below is
the hypothesis that the research will aim to verify.
a. Distinct types of teaching affect children wrong response to the mathematical task
b. Diverse types of learners need to be taught using different techniques
c. Memory contributes to recalling mathematical knowledge
Literature review
Cognitive psychology
Cognitive psychology is the study of the mind as a processor of information. The aim
of the psychologists in this field is to build a model of the mental information processing
system (Anderson, 2010). This includes perception, memory, thinking, consciousness,
attention and language. The study of cognitive psychology shifted the emphasis of
psychology from concentrating in conditioned behaviour and psychoanalyst to the study and
understanding of human’s mind information processing system (Hasher and Zacks, 1979).
Through the introduction of the computers scientists have been able to model and have a
clearer understanding of the human thinking process than before.

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How distinct types of teaching affect children wrong response to mathematical task
Memory
The mental records that are maintained in the human brain are what is referred as
memory. This is what enables people to retrieve past information which includes even the
skills that we possess (Hasher and Zacks, 1979). The human memory is divided into three
sections; long-term, short-term, and sensory memory processes. The long-term is what
humans normally utilise in their day to day activities. The types of memory each have a
unique mode of operation but the three collaborate so to complete the memorization process
(Ginsburg, 1997).
The memory works in three stages encoding, storage as well as retrieval. The
encoding stage involves sending the information to the brain where it is dissected into
significant elements. This is followed by the storage phase where the brain must maintain the
encoded information for a period (Baddeley, n.d.). Retrieval on the other hand involves the
ability to access the stored information and bring out the old information from the permanent
memory to the short-term memory which allows for mental manipulation for usage (LaBar
and Cabeza, 2006).
Learning can be defined theoretically as the capacity to modify the information stored
in the memory regarding the latest information and experience. Being that memory depends
on the prior learning the initial step in memory is therefore learning . Sensory information
makes its way to the brain consciously in two subtypes iconic and echoic memories. Vision
has a longer duration in the human brain and pupils can therefore quickly if they visualize
while studying (Anderson, 2000).
Types of learners
Students normally develop a variety of techniques so as to memorize contents taught,
these methods do vary from student to student and can be used to develop a model of types of
learners (Denig, 2004). The pupils respond to a method of teaching is guided by the type of
learner they fall under. In general, four types of learners exist; auditory, visual, reading and
kinesthetic (Lambert and McCombs, 1998). Auditory learners master contents well by
reciting the information back to the presenter while kinaesthetic ones master more contents
through participating in a number of activities (Galeet, 1999). Just as the name suggests
visual learners learn best through use of imagery while writing one’s master best when they
take notes of the contents taught.

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How distinct types of teaching affect children wrong response to mathematical task
A geometry teacher must consider all the four groups of learners to effectively ensure
the student's mastery of the contents. To cater for the full set of students the teacher should
review the teaching methods and come up with a mixture of methods that fits the entire group
(Binet, 1916).
Methodology
Research design
The design of the study will be a case study. This will involve concentrating the
research to the pupils of grade 5 to 7 in a local school situated within Liverpool city in the
United Kingdom. The research will derive data from the teacher, administrators and the
pupils within the school. the students will undertake several tests whose results will be
analysed to come to conclusions. As a way of giving more highlight to the pupils’ responses
their teachers and school administrators will be interviewed.
Sampling
The research will be concentrated on understanding children responses when solving
mathematical problems. The population of concern is that of pupils in grade six who are
undertaking geometry. To come up with the research sample a school will be selected at
random within the city of Liverpool. From here the pupils of grade 5-7, their teachers and
administrators in the current year will be identified and used as the research participants. To
participate in the study the pupil should be between the age of 10 to 11 years. The gender of
the pupil will not be considered during the study.
Instrumentation
The collection of the research data will involve the use of interviews and
experimentations. Secondary data sources will be used to complement the study. The major
instrument will be the observation grids. This will record observed data from the tests
administered to the students. Afterward interviews will be used to gather information from
the teachers and the administrators to supplement the one collected by the experiments
conducted. The variability of the study will be enhanced by only relying on the use of experts
and secondary sources of information to assist interpret the findings and come up with
valuable conclusions.
Procedures for data collection and analysis

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How distinct types of teaching affect children wrong response to mathematical task
The data collection will be conducted in two phases the first phase will involve the
pupils only. A simple geometry question will be taught to them and a short test conducted to
gauge their understanding of the contents. Afterward the teaching methods will be changed
and again tests conducted. The results f the tests will be used to gauge the students’ reaction
to various teaching methods and to classify the pupils based on their types as indicated by the
teaching method they understand best.
The second phase of the study will involve the teachers and administrators who will
require answering interview questions based on a questionnaire.
The data analysis will be done qualitatively as well as quantitatively. The qualitative
data analysis will mainly involve the use of expert’s opinion to interpret the results. On the
other hand, the Microsoft Excel software will be relied on when carrying out statistical
analysis. The statistical tests will be mainly parametric where the sample will be assumed to
follow normal distribution some of the analysis that will be carried out will be the t-0tests,
ANOVA tests and the descriptive statistics summary.
Ethical considerations
To protect the rights of the participants, the participation in the research will be
voluntary and no form of incentive will be used to allure individuals to participate. Due to the
involvement of minors in the study their teachers, administrators as well as parents will be
required to give confirmation before they can be used as participants. Furthermore, personal
information regarding the participants will not be collected to seal identity and maintain
confidentiality and privacy.
Discussion
In every society there exist a range of students depending on the techniques they use
to master concepts. Having understood the knowledge surrounding cognitive psychology,
types of teaching methods and types of students, it is important to understand how teaching
contributes to wrong response among the pupils when undertaking maths problems. This
study is specifically designed to fill this gap. The study’s importance relies on how this
analysis will be applicable in improving teaching especially in the area around geometry.

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How distinct types of teaching affect children wrong response to mathematical task
References
Anderson, J. (2010). Cognitive Psychology and Its Implications, New York: Worth
Publishers.
Anderson, J. R. (2000). Learning and memory: An integrated approach. 2nd ed. Hoboken,
NJ, US: John Wiley & Sons Inc.
Baddeley, A. D. (n.d). The Psychology of Memory. 1 ed. New York: Basic Books Inc..
Lampert, M. and Ball, D. L. (1998). Teaching, Multimedia, and Mathematics: Investigations
of Real Practice. The Practitioner Inquiry Series, New York: Teachers College Press.
Binet, A. and Simon, T. (1916). The development of intelligence in children, Baltimore:
Williams & Wilkins.
Denig, S. J. (2004). Multiple Intelligences and Learning Styles: Two Complementary
Dimensions.. Teachers College Record, 106(1), pp. 96-111.
Galeet, B. (1999). An analysis of kinesthetic learners' responses: teaching mathematics
through dance. Doctoral Dissertation, Washington D.C: American University.
Ginsburg, H. (1997). Mathematics learning disabilities: a view from developmental psychology. US
National Library of Medicine, 30(1), pp. 20-33.
Hasher, L. and Zacks, R. T. (1979). Automatic and effortful processes in memory. Journal of
Experimental Psychology, 108(3), pp. 356-388.
LaBar, K. S. and Cabeza, R. (2006). Cognitive neuroscience of emotional memory. Nature
Reviews Neuroscience, 7 (1), p. 54–64.
Lambert, N. M. and McCombs, B. L. (1998). How students learn: Reforming schools
through learner-centered education. Eds ed. Washington, DC, US: American Psychological
Association.
Carpenter, T. P., Fennema, E., Fuson, K., Hiebert, J., Murray, H. and Wearne, D. (1997).
Making Sense: Teaching and Learning Mathematics with Understanding. 1st ed.
s.l.:University of Wisconsin Foundation.
Katz, V. J. and Parshall, K. H. (2014). Taming the Unknown: A History of Algebra from
Antiquity to the Early Twentieth Century (2014), s.l.: s.n