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 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.
The secondary questions are;
The research questions are the basis from which the hypothesis was computed. Below is the hypothesis that the research will aim to verify.
- Distinct types of teaching affect children wrong response to the mathematical task
- Diverse types of learners need to be taught using different techniques
- Memory contributes to recalling mathematical knowledge
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.
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.
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).
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.
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
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.
References
Anderson, J. (2010). Cognitive Psychology and Its Implications, New York: Worth Publishers.
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Lampert, M. and Ball, D. L. (1998). Teaching, Multimedia, and Mathematics: Investigations of Real Practice. The Practitioner Inquiry Series, New York: Teachers College Press.
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Denig, S. J. (2004). Multiple Intelligences and Learning Styles: Two Complementary Dimensions.. Teachers College Record, 106(1), pp. 96-111.
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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.
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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.
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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
