We have been facing increasing failure in school mathematics for years, in spite of intensive efforts to improve. It is a fact that we are missing something fundamental about the schooling process. But we do not even seem to be sincerely interested in this. We push for excellence without regard for causes of failure or side effects of interventions. We try to cure symptoms in place of finding the underlying disease, and we focus on the passing of tests instead of meaningful goals.
Maths is not a difficult subject but it is made abstract by poor quality of teaching and hence students find it difficult to comprehend. More over , not only do we fail to teach children mathematics, but we teach many of them to dislike it.
Learning mathematics is as much a matter of psychology as it is of intellectual understanding. Studies on the psychology of mathematics suggests that students limit themselves with their beliefs about their mathematical ability and also claims our understanding of cognitive psychology influences how math should be taught . A 2010 article in Psychology Today suggests that students are overwhelmed with too much math instruction and consequently cannot perform well.
Mathematics and Psychology
Psychology , being the scientific study of the relationships between mental processes, emotions, and behavior is linked with maths in three major ways.
1) Psychologists study mathematical cognition, i.e., the development of brain, acquisition, and application of mathematical skills.
2) They investigate people's feelings and attitudes regarding mathematics.
3) Psychologists use mathematics, particularly statistics, as a professional tool to quantify and analyze their scientific findings.
Psychologists working in the field of mathematical cognition study how humans process information, interpret mathematical symbols, and develop and use strategies to solve mathematical problems. For example, these skills are particularly important for so-called "word" problems, where written descriptions must be translated into equations. Most students consider "word" problems more difficult to solve than other types of math problems. This is because "word" problems require a variety of skills from the brain, including the ability to read and comprehend the meaning and context of the words, the ability to perceive and define the mathematical problem, the ability to assign mathematical symbols to unknown variables, and finally, the ability to apply problem-solving strategies and calculate the correct answer.
Mathematical cognition is a very important field in psychology. It benefits scientists and doctors studying the brain, and it helps educators develop better teaching methods for mathematics. In addition, its study is crucial to the development of "smart" computers, neural networks, fuzzy logic, robots, and artificial intelligence. Researchers also study how people feel about maths, because a person's feelings about a subject influence their willingness to learn and use it. For example, cultural and gender differences in attitudes about maths affect test scores. Another area receiving a lot of attention is called maths phobia or maths anxiety. Maths phobia is a fear of maths. People with maths phobia become so uncomfortable and anxious when confronted with mathematical tasks that they can experience physical symptoms including increased heart rate, nervous stomach, and breathing difficulties that prevent them from concentrating and learning. These feelings have been traced to a variety of sources, including negative experiences in the class room, poor self-image, lack of appreciation for the application of maths to "real life," and shyness that prevents asking questions.
The third major link between psychology and mathematics is that psychologists use mathematical and statistical tools to quantify and analyze their research findings. This use is called psychometrics and arises from the application of the scientific method in psychology, i.e., a systematic method of data collection, hypothesis development, and experimental testing that can be duplicated and verified by other scientists.
One example of psychometrics is the Intelligence Quotient (IQ) test, a standardized test that measures a person's relative intelligence. An IQ score is a relative measurement; it is compared to a reference IQ of 100 for the average score. IQ scores for a large population are an example of a statistical function called the normal distribution. Normal curves or Gaussian curves are the familiar bell-shaped curves in which measurements are graphed along the x-axis and frequency is graphed along the y-axis. The majority of IQ scores fall in the wide part of the curve near the mean value of 100. As scores deviate negatively or positively from 100, they decrease in frequency.
Q methodology is a type of analysis used in psychology to measure and quantify the feelings of a group of people regarding a particular subject. For example, a large group of students could be asked the following question: "How do you feel about your school?" A wide variety of answers would be collected ranging from "I hate it" to "I love it" with many opinions in between pointing out good and bad qualities of the school. This entire opinion set is called the concourse. From it, a limited number of opinions (the Q sample) would be selected that represent the spectrum of responses. During the next interview, the students would read the Q sample and rank their level of agreement with each opinion using a scale of -4 to +4, where -4 indicates strong disagreement and +4 indicates strong agreement with the opinion. This process is called Q sorting. The resulting numerical data can be analyzed using statistical functions to provide a mathematical description of student opinions about their school.
Common statistical concepts and tools studied and used by psychologists include correlation, regression, sampling distributions, probability density functions, and factor analysis.
Factors affecting learning of Mathematics
A genuine interest and skill in maths is based on several factors. Some of them are listed below.
1) Fear of mathematics
widespread fear of the subject. Fear may inhibit students from attempting to study mathematics or cause them to blank out when taking math tests. Successful mathematics teachers approach the subject with the right balance of encouragement and instruction to reduce students' fear.
2) Myths and self-limiting beliefs
Students' beliefs about maths may interfere with their ability to grasp mathematical concepts. For example, some female students may believe that girls cannot do as well in math as boys. These students may not try as hard because they do not believe they are capable of success.
3) Cognitive Psychology and Mathematics
Cognitive psychology is the branch of psychology that studies how we learn. For example, earlier drilling and repetition were key components of maths education. In more recent times, maths education has included hands-on activities because psychologists believe that children learn best through activity.
4) Over saturation of mathematical education
Psychology Today says that current educational philosophy appears to be to subject children who are not learning a subject to even more hours of that subject in school instead of learning, though, children may become overwhelmed. As far back as 1929, studies were being done to assess the effects of over saturation of mathematical education on children's mathematical knowledge. Psychology Today describes the results of one such study, in which students were not subjected to arithmetic until the sixth grade. The results of this study showed that students who did not study mathematics until sixth grade did as well as or better than students who began learning arithmetic in first grade.
5) Characteristics of Math Teachers
Maths teachers must possess certain characteristics for students to learn maths. The teachers must be encouraging, and they must not be afraid of maths themselves. A study republished in Psychology showed that the majority of teachers did not know basic mathematical concepts and were afraid that students would realize that they lacked knowledge. These teachers discouraged questions from students for fear of being found out. Many of them did not grasp mathematical concepts because they themselves were afraid of math.
When teachers love their students and understand the basic learning processes , they can make wonders to make their students love maths and apply mental ability in life.
SREEKUMARAN UNNI . A
HSST (Psychology)
Govt.HSS Mankada pallippuram
Maths is not a difficult subject but it is made abstract by poor quality of teaching and hence students find it difficult to comprehend. More over , not only do we fail to teach children mathematics, but we teach many of them to dislike it.
Learning mathematics is as much a matter of psychology as it is of intellectual understanding. Studies on the psychology of mathematics suggests that students limit themselves with their beliefs about their mathematical ability and also claims our understanding of cognitive psychology influences how math should be taught . A 2010 article in Psychology Today suggests that students are overwhelmed with too much math instruction and consequently cannot perform well.
Mathematics and Psychology
Psychology , being the scientific study of the relationships between mental processes, emotions, and behavior is linked with maths in three major ways.
1) Psychologists study mathematical cognition, i.e., the development of brain, acquisition, and application of mathematical skills.
2) They investigate people's feelings and attitudes regarding mathematics.
3) Psychologists use mathematics, particularly statistics, as a professional tool to quantify and analyze their scientific findings.
Psychologists working in the field of mathematical cognition study how humans process information, interpret mathematical symbols, and develop and use strategies to solve mathematical problems. For example, these skills are particularly important for so-called "word" problems, where written descriptions must be translated into equations. Most students consider "word" problems more difficult to solve than other types of math problems. This is because "word" problems require a variety of skills from the brain, including the ability to read and comprehend the meaning and context of the words, the ability to perceive and define the mathematical problem, the ability to assign mathematical symbols to unknown variables, and finally, the ability to apply problem-solving strategies and calculate the correct answer.
Mathematical cognition is a very important field in psychology. It benefits scientists and doctors studying the brain, and it helps educators develop better teaching methods for mathematics. In addition, its study is crucial to the development of "smart" computers, neural networks, fuzzy logic, robots, and artificial intelligence. Researchers also study how people feel about maths, because a person's feelings about a subject influence their willingness to learn and use it. For example, cultural and gender differences in attitudes about maths affect test scores. Another area receiving a lot of attention is called maths phobia or maths anxiety. Maths phobia is a fear of maths. People with maths phobia become so uncomfortable and anxious when confronted with mathematical tasks that they can experience physical symptoms including increased heart rate, nervous stomach, and breathing difficulties that prevent them from concentrating and learning. These feelings have been traced to a variety of sources, including negative experiences in the class room, poor self-image, lack of appreciation for the application of maths to "real life," and shyness that prevents asking questions.
The third major link between psychology and mathematics is that psychologists use mathematical and statistical tools to quantify and analyze their research findings. This use is called psychometrics and arises from the application of the scientific method in psychology, i.e., a systematic method of data collection, hypothesis development, and experimental testing that can be duplicated and verified by other scientists.
One example of psychometrics is the Intelligence Quotient (IQ) test, a standardized test that measures a person's relative intelligence. An IQ score is a relative measurement; it is compared to a reference IQ of 100 for the average score. IQ scores for a large population are an example of a statistical function called the normal distribution. Normal curves or Gaussian curves are the familiar bell-shaped curves in which measurements are graphed along the x-axis and frequency is graphed along the y-axis. The majority of IQ scores fall in the wide part of the curve near the mean value of 100. As scores deviate negatively or positively from 100, they decrease in frequency.
Q methodology is a type of analysis used in psychology to measure and quantify the feelings of a group of people regarding a particular subject. For example, a large group of students could be asked the following question: "How do you feel about your school?" A wide variety of answers would be collected ranging from "I hate it" to "I love it" with many opinions in between pointing out good and bad qualities of the school. This entire opinion set is called the concourse. From it, a limited number of opinions (the Q sample) would be selected that represent the spectrum of responses. During the next interview, the students would read the Q sample and rank their level of agreement with each opinion using a scale of -4 to +4, where -4 indicates strong disagreement and +4 indicates strong agreement with the opinion. This process is called Q sorting. The resulting numerical data can be analyzed using statistical functions to provide a mathematical description of student opinions about their school.
Common statistical concepts and tools studied and used by psychologists include correlation, regression, sampling distributions, probability density functions, and factor analysis.
Factors affecting learning of Mathematics
A genuine interest and skill in maths is based on several factors. Some of them are listed below.
1) Fear of mathematics
widespread fear of the subject. Fear may inhibit students from attempting to study mathematics or cause them to blank out when taking math tests. Successful mathematics teachers approach the subject with the right balance of encouragement and instruction to reduce students' fear.
2) Myths and self-limiting beliefs
Students' beliefs about maths may interfere with their ability to grasp mathematical concepts. For example, some female students may believe that girls cannot do as well in math as boys. These students may not try as hard because they do not believe they are capable of success.
3) Cognitive Psychology and Mathematics
Cognitive psychology is the branch of psychology that studies how we learn. For example, earlier drilling and repetition were key components of maths education. In more recent times, maths education has included hands-on activities because psychologists believe that children learn best through activity.
4) Over saturation of mathematical education
Psychology Today says that current educational philosophy appears to be to subject children who are not learning a subject to even more hours of that subject in school instead of learning, though, children may become overwhelmed. As far back as 1929, studies were being done to assess the effects of over saturation of mathematical education on children's mathematical knowledge. Psychology Today describes the results of one such study, in which students were not subjected to arithmetic until the sixth grade. The results of this study showed that students who did not study mathematics until sixth grade did as well as or better than students who began learning arithmetic in first grade.
5) Characteristics of Math Teachers
Maths teachers must possess certain characteristics for students to learn maths. The teachers must be encouraging, and they must not be afraid of maths themselves. A study republished in Psychology showed that the majority of teachers did not know basic mathematical concepts and were afraid that students would realize that they lacked knowledge. These teachers discouraged questions from students for fear of being found out. Many of them did not grasp mathematical concepts because they themselves were afraid of math.
When teachers love their students and understand the basic learning processes , they can make wonders to make their students love maths and apply mental ability in life.
SREEKUMARAN UNNI . A
HSST (Psychology)
Govt.HSS Mankada pallippuram
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