"Mathematics is a game played according to certain simple rules with meaningless marks on paper." -- David Hilbert
Since the beginning of society, mathematics has been used as a tool for solving problems and answering questions in the cultures. Mathematics was vital for equivalent trades and accurate measurements, therefore it was the key to controlling the economic profits coming in and out. As time flew, mathematics developed from the work of several intellectuals discovering concepts and formulas of math. Presently Mathematics has become the main axis in most of the academics, it is now almost impossible to look at subjects without concept of math. As a result, obviously mathematics has evolved into a necessary subject in education. However, the way of teaching math is slightly turning from making students learn the way of finding out the solution to the answer to memorizing the ways to solve certain problems. I believe that Problem Based Learning for math is worth fighting for.
Mathematics education is losing it’s definition of acquiring certain knowledge or skills of math nowadays. Students desire to focus on the types of problems that are coming out in the test which they can simply memorize, and it is surely not the ways to understand concepts or basic knowledge. Their way of studying is memorizing the processes and formulas in order to solve a problem, not to understand how the processes are done or the formulas created. They believe that if they toy a little with simple rules, they would easily get an answer for the problem and ace the tests. This is actually a true and effective ways to solve problems on a test. However, information achieved just from memorizing, fades out rapidly as fast as students in math class leave when the class time is over, which wastes all the time of learning certain part of math again by making this part a weak spot for them. The worst case is having a brain mix up with the memorized concepts with other concepts of math which requires much more sacrifices than losing the memory. One such case happened in school when a student who was taking a mathematics test was confused with the multiplication and division of negative numbers with powers of negative numbers because of his imperfect memorization mixed up with other mathematical concepts and screwed up the whole test. Although the ultimate result of memorization instead of understanding in math is an absolutely ineffective way, current students are not descrying that fact and maintain their positions of memorizing. However, Problem Based Learning is perfectly capable of enlightening students to the right way of studying mathematics.
Problem Based Learning-also called PBL- is basically a way of teaching by problems given by the teacher. The participants struggle to solve a problem with all the knowledge and creativity they have, as it usually is not a problem that can be solved by the memorization of ‘simple rules’, which absolutely improves critical thinking skills that are considered as necessary factors in solving mathematical problems. Mostly the participants get assigned with other students and form small groups in which they discuss the problem and concepts that might help them to solve the problems. Through these stages of discussion, researches have found that Problem Based Learning also supports the development of collaboration skills including the ability of communication. Even later on it has been discovered that employers are appreciating about students’ attitudes on the work. Throughout the experiments and surveys it has been demonstrated that Problem Based Learning is affecting students in positive ways, and it completely redeems the improvements mathematical education needs.
Problem Based Learning supports the students’ understanding of mathematical concepts. Psychological research demonstrates the fact that PBL helps students improve thinking strategies via experience of solving problems given by teacher. Students having PBL for their learning, achieve knowledge by constructing over the previous ones, whereas students having instructions from teacher for their lesson learn by mechanically filling up the information causing imperfect memorization with danger of oblivion. Therefore, this requires participants to recall their previous knowledge in order to learn the new concept, which fixes the complication of incorrect knowledge by confirming it again through deliberating and discussing over the group to come up to the solution, and PBL also prevents another misunderstanding of the concept since students themselves would be the ones teaching it. Problem Based Learning operates inductive ways of explaining a concept whereas common teaching by teacher instructions uses deductive ways of describing. As explained, PBL’s first step of learning comes from the problem given by an instructor, which means that explanation and understanding comes before the result, causing the process of getting to the solution to be stored at the basic knowledge than the result that came out. In these ways, Problem Based Learning effectively builds up the participants’ knowledge from the basic part, and it is being proved through real scenarios.
Cycles with negative effects are covering around mathematical education and students are being affected. Although memorization of ‘simple rules’ in math is just an instant way of increasing mathematics grade, it is definitely not a way of developing mathematical skills. Some people indicate that such complicated mathematical skills are not needed in real life, and there are no need for improvements in education anymore. However, they have to understand that, although math is only used in professional areas, mathematical education develops sense of logic and affects the brain in a great way. Mathematical education absolutely requires improvement, and therefore I strongly insist that PBL, is worth fighting for.
Since the beginning of society, mathematics has been used as a tool for solving problems and answering questions in the cultures. Mathematics was vital for equivalent trades and accurate measurements, therefore it was the key to controlling the economic profits coming in and out. As time flew, mathematics developed from the work of several intellectuals discovering concepts and formulas of math. Presently Mathematics has become the main axis in most of the academics, it is now almost impossible to look at subjects without concept of math. As a result, obviously mathematics has evolved into a necessary subject in education. However, the way of teaching math is slightly turning from making students learn the way of finding out the solution to the answer to memorizing the ways to solve certain problems. I believe that Problem Based Learning for math is worth fighting for.
Mathematics education is losing it’s definition of acquiring certain knowledge or skills of math nowadays. Students desire to focus on the types of problems that are coming out in the test which they can simply memorize, and it is surely not the ways to understand concepts or basic knowledge. Their way of studying is memorizing the processes and formulas in order to solve a problem, not to understand how the processes are done or the formulas created. They believe that if they toy a little with simple rules, they would easily get an answer for the problem and ace the tests. This is actually a true and effective ways to solve problems on a test. However, information achieved just from memorizing, fades out rapidly as fast as students in math class leave when the class time is over, which wastes all the time of learning certain part of math again by making this part a weak spot for them. The worst case is having a brain mix up with the memorized concepts with other concepts of math which requires much more sacrifices than losing the memory. One such case happened in school when a student who was taking a mathematics test was confused with the multiplication and division of negative numbers with powers of negative numbers because of his imperfect memorization mixed up with other mathematical concepts and screwed up the whole test. Although the ultimate result of memorization instead of understanding in math is an absolutely ineffective way, current students are not descrying that fact and maintain their positions of memorizing. However, Problem Based Learning is perfectly capable of enlightening students to the right way of studying mathematics.
Problem Based Learning-also called PBL- is basically a way of teaching by problems given by the teacher. The participants struggle to solve a problem with all the knowledge and creativity they have, as it usually is not a problem that can be solved by the memorization of ‘simple rules’, which absolutely improves critical thinking skills that are considered as necessary factors in solving mathematical problems. Mostly the participants get assigned with other students and form small groups in which they discuss the problem and concepts that might help them to solve the problems. Through these stages of discussion, researches have found that Problem Based Learning also supports the development of collaboration skills including the ability of communication. Even later on it has been discovered that employers are appreciating about students’ attitudes on the work. Throughout the experiments and surveys it has been demonstrated that Problem Based Learning is affecting students in positive ways, and it completely redeems the improvements mathematical education needs.
Problem Based Learning supports the students’ understanding of mathematical concepts. Psychological research demonstrates the fact that PBL helps students improve thinking strategies via experience of solving problems given by teacher. Students having PBL for their learning, achieve knowledge by constructing over the previous ones, whereas students having instructions from teacher for their lesson learn by mechanically filling up the information causing imperfect memorization with danger of oblivion. Therefore, this requires participants to recall their previous knowledge in order to learn the new concept, which fixes the complication of incorrect knowledge by confirming it again through deliberating and discussing over the group to come up to the solution, and PBL also prevents another misunderstanding of the concept since students themselves would be the ones teaching it. Problem Based Learning operates inductive ways of explaining a concept whereas common teaching by teacher instructions uses deductive ways of describing. As explained, PBL’s first step of learning comes from the problem given by an instructor, which means that explanation and understanding comes before the result, causing the process of getting to the solution to be stored at the basic knowledge than the result that came out. In these ways, Problem Based Learning effectively builds up the participants’ knowledge from the basic part, and it is being proved through real scenarios.
Cycles with negative effects are covering around mathematical education and students are being affected. Although memorization of ‘simple rules’ in math is just an instant way of increasing mathematics grade, it is definitely not a way of developing mathematical skills. Some people indicate that such complicated mathematical skills are not needed in real life, and there are no need for improvements in education anymore. However, they have to understand that, although math is only used in professional areas, mathematical education develops sense of logic and affects the brain in a great way. Mathematical education absolutely requires improvement, and therefore I strongly insist that PBL, is worth fighting for.
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