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An essay on the history of mathematics
An essay on the history of mathematics
An essay on the history of mathematics
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Math Methodologies It is evident that methodologies in education, including Math, have in their crude forms existed long before theorist began coining catch phrases and terminologies. With the onset of higher learning and the desire to explore their world men have lived and learned by many of the teaching/learning methodologies that are being adapted today. What men have discovered through natural learning long ago is now being refined in order to support and strengthen modern day educational practices across academia.
Problem Based Learning (PBL) Problem-based learning (PBL) is a method of learning and teaching in which students are given the opportunity to focus on how and what they will learn. Students are presented by a teacher or lecturer
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The three main attributes of discovery learning are: exploring and problem solving to create, integrate, and generalize knowledge; it is student driven; includes interest-based activities in which the students determine the frequency and order; and entails activities which facilitate the adaption of new knowledge into the student’s existing knowledge base. The first attribute of discovery learning is a very important one: through exploring and problem solving, students take on an active role to create, integrate, and generalize knowledge. Instead of engaging in passively accepting information from teachers or from drill and practice, students establish broader applications for skills through activities that encourage risk-taking, problem solving, and an examination of unique experiences (Bicknell-Holmes & Hoffman, …show more content…
It also permits students to dictate the rate and pace of learning. Another important characteristic of discovery learning is that it is founded on the principle of using existing knowledge to build new knowledge. Discovery learning may be difficult for traditional educators to grasp or implement since it is a departure from the teacher centered lessons that have dominated the teaching profession for so long. A method that places the responsibility of learning in the hands of the learner may seem asinine to traditionalists. Fundamentally, discovery learning differs from traditional learning because it promotes active learning rather than passive; learning is also seen as process-oriented rather than content-oriented; failure is a welcomed and important part of the discovery process; feedback is necessary and critical for effective learning to occur; also discovery learning promotes a more profound level of understanding rooted in real world
The second part of this memo contains a rhetorical analysis of a journal article written by Linda Darling-Hammond. Interview The following information was conducted in an interview with Diana Regalado De Santiago, who works at Montwood High School as a mathematics teacher. In the interview, Regalado De Santiago discusses how presenting material to her students in a manner where the student actually learns is a pivotal form of communication in the field (Personal Communication, September 8, 2016).
Throughout my education journey, I have had the opportunity to learn theories that have helped others including me in the past. Jean Piaget’s theory is a great example. Piaget’s theories have helped a lot of students overcome difficulty in learning. While I consider his theory to my knowledge, I have been given the opportunity to come up with my own personal learning theory that has been a big help to my learning experience. I am very encouraged because I have had educators in the past who have helped me figure out what works best for me. Thomas Shuell helps us realize that; “learning is one of the most important activities in which humans engage” (2016, para.1). We learn new things in life and when we learn, it gives us the opportunity to gain experience and use these skills for real life situations. “It is at the very core of the educational process, although most of what people learn occurs outside of school” (Shuell, 2016, para.1). A lot of us become great problem solvers because of different types of learning theories.
Kieren, T., Gordon-Calvert, L., Reid, D. & Simmt, E. (1995). An enactivist research approach to mathematical activity: Understanding, reasoning, and beliefs. Paper presented at the meeting of the Ame rican Educational Research Association, San Francisco.
What is the most effective way to teach? Can students really learn and fully understand the material teachers convey to them on a day to day basis? According to a middle school mathematics teacher, his methods of teaching the traditional way was not as effective and producing a long-term impact as he would have liked. The article "Never Say Anything a Kid Can Say!" enriches us to the possibility of applying slight gradual modifications to our teaching methods and how we could find ways to utilize that information in the search for more effective teaching methods to encourage students to explain their thinking and become more deeply involved in the classroom discussions, thus developing their questioning skills (Reinhart, 2000). After analyzing his research, I can say as an aspiring Mathematics teacher myself, there are some positive aspects to his newfound teaching methods, as well as some questions of concern that I have pertaining the longevity of this approach to teaching.
Wu, Y. (2008). Experimental Study on Effect of Different Mathematical Teaching Methodologies on Students’ Performance. Journal of Mathematics Studies. Vol 1(1) 164-171.
Using literacy strategies in the mathematics classroom leads to successful students. “The National Council of Teachers of Mathematics (NCTM, 1989) define mathematical literacy as an “individual's ability to explore, to conjecture, and to reason logically, as well as to use a variety of mathematical methods effectively to solve problems." Exploring, making conjectures, and being able to reason logically, all stem from the early roots of literacy. Authors Matthews and Rainer (2001) discusses how teachers have questioned the system of incorporating literacy with mathematics in the last couple of years. It started from the need to develop a specific framework, which combines both literacy and mathematics together. Research was conducted through
Providing the explicit information they need through instruction is practical because it takes into account cognitive load theory, the link between working memory and long-term memory. Studies observing students in a classroom discovered that “when students learn science in classrooms with pure-discovery methods and minimal feedback, they often become lost and frustrated, and their confusion can lead to misconceptions” due to the lack of instruction (Kirschner et al., 2006). On the other hand, studies involving strongly guided learning showed that students learn more deeply and their quality of education is improved when they are given instruction and feedback on their work. Instructed learning provides a superior quality and amount of learning because it decreases cognitive load, provides worked examples that show students how to solve a problem, and employs methods such as process worksheets which assists students in providing more accurate answers than students who rely on discovery learning (Kirscher et al.,
I have ensured that I meet my students’ science needs by assuring that the material needed to be cover in the class was covered. Furthermost, the students are able to learn from exploring, which is different from teaching the students how to and giving them the information needed. The students were still able to learn the material needed to be covered by discovering the content.
As a secondary subject, society often views mathematics a critical subject for students to learn in order to be successful. Often times, mathematics serves as a gatekeeper for higher learning and certain specific careers. Since the times of Plato, “mathematics was virtually the first thing everyone has to learn…common to all arts, science, and forms of thought” (Stinson, 2004). Plato argued that all students should learn arithmetic; the advanced mathematics was reserved for those that would serve as the “philosopher guardians” of the city (Stinson, 2004). By the 1900s in the United States, mathematics found itself as a cornerstone of curriculum for students. National reports throughout the 20th Century solidified the importance of mathematics in the success of our nation and its students (Stinson, 2004). As a mathematics teacher, my role to educate all students in mathematics is an important one. My personal philosophy of mathematics education – including the optimal learning environment and best practices teaching strategies – motivates my teaching strategies in my personal classroom.
Helping students acquire and integrate new knowledge is another important aspect of learning. When students are learning new information, they must be guided in relating new knowledge to what they already know, organizing that information, and then making it part of their long-term memory. When the students acquiring new skills and processes, they must learn a model or the steps, then shape the skill or process to make it efficient and effective for them, and finally, internalize or practice the skill or process so they can perform it easily.
In this course I experienced an important change in my beliefs about teaching; I came to understand that there are many different theories and methods that can be tailored to suit the teacher and the needs of the student. The readings, especially those from Lyons, G., Ford, M., & Arthur-Kelly, M. (2011), Groundwater-Smith, S., Ewing, R., & Le Cornu, R. (2007), and Whitton, D., Barker, K., Nosworthy, M., Sinclair, C., Nanlohy, P. (2010), have helped me to understand this in particular. In composing my essay about teaching methods and other themes, my learning was solidified, my knowledge deepened by my research and my writing skills honed.
Reid (2003) also stated that discovery learning works by “ activating the relevant knowledge in learners memories, enhancing problem representation and hypothesis generation based on their existing background knowledge, eliciting more explanation activities toward the experiments and promoting access of knowledge base.” From this information we can then say that discovery learning works better due to the fact that it involves the participant more and has a active learning aspect to it that allows the participant to assign meaning to the task and overall increase
A somewhat underused strategy for teaching mathematics is that of guided discovery. With this strategy, the student arrives at an understanding of a new mathematical concept on his or her own. An activity is given in which "students sequentially uncover layers of mathematical information one step at a time and learn new mathematics" (Gerver & Sgroi, 2003). This way, instead of simply being told the procedure for solving a problem, the student can develop the steps mainly on his own with only a little guidance from the teacher.
The overall essence of education or knowledge acquisition is reflected in an axiom by Confucius which says “Tell me, and I will forget; show me, and I will remember; but involve me, and I will understand. Back then, it was clear that learning was a comprehensive process which involves passionate exchanges between students and their teachers; unfortunately this is not the case in most modern classrooms. Instead of the expected bidirectional communication between learners and teachers, in the modern learning environment there is a unidirectional system which involves the teacher incessantly hurling facts at students who, due to their passive roles as mere receptacles, have fallen asleep or; in the case of “best” students are mindlessly taking notes. This leads to a situation where knowledge has neither been conferred nor acquired.
Throughout out this semester, I’ve had the opportunity to gain a better understanding when it comes to teaching Mathematics in the classroom. During the course of this semester, EDEL 440 has showed my classmates and myself the appropriate ways mathematics can be taught in an elementary classroom and how the students in the classroom may retrieve the information. During my years of school, mathematics has been my favorite subject. Over the years, math has challenged me on so many different levels. Having the opportunity to see the appropriate ways math should be taught in an Elementary classroom has giving me a