Research on and information about mathematics and the learning of mathematics has evolved over the last one hundred years. In the first half of the 20th century much of the focus was on computational approaches such as drill and practice and incidental learning (Brownell, 1947; Thorndike, 1924). This emphasis can certainly be attributed to the lack of technology available along with the needs of society for efficient computation (Jones et al., 2002).
The development of the new math in the second half of the 20th century was a positional change for mathematics educators and researchers. The shift was towards the structure of mathematics (Jones & Coxford, 1970) as well as reflecting the current needs and state of mathematics at the time. Questions arose regarding what the content focus should be and what should the structure of the classroom involve. Advances in knowledge and technology characterize the 21st century. Kiong & Yong (2001) emphasize that these advances bring forth the need for a restructuring in mathematics education. The researchers accentuate imaginative methods in the learning and teaching of mathematics that can promote problem-solving skills, higher-order thinking skills, independent learning, collaboration, and communication skills. The skills and processes emphasized in mathematics curriculum in the past will not be sufficient in the knowledge-based era now present in our world.
What is certain is that mathematics is indispensible in generalizing, modeling, and understanding the world in which we all function and interact. Furthermore, mathematics has led the way for an increase in scientific and technological advancements. The end result is that there has been a significant amount of focus on mathematics ...
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... when a mathematical concept is presented under conditions in which the relevant variables remain constant but irrelevant variables are changed the ability to generalize is enhanced. The constructivity principle states that students should be allowed to build their own concepts by manipulating concrete materials in order to form mathematical relations.
Through interactions with the learning environment is how the principles attributed to Dienes stress the importance of learning mathematics. The phrase “mathematics is not a spectator sport” would apply to the theories developed by Dienes in that the classroom environment must include physical and mental involvement of the student (Post, 1981). The influence of Dienes can also be found in the work of Lesh & Doerr (2003) and their work related to the design of authentic models and model-eliciting activities.
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.
Robert, A. Wayne and Dale E. Varberg. Faces of Mathematics. New York: Harper & Row Publishers, Inc., 1978.
The article “Tying It All Together” by Jennifer M. Suh examines several practices that help students to develop mathematical proficiency. It began with a mathematics teacher explaining that her students began the year struggling to understand basic mathematics concepts, but after implementing the following practices into the classroom throughout the year, the students began to enjoy mathematics and have a better understanding of math concepts.
This class made me realize that there is more to math then just numbers and calculations. One interesting concept
Mathematics has played an integral part in daily life since the beginning of time. There have been many individuals responsible for paving the road to higher mathematics. Among these individuals is a man who was a physicist and scholar and helped to bring life to modern mathematics. His name was Leonhard Euler. Although he was born in the 18th century, Euler’s mathematic innovations still apply to the world of mathematics that we experience today.
Pateman, Neil A., Ed, et al. Proceedings Of The 27Th International Group For The Psychology Of Mathematics Education Conference Held Jointly With The 25Th PME-NA Conference (Honolulu, Hawaii, July 13-18, 2003). Volume 3. n.p.: International Group for the Psychology of Mathematics Education, 2003. ERIC. Web. 23 Apr.
The curriculum implies that teachers will teach students the skills they need for the future. Valley View’s High School math department announces, “Students will learn how to use mathematics to analyze and respond to real-world issues and challenges, as they will be expected to do college and the workplace.” Also, the new integrates math class allows students to distinguish the relationship between algebra and geometry. Although students are not being instructed a mathematical issue in depth, they are rapidly going through all the different topics in an integrated math class. Nowadays, students are too worried to pass the course to acquire a problem-solving mind. Paul Lockhart proclaims the entire problem of high school students saying, “I do not see how it's doing society any good to have its members walking around with vague memories of algebraic formulas and geometric diagrams and dear memories of hating them.” A mathematics class should not be intended to make a student weep from complicated equations, but it should encourage them to seek the numbers surrounding
Mathematics education has undergone many changes over the last several years. Some of these changes include the key concepts all students must master and how they are taught. According to Jacob Vigdor, the concerns about students’ math achievements have always been apparent. A few reasons that are negatively impacting the productivity of students’ math achievements are historical events that influenced mathematics, how math is being taught, and differentiation of curriculum.
In a musty and bleak portable classroom outside of Henry Clay High School, younger me sat and tried to understand the hardest foreign language of all, math. But this tutoring session was different, I was finally going to have a breakthrough and understand something in mathematics.
I also learned that mathematics was more than merely an intellectual activity: it was a necessary tool for getting a grip on all sorts of problems in science and engineering. Without mathematics there is no progress. However, mathematics could also show its nasty face during periods in which problems that seemed so simple at first sight refused to be solved for a long time. Every math student will recognize these periods of frustration and helplessness.
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.
To most people English or Language Arts is a creative course and math is just a logical, you get it or you don’t class. My purpose writing this paper is to change your mind. I believe that Math is just as, or more creative than English. I will demonstrate this through a couple of examples.
Devlin believes that mathematics has four faces 1) Mathematics is a way to improve thinking as problem solving. 2) Mathematics is a way of knowing. 3) Mathematics is a way to improve creative medium. 4) Mathematics is applications. (Mann, 2005). Because mathematics has very important role in our life, teaching math in basic education is as important as any other subjects. Students should study math to help them how to solve problems and meet the practical needs such as collect, count, and process the data. Mathematics, moreover, is required students to be capable of following and understanding the future. It also helps students to be able to think creativity, logically, and critically (Happy & Listyani, 2011,
What is math? If you had asked me that question at the beginning of the semester, then my answer would have been something like: “math is about numbers, letters, and equations.” Now, however, thirteen weeks later, I have come to realize a new definition of what math is. Math includes numbers, letters, and equations, but it is also so much more than that—math is a way of thinking, a method of solving problems and explaining arguments, a foundation upon which modern society is built, a structure that nature is patterned by…and math is everywhere.
When I graduated from high school, forty years ago, I had no idea that mathematics would play such a large role in my future. Like most people learning mathematics, I continue to learn until it became too hard, which made me lose interest. Failure or near failure is one way to put a stop to learning a subject, and leave a lasting impression not worth repeating. Mathematics courses, being compulsory, are designed to cover topics. One by one, the topics need not be important or of immediate use, but altogether or cumulatively, the topics provide or point to a skill, a mastery of mathematics.