Teaching mathematics has evolved from the traditional instrumentalist view where the focus is on knowledge mathematical facts, rules and methods as independent concepts, to the more contemporary constructivist approach which focuses on building on prior knowledge and experiences incorporating mathematical facts, rules and methods to problem solve and investigate new mathematical concepts. This will in turn, enable students to apply concepts in real life situations. Teaching thematically is an approach which allows concepts to be applied to real life situations. While the benefits and success of the constructivist approach for long term learning are widely acknowledged, a teacher’s ability to engage with and implement this approach to teaching numeracy relies largely on their knowledge, experiences, attitudes and beliefs.
Ma (1999) explains that the understanding of elementary mathematical ideas in essence underpin the development of all mathematics. Ma (1999) further suggests that these elementary mathematical concepts establish the basis on which future mathematical thinking is constructed. Mathematics can often be taught in discrete and separate ways to cover a specific curriculum. However Richhart (1994) and Nodding (1993) imply that teachers should not simply cover the curriculum but rather uncover it. Booker (2010) supports these suggestions by explaining that mathematics needs to be viewed as a cohesive body of knowledge rather than as a series of fragmented ideas.
It is important for teachers to understand and foster new and ever evolving productive pedagogies. As previously briefly outlined, there has been a change in the way leading theorists believe to be the ideal way students should be taught for students to better ...
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...who are teacher-taught by rote.
References
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Before the article discussed the teacher implementing the practices into the classroom, it broke down the five strands of mathematical proficiency. Those five strands of mathematical proficiency include conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive
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.
I remember how mathematics was incredibly difficult for me and because of this I can relate to the struggles students have with math. For a teacher to be successful they need to create relevance for the students. I understand how to relate the various topics of mathematics to topics of the world, which for most students is difficult to do, For example, I remember at the CREC School I was observing at, there was a student of Bosnian decent who was having trouble understanding how to read a map of the United States. So I showed her a map of Bosnia with the same map key, and we discerned what everything meant (where the capital was, where the ocean was, major port cities were, etc…). She caught on quickly as she already had an understanding of Bosnia and it quickly transferred over to the map of the thirteen colonies. This skill is easily transferrable to mathematics by using relevant, real-world examples of concepts learned by
Being that the subject of mathematics is so complicated it takes an efficient teacher to be able to successfully teach students the correct steps in solving mathematical equations. Teaching math cannot be done successfully by reading some vocabulary words, filling in the blanks on a worksheet, and then taking a quiz, mathematics needs to be taught in ways were students get to explore problems and follow the necessary steps to solve the problem. Most importantly students need practice in math and that can be done in many different ways. Many teachers today think and teach the same way to all of their students, ignoring their individual ways of learning. “Teachers need to employ strategies that will help them develop the participation essential to engaging students in mathematics.” (National). It is also a proven fact that students tend to learn more and have higher participation when they work in groups. Effective teachers in the classroom will provide students with opportunities to work independently and collaboratively to make sense of the math curriculum in which they are learning. (Anthony & Walshaw, 2012). By working in groups students can ask questions to their peers as the arise and the students take more responsibility in t...
While children can remember, for short periods of time, information taught through books and lectures, deep understanding and the ability to apply learning to new situations requires conceptual understanding that is grounded in direct experience with concrete objects. The teacher has a critical role in helping students connect their manipulative experiences, through a selection of representations, to essential abstract mathematics. Together, outstanding teachers and regular experiences with hands-on learning can bestow students with powerful learning in
Mathematics has become a very large part of society today. From the moment children learn the basic principles of math to the day those children become working members of society, everyone has used mathematics at one point in their life. The crucial time for learning mathematics is during the childhood years when the concepts and principles of mathematics can be processed more easily. However, this time in life is also when the point in a person’s life where information has to be broken down to the very basics, as children don’t have an advanced capacity to understand as adults do. Mathematics, an essential subject, must be taught in such a way that children can understand and remember.
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
Sherley, B., Clark, M. & Higgins, J. (2008) School readiness: what do teachers expect of children in mathematics on school entry?, in Goos, M., Brown, R. & Makar, K. (eds.) Mathematics education research: navigating: proceedings of the 31st annual conference of the Mathematics Education Research Group of Australia, Brisbane, Qld: MERGA INC., pp.461-465.
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
Mathematics teachers teach their students a wide range of content strands – geometry, algebra, statistics, and trigonometry – while also teaching their students mathematical skills – logical thinking, formal process, numerical reasoning, and problem solving. In teaching my students, I need to aspire to Skemp’s (1976) description of a “relational understanding” of mathematics (p. 4). Skemp describes two types of understanding: relational understanding and instrumental understanding. In an instrumental understanding, students know how to follow steps and sequential procedures without a true understanding of the mathematical reasons for the processe...
The early acquisition of mathematical concepts in children is essential for their overall cognitive development. It is imperative that educators focus on theoretical views to guide and plan the development of mathematical concepts in the early years. Early math concepts involve learning skills such as matching, ordering, sorting, classifying, sequencing and patterning. The early environment offers the foundation for children to develop an interest in numbers and their concepts. Children develop and construct their own meaning of numbers through active learning rather than teacher directed instruction.
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.