Teaching Mathematics through Guided Discovery
As with every academic subject, there are a variety of strategies for teaching mathematics to school-aged students. Some strategies seem to be better than others, especially when tackling certain topics. There is the direct instruction approach where students are given the exact tools and formulas they need to solve a problem, sometimes without a clear explanation as to why. The student is told to do certain steps in a certain order and in turn expects to do them as such at all times. This leaves little room for solving varying types of problems. It can also lead to misconceptions and students may not gain the full understanding that their teachers want them to have. So how can mathematics teachers get their students to better understand the concepts that are being taught?
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 ability for children to discover is innate. From birth children discover all sorts of different things about the world around them. It has even been said that "babies are as good at discovery as the smartest adult" (Gopnik, 2005). Discovering is the natural way that children learn. By interacting with the world around them, they ar...
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... a sense of accomplishment, something they cannot get through direct instruction alone. This sense of accomplishment will raise their mathematical self-esteem. This can, in turn, help students appreciate and enjoy mathematics even more. Few would argue against the idea that any teaching strategy that gets students to believe in themselves and enjoy the subject is a good one.
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From two studies in mathematics, a total of four relationships between teachers' content knowledge and student learning were examined. In three instances, a positive relationship was found, for two cohorts of elementary grades students over a three year period and for grade 3 students' learning of advanced concepts. In one instance, grade 3 students learning of basic concepts, no relationship was found. In science, a total of three relationships between teacher content knowledge and student learning were examined. In two instances, a relationship was documented between teachers' content knowledge, both correct and incorrect, and their grade 8 students' development of correct and incorrect understandings, respectively. In the third instance, high school biology teachers' knowledge of the nature of science was not found to relate to their students' learning about the nature of
...ts work on the lessons independently or with a preservice teacher by using manipulatives or other mathematical tools it will allow them to fully grasp the concept that is being taught so they can do well in the long run of learning more complex mathematics.
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.
Now days we can see that young children are very inquisitive about finding the reason behind every occurrence. They are self motivated to learn about the “Hows” and “Whys” of the world. It can be said that the children are almost like scientist as they collect evidences by scrutinizing and experiencing the world. Children are generally involved in the process making hypotheses; they are also engaged in evaluating the statistical data and releasing prior beliefs when they are presented by other stronger evidences. All this they are doing even when they are searching for their toys, arranging blocks in any random manner or playing with toys with their friends. Children also show amazing psychological intuition by watching the actions of other people and can also determine underlying enthusiasm, desires and preferences (Kushnir and Wellman, 2010).
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.
By the age of three a child's brain is three quarters of its adult size. From infancy to the age of two development is very rapid (Santrock, 1996). For this reason it is essential for the child to be able to explore their world around them. By exploring children will increase their knowledge and understanding of the world.
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
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The most successful teaching begins with clarity about important learning outcomes and about the evidence that will show that learning has occurred (Marzano, 2010, p. 74)
Allowing children to learn mathematics through all facets of development – physical, intellectual, emotional and social - will maximize their exposure to mathematical concepts and problem solving. Additionally, mathematics needs to be integrated into the entire curriculum in a coherent manner that takes into account the relationships and sequences of major mathematical ideas. The curriculum should be developmentally appropriate to the