Mathematics Education

Mathematics education needs an improved strategy for developing students' quantitative skills in order to prepare them for daily interaction in today's society.

In order for students to become quantitatively fit for our society, their teachers must obtain more knowledge of the subject material. Many math teachers at the elementary level do not have degrees in the area, and this lack of knowledge can cause major concerns in the development of students' quantitative skills. It is also possible that teachers may not fully understand the meaning behind certain concepts, which can ultimately contribute to uncertainty and a lack of developed mathematical reasoning. Changing the teacher's knowledge of the material will give students the opportunity to enhance their understanding of mathematical concepts and quantitative skills. In Mathematics and Democracy-The Case for Quantitative Literacy it states, "No matter what we say or what curriculum we teach, students will remain unconvinced of the need for quantitative literacy if they do not perceive their teachers as being quantitatively literate" (NCED, p 97). If a teacher is uncomfortable presenting the material to the class, the development of the students' mathematical skills will be inadequate. Math is a subject that is frequently overlooked and short-changed at the elementary level. However, it is essential for students to grasp certain topics and have an intuitive understanding of mathematics at a young age. This understanding at the beginning of a student's education will contribute to the further development of the student's quantitative skills later on in his learning career. The improvement of teacher's understanding of mathematical concepts will allow students to hone their skills to a greater extent, contributing to the overall enhancement of student's quantitative literacy.

Not only can the education of teachers change to improve quantitative skills, but teaching mathematics and quantitative literacy simultaneously will help enhance students' practical problem solving and mathematical common sense. It is crucial for people to think logically and use mathematical reasoning to actively participate in today's society. One must be able to interpret graphs when reading the newspaper and be capable of analyzing numbers and symbols in various situations. The most common skills individuals use in real world situations are taught and developed at a very young age. Therefore, mathematical education needs a balance between concrete formulas to solve problems and an ability to work with numbers in different contexts. In Numerical Common Sense for All it says,

"Some suggest in response, that we should change the entire secondary school curriculum to more clearly emphasize abstract symbolic reasoning, even if it is at the expense of real-world, data driven analysis and problem solving; however, because we are only talking about a few hundred mathematics Ph.D.'s per year, common sense suggests that the benefits may not outweigh the cost of such a drastic change in pedagogical practice. Others say that applied real-world problems are so important that they should be taught in every discipline, even if at the expenses of abstract pure mathematics. Clearly neither of these extremes will serve the country well. A balance is required and will eventually be reached. I believe in the multiplication tables and the distributive law, not only because they are needed to understand algebraic problem solving well enough to get correct answers but also because they are the basis of quantitative literacy- which encompasses citizenship, personal finance, personal medical decisions, and work-related spreadsheet analyses" (NCED, pg. 64).

The ideal curriculum consists of a combination of pure mathematics and logical problem solving. The appropriate skills need to be taught to students at a young age, keeping in mind the idea that individuals in today's society are daily users of math. Many of the basic skills taught in mathematics are the building blocks for a quantitatively fit individual. These two unique areas have many connections with one another and should be taught collectively because an individual can use mathematics to develop his quantitative skills.

Along with mathematics education and quantitative literacy being taught together to provide a balance of the necessary skills needed to interact in today's society, the way teachers teach also contributes to the development of students' quantitative skills and practical problem solving. Teachers' personal experiences can affect the way they teach the course because specific methods may be more appealing to them than others. For example, a teacher may instruct a student to perform a calculation in an explicit manner, limiting the student's potential understanding and reasoning. It is important for students to have an approach that works best for them because every student is unique and learns differently. Students can go about solving problems in a way that satisfies them, not the teacher, allowing them to actually enjoy logical thinking and practical reasoning. They learn about their personal preferences through mathematical experience and may be eager to learn, further developing their quantitative skills. The Trends in International Mathematics and Science Study (TIMSS) compares mathematics achievements of U.S. students to students of other countries. A video study was done in 1995 to evaluate classroom practices of eighth grade mathematics lessons in America, Japan, and Germany (Kilpatrick, pg. 49). There were some noticeable contrasts between the instructions of the German and Japanese classes and those of the United States. The teachers in U.S. classes presented a few problems to the class and proceeded to demonstrate how to solve them. This method of teaching is somewhat repetitive and varies with the Japanese and German approaches. The teaching patterns of Japan and Germany consisted of students developing mathematical topics through examples and justifications. These students could approach different problems however they wanted, expanding the students' thinking and logical reasoning. The 1995 TIMSS assessment results showed that Japan scored in the top four out of forty one countries while the United States scored slightly below the overall average. These statistics have a direct correlation with the teaching patterns of the United States, Germany, and Japan. The difference between lectures and small group work is drastic as students in small groups can interact more closely with one another and go about solving problems in a manner that works best for them. These methods for problem solving are not explicit as students can approach situations in different ways and reach the same solution. The results from various studies show that some strategies may be more appropriate than others. A better design of mathematics education will naturally lead to a more developed quantitative literacy.