Elementary Methods : Teaching Mathematics

In this paper, I will be writing about the math curriculum, including geometry, taught in schools across America in grades first through twelfth. In addition, I will also discuss what students in other countries are taught in the areas of mathematics. Then, we will look at the level of mathematical knowledge of students in the United States compares to those other countries. Finally, we will find out if there is a way we can improve our educational system to better our future generations understand of mathematics.

The first of the eight common core mathematical practices helps students know what to address before, during, and after they are presented with a problem. The key is to make sense of the problems and persevere in solving them. When a student is presented with a problem, common core can help them to make a plan, carry out the plan, and evaluate its success.

Therefore, although numeracy and mathematics are not the same, their shared focus on problem-solving skills, reasoning, and critical thought means they are inextricably linked.

America has been experiencing problems with math in education. Internationally we are not doing very well in math. This is not good for us as a country because math is an important part of our country’s growth. One reason for our failures in mathematics is because of the inadequate teachings of math in school. Some reasons why Americans are not good in math is because we teach memorization, teaching to the test, and teaching only the procedure.

I believe every child can succeed in mathematics, and it is my role to unlock this potential. I aim to teach in ways that help children develop cooperation, assertion and responsibility, as well as a good understanding of subject matter. I believe this can be achieved by creating a culture in the classroom that is built gradually on trust, with a common language, through rules that we create together, and by practicing procedures until they become nearly automatic. I aim to use the resources, materials, and curriculum requirements I have to work with, to engage my students in meaningful learning. I believe that children want to learn, and that it is motivating for pupils when they and their teacher’s are enthusiastic about learning, too.

Algebra is the gateway math for all things higher education. As stated in the article, many students who don’t go on to complete algebra in high school, will not get into post secondary schools or achieve the higher level of critical thinking. While the current phrase is “algebra for all”, we should be introducing algebra to early education as well. This article was focused on the four mathematical ideas that need to be incorporated in early education: Patterns, mathematical situations and structures, models of quantitative relationships, and change.

- The Math area in the classroom is composed of concrete materials for learning numbers and quantities. Children gain a strong foundation in the basic concepts, and can move on to more complex mathematical procedures and concepts as they are able—at their own pace.

Mathematics and numeracy are vital components of everyday life and are intertwined within our natural world. Combined, they are used to solve problems, conceptualize how things work, describe why certain patterns appear in nature and to help us manage day to day activities. Mathematics can be used to explain the phenomena of our natural world and how the world around us is built while numeracy is the ability to confidently use mathematical skills to solve problems and contribute to society. While they work interchangeably, there are key differences within the two which will be discussed later in the essay. As a future educator, it is imperative that maths and numeracy are understood in a real-world context so that students

Ma interviewed 23 teachers from the United States and 19 out of the 23 or 83% focused on the procedure of subtraction with no context as to why. (pg. 2) When given the problem of 23-17 the majority of teachers stated that the best way to solve the equation was to “borrow” one ten from the tens place and add it to the three in the ones place because you could not subtract a bigger number from a smaller one. By doing so you can then subtract the 7 from the 13. (pg.2)This however, does not show the true meaning of why we are able to do that. It focuses on the procedure itself and does not elaborate to the student what is really going on. (pg. 3) The reason the teacher was not able to go further than this computation was due to lack of content knowledge on the subject. (pg. 3). This however makes it seem like there are really two problems going on when really there is only one. (pg. 4) These misconceptions can in the long run cause more distress on the part of the student who will later be solving problems where they can subtract a larger number from a smaller one. If the previous teacher has instilled a belief that it could not be done, it will frustrate the student to

Teaching students effectively in areas of multiplicative thinking, fractions and decimals requires teachers to have a true understanding of the concepts and best ways to develop students understanding. It is also vital that teachers understand the importance of conceptual understanding and the success this often provides for many students opposed to just being taught the procedures (Reys et al., ch. 12.1). It will be further looked at the important factors to remember when developing a solid conceptual understanding and connection to multiplicative thinking, fractions and decimals.

It is imperative that learners have a rich understanding of numerical concepts. Many of the later math disciplines and skills that students will encounter are going to require knowledge and application of basic numeracy skills. Merely following steps in a process (e.g. multiplying fractions) or using an algorithm without knowing what is happening to the numbers, will leave the student void of true understanding and in turn, inhibit the path of learning. For example, imagine a scenario where a student who was never able to understand primary concepts related to prime and composite numbers finds him or herself in a classroom years later that requires factoring trinomials. Teachers may never be able to make math easy for their students, but they can support students in a way that enables them to be successful by ensuring they teach it in a way that promotes genuine understanding and knowledge of numerical content.

In today’s society mathematics is a vital part of day-to-day life. No matter what a person is doing at home or at the workplace, he/she is constantly using different mathematics skills to simply function. Then what does this mean for mathematics education? When someone needs to utilize a skill every day then he/she needs a strong background in the skill. Therefore, today’s students need more than a just a working knowledge of mathematics or enough knowledge to pass a test. Today’s students need to understand how mathematics works and how to utilize mathematics skills in the best way possible.

Maths is ubiquitous in our lives, but depending on the learning received as a child it could inspire or frighten. If a child has a negative experience in mathematics, that experience has the ability to affect his/her attitude toward mathematics as an adult. Solso (2009) explains that math has the ability to confuse, frighten, and frustrate learners of all ages; Math also has the ability to inspire, encourage and achieve. Almost all daily activities include some form of mathematical procedure, whether people are aware of it or not. Possessing a solid learning foundation for math is vital to ensure a lifelong understanding of math. This essay will discuss why it is crucial to develop in children the ability to tackle problems with initiative and confidence (Anghileri, 2006, p. 2) and why mathematics has changed from careful rehearsal of standard procedures to a focus on mathematical thinking and communication to prepare them for the world of tomorrow (Anghileri).

Mathematics, like every creation of man, have evolved without really knowing how far you can get with them: the scope of the computer, physics, chemistry, algebra, all are evidence of this. Every aspect of our culture is based in some way or another in Mathematics: language, music, dance, art, sculpture, architecture, biology, daily life. All these areas of measurements and calculations are accurate. Even in nature, everything follows a precise pattern and a precise order: a flower, a shell, a butterfly, day and night, the seasons. All this makes mathematics essential for human life and they can not be limited only to a matter within the school curriculum; here lies the importance of teaching math in a pleasure, enjoyable and understandable way. Mathematics is an aid to the development of the child and should be seen as an aid to life and not as an obstacle in their lifes.

Mathematics is a type of reasoning. Thinking mathematically includes thinking in a rational way, developing and checking conjectures, understanding things, and forming and validating judgments, reasoning, and conclusions. We show mathematical habits when we acknowledge and explain patterns, build physical and theoretical models of sensations, develop sign systems to assist us stand for, control, and review concepts, and create treatments to address issues (Battista, 1999).