TEACHING MATH (sample essay canceled)

ESSAY ON TEACHING MATH

Introduction

Teaching math and science to middle school students can be challenging. The main thing to remember in terms of strategies in this report's opinion is conditioning. Classical conditioning states that a certain kind of stimulus acquires value when it is repeated and it is also paired with a sort of positive response. From this view, students learn by sorting out their responses to different stimuli in general ways and in specific ways. Operant conditioning states that individuals will determine their own actions and then learn from the response that comes from these actions, whether it is positive or negative. Reinforcement is about keeping that action viable while punishment is about stopping the action or behavior. Making a cue for a student or prompting them involves getting them to respond in the right way to a situation. Understanding by design can improve student outcomes. "According to Schoenfeld (1989), the way people engage in mathematical activities is shaped by their conceptions of mathematics. There have been many studies that confirm that effective factors shape how students behave" (Tsao).

Many students have short attention spans, especially these days, and there are also common problems of lack of organization, poor sociality, and poor skills. In the current model, the affective model of participation suggests that participation leads to attainment of student higher order needs which in turn leads to more productive learning of important negotiation and problem solving skills. Students should learn from the centered approach that there is a danger of a situation where there is more concern with maintaining group relations than there is with making high quality decisions and learning the lesson. Students should be able to take various roles with this method as well. For example, students could be given a situation in which competing groups have the same goal, and must somehow work together to focus on the goal. Actively fostering a connection between the students' goals and the teacher's objectives through systems of participation is called upon in the centered approach to help the students work in teams to solve problems as well as negotiate solutions between competing goals. Teachers can also use the centered approach to teach content application, and improve mathematics scores for middle school students. There are many ways of teaching students mathematics knowledge.

Article Review

The article shows a comparison of American and Taiwanese students in mathematics skills, with the Americans losing. "Poor performance by American students on tests of mathematics and science has reached the level of a national crisis. Why is this? Study after study has reported on one or another facet of the low standing of Americans in international competition. For example, in a recent cross-national study of mathematics achievement, Americans scored low" (Tsao, 2007). Math classroom communities can help by bringing students into contact with each other in groups and having them work as teams to solve relevant problems over distance. This type of problem solving instruction can also be used for individual students. Cooperative learning assesses students on their success in mixed groups functioning as teams There are many different types of assessment that are available for the teacher, from standardized testing to other more alternative types of assessment. Teachers need to choose as thinking individuals to find the right assessment measure that reflects their own classroom philosophy and their ability to react as a teacher who is able to give student assessment total priority. But this assessment must focus on the higher level. Assessment needs to consider verbal input as well as mathematical awareness, but some standardized testing measures or assessments have less well rounded input. In other words, in standardized assessment measures, there might not be as many variables being measured by the teachers, and the students might be choosing in a multiple choice format. In a more dynamic assessment, children might be graded on how they are able to interpret information from a problem to create a presentation or show the teacher processes of proof writing. "American students in the eighth and twelfth grades were below the international average in problem solving, geometry, algebra, calculus, and other areas of mathematics. In contrast, Japanese eighth graders received the highest average scores of children from 20 countries, and, at the twelfth-grade level, Japanese students were second only to Chinese students in Hong Kong" (Tsao). Diagnostic and non standardized tests have a lot of relevance in the educational environment for reading lessons of students. The main question addressed in Tsao is how we can use assessment to help the teacher better address the instructional needs of children. Generally the current educational platform is a performance-based system that relies primarily on high-stakes tests for its program. But there is a lot of uneven argument in the environment of education, and some people think that these high stakes test are less effective than more holistic methods. The article showed how far behind American students are often falling, for various reasons.

Topic: Understanding by Design

Understanding by design has understanding at its impetus, but the school has to watch out in the long term not to cripple what power of standardization it may have been advocating immediately, which is essentially a way of misleading the public. Another short term objective would be to get the school to align state standards with behavior problems in students who are bored in class, or too busy to do their class work. The state standards don't really go into accommodating different learners and understanding by design in this way. From a long term perspective, standards however are becoming more and more important with new programs and initiatives, so it is disturbing that the performance of students in lower socio-economic level urban areas are still showing low scores on these tests. The issue must be addressed in the short as well as the long term. In many cases poor performance on these standards and poor academic achievement is labeled as being a cause of socio-economic conditions. "The Singapore Math curriculum is sequential in nature and builds on students' prior knowledge. The MCPS revised curriculum uses the same principle and techniques. Concepts of fact families are integral to Singapore Math, and one will find those same concepts in the MCPS math curriculum as well" (Miracle, 2007). Many different curricula can light the way for the free thinking teacher.

Understanding by design can facilitate progress in math and science because it focuses on regulating the type of learning style that the student will have and relating it to their self-esteem and self-concept, or their self-efficacy within a social group, or how much they feel they are going to succeed at a given task or at solving a given problem. Students may use different strategies such as taking notes or using flash-cards before finding the one that is right for them, so the teacher needs to realize that cooperative learning is not just about their directives, but also about listening to the students' input. The effective teacher will have a master plan going but at the same time they will not be so absolutely dedicated to this plan that they will not consider straying from it when the opportunity presents itself, which it often does, and they will not be afraid of changing the plan to fit the situation, and giving more responsibility to the students for problem-solving as well as cooperative learning. The independent teacher knows how to adapt to his/her situation.

Teachers can plan in many different ways and can provide their students with many different types of work, and these should be based on creating a warm and supportive atmosphere in which students can feel that their work is valued. This perspective seeks to categorize the problem without solving it or reaching a resolution, and therefore it is not a perspective that works very well in the short or long term, because it does not really address any of the root problems inherent to the situation.

Understanding by design is a less teacher oriented and more student oriented instructional method. "It would fall midpoint in the classroom inquiry continuum. In this approach, students are guided in exploration of materials. They observe phenomena, gather data, make comparisons, and arrive at conclusions" (Peters, 2008). When thinking of organizing strategies in creating and timing lessons, the chief tenets observed throughout my experience stress the importance encouraging all aspects of growth and development in the student. The completeness of a teaching philosophy must be reflected in the evenness and completeness which is encouraged in the children whom the teacher is instructing. It is a symbiotic and organic process of organization that stems from both the teacher's effective leadership and their ability to communicate with their fellow professionals. The children in an effective math classroom should develop socially through sharing and interacting, emotionally by learning to respect everyone equally, physically by playing active games and getting exercise, and cognitively by learning key assessment requirements on a corporate level. "This welcome support from AT&T will help create a new generation of math and science teachers in the United States," said Dr. Mary Ann Rankin, president and CEO of NMSI. "Our nation needs an additional 280,000 math and science teachers by 2015, and the UTeach program is playing a key role in providing those teachers." (AT&T, 2012). Understanding by design can take many different forms.

One teaching strategy used in teaching mathematics by design is encouraging inference. This means that the students concentrate on process over product and therefore can enhance observational and logical problem solving skills. "The usual meaning of inference is to interpret or explain what we observe. If Wallie smiles when she greets us, we may infer that she is pleased to see us. The accuracy of our inferences usually improves with more chances to observe" (Peters, 2008). Direct instruction is a more traditional choice which may be used when students present problems with authority. Teaching mathematics also involves integrating concepts of cooperative learning. This cooperative type of student-directed model matches many teachers' patterns most closely, because I think that this model has the balance of respect and activity that is necessary and allows students to really own the concepts. This process of growth and development is framed by teacher ideals in that it is their goal to provide an atmosphere where everyone benefits through education, where the children can learn socially and cognitively in an environment that encourages their curiosity and creativity as well as their problem solving and logic skills. "The system's new math curriculum is aligned with state, national, and world standards and has led to unprecedented student achievement. Singapore Math's strategies, called "bar modeling," as an ideal way to solve math word problems. MCPS agrees and has incorporated bar modeling into the revised curriculum" (Miracle, 2007). Understanding by design can also be used in kinesthetic ways.

Manipulative materials is also an important strategy to use to get students really engaged with the material. Still the teacher must have their teaching philosophy in mind, trying their best to provide a relaxed, calm, and comfortable environment in which the children can grow, because too much control in a classroom can be a bad thing to encouraging student cooperation. "In short we want to use the learning cycle to develop students' scientific knowledge and understanding and skills. The learning cycle is generated as a do talk do cycle. In the do parts of the cycle, sills are being used. What specifically are the scientific skills? Which skills are appropriate?" (Peters, 2008). Basically the same thing can be said for mathematics skills, in terms of learning when they are used. It may seem like it is just problem solving strategies that fit with mathematics work, but there are other strategies that can go across different disciplines as well. I would say personally that a mixture of problem solving and cooperative learning strategies leads to "It is also important for children to have access to the right kind of materials.

To address these concerns, teachers need to think more and more about how they can make applied behavior analysis to see what works best in a given situation in a way that is creative and kinetic rather than rigid and unmoving. For example, teaching social skills to a student who lacks them should not be used as an end of itself: it should be accompanied with an explanation of what the student is doing creatively so that they learn from the experience and it becomes useful. Students who have problems such as those mentioned above can also be encouraged by a group system. In general, "the most effective contexts leading to optimum student achievement are classrooms where all students feel valued, respected, and capable of succeeding despite their differences" (Peters, 2008). This reflects a substantive view as well, in terms of students getting together and forming a creative solution to the problem or conflict rather than displaying personal conflict, which, as demonstrated by the negative behaviors above, also exists in the classroom environment. "Classroom environments that work require personal reflection about teachers' roles, an understanding of what works in classroom organizations, a view of the relationship between management and instructional decisions, and the ability to use multiple methods" (Making, 2008). This understanding of what works in the classroom environment must also include creativity awareness in the children, and also must make the teacher think about how to be more creative as a teacher in their expression within the classroom. Understanding by design is all about getting the student involved.

I have observed the value of a solid teaching strategy many times throughout experiencing lessons. My school has a very strong mathematics program that involves the children in integrative learning. Creativity is encouraged among students and we have sent several students to the Math Olympics competition for the last three years. The school also has a special gifted and talented mathematics program which caters to students who have more advanced skills and would be bored and unchallenged in a normal class. "The National Math and Science Initiative (NMSI) announced Thursday that AT&T has contributed $500,000 to support the highly regarded UTeach program to train math and science teachers on five university campuses: the University of California at Berkeley, the University of California at Irvine, University of Northern Arizona, the University of Florida, and Florida State University" (AT&T, 2012). There are many different teacher strategies.

Generally by operating without secrecy and with a high level of accountability, the classroom will be looked upon as possessing integrity and fairness in its operations, and will gain the trust of the student and increase the level of responsibility required of its own employees and society as a whole. Theoretically, it all seems rather simple for codes of ethics to promote this sort of behavior through problem centered learning. "Problem centered learning moves us even further from teacher control to learner control lesion models. Now students become more involve4d in the planning and implementation of lessons. Following the development of an initial question, students continue their investigation until the problem is solved" (Peters, 2008). In reality, the situation is much more complex, since a school is by nature made up of many different individuals. A school is a large organizational structure, and within this structure, there may be many individuals, both teachers and students. There has to be open communication between everyone.

REFERENCES

AT&T Contributes $500,000 for UTeach Program to Train Math and Science Teachers (2012). Business Wire

Peters, J. Math and Science in Education. New York: Pearson.

Tsao, Y (2007). A comparison of American and Taiwanese students: their math perception. Journal of Instructional Psychology. Making math meaningful.

Miracle Math. Education Next.