Mathematics is one of the difficult subjects from the standpoint of students because of heavy and hectic calculations (Rees, 1995). This particular subject is extremely useful in almost every field of life, because its implications are applied on every subject of life. Standards are of everywhere and to walk on the standard is the actual power of a person (Cinnamon & Larsen, 2006). Math is a subject which is surrounded by formulas, theorems and standards, likewise other subjects which have been based on theories. The main perspective of this work is to answer some questions related to mathematics.

What Is the Importance of Having Standards in Mathematics?

The entire field of mathematics depends on standards, theorems and formulas which mean nothing can be done apart from the given standards. Due to this particular thing, the filed of mathematics is in the pressure of criticism because of the low innovation. It is the only field, which has not been developed like other fields and subjects of the world. Herein, the importance of the standards is required (Rachev & Fabozi, 2008). One can say that the standards in the field of mathematics is important, but not always because of the low innovation and techniques

How Do Standards Improve Mathematics Instruction?

This particular question is about to analyze, how the standards can improve the instructions of mathematics. It can be said that the field of mathematics is divided into two different parts. One is an understanding, and the 2^{nd} is applying relevant formula and standards. The standard of mathematics can improve the instruction embedded with the question and the solver can solve and understand the entire questions even the complex mathematical problems.

The standards of supposition are extremely important in the field of mathematics because these particular provisions help the solver to solve any complex problems. The standards used in algebra and complex matrix problems are not only sophisticated but they are extremely beneficial for the instruction of mathematics, especially to understanding and applying the standard procedures on it.

Compare and Contrast Traditional Mathematics Programs versus Constructivist-type Programs in Addressing the Standards

In the recent years, there has been a debate in the public schools over the different approaches to how mathematics is taught in public schools. In the past, at schools people believed that teaching mathematics was the traditional way with direct instructions and route memorization of facts and procedures. In the recent years, there has been a shift in the educational system in moving towards a more constructivist approach to the teaching of mathematics. School are beginning to adopt the new mathematics curriculum with includes the use of manipulative, small group work and developing cognitive thinking skills.

Mathematics has the ability to confuse, frighten and frustrate learners of all ages. If a child has a negative experience in mathematics, that experience has the ability to affect his/her attitude towards mathematics as an adult. Every daily activity includes mathematic procedures, whether people are consciously aware of it or not. Possessing the solid mathematical computational ability will help to make additional skills come easier to the learner. The current debate in the school system is based on two different approaches to mathematics, constructivist or traditional. Constructivist teaching or constructivism is influenced by Jean Piaget and based upon the student being actively engaged in the learning process. Students build on their prior knowledge or schema, to aid in their learning. (Singer & Revenson, 1999; Marek & Cavalla 1997). The traditional mathematics instruction was influenced by Skinner, holds a scientific approach to learning.

Rote memorization, drills and recitation are the foundation for traditional teaching methods. Traditional mathematics instruction (also referred to as direct instruction) emphasizes the learning procedures and number facts and uses drill and recitation to reinforce and assess learning. During one case study conducted by Jennings and Pawat, (1997) the researchers recorded and observed both constructivist and traditional mathematics teachings. The study showed that the teachers believed that the traditional mathematics teachings resulted in better student achievement. The participants in the case study attempted the constructivist teaching methods, but showed resistance to change and did not believe it to be more effective. Hollar and Norwood (1999) sought to find that students achieved higher results in algebra using a graphing calculator. They found that students in the experimental group who used the calculators in math had a higher positive attitude towards mathematics and their abilities. However, no difference in their academic achievement was found. Arra and Bahr (2005) found no differences between which the instructional method and constructivist or traditional that students preferred more.

It is investigated that the mathematics achievement in relation to students with learning disabilities. Groebecker focused the study on two students (one male and one female) with learning disabilities and found that the female student would benefit from constructivist teachings while the male student would benefit from a more traditional approach to mathematics. Witzel (2003) compared a new algebra curriculum that focused on the traditional approach to constructivist mathematics and found that the students with learning disabilities had a higher achievement when engaged in the constructivist curriculum.

Thompson (2005) sought to understand how to predict when a child might have a learning disability in mathematics. To investigate this question they conducted a four year study on the kindergarten students. The researchers found a correlation between the students with a mathematics learning disability and the education of the mother, the higher the education of the mother was, the less likely it was for the student to have a learning disability. The research showed that the students with a mathematics learning disability scored lower in the areas of cognition, memory and processing.

Limitation of Programs

There are different limitations of both programs which can be regarded as important from the standpoint of this subject. In the constructive mathematics, theoretical aspects like theorems complex the entire structure, while in destructive type the aspects are so dry to digest.

Classroom Implications

Students being taught using the constructivist mathematics methods would become active learners in their own environment, develop cognitive thinking and be able to relate mathematics on the real world applications. One constructivist mathematics curriculum is the Everyday Mathematics Curriculum as outlined in the section two. The majority of the research presented that students achieved higher mathematical skills and higher attitudes about mathematics when the Everyday Mathematics Curriculum was used in the classroom. Several studies from the section three indicated that student were able to achieve better skills and achievement when being taught with the traditional, route memorization of mathematics. One study found that at risk students had higher achievement rates and were more attentive in class when given the direct instruction. While the study stated that student’s scores had improved significantly from the previous instruction, it failed to note what the previous instruction was, and or any relevant test results. In the section four, while the research explored both the traditional and constructivist instruction, it was impossible to find any significant differences between the types of instruction and the student achievement. The research in the section five and section six presented mixed results in relation to student with learning disabilities and which instructional methods would best benefit the student.

How Technology Can Be Used in Education

Our world constantly changes; it becomes bigger and smaller at the same time. Our world gets smaller because the technologies let us stay in touch with our friends from different parts of the planet (Vernimmen, 2000). On the other hand, the increase in information makes our horizons wider. Because of the opportunity of the global communication, we have to change methods of our education. Some people would consider that there is no need in the change, however, change is already behind our backs, whether we want it or not. The main task for us is to prepare our children for the future is waiting for them; new professions and new technologies that are yet to be discovered (Witzel 2003). As we see, the driving forces of Moore's Law, Metcalfe's Law, technology fusion and a changing world economy are redefining the way our children need to be taught. Technology can be used in mathematics education and currently it is being used in many countries.