Mathematics Education

Posted: August 29th, 2013

Mathematics education

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Mathematics education

The purpose of this paper is to analyze about the current effective practices in teaching mathematics in primary schools. This is as opposed to the back to basics that parents want to be used while teaching their children. The paper analyses carefully the reasons why parents think that going back to the basics is important in teaching their children mathematics. While, on the other hand, the world today demands children be taught the concepts of mathematics together with the knowledge of how to apply it in the twenty first century. Parents are worried that the methods used to teach their children mathematics are not adequate since it is different from what was used in the sixties and seventies.

Thelma Perso in her article explains what back to basics means, which is teaching mathematics like it was done in the sixties and seventies. Concentrating on the basic computation skills like addition, subtraction, multiplication and division. In addition, the parents also demand that some basic foundational measurement skills be taught in mathematics. Thelma points out that the reason why parents feel that their children are not being taught the basics is because, in this era children are exposed to computational technology like computers and calculators. She points out that when parents were being taught mathematics back in the day, they used to be drilled and made to practice the basic computation since they were necessary for employment and life tasks like budgeting, accounting and reckoning. Thelma insists that its untrue about the parents claims that these basics are being taught to children because if anything, they are overtaught which is problematic. The other points that she points out is that focusing on computation at the expense of other mathematics curriculum that are necessary for current teaching is flawed. It is flawed in the sense that it would be ignorant on the parents’ side to assume that the availability of computing technology such as calculators has no effect on school mathematics. The other reason is it would be a denial of the research done over the years on how children ought to learn mathematics as opposed to how mathematics should be taught. Lastly, it would be wrong to ignore that in the 21^st century the western society is a knowledgeable society and the effects it has on characteristics of the student cohort.

She addresses the concern of parents, which is that with calculators available children will learn to rely on this computing tool rather than learn the core computing skills. On the other hand, there is the concern that teachers believe it is their duty to teach mathematics like back in the sixties when calculators were not in existence. She points out that in the past, long division was used as a bench mark to determine if one was good in mathematics and to pass the exams. On the other hand, today it is used as a part of solving a certain problem that starts in recognizing that division is required. She states that long division is a procedure for determining an answer to a certain problem but is not the only method of computing that particular answer. Hence, it is wrong for students to learn just one method of solving problems as parents are asking in teaching the basics. She points out that what is essential is for students to learn when to apply division and   estimate how to go about it. This is achieved by using their mental computation depending on what they have been taught about numbers and performs the calculation either by calculator or by long division. This in the end will determine whether the answer arrived at is reasonable or not. Hence, they will have incorporated computation technology in solving mathematics problems with the core basic computation methods. Therefore, she points out that as much as division is important it should not be a key focus in classrooms because it is a small part of the process and not sufficient in mathematics learning.

She says in her article that a balance between basic computing skills and meta-cognition that, is the knowledge used in making decisions, analysis and judgments on performing these skills should be balanced when children are taught mathematics. The media would have the public believe that it is useless to teach the high order Meta-cognition to students in mathematics in today’s era. However, in today’s world, it is required of students to apply what they learn to real life and they cannot do that without meta-cognition being incorporated in mathematics. This outweighs the performance of procedures of the sixties and seventies since the meta-cognition required nowadays if far more superior than these procedures. However, Thelma points out that these procedures are still used extensively in many classrooms to teach mathematics, which is very unfortunate. Thelma argues that compared to the seventies, where specialist mathematics and other meta-cognition skills were taught on the job, these days the demands for work and life have changed and is different from then. Therefore, it is important to incorporate these in today’s teaching of mathematics unlike in the past where only basic computations were taught. Therefore, she states that it is impossible for the mathematics curriculum to stay the same given the changes in work and life today hence those calling for back to basis should consider this.

Thelma points out that student of the 21^st century need to be presented with knowledge in different ways compared to the past where knowledge acquired in school was deemed enough to last a lifetime. In the 21^st century a student, need to know how to apply the knowledge they have acquired to different careers since young people may have more than one career. In the past students were though not to posses any knowledge, hence they were fed with the knowledge to take them through their career. However, in the 21^st century knowledge has expanded substantially hence, students need to be taught how to learn on their own. They are equipped with the skills to enable them learn on their own. Moreover, they need to make sense of knowledge and use it in a transformative way. In addition, teaching them this way enables them to be creative and flexible in this era of technology. She adds that knowledge, as much as it requires to be incorporated with meta-cognition, is also necessary to add social interaction and individuals’ effective performances to enable students improve on knowledge. She says that for a student to work with knowledge, they need to share it, represent it, view it from different aspects, understand it is subject to revision and improvement, know they can create it and identify that it can be manipulated and judged.

She points out the tensions that exist between teaching mathematics content and teaching the required processes and skills to apply in mathematics. One group argues that learning mathematics content is far much more important than learning how to apply. On the other hand, a second group is adamant that learning the meta-cognition of how to apply mathematics content is important than learning the mathematics content. So often, the schools are caught between the arguments and are unable to please either group or balance between the two, as it should be. She points out that in Australia; the mathematics curriculum has been upgraded to include both the content and meta-cognition processes and skills to go hand in hand with the 21^st century. This in turn is viewed by parents and critics as a way of ignoring the content yet the content taught is similar to the one taught in the past. The meta-cognition processes included in the curriculum include emphasis on critical thinking, analysis, reflection and justification (Bishop, (2010). This makes the parents feel that the curriculum is too complicated since they expect the curriculum to consist computational skills only like in the past. Parents expect the computational skills to be presented as whole instead of as part of the problem that brings the call for basics agenda. This contributes to derailment of implementation of the new curriculum by the states as they face a huge opposition from parents and critiques alike.

She points out that the cry for back to basis should be changed to be 21^st century cries which should include both the basics that were there in the past and the meta-cognition skills needed for the 21^st century (Frame & Mandelbrot, 2002). The 21^st century basics should include understanding of numbers and their work in different ways, understanding operations, estimating them mentally, working out solutions using different methods including computational technology and recognizing 2D and 3D shapes among many other basics. This curriculum ensures that the basics from the past are included because they are very vital, although they are just but a small important part of the curriculum. She concludes in saying that it is the duty of teachers to explain to parents the importance of teaching both the past basics and meta-cognition processes required for this century. She points out that unlike in the past where a teacher’s work was to teach the basics, these days students need to learn the meta-cognition skills to be fit for the work force. In addition, she cautions the teachers to be careful not to give in to the paren6ts demand and disadvantage the students rather they should meet their demands together with those of the 21^st century.

The activity the students focused on was the estimation of how many animals’ are in Yellowstone using estimates given by the teacher, a map of yellow stone in square meters and measurement tools (Annenberg learner, ssss2012). The other activity was determining the shapes from squares given to them by the teacher. The third activity was to subdivide square top recreate a rocket shape and later discussing in class what challenges they faced. The fourth activity was counting the number of seeds in a pumpkin to develop their large number skills. The fifth activity involved division, fraction, decimals, reasoning, numeration and  communication These activities relates to the Australian curriculum in the sense that the students were not just given the measurement to calculate in their books but rather they were given maps, shapes, pumpkins, squares and measurement tools to estimate. In addition, the students were expected to show how they arrived at the solution and the factors behind it. The children were grouped in groups of three where necessary, and individually they were to interact with each other in discussion on what number to choose, how to measure the size of the area and number of shapes,  and calculate the exact number of animals, squares, fractions and pumpkin seeds. The students showed mathematical learning on calculation of distance, knowing and counting numbers, identifying fractions and labeling graphs on the blackboard, which relates to the basics of computational skills. These activities fit with the new curriculum introduced because what the students learnt from the activities required them to use both computational skills and meta-cognition skills. In addition, social interaction was vital through discussions the students held. These activities relate to best practices of mathematics because they incorporated the concepts of mathematics together with the skills on how to apply these concepts. Moreover, social interaction was evident through the discussions the students were involved with themselves and with the teacher. The students were glad to participate in the group discussion because it made them understand mathematics better and improve on their social interactions. In addition, it strengthened their team building capacity and brought out their effective individual performance.

In conclusion, what Thelma is pointing out in the article is true that as much as parents and critics are calling for back to the basic teaching, times have changed in the mathematics world; hence a different curriculum is necessary, one that will address these changes in the workforce, technology and life in general (Taylor & Francis, 2011). In this era, knowledge has expanded, and students need to be self reliant in learning on their own to cope with the career changes, creativity and flexibility. Students can only achieve this if basic mathematics concepts are taught as part of the problem rather than whole and taught together with meta-cognition processes and skills. The teachers also have a part to play in creating awareness to parents about the need to change the curriculum to suit the needs of this era.