The comparison of numeracy learning and development - Essay Example

? Introduction There is a widespread interest in improving mathematics achievements in schools across the world (Kaiser, Luna, & Huntley 1999). Apartfrom economic benefits of mathematics, such as preparing young men and women for the numeracy requirements of the modern workplaces, and improving the skill levels of the personnel, there are social benefits tied to bettering access for many young people to training opportunities and post school education and laying firm foundations to skills for womb-to-tomb learning. The interest in heightening levels of achievement has resulted in a focus on recognizing the range of factors that determine achievement as well as interpreting how these factors operate to enhance or limit the achievement of varied groups of students (Kaiser, Luna, & Huntley 1999). This paper considers the comparison numeracy learning and development of two students, which should focus on various key aspects, such as the background of the learners and the support teachers provide for the learners. Student background variables determine differences in achievement in mathematics, school and classroom variables. Case study In this case study project, I will consider two students, namely Christopher and John. Christopher has a British background, and he is a gifted learner. He understands the background meaning and culture of a variety of questions. Christopher is a fast learner, and he always finds a hard time with curriculum demands as well as teachers because they comfortably cater for students with normal learning abilities. John is a Vietnamese who is in England for his studies. He has been in England for five one year and he has a problem with understanding English language, especially in speaking. John does not understand the cultural context of a variety of mathematical questions, and he is in need of constant assistance with understanding key English words. Christopher Christopher is a 42-year-old father of four. Three girls aged 12, 16 and 18, and a boy aged 8 years. He completed his ‘O’ levels about 31 years ago. Christopher has three ‘O’ levels and five different subjects at CSE. He studied a Software Development Course and accounting packages with the City and Guilds as the examining board. Christopher got married at the age of 20 years, and his academic studies stopped for about five years, after which he enrolled into a higher learning institution to study Software Security Course. He sired his first child eight years after marriage and, later, after two years, he sired another child. The second child had some mental disability, which called for more care. He took most of his time taking care of his disabled daughter, but he continued with his studies on the part time basis. Christopher decided to enrol on the numeracy level 1 in order to better his numeracy skills because he encountered many calculations including daily purchases. He passed well in level one examination and proceeded to numeracy level two. According to the results of his initial diagnostic test, he had a ‘spiky’ profile. He excellently understood some topics, and at the same time, it was difficult for him to understand other topics regarding numeracy. However, he committed himself to understand the difficult areas, which resulted to a substantial improvement and success in his level 1 examinations. Now, when he proceeded to numeracy level 2, all topics became equally manageable. It was easier for Christopher to understand every topic because he had gone through the English Education System. His accent and approach enabled him to do well in numeracy because he could ask the lecturer for clarification every time he experienced a problem. When I started to teach in Christopher’s class, Christopher experienced some problems regarding my teaching methods as well as my accent. This was because my approaches were significantly different from the approached that the previous teachers employed in teaching. Therefore, he failed to understand some key concepts concerning numeracy. I did not hesitate to set him free to use his methods in order to make him comfortable and at the same time, understand all the concepts. Afterwards, Christopher did not exhibit any problem when we were covering new topics because he would not be having any experiences. Therefore, it is apparent that learners will learner better within an environment that brings about experiences that the students had come across or experiences that have a close relationship with their previous experiences. Christopher connected to his previous experiences, which enabled him to understand the new concepts easily. The key ideas that underlie this approach to concept formation include classification, abstraction, similarity, and concept. Price (2006, pg.46) defines abstraction as the act developing general concepts through abstracting. An abstraction is a lasting change, which is the result of abstracting that enables students to recognize new experiences because of the similarities of the previous experiences. Classification is the processes through which an individual puts together experiences based on the similarities. Therefore, my teaching method was going against Christopher’s collection of experiences based on similarities thereby hindering his learning process. The progress of a student through various stages, namely Allegorization, Integration, Analysis, and Synthesis is extremely significant in determining the learning style of the student (Price 2006). During the stage of Allegorization, a teacher describes a new concept figuratively within a familiar context in terms of the already known concepts. In the stage of Integration, the learner uses comparison, exploration, and measurement to distinguish the new concepts from the already known concepts. During analysis, the new concepts become part of the knowledge base that exists (Pearse & Walton 2011). Connections and explanations are significant in elaborating the new concepts. In the stage of Synthesis, the new concept takes a unique identity, and, therefore, becomes a tool for further allegorization and strategy development. The Role of a Teacher in Numeracy Achievement The four stages, namely Allegorization, Integration, Analysis, and Synthesis can also be significant in determining the role of a teacher in numeracy achievement. Synthesis refers to a creative act, and, therefore, many students experience problems in synthesising with various concepts in numeracy. Although, Christopher is extremely good in numeracy, he has trouble in grasping advanced concepts in numeracy, for instance, when I was explaining issues of multiplication and division of numbers with the same base and different indices. Multiplication of such numbers results in the addition of indices while division of the numbers results in subtraction of the indices. Christopher could not understand the laws of indices. However, I tried to prove a number of problems concerning the multiplication and division laws of indices until Christopher conceptualized various instances. Furthermore, suitable allegories depend on the cultural background of the student, and as a result, it is crucial to develop new allegories continually. Different concepts require varied integration, analysis, and allegorization. There must be a teacher who will determine how much analysis, allegorization, and integration should be appropriate in presenting a concept, who will develop allegories for students, and who will ensure that students develop critical thinking skills regarding each concept. A teacher creates new allegories and present problem solving strategies in order to synthesis for students (Pearse & Walton 2011). During allegorization, the teacher acts as a storyteller. The teacher brings forth a mathematical concept and ensures that he or she explains it in the most suitable approach for students to understand. During integration, the teacher guides students in the classroom throughout the learning-teaching process. A teacher uses measurement, exploration, and comparison to distinguish new concepts from the already known concepts. In the analysis, the teacher acts as an expert. The teacher uses connections and explanations to elaborate the new concepts to engage his or her learners. During synthesis, the teacher acts as a coach, and the new concept attains a unique identity, and, therefore, becoming a tool for further allegorization and strategy development. Teachers will also ensure that gifted students do not get stifled or bored in the normal educational system by offering a thorough guidance. Christopher is a talented man and he could get stifled in the current educational system, but due to the tutor’s guidance and the requirements of numeracy level 2, he is learning comfortably. He has enthusiasm and capability to learn faster, but he must learn normally following the teachers’ efforts. This education system is boring to Christopher, and it has suppressed his progress to join higher education. John John is a 42-year-old Vietnamese who is in England for his studies. He migrated to England five years ago. John is a married man, and he has sired a son. He scored a pass in Mathematics and a credit in the other seven subjects when he did his equivalent to GCSE in Vietnam. He has a problem with understanding English language, especially in speaking. John does not understand the cultural context of a variety of mathematical questions and he is in need of constant assistance with understanding key English words. John decided to enrol at the college and study numeracy in order to better his numeracy skills. He did a diagnostic test, which showed that he could start his studies at level 2. This was his first time to study in English language, and, therefore, he had trouble to follow instructions during lessons and when doing continuous assessment tests or examinations. However, John could be able to solve many questions when the teacher explained the requirements. It is evident that students can perform well in numeracy or any subject when they understand the language that the examiners used to set the questions (Westwood 2008). Therefore, teachers should make sure that their students understand mathematics vocabulary. Students should be proficient in English language in order to follow instructions and solve word problems correctly. Even if, people tend to think that mathematics does not require a strong command of language, mathematical problem solving and reasoning have a close relationship with language, and depend on a strong understanding of mathematics vocabulary. John experiences problems in his studies because he is not proficient in English language. The new situation of having a student who is not proficient in English is challenging me as a mathematics teacher. It is very crucial to teach academic language, increase student language production, and build background knowledge. This has forced me to develop a new set of instructional techniques, which will enable John to learn the content in numeracy and at the same time learn English language. Because of a more effective instruction, John can be able to understand the content better, and he is comfortable with mathematics. John asks questions in case he does not understand various concepts in mathematics. Academic Vocabulary Students can perform well in numeracy given that they are proficient in mathematics vocabulary (Olsen 2010). For instance, some questions in mathematics depend on the use of letters to represent the unknown values. The most common letters that represent the unknown values include x and y. I presented the following simultaneous equations to students: 1. Solve for x and y in the following simultaneous equations: 4x + 5y = 30 8x - 10y = 20 This question requires students to find value that x and y represent. John failed to understand the requirement of the question. I explain the requirements of the question by informing the students that they should find the values, which x and y represent. The literal use of words is among the problems that I experienced with John during the mathematics lessons. I found that it is useful to be able to read and understand written mathematics problems. Students should also be conversant with the building background knowledge of numeracy in order to perform well in mathematics (Olsen 2010). Students whose first language is not English have trouble with working out written word problems in mathematics. This is because students must read and understand the text of the problem, identify the question, create a numerical equation, and solve the equation. Therefore, those learners who acquire formal education within their home countries rarely have trouble with word problems in numeracy. John can do well in mathematics if the teacher explains the key words used in questions. Having the background knowledge in numeracy also enables learners to perform better grades. References Kaiser, G, Luna, E, & Huntley, I 1999, International comparisons in mathematics education, London, Falmer Press. Olsen, A E 2010, Academic vocabulary: academic words, White Plains, N.Y., Longman. Pearse, M, & Walton, K M 2011, Teaching numeracy: 9 critical habits to ignite mathematical thinking, Thousand Oaks, Calif., Corwin Press. Price, A 2006, Creative maths activities for able students: ideas for working with children aged 11-14, London, Paul Chapman. Westwood, P S 2008, What teachers need to know about numeracy, Camberwell, Vic., ACER Press. Read More