Mathematics Curriculum in Education - Assignment Example

?Mathematics Curriculum in Education (Teaching Mathematics in the Modern room) Over the years, teachers have employed a number of different strategies to teach mathematics effectively. In the past, mathematics classes were teacher-centered, deductive, theory-focused, structural (Ernest, 2000), and often times, boring. Teachers did not realize the importance of relating the lesson to the real life experience of the students. Later, educators and philosophers realized that the content of math education should be close to the students’ personal experience or to realia, hence math education geared towards a more practical approach in which learning concepts were discussed and examples from real life experiences were given. Today, efforts to improve mathematics teaching have grown immeasurably, thus allowing teachers to teach math effectively. This paper discusses some of the modern approaches useful for attaining goals in the upper primary math classrooms. In particular, the approaches mentioned are relevant to the teaching of Mathematics in the upper primary level in (name of school), which is located in Brunei Darussalam. The Mathematics curriculum in (name of school) adopts a modern approach to teaching. In particular, the curriculum emphasizes the teaching of math in relation to the real life setting. This means giving particular attention to how math is used in the real world, such as government, business, home, and school. In the curriculum for upper primary (Grades 4–6) students, the syllabus includes topics that relate to real life experiences of using numbers and math concepts. Specifically, the goals of instruction include the following: Communication of math ideas in oral and written form Application of math concepts into real life experience Problem solving activities that connect math concepts to each other and to experiences in real life Infusion of Islamic values and Malay Islamic Monarchy philosophy Noticeably, the curriculum sets out very specific goals for instruction. Each goal is highlighted in the next part, together with approaches and activities that could best lead to the attainment of goals. Communication of math ideas in oral and written form The first goal, that is, communication of math ideas in oral and written form, directs teachers to an interactive way of teaching mathematics. This denotes the use of modern approaches that promote communication among students, especially in spoken language. Such approaches include Cooperative Learning, Cooperative Learning entails class activities that allow students to interact with each other and perform tasks in groups. Murdoch and Wilson (n.d.) define cooperative learning as an approach that requires students to work together towards a common goal. Merely working in groups without specific goals and measurements cannot be considered cooperative learning. For activities to be considered as cooperative learning activities, they should have clearly set goals and rules, for instance, each student in the group plays an important role in the performance of a particular activity. One way of applying Cooperative Learning is asking students to solve math problems. For example, students will be asked to solve for the average of annual GDP growth of the country in 10 years. In the given problem, each member of the group will be assigned to solve the GDP growth for (a) particular year/s. Hence, in a group of four, one can be assigned to solve for the growth from 2002-2005, another for 2005-2008, still another for 2008-2012, then finally another member averages the total GDP growth from his/her classmates. This way, each member of the group contributes effort and knowledge to come up with the final answer. The answer to the problem cannot be obtained without the output of each individual. Thus, assigning each member a role will make the student collaborate with others. Without the contribution of each member, the group will not be able to arrive at the final answer. Brown and Ciuffetelli (2009) and Siltala (2010) identify five basic and essential elements of cooperative learning, namely, positive interdependence, face-to-face promotive interaction, individual and group accountability, social skills, and group processing. These elements can be attained if teachers ask students to draw graphs then explain the contents, make a skit and dramatize word problems, and make graphic organizers to illustrate math concepts. Positive interdependence will be ensured by giving each member a task to fulfil. Face-to-face interaction is also important from the planning to the presentation stage. Making graphs or graphic organizers are the best activities to promote interaction among students. Individual and group accountability are also ensured as students contribute their knowledge in the performance of the task and presentation. Meanwhile, social skills will be enhanced more if students will be assigned in different groups and not in a permanent one. Being assigned in different groups, students will get a chance to meet different personalities, which could lead them to develop better social skills and communicative competence. Furthermore, each student should get a chance to be a leader in order to harness leadership qualities. The leader should be the one to assign roles to members, and provide introduction/synthesis during presentations. This way, every student will get a chance to speak in front of the class and experience being a leader. Finally, group processing may be attained by having each group evaluate its own performance. Evaluation forms should be provided by the teacher. These forms should include specific questions to facilitate evaluation. Cooperative Learning is especially good for upper primary students. Basically, students in the upper primary level can already work well in groups. In fact, they would love to work with their peers, thus group activities will be best for them. Likewise, Cooperative Learning will let them engage actively with the members of the group, thus every student will learn math concepts not from the class/teacher discussion but from the collaborative effort they do in each group. As they interact, students will act as what Vygotsky (1978) call, the more knowledgeable other (MKO). The MKO is anyone equipped with a better understanding or higher ability than the learner. In the traditional approach to teaching math, the MKO is usually identified as the teacher. Teacher-centered instruction usually has the teacher as the source of knowledge and the most well-informed and skilled individual in the classroom. However, based on Vygotsky’s definition, the MKO could be anyone, including students themselves or computers, whatever it is that has a better knowledge and could guide the student in understanding the subject matter. In the Cooperative Learning classroom, students are not treated as mere receivers of information. They do not just sit passively in the classroom, take down notes, and answer when called. Rather, they actively engage in discussions, share their knowledge on the subject matter, investigate, discover, and actively participate in group activities, acting as the source of knowledge at times and a receiver of knowledge on the other. Given this, students in Cooperative Learning classrooms serve as MKO to each other. Conversely, teachers are not only the source of knowledge; they act as facilitators, provide stimuli to activate the skills of students, and let them perform learning activities to attain specific goals. In the abovementioned examples, students assigned to illustrate mathematical concepts through graphic organizers will interact with each other, discuss the concepts, and assign each member of the group to draw, paint, paste, label, etc. the organizer to illustrate concepts. The process of making organizers will lead the students to understanding the concepts more, and communicating their views with others. As such, they will serve as MKOs to their peers and vice versa. In role-playing word problems, students will likewise actively engage in the preparation process. They will discuss ideas based on the prompt, assume roles in the presentation, and deliver lines that communicate their thoughts. The active learning that will take place will lead students to have higher interest and retention of the subject matter, which may not occur when having board problems. This is so because in the latter, only those who are good can go to the board and be recognized, whereas in Cooperative Learning activities, everyone can shine. The only drawback of Cooperative Learning activity is the length of time needed to complete each unit. Compared with boardwork, every group activity will take more than thrice the time needed to complete word problems. Nevertheless, such activities are more worthwhile because they emphasize learning skills and understanding concepts wholly. Application of math concepts into real life experience The second goal of math instruction in (school) is the application of math concepts into real life experience. The syllabus speaks much about this goal, thus suggests activities that relate concepts into the real setting. For example, students will be asked to compute statistical records based on their level, measure length/area/volume/time, etc., convert units of measurement, and present concepts related to personal experiences. To reach the goal, teachers may further use the Social Development Theory developed by Lev Vygotsky. Aside from acknowledging students as MKOs, this theory supports the view that students learn better in context. This means presenting lessons using the social context of the students or the environment where they belong. The theory entails providing social situations to introduce math concepts. For example, to teach statistics, examples should be based on the community where students belong. Instead of just computing for population, students may be given data regarding the number of children born to mothers in their community at a given time. To make the activity more relevant, students may be asked to conduct their own census, for instance, ask them to go to a community hospital to obtain records or to local government units, guided by the teacher during an educational visit. Such activity will make students become more aware of the social environment they are in. Active Learning and Guided Discovery are likewise embedded in the said activities. These learning theories require the involvement of the students, their active participation, and collaboration with peers. The educational visit will lead them to be familiar with places in their community, expose them to different professions, and provide a deeper understanding of the math concepts in use. Further to Active Learning and Guided Discovery approaches, activities may be designed in a way that would make students perform actively. Thus, instead of staying in the classroom and computing word problems, students may be asked to obtain actual measurements of certain areas within the school premises such as the school’s playground, room, library, etc. Importantly, asking students to obtain actual measurements will make learning more personal, effective and fun as students work in pairs or groups. Social interaction will also be enhanced as they communicate while doing their tasks, and fostering creativity. Infusion of Islamic values and Malay Islamic Monarchy Philosophy Part of any curriculum in (school) is the infusion of Islamic values and Islamic Monarchy Philosophy. As such, word problems are infused with family values, love of Allah, and social responsibility. Particularly, students are guided to understand that studying diligently is a way to please Allah and serve one’s parents. To emphasize this value, students should keep a journal where they can express and provide evidence of their efforts in studying. This should be implemented not only in the math curriculum but likewise in all subjects. When working in Cooperative Learning groups, the teacher should remind students of Islamic values that they should practice while working in groups. This would serve as guide so students will always keep a humble and non-competitive behavior. Instead of competing with each other, students will monitor their own performance using evaluation sheets and journal reflection. Assessments and Quality Assurance Processes Instructional plans will not be complete without assessments or quality assurance processes. These processes should be in line with curriculum objectives and goals. On one hand, assessments should be relevant to the learning procedures or activities done in class. For example, using Cooperative Learning, Active Learning, and Guided Discovery Approach, students should be evaluated using not only formal or pen-and-paper assessments but also informal assessments. Formal assessments are curriculum-based assessments, either standardized or teacher-made tests, usually in the form of quizzes (Van Blerkom, 2009). These assessments measure the learning achievement of students using pen and paper. In contrast, informal assessments are assessments that do not require the use of pen and paper but other means such as oral assessment or teacher observations (ibid.). In terms of purpose, the formal assessment assesses the learning performance of students, the percentage of learning they gained against that which was required. Informal assessments are designed not only to guage student learning but likewise to know the effectiveness of the strategy used for instruction. Moreover, formal assessments are designed to identify who else needs enrichment and who can advance to a higher level of instruction. In the curriculum for upper elementary, informal assessments are more frequently used than formal assessments. This is so because one of the main objectives of the curriculum is to equip students with the ability to communicate math concepts. In line with this, informal assessments such as oral recitation are common in everyday instruction. Short recap of concepts learned may already serve as informal assessment. Additionally, using Cooperative Learning, the group activities and outputs that students produce may also be considered as informal assessments, themselves. However, due to the difficulty to monitor whether students actually learned, it is better from time to time to still give formal assessments after the group activity. Worksheets, individual projects, and reflection journals may likewise be used to assess mastery of concepts and linguistic skill at the same time. The current use of word problems relevant to the context of the students is also recommendable. Observation sheets to be accomplished by the teacher while activities are going on are worthwhile to keep track of the performance of students and of recommendations for future activities. Teachers should use these sheets to track down progress of students not just in math but also their ability to interact, lead, follow instructions, and so on. To ensure effective Cooperative Learning activities, group work should be aided with evaluation checklists to record student contribution and behavior, which should be noted by the group leader. Additionally, checklists may include the comments of students regarding the activities, their accomplishments, a statement expressing their learning progress (what additional information/skill they have learned), or suggestions for future activities. These evaluation checklists will serve two purposes, one as informal assessments and another as bases for future lesson plans and line up of activities. Suggestions for Curriculum Improvement The current curriculum for upper primary mathematics implemented in (school) highlights the use of word problems related to the personal experience of the students. Situations usually mention children of the same age as the learners to make it easier for the students to relate with the problem. In addition, Cooperative Learning is adopted to help struggling students cope with the lessons while enjoying interaction with other students. To help advance in communicating math concepts, Altieri (2010) suggests the use of “quick writes,” which requires students to make short notes on math concepts, for instance, after discussing about area measurement, the teacher will ask students in pairs to write on small boards an explanation they can give regarding the area of a place or object. To avoid rote memory or what O’Brien (1999) calls as “Parrot Math,” students will be asked how they should measure a certain object and not to recall the definition of the term. Students may do this individually but it is more preferable to do it in pairs so that there will be interaction. To improve the current curriculum, additional Active Learning and Guided Discovery activities as mentioned above should be included. Community-related activities are strongly recommended to help learners understand the application of math concepts in situations outside the school. The said activities will also increase interaction with MKOs, for example, government officials, community helpers, and other professionals in their own field. Enrichment activities should be varied along with materials for instruction. Tipps, Johnson, and Kennedy (2010) suggest maximizing the use of manipulatives such as blocks, puzzles, shapes, flip charts, clay, rulers, etc. These manipulative materials will make learning more fun and memorable. Likewise, it will provide fine motor skill practice. Furthermore, games, group dynamics, and oral activities should be part of every lesson so that students will be more active and comfortable to be themselves. References Altieri, J. (2010). Literacy+math=creative connections in the elementary classroom. Chicago:IRA. Brown, H. & Ciuffetelli, D.C. (Eds.). (2009). Foundational methods: Understanding teaching and learning. Toronto: Pearson Education. Ernest, P. (2000). Teaching and learning mathematics. in Koshy, V. et al., Mathematics for primary teachers. London: Routledge; p. 22. Murdoch, K. & Wilson, J. (n.d.). How to succeed with cooperative learning. Retrieved March 31, 2012. http://www.curriculumpress.edu.au/sample/pages/clearning.pdf O’Brien, T. (1999). Parrot math. Phi Delta Kappan, vol. 80. Riley, J. E. (2003). The use of traditional and contemporary instructional strategies and materials in the elementary mathematics classroom. The Journal of Mathematics and Science: Collaborative Explorations, volume 6; 179-189. Siltala, R. (2010). Innovativity and cooperative learning in business life and teaching. University of Turku. Tipps, S., Johnson, A. & Kennedy, M. (2010). Guiding children’s learning of mathematics. CA: Cengage Learning. Van Blerkom, D. (2009). Measurement and statistics for teachers. NY: Taylor & Francis. Vygotsky, L.S. (1978). Mind and society: The development of higher mental processes. Cambridge, MA: Harvard University Press. 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