Assessment in Mathematics - Coursework Example

 Assessment in Mathematics Name Institutional affiliation Tutor Date Assessment in Mathematics Abstract Assessment is alienable in the educational setting. This paper shall focus on teaching that is based on inquiry and how questioning has proven beneficial to the learners. Analysts argue that teachers must always be responsible for what they impose on their learners in the form of learning through questioning, and whether they are willing to maintain the trend on a particular learner. Use of reasoning can only be achieved through questioning, a major theme in this essay. Additionally, learning cannot be termed successful if the learners have not been assessed (Black & William, 2001). From a simple question, a lot can be derived from just a single concept. This essay shall center on the implications of assessment on the teaching and learning environment in relation to the national and school’s policy. 1.0. Introduction In the course of teaching and learning, it is of the essence that a myriad of tests are given to learners so as to make certain that the learners are well tested on the concepts taught in the classroom. With the concepts trained in Mathematics are mostly concerned with solving problems, the teachers cannot confine themselves on multiple choice questions, but quizzes that are meant to define the weight of understanding of the whole concept by the students. With the learners being subjected to challenging concepts by the day, the learners are at mot times at par with the concepts being taught in the classroom setting. This leads to the theory that both the formative and summative assessments cannot be estranged in the success of teaching and education and Mathematics. Analysts and researchers in the field of schooling claim that, no learning structure can be viewed as successful if the students have not been evaluated, and given a chance to improve on the previously achieved scores. With the learners having a chance to assess their improvement, learning becomes a joint approach between the educators and the learners. According to Donald &Ainsworth (2006), formative evaluation as compared to summative evaluation allows learners have an immediate assessment strategy on the concepts being taught in the learning environment. Detection of limitations they have on a certain concept, they are able to take charge of what they need to improve on, in the course of learning. Summative assessment on the other hand, is only designed for the long term results and grading of the learners. Critics argue that summative assessment is more of a tool that shifts its energies to general assessment of the learners, not considering the aspect of improving the learners’ ability on an immediate manner. In this case, it is warranted to make the assumption that formative assessment are of great importance to teaching and learning as compared to summative education (Stanley & Moore, 2009). Additionally, Lester & National Council of Teachers of Mathematics (2007) indicate that if educators select formative assessments over summative assessments, their learners stand a better chance to have close monitoring of the learner progress and assistance on the tasking topics in the course of learning. Positive results are likely to be yielded in the learning environment with the educators devising the best approaches to apply while teaching. Positive results, new trends picked by the learners and varying responses can be well recorded in the learning environment in the case of formative assessment, since the entire process is continuous. This essay shall focus on the current national policy on assessment in Mathematics, the school policy on assessment, after that give a critical reflection of my personal classroom practice with assessment in Mathematics. Finally, the essay shall make a conclusion on the importance of theories of assessment in Mathematics among my learners. 2.0. Body 2.1. Current national policy on assessment in Mathematics Maughan & Cooper (2010) indicate that in the UK, there have been massive attempts by the UK government to update the current policies that relate to assessment of Mathematics in England. The government aimed at coming up with forms of means that would lead to proper learning of the subject through engagement of the learners; thus, better participation of the same in the learning process. On another view point, the government of UK was much more concerned with making the learners embrace the fact that learning is not a formality, but it must come from within them. In the long run, analysts and researchers of education in England argue that these policies have in a number of ways been beneficial in teaching and learning of Mathematics. The policies also aimed at highlighting the implications of the study of Mathematics outside teaching and learning, but also in the life after schooling. According to the research conducted by Maughan & Cooper (2010), proper assessment of Mathematics in the UK educational system, has been defined as a form of assessment that allows learners to develop attributes of problem solving skills, whilst under instruction of Mathematics. The government undertook measures of setting up accountability measures that would see the implementers of education policy in the classroom would come up with tests that would measure the ability of learners in a particular test. This interprets the fact that the educators must involve putting much weight on skills taught in the classroom setting. This according to the policy set by the UK educational programs relates to selecting the best content that would see the learners be in a position to succeed in the tests (Maughan & Cooper, 2010).According to the UK Smith Report, suitable methodologies of assessing Mathematics would be beneficial for evaluation of proficiency skills among the learners in the context of Mathematics (Maughan & Cooper, 2010). Prior to the selection of a single model to assess Mathematics, the assessors must exhaust all the existing options that would be beneficial in setting an appropriate model. The current national policy on assessment in Mathematics in UK, advocated for the tests being of varying genres, and with rich content that would boost the learners reasoning ability. The policy, according to Maughan & Cooper (2010) seek to establish a means in which the learners would be first tested on the uncomplicated questions, then progress to those that require a bit of thinking. Time allocation is also of great importance if the learners have to achieve the goals and objectives of the test. Educators must make sure that all questions have a considerable amount of time for proper answering. 2.2. Critical reflection on classroom practice In the course of learning, it is imperative that execution of formative assessment is properly done by the educators. As a Mathematics teacher in a mixed secondary school of year 7, 8, 9 and 11, I ensure that I incorporate the use of various teaching methodologies so as to fit the learners of varying mixed abilities in my classroom. It is evident that these learners work within the range of varying grades; thus, it is of great essence that the educators come up with forms of assessment that will include all these learners in the classroom practice. In the course of my teaching Mathematics, formative assessment according to Hodgen &Williams (2006) must be well designed. The use of whiteboards has been of great benefit to my learners. Mini –whiteboards have been of great benefit to the teaching of my learners especially on topic that relate to drawing, for example drawing graphs. This works when I introduce the topic on the writing board, and require direct and quick response from the learners. The next step includes the learners lifting up their mini –whiteboards so as I can have a quick check whether they have grasped the concepts being taught in the classroom. With this, I am able to detect if the learners need correction and whether the concepts introduced have been understood. Secondly, through the use of mini –whiteboards, one on one learning is possible with my learners. I would give my learners a chance to lift up their boards after solving questions on basic multiplication that would have otherwise taken time moving round the class checking the answers by all learners. I am very ken especially on learners of slow ability to learn, who are also motivated to learn by the other learners in the classroom. It is also of benefit to group learners of varying abilities and assessing their ability in relation to the concepts being taught. This coincides with the policy of assessment, as through the mini-whiteboards, I consistently monitor the progress of the learners from the feedback of the learners. With my comments on ‘calculate the.., demonstrate using a drawing or a graph on …..’ during learning is a mere explanation of the use of assessment during teaching and learning on Mathematics in my class. Additionally, I have incorporated the use of posters to teach quite a number of concepts in the teaching and learning of Mathematics. I have done this by grouping my learners and getting them to work collaboratively to come up with answers that relate to certain concepts in the learning process. This is done by the learners carrying out research on the steps towards coming to the correct answers. For instance, I have taken my learners through the factorization process through calculations and each group presents its poster in the class during normal lessons. An assessment of the presentation by each group gives me an opportunity to assess what group has performed well, and what group needs re-emphasis on the concepts taught in the classroom. Posters have really been beneficial in an assessment of what is the best for the learners by weighing the ability of these learners to link up the steps towards coming up with the correct answer. Furthermore, use of questions, according to the research conducted by Lee (2002) indicates that no form of assessment can be of benefit if the questions are not administered in the learners. QCA (2005) cautions that through the use of questions by the educators should not be taken for granted, but carefully researched by the educators prior to subjecting them to the learners. If the questions are well though of by the examiner, there is a great likelihood that the learners will also be comfortable with the tests subjected on them. The learners are also in a position to come up with answers that will determine whether they have grasped the concepts taught or not. In my case, questions comprise the greatest percentage of the assessments subjected on my learners. My questions range from the known concepts to what is unknown. This enables my learners link the concepts being taught and what they already know in the lesson. At times, I have grouped my learners based on their abilities, and gave them questions which they solve as a group. The learners are able to internalize the questions, and then come up with the best answers which are presented in the classroom. Keeley & Tobey (2011) indicate that in the case of formative assessment of Mathematics in the classroom the educators must be very keen whilst giving feedback. They recommend that the educators give comments that will boost the morale of the learners as compared to grades that demotivated the learners. With the concern by the stakeholders of education in the UK on the inability of the educationists to apply the use of questions during learning, the concept of formative assessment is seemingly out of question by the educators. In my classroom, I have always been keen to ensure that my questions improve learning of Mathematics. My questions have always been rich in content and those that see the progress of the learners by step by step analysis of the concepts being asked. OFSTED (2003) indicates that it is evident that through questions, an understanding of the concepts being taught in the classroom can be assessed in a sensible way. With the use of questions, I have been better placed to plan my future lessons from a correction of the past mistakes by my learners. This leads to my belief that, through questioning it is possible to access important information regarding formative assessment. Peer and self assessment is very useful in the field of education, especially in the teaching of subjects of complexity such as Mathematics. According to the research conducted by Garber (2008) use of peer and self assessment aids in minimizing the fear of asking among the learners. With the learners marking their own homework, they are likely to discuss freely on the outcome as compared to the teachers. Some learners fear their teachers; thus, most of them end up creating a chain of questions that have no set timeline for asking. For a subject that needs calculations and constant repetition, such learners are likely to be completely locked from the coursework and demands by the UK educational system. In the case of my classroom, I incorporate the use of peer assessment at least twice in a week so that the learners can discuss amongst themselves. This is not only of benefit to the slow learners, but also the bright learners who end up perfecting their previously acquired skills. Black & William (1998) indicate that, it is of vital importance that the educators always reflect on the responses of the learners, if they have to assess the strong and weak points of the learners. Through peer assessment in relation to the facts by the Department for Education and Sills (2007), my learners have shown exemplary responses in personal assessment on concepts I introduced in the classroom. I have always emphasized the fact that learners always be keen on all the minute details I introduce in the lesson. I, therefore, believe in the fact that through peer and self assessment, learners can substitute my place in the classroom, but with minimal supervision (Garber, 2008). After subjecting learners to any form of tests, it is of essence that the educator devises a strategy that will ensure that feedback gets to the learners. In my Mathematics classroom for example, I always ensure that I mark all the assignments and give appropriate feedback through giving my comments at the end of the test. For instance in the case of fractions, I am careful to check if all the steps in the classroom have been well understood by the learners, by giving feedback on why some parts are wrong and why others are right. This kind of feedback allows the learners devise a strategy of what is right and what is wrong and what steps to undertake to improve their grades (Qualifications and Curriculum Authority, 2008). Formative assessments should be designed in such a way that the learners are assessed on the basis of their levels of understanding (Black & William, 1998). Assessing the learning in relation to outcomes (levels), the educator is able to keep track of the progress of the learners. Since my class is a mixed ability one, at times I group my learners together, according to their abilities then assess them in small groups. If this process becomes monotonous during learning, the educator manages to come up with a culture of never leaving the classroom without checking the progress of the learners. The educator is able to devise plans that allow the learners understand the objectives and aims of the lesson prior to any form of assessment. In my Mathematics class, I have incorporated the use of thumbs up and down, as well as the traffic lights approach. Through the thumbs approach, my learners put their thumbs up to show that they have grasped the concept taught and thumbs down to show that they have not understood. The same concept applies for the traffic system that allows the learners go with green if they are good to go to the next level in the study of Mathematics. If they are not completely sure that are not comfortable with the topic, they go with yellow, and completely unaware for color red. With this information at hand, I am able to detect which learners are fit to move to the next level and which learners need a lot of coaching to join the rest of the class. This makes work easier, as the concepts of formative assessment in this case are well defined to the learners. Online assessment tools have been of help in my classroom especially those that can be printed. With a lot of tasks being subjected on my learners, they are constant in the learning process. The online assessments also provide the learners with a unique experience as compared to the normal questioning that take place in the classroom setting. I ensure that I record all the responses for future responses. This has been of help in my quest for implementation of formative assessment in the classroom setting and learning in general. 2.3. School’s policy The school’s policy requires that all forms of assessments must be geared towards the success of the learners. This interprets that the tests must be suitable enough to cater for the needs of the learners inclusive of the learners with a lot of weaknesses. Of essence, the tests according to my school relates to the fact that the learners ability and understanding of concepts must be boosted through tests and not condemning the learners. Detection and correction of the weak points, essentially, is my school’s slogan. 3.0. Conclusion Conclusively, it is justified to argue that assessments are the basis of apposite learning in the educational setting. As discussed above, educators must be very keen to check the practicability of different forms of assessments and the repercussion that they will have on the learners. Educators who have introduced a culture of continuous and consistent assessments have, indeed had an easier time dealing with the advancement of their learners especially the slow learners in the course of learners. References Black, P. & William, D. (1998). Assessment and Classroom Learning. Assessment in Education: Principles, Policy and Practice 5, 1998: 7–68. ---------------------1998. Inside the black box. NferNelson: London. ------------------ 2001. Inside the Black Box Raising the Standards through. Available from: http: Ilwww.powavschools.com/projects/literacy/SSTTL/AssessDocs/PDPs/BlackBoxArticle.pdf Department for Education and Sills (DfES), 2007. Secondary National Strategy for school Improvement Tracking for Success in Mathematics. London: DfES Donald, V., &Ainsworth, L., 2006. Common formative assessments: how to connect standards-based instruction and assessment. London: Corwin Press. Garber, L., 2008. The effect of written feedback on formative assessments on students' performance in a high school mathematics class. Delaware: University of Delaware. Hodgen, J., &Williams, D., 2006. Mathematics inside the black box. London: NFER. Keeley, P., & Tobey, C., 2011. Mathematics Formative Assessment: 7 Practical Strategies for lining Assessment, Instruction and Learning. London: Corwin in association with NCTM. Lee, et al., 2002. Working inside the Black Box. London:  King's College. Lester, K., & National Council of Teachers of Mathematics., 2007. Second Handbook of Research on Mathematics Teaching and Learning. Charlotte: IAP. Maughan, S., 2009. What is a good Math assessment? Presented at the International Association for Educational Assessment conference, Brisbane, September 2009. Maughan, S., & Cooper, L., 2010. Policy and developments in mathematics assessment in England. Paper presented at the 36th International Association for Educational Assessment Conference 'Assessment for Future Generations', Bankok, 23 August. Available at: http://www.nfer.ac.uk/nfer/publications/44413/44413.pdf OFSTED., 2003. Good assessment practice in mathematics Document ref number: HMI 1477  QCA., 2005 2004/5. Annual Report on Curriculum and Assessment. Qualifications and Curriculum Authority. 2008. Assessing Pupils’ Progress, Assessment at the heart of learning. QCA Online. Stanley, T. & Moore, B. 2009. Critical Thinking and Formative Assessments: Increasing the Rigor in Your Classroom. Larchmont, NY: Eye on Education. William, D., 1999. Formative Assessment in Mathematics: Part 1: Rich Questioning. Summer 1999; Vol 5: No 2. Read More

Additionally, Lester & National Council of Teachers of Mathematics (2007) indicate that if educators select formative assessments over summative assessments, their learners stand a better chance to have close monitoring of the learner progress and assistance on the tasking topics in the course of learning. Positive results are likely to be yielded in the learning environment with the educators devising the best approaches to apply while teaching. Positive results, new trends picked by the learners and varying responses can be well recorded in the learning environment in the case of formative assessment, since the entire process is continuous.

This essay shall focus on the current national policy on assessment in Mathematics, the school policy on assessment, after that give a critical reflection of my personal classroom practice with assessment in Mathematics. Finally, the essay shall make a conclusion on the importance of theories of assessment in Mathematics among my learners. 2.0. Body 2.1. Current national policy on assessment in Mathematics Maughan & Cooper (2010) indicate that in the UK, there have been massive attempts by the UK government to update the current policies that relate to assessment of Mathematics in England.

The government aimed at coming up with forms of means that would lead to proper learning of the subject through engagement of the learners; thus, better participation of the same in the learning process. On another view point, the government of UK was much more concerned with making the learners embrace the fact that learning is not a formality, but it must come from within them. In the long run, analysts and researchers of education in England argue that these policies have in a number of ways been beneficial in teaching and learning of Mathematics.

The policies also aimed at highlighting the implications of the study of Mathematics outside teaching and learning, but also in the life after schooling. According to the research conducted by Maughan & Cooper (2010), proper assessment of Mathematics in the UK educational system, has been defined as a form of assessment that allows learners to develop attributes of problem solving skills, whilst under instruction of Mathematics. The government undertook measures of setting up accountability measures that would see the implementers of education policy in the classroom would come up with tests that would measure the ability of learners in a particular test.

This interprets the fact that the educators must involve putting much weight on skills taught in the classroom setting. This according to the policy set by the UK educational programs relates to selecting the best content that would see the learners be in a position to succeed in the tests (Maughan & Cooper, 2010).According to the UK Smith Report, suitable methodologies of assessing Mathematics would be beneficial for evaluation of proficiency skills among the learners in the context of Mathematics (Maughan & Cooper, 2010).

Prior to the selection of a single model to assess Mathematics, the assessors must exhaust all the existing options that would be beneficial in setting an appropriate model. The current national policy on assessment in Mathematics in UK, advocated for the tests being of varying genres, and with rich content that would boost the learners reasoning ability. The policy, according to Maughan & Cooper (2010) seek to establish a means in which the learners would be first tested on the uncomplicated questions, then progress to those that require a bit of thinking.

Time allocation is also of great importance if the learners have to achieve the goals and objectives of the test. Educators must make sure that all questions have a considerable amount of time for proper answering. 2.2. Critical reflection on classroom practice In the course of learning, it is imperative that execution of formative assessment is properly done by the educators. As a Mathematics teacher in a mixed secondary school of year 7, 8, 9 and 11, I ensure that I incorporate the use of various teaching methodologies so as to fit the learners of varying mixed abilities in my classroom.

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