Assessment in mathematics teaching in regards to the National Curriculum

The subject of detecting what goes on in a schoolroom and reflecting on whether it is every bit good as it heap be, improves the part of a teacher s ain instruction and their ability to region it with others. ( Mason, in Lee, 2006, p10 ) in that location atomic number 18 many methods of reflecting upon one s ain work, but carried unwrap critic everyy and positively, all should take to an ability to better the quality of that work. The cardinal word here is should . Improvement bequeath simply take topographic point if, following the musing, some stairss argon identified and implemented to convey ab surface betterment. It is the confined of this paper to help that contemplation and contemplation cognitive operation.The rubric of the essay requires rating of my instruction. The word evaluate is taken to intend to judge or find the signifi batchce, worth, or quality of , as defined by Dictionary.com. The paper w laid low(predicate) total, in a chronological order, the instruction I carried proscribed over a devil hebdomad period. In peculiar it ordain analyze the estimation techniques that I apply at each phase, and will critique the effectivity of the judgement. Where appropriate the paper will propose where things could h darkeneder been make better.As the rubric dictates, this paper is a contemplation upon learning that I carried out during my first arrangement, as set of my PGCE class. As such(prenominal), it refers in the most portion to personal experience and contemplations upon that experience. The paper will thus be written chiefly in the first individual, with mentions from other parties in the 3rd individual.Having considered the appraisal employed throughout the instruction, I will so see a figure of general findings, and how assessment whitethorn impact those findings.What Is Assessment and Why Is It ImportantAssessment is a portion of all of our lives from the minute we are born, as the accouche affair places a babe on the graduated tables. It follows us through early childhood ( as pistillate parents and wellness visitants assess what a babe can make at each phase in their development ) , into school and beyond into employment.The facet of appraisal with which this paper is concerned is the appraisal carried out within the mathematics schoolroom. The word appraisal is habituated to denote any witting activity intended to tack on information about a disciple s fulfillment or attainment.There are four chief types of appraisal, ( as defined by Weeden, spend and Broadfoot, 2002, p19 )Diagnostic to place students original public presentationFormative to help eruditeness ( including equal and self appraisal )Summational for reappraisal, transportation and enfranchisementmeasure to see how well instructors or establishments are executing.Of these, formative and summative appraisal will have the most focus, with conside balancen being given to the effects these types of appraisal have on students acquisition. Appraising appraisal is non considered within the range of this essay.Whether appraisal is good to a student s acquisition or non depends on the utilization to which the information gained is put. For illustration, wellness visitants may place a nutritionary demand of a immature kid which can be corrected with the appropriate input, and also instructors may place an educational demand of a student which they can take stairss to turn to. William ( in Weeden, Winter, Broadfoot, 2002, p29 ) suggests all four maps of appraisal require that case of public presentation or attainment is elicited, is so interpreted, and as a consequence of that reading, some action is taken . Weeden, Winter, Broadfoot ( 2002 ) besides conclude that appraisal becomes formative when the information gained is used by the instructor and student within the learning procedure. I would besides add that it requires the consequences of the appraisal to be acted upon within a trivial cli p frame, while feedback is still relevant.Further much, inventions that include beef uping the pattern of formative appraisal green goods important, and frequently significant, larning additions . ( filthy et al. 2003, p9 ) .The purpose, whence, is to justify that appraisal, of all types, is used formatively wherever possible.The Class That Was TaughtThe course of instruction that I taught was a Year 9 category of 20 students. Although they were classified as a lower-attaining category ( Set 3 out of 4 ) , the scope of abilities within the category and the particular demands of a few persons warrant some brief description. matchless male child had arrived late from Somalia and had a limited appreciation of English, but no other particular demands.Several of the students had low reading ages, typically in the age 8 9 scope, and were hence challenged by some word jobs. Additionally, one of these students had moved into mainstream categories at the start of yr 9, after two old ages support by the school s nucleus programme , and hence sometimes needed extra support as respects concentration.Four of the students in the category were on the school s SEN registry as BESD, i.e. they had behavioral, emotional or societal throw out of kilters which without careful handling could take to disruption in lessons.One-half of the category entered twelvemonth 7 with a National Curriculum assessment degree of 3b or 3a, with the balance at low degree 4. By the terminal of twelvemonth 8 all were accessed at degree 4 or 5c. Several of the students moved up by merely one or two degree points during their first two old ages at Secondary school, bespeaking some cause for concern.The category was routinely supported by a Teaching Assistant, whose function was chiefly to back up the student with EAL, but besides to supply general support as required to other students.The Topic TaughtThe subject taught was Ratio and Proportion.The Scheme of Work indicated five hours of inst ruction, the identical of six 50 minute lessons, and I set about dally forthing a subject program consequently. The really first Standard which a trainee instructor must accomplish is to hold postgraduate outlooks of kids and immature people ( Training and Development Agency for Schools ( TDA ) , 2010 ) . With the benefit of hindsight, I can see that the word high in this criterion is a word that requires considerable thought and single application to each student. At the clip, nevertheless, I took this to intend that I should anticipate all my pupils to be able to hold on the rudimentss of a given subject within a period of learning clip, determined by me, their instructor. Low outlooks by instructors are regarded as a much bigger job than high outlooks. ( Weeden, Winter and Broadfoot, 2002, p64 ) . Determined that my learning would non be portion of this bigger job , I set about my planning with high outlooks for all my students. This position was proven to be instead excessively simplistic during the instruction, but this will be enlarge upon subsequently. The subject of ratio and proportion, harmonizing to the strategy of work, is pre-dominantly a degree 5 6 subject, so would by necessity be disputing for most of the students.With a comparatively unfamiliar with(predicate) category I felt it was of import to get down by measuring how good the category would get by with some of the cardinal mathematical constructs which would be necessary for the subject. The first activity in the instruction, hence, was to re-cap fractions understanding. In peculiar, could the pupils cut down fractions to their simplest signifier, and could they happen fractions of measures? This was mostly a diagnostic appraisal, to set up a starting point for my instruction.Having established that all students had a sound appreciation of simplifying fractions, I introduced the construct of ratios and simplifying of ratios. This was followed by sharing a showd measure by a given ratio, and happening a missing measure given one measure and a ratio.The concluding instruction activity was to present the intellection of proportion and to specify the difference between proportion and ratio.The subject was completed with a summational appraisal, and by self- and peer-assessment in the signifier of production of a posting.For the mantleds of this paper, I will concentrate chiefly on the start of the subject and the decision of the subject, and the appraisal strategies employed at these points. Some reference will be do of the interim instruction, peculiarly with mention to the effectivity or otherwise of appraisal carried out at this phase.The TeachingRe-cap FractionsMy determination to get down this subject with a re-cap of fractions was found on the similarities that I perceive between fractions and ratio. It hence seemed logical, before get downing on a stark naked and potentially ambitious subject, to set up how much the category already knew abou t fractions. As claimed by Ausubel, ( in Clarke, 2005, p12 ) , The most of import individual factor act uponing acquisition is what the scholar already knows. Determine this and learn him consequently. Therefore, the intent of this lesson was diagnostic appraisal to be used to inform the instruction for the balance of the subject. Although diagnostic appraisal has been found to be unproductive if it is simply used for puting intents, it has had benefits if used to place the single acquisition demands of a student. ( Black et al. , 2003 ) .A starter activity ( of fiting braces of tantamount fractions ) indicated that the bulk of the category had an first-class appreciation of this construct. I established this by leting students to work in braces to fit the fractions, and so inquiring persons, or their spouses, for replies. I attempted to use a no hands up attack, as recommended by Lee ( 2006 ) , sometimes utilizing lollipop sticks to choose students to reply. No hands up was a new attack for the category, and many found it hard to defy seting custodies up or shouting out ( or both ) . I would hold with Lee s averment that seting hands up can take to a competitory environment for some students. I would besides propose that it can take to neutrality from other students who see no demand to acquire manifold.Having established that the students possessed an ability to simplify fractions, the following relevant facet of fractions was the ability to happen a fraction of a measure, e.g. A? of 36.Using mini white boards, I was able to set up that all students could work out simple measures. It was so of import to cognize the methods they had employed and to understand their idea procedures, and I used oppugning and synergistic treatment to set up students methods. As Morgan, Watson and Tikly ( 2004, p133 ) put it, cognizing that they can bring forth the right solution is a instead dead-end piece of cognition for the instructor. It would be more helpful to happen out the restrictions of the manner they shortly see the undertaking. Knowing how they see the procedure and what they say to themselves while making it, provides you with a get downing topographic point to learn them to work out more complicated jobs. The popular method of happening A? was halving and halving once more, which led me to revision the inquiring by inquiring how to happen 1/fifth of 30. This in bend led to treatment of division and generation, and through the discourse it became evident that many had troubles with times tabular arraies. As it was non my aim in this lesson to revise times tabular arraies, generation grids were made available to students who asked for them. More students asked for the grids than I had expected, which I view was declarative of a general deficiency of assurance with mental maths. As a signifier of distinction this was powerful for those who needed the grids, but may besides hold led to others seeking an easy option . In the h ereafter I would seek to administer such AIDSs to merely those I believed actually needed them.However, with the usage of the generation grids it was a straight-forward following measure to conk to non-unit fractions, and all students stateed sensible ability to happen fractions of measures.I stated in the debut that the intent of this lesson was mostly to execute a diagnostic appraisal. As a consequence of the lesson I had gained a assurance in my students ability to manage fractions sufficiently good to come on to the following phase. I had non, nevertheless, asked my students to self-assess whether they felt the same. As a consequence, when, towards the terminal of the whole subject, I asked the students to self-assess how they felt about the interact parts of the subject, I was surprised to detect that about all felt that they were ineffective to make fractions . It would look evident that although I believed my students had achieved the acquisition result, by the termin al of the subject they did non portion that persuasion. If I had instigated self-assessment during this lesson, the consequence may hold been different, but I will neer cognize for certain. I agree, with the suggestion of Weeden, Winter and Broadfoot ( 2002, p73 ) , that using effectual signifiers of ego appraisal will do students more responsible for and involved in their ain acquisition .This is an uncouth that I will necessitate to look to better as I move frontward into my following confront of instruction, as it is far more valuable for pupils themselves to take part in the appraisal procedure than for instructors to be the exclusive proctors of advancement. ( Morgan, Watson and Tikly, 2004, p134 ) .Even though the declared intent of the lesson was diagnostic appraisal, I made some effectual usage of formative appraisal during the lesson. For illustration, I used oppugning to place the students methods, and so adjusted my oppugning in repartee to their replies. While t his was effectual, there was range for improved usage of oppugning, to examine deeper into their degree of apprehension.Ratio and ProportionThe chief instruction of ratio and proportion was spread over three lessons. everyplace that period we progressed from basic apprehension of the algorithms to application of the algorithms to existent life type jobs.As the work was spread over three lessons I was afforded the chance to reexamine the work in students books. Mindful of the research findings ( Black et al. Butler Clarke Thorndike in Stobart, 2006 ) , I restricted my marker to placing errors and doing remarks.The research of Thorndike, carried out about a 100 old ages ago, highlighted the comparative consequence of delegating classs to work, i.e. the assignment of classs taking to pupils comparing themselves against one another. This is supported by more recent research summarised by Clarke, ( 2005 ) , to smasher doing a nexus to the impressiveness of measuring attainment against the larning aims instead than against other students.My purpose in placing students errors was to be able to turn to mistakes and misconceptions in subsequent lessons. I was able to make this to some extent, but I do non hold the grounds of a follow-up appraisal to be able to corroborate whether this was all in all successful.The comment-only marker should hold been followed up by leting the pupils clip to reexamine the remarks, and re-work their replies in line with the remarks, as stressed by Black and William ( in Clarke, 2005 ) . I did non let sufficient clip for this to be done. It may besides hold been good at this phase if I had asked the students to notice for themselves on their work, as recommended by Clarke ( 2005 ) . She suggests this as a signifier of self appraisal, whereby the student, holding identified an country for betterment, would discourse the suggestion with the instructor. The in agreement betterment would so be made both in lesson clip or as a pre p activity. In general, the planning of clip to let students to employ the feedback they have received, and the subsequent appraisal of the effects, is an country of failing that I will necessitate to better if my feedback is to be genuinely formative.Another country of appraisal which I was nerve-racking to utilize during this instruction was effectual inquiring. I found a figure of troubles with effectual oppugning in this category, which may good be common across most categories.The first challenge was trying to guarantee all students were involved, without seting undue force per unit area on students who are non comfy replying inquiries in forepart of the whole category. The usage of mated activities helped in some instances, as students were able to give squad replies and support each other if required. Team- or pair-working is a method which I should look to widen in the hereafter, for usage with higher-order inquiries, and to promote the usage of more mathematical lingua l communication. The usage of Study Buddies has been shown to promote non merely mathematical talk and look, but besides peer-assessment and self-reflection ( Lee, 2006 ) .My efforts to guarantee all students were involved in replying inquiries led to some really awkward silences as I allowed the recommended ( Black et al. , 2003 ) wait-time. With one peculiarly quiet student whom I neer persuaded to reply a inquiry, the issue turned out to be merely one of being afraid to acquire it incorrect this was a truly unfortunate state of affairs as it transpired from the terminal of topic trial that she had an first-class appreciation of the work. Not merely was her reserve making her a ill service, but the remainder of the category would besides hold benefited greatly from her part. In add-on, even if she had got it incorrect , this excessively would hold been of benefit. As Lee ( 2006, p26 27 ) states a incorrect reply, possibly more than the right one, helps the instructor b uttocks what further larning students need. End of TopicAt the terminal of the subject I decided to transport out two pieces of assessment a summational trial and a brooding self-assessment.The summational trial besides included some points from the old subject I had taught this group. Its intent was to set up how good the students had remembered subjects they had been taught throughout the old six hebdomads.I was fortunate that this trial took topographic point at the start of Christmas hebdomad , when it was general pattern in the school for lessons to be more relaxed. This allowed me clip to speak separately with each student, to discourse what they had done good and where they may hold had misinterpretations. I was concerned that the students were more interested in the grade they had achieved than in the feedback I was able to give them about their acquisition. Harmonizing to Weeden, Winter and Broadfoot, ( 2002, p115 ) this is non uncommon, as the accent is ever on grade or class and seldom do students truly care about what they really achieved. Although this was designed as a summational appraisal, I was besides able to utilize it formatively by placing a common job with algebra, and turn toing this in the last lesson of term, thereby utilizing the wake of trials as an chance for formative work. ( Black et al, 2003, p55 ) They besides conclude that summational trials should bea a positive portion of the acquisition procedure. ( 2003, p56 )The self-assessment took the signifier of the production of postings summarizing all they had learnt about Ratio and Proportion. The appraisal showed a assorted degree of apprehension, and ability to pass on that apprehension, within the category. One group showed an first-class apprehension and had clearly referred back to their books to guarantee that they included all the freeze right. The EAL pupil had trouble with this activity, so I encouraged him to be really ocular with his posting. Others had taken h apless notes during the instruction and struggled to remember the information this, in itself, was a utile acquisition point for them, as they consider the quality and utility of what they write in their books. ( Two ( contrasting ) postings are included in supplement A ) . Overall, this was an effectual drawing together of the subject, and enabled the students to self-assess their ain acquisition, as the production of postings a requires pupils to reflect upon and organize their cognition in order to pass on it ( Morgan, Watson and Tikly, 2004, p151 )Although this self-assessment enabled students to reflect upon their acquisition, as it took topographic point at the terminal of the subject I was unable to supply an chance for students to set their contemplations into pattern. The appraisal can non hence be findd as genuinely formative. An excess lesson would hold enabled the students to move upon their contemplations, thereby doing the assessment formative.General FindingsExce ssively Much MaterialA repeating job with many of my lessons was trying to grounds excessively much stuff into each lesson. This resulted in me travel rapidlying to acquire through the lesson. I therefore allowed deficient clip for examining and higher-order inquiries. This was to the hurt of my instruction and my students acquisition as instruction is more than make fulling a kid with facts. It starts with presenting hard inquiries ( Spendlove, 2009, p32 ) . I was losing chances, non merely to dispute and excite some of the students, but besides to measure the deepness of their apprehension and place misconceptions at an early phase.Communication and QuestioningMuch formative appraisal can be achieved by effectual communicating and oppugning. Black et al. , found effectual oppugning a led to comfortableer discourse, in which the instructors evoked a wealth of information from which to judge the current apprehension of their pupils. ( 2003, p41 ) However, many secondary sch ool students appear to be fresh to constructive treatment in a lesson environment, and there are considerable challenges involved in altering this state of affairs, particularly if outlooks of communicating are non consistent across a school. Add to this the excess linguistic communication dimension of the mathematics registry as Lee ( 2006 ) calls it, and it goes some manner to explicating the trouble I had in promoting students to speak about their mathematics.While it may be disputing, the benefits of effectual communicating to pupils larning justify attempt being spent to better the quality of communicating in lessons, as larning can non take topographic point in a vacuity and it is at its best when there is a rich bipartisan duologue between instructor and scholar and scholar and scholar. ( Spendlove, 2004, p44 )The countries of communicating in which students are encouraged to go involved include replying inquiries, and explicating their thoughts and methods. This can sho w farther troubles with the usage linguistic communication, peculiarly for students with EAL, who may happen themselves wholly excluded from the discourse. Another group of students who may hold a similar job are those for whom such communicating is unfamiliar outside school. Children aa . from families where English is non the first linguistic communication may be disadvantaged by trust on unwritten interaction. ( Morgan, Watson and Tikly, 2004, p150 )The fact that all students are larning a new mathematical linguistic communication together could be seen as a leveler for the EAL pupils, as all pupils aneed to larn how to utilize mathematical linguistic communication to make, control and show their ain mathematical significances. ( Pimm, in Lee, 2006, p18 ) . Much of the linguistic communication will necessitate to be learnt by both EAL and non-EAL students.As a instructor purpose on promoting the usage of mathematical discourse as portion of formative appraisal in my instruct ion, I will necessitate to run into these challenges creatively.ExpectationsAs mentioned earlier, I set unvarying high outlooks for all my students, but I had given deficient consideration to the comparative nature of the word high . Whilst I believe that I am right to anticipate all of my students to accomplish an apprehension of what they are being taught, how fast and to what degree are things that need to be separately agree. This so leads to the ability of students to measure their ain advancement against agreed marks and aims.I found that one student in the category neer did any work in the lesson until his outlook for that lesson had been separately negotiated with him. He would so bring forth some first-class work, by and large transcending my outlooks. Ollerton, ( 2003 ) relates the importance of students disputing themselves against their ain marks, instead than viing against one another, and that in such a civilization, outlook can be high but accomplishable, holding been negotiated and agreed between student and instructor.Assessment Against LevelsA trouble which has permeated my first instruction pattern has been the definition of degrees at which students are working. There has been an accent placed upon students being cognizant of the degree at which they are working, and being able to measure for themselves how they are come oning against those degrees. There is a danger, nevertheless, that this can take to clicking boxes for each point required within the degree, without needfully developing the apprehension behind the capable stuff. This is similar to the issues liftd by Skemp ( 1976 ) , sing the importance of Relational Understanding as opposed to Instrumental Understanding. It is certainly possible for a student to be assessed, both by themselves and their instructors, to be working at degree 5, for illustration, while missing the relational apprehension to use their accomplishments in other countries.I tested this concern with a Y ear 6 student, with current maths degree ( instructor and trial ) assessed as degree 4a/5c. Without any learning about the topic of ratios ( other than a definition of the word ratio ) , this student was able to use bing mathematical cognition and apprehension to right work out ratio and proportion inquiries graded at degree 6. My twelvemonth 9 students on the other manus, while theoretically working at the same degree, and after several lessons on the topic, were unable or unwilling to utilize their accomplishments to reduce jobs which differed from 1s they had seen antecedently. ( I say unwilling, as I suspect some of their reserve was due to a deficiency of assurance in their ability to undertake more ambitious inquiries. )So, while both the twelvemonth 6 student and the twelvemonth 9 students are assessed as working at the same degree, my belief is that the twelvemonth 6 student shows a far greater relational apprehension, while the twelvemonth 9 students show about merely inst rumental apprehension. This is supported by findings which indicate learning how to go through trials means that pupils may be able to go through even when they do non hold the accomplishments and understanding which the trial is intended to mensurate ( Gordon and Reese in Harlen, 2006, p79 ) .The two groups come from different backgrounds and different acquisition experiences, so it is non possible to pull any decisions, other than to state that the assignment of degrees would look to give small information sing mathematical apprehension and attainment. It is possible that the twelvemonth 6 student has been encouraged to transport out more self find of mathematical constructs, an activity in which the twelvemonth 9 group were loath to prosecute. It concerns me that students are encouraged to mensurate their accomplishment by being able to click boxes instead than understand and use their mathematics. This leads to the consideration of students motive what they want to acquire f rom their instruction.Motivation to LearnA uninterrupted challenge in all lessons has been promoting students to trust to larn. Pupils frequently ask the inquiry, Why do I need to cognize this? , and I confess to sometimes happening this a hard inquiry to reply. One of the primary countries I would seek to better in my instruction is my ability to actuate my students to larn, but first I must understand motive.There are two chief types of motive which encourage students to be in lessons ( as defined by Harlen, 2006 ) extrinsic, where they are motivated by an external end such as deriving a making, and intrinsic, where they are motivated by the end of larning itself. Intrinsic motive is seen as the ideal, since it is more likely to take to a proclivity to go on larning, than larning motivated extrinsically. ( Harlen, 2006, p62 ) , and intrinsic motive is associated with degrees of battle in larning that lead to conceptual apprehension and higher degree believing accomplishment s ( Kellaghan et al. , in Harlen, 2006, p63 ) .So, possibly I could hold used appraisal more efficaciously to increase the intrinsic motive of my students.The work of Harlen, ( 2006 ) identifies possible negative effects of appraisal on student motive, which mostly relate to summative appraisal and judgmental feedback. She besides goes on to depict patterns that maintain motive degrees, including affecting students in self-assessment ( Schunk ) , and the usage of feedback from uninterrupted classwork.None of this, nevertheless, leads to a decision that appraisal can assist increase intrinsic motive. Further factors need to be considered in finding whether this is the instance.There is sure grounds that formative appraisal can raise achievement degrees, as identified by Black et Al ( 2003 ) , but I do non believe that is needfully the same as raising intrinsic motive. Increased intrinsic motive is most likely to originate from bring forthing a echt battle in what is being learnt, and hence lead to a desire to go on that larning throughout life. As Clarke ( 2005 ) claims, affecting pupils in their ain acquisition procedure has had the proved consequence of making life-long, independent scholars.Harlen ( 2006 ) describes two types of involvement single involvement and situational involvement. Students with single involvement in mathematics will persist more and are likely to accomplish good. Sadly, nevertheless, non all students will hold single involvement. Either signifier of involvement will promote students to be involved in acquisition, so the instructor must try to make situational involvement, for illustration, through games. Having encouraged the students engagement through situational involvement, non merely will they get down to larn, but they may besides develop single involvement.One of the keys to making situational involvement is guaranting the students know what they are larning and why, and so supplying formative feedback to the student. Hen ce the importance of formative feedback in making involvement, taking to intrinsic motive. no curricular inspection and repair, no instructional invention, no alteration in school administration, no toughening of criterions, no rethinking of instructor preparation or compensation will win if pupils do non come to school interested in, and committed to, larning. ( Steinberg, in Weeden, Winter, Broadfoot, 2002, p9 )It appears, hence, to be of critical importance that instructors use formative techniques to increase the intrinsic motive of their students to larn. At the same clip, they should avoid actions which will cut down their intrinsic motive.DecisionsThere have been several surveies over the old ages sing the impact of appraisal on students acquisition, notably the work of Black and William, at the abetment of the Assessment Reform Group. These surveies have concluded that for appraisal to raise the criterions of students attainment it must be used formatively. ( Black et al. , 2003 )Reflecting upon my ain instruction and my students acquisition, I must admit that there are many ways in which my pattern can be improved. These include usage of higher-order inquiries, leting for self-discovery of mathematical constructs and leting clip for students to move upon feedback.It is still a duty of the instructor to fix students for external scrutinies, and to describe advancement to interested parties. As such it is necessary to strike a balance between the usage of formative appraisal to back up acquisition, and summational appraisal for coverage intents, but besides to fix students for taking external scrutinies. However, There is ample grounds that the alterations involved ( in bettering formative appraisal ) will raise the tonss of their pupils on normal, conventional trials. ( Black et al. , 2003, p2 )The expression goes, the hog does nt acquire fatter merely by being weighed . Harmonizing to Weeden, Winter, Broadfoot, 2002, p36, Formative Assessment could be an exclusion to this regulation. In this peculiar instance, repeated and ongoing appraisal could really assist to better the quality of acquisition, if the information gleaned from the appraisal is used to do it go on.