A particular understanding that is not yet fully understood by a pupil may not be essential providing the topic will be encountered again. Yet judgements whether a particular idea is necessary to be understood will often be unclear so
The practice of formative assessment has to be informed by a model that is quite detailed, in that it has to provide some guidance about the ways in which a pupil might progress in learning, linked to a clear conception of the curriculum and its learning goals. (Black 1998: 26).
From my experience in school I have seen mathematics teachers’ use formative assessment in many different ways. One of the most common applications of formative assessment that I have observed was an almost instantaneous assessment of the body language and facial expressions of the pupils when explaining the task, the teacher decided to explain the task again in a different way, as she felt the pupils misunderstood the first explanation. Clearly, if formative assessment is used and applied in a structured manner it will be advantageous for the pupil’s progression through the curriculum and help clarify any misconceptions pupils may have.
Schools are accountable to the pupils who attend. One responsibility of the school is to provide evidence that they are promoting the learning of their pupils. One method to provide this evidence is to publish public examination results that are related to a common criteria and standard in order to show pupils progression. However this does not paint a valid portrait of the school, as poor exam results would show the school is not taking responsibility for pupils, as learning is clearly below standard, but in reality pupils may have significantly improved if they came from a poor educational background so linking the results with detailed data such as the school’s intake and context will make the data fairer. Providing evidence that pupils are learning by the means of assessment will only develop further learning if the results can be designed and communicated so that they can serve the improvement in the school, otherwise this assessment for accountability will not provide any benefit to the pupil (Black 1998: 31-35).
In the classroom feedback from assessment is important for both the teacher and the pupil. From the teachers perspective it can be used in the classroom to measure the understanding the pupils have from the lesson objectives which links it closely to formative assessment. Pupils can receive feedback on their performance in many different ways such as grades, comments or praise such as very good.
The combination of goal-setting and feedback had been compared with either alone, that, despite the difficulties of isolating the two effects and a variety of methodological flaws, the results were ‘remarkably consistent ... neither is really effective without the other (Locke and Latham 1990: 197).
There has also been a significant amount of research trying to find which type of feedback is the best for improving performance Wiliam (1999: 10) states that, ‘If you are going to mark a piece of work, you are wasting your time writing carful diagnostic comments’. This is because pupils tend to be blinded by the grade they receive and do not recall the comment for improvement, which is the more effective form of feedback for further learning. Evidence of this is provided by Ruth Butler (1987) in a study showing that giving marks or grades, or otherwise focusing on judgment or competition, as part of feedback can actually inhibit the learner’s attention to any substantive advice on improvement. Therefore feedback to the pupils can promote further learning for the pupils, if it is used effective and relates performance to goals, make people focus on the task, not themselves, nor compare them with others, compare their performance with their own past performance, be seen as informative, but not controlling and make people feel confident, but not complacent (Coe 1998: 43-66).
There are many different strategies that can be implemented by the classroom teacher to assess pupils’ achievement and understanding in mathematics. Some strategies are outlined by The National Strategy from the Department for Children, Schools and Families. They have provided an assessment criterion, which shows what pupils should have an understanding of at the level they are working at in mathematics. It is recommended by the DCSF this criterion can be used when
Assessing; the work in pupil’s exercise books, observing and listening to pupils when they are working, dialogue with pupils, initiated by careful questioning to explore and probe their understanding and evidence from the occasional test. (DCSF, 2009: 6).
New approaches to assessment are being implemented in some classrooms. Naylor and Keogh (2009: 215) describe, ‘An Active Assessment approach...strategies that actively involve learners in the purposeful assessment activities and sow the seeds for further learning’. Active assessment is often implemented by using activities that include misconceptions, misinterpretations or deliberate mistakes, making pupils experience a degree of uncertainty, including high achieving pupils. These activities put pupils in a position where they have to explain and justify their ideas through collaborative discussion. Activities such as sorting cards with statements on them into groups such as agree, disagree or partly agree could be used to encourage discussion amongst the pupils. Other examples of activities that support Active Assessment are odd one out activities and creating a wanted poster about a particular shape where the pupils describe a given shape. Active Assessment is allowing the teacher to integrate assessment, thinking and learning in their classroom, and make assessment for learning much more manageable (Keogh and Naylor 2009: 35-37).
The past decade has seen significant rises in mathematics for all pupils, but still more pupils should be attaining higher GCSE grades. Current teaching focuses on strategies to improve exam performance and focuses heavily on preparation for the test. Many pupils described typical maths lessons as concentrating on the acquisition of skills, solution of routine exercise and preparation for tests. When asked by inspectors pupils understood the difference between getting the right answer and understanding the work. However many were content to have the right answers in their book when they did not know how to arrive at them. Often replicating steps in a method without thinking, or waited until the teacher read out the answers. Most secondary maths teachers recognise the importance of pedagogic skills in maths, but feel the pressures of external assessments on them and their pupils. They feel restricted by these pressures and by time, so many concentrate on approaches they believe prepare pupils for tests and examinations, in effect ‘teaching to the test’. This practice is widespread and is a significant barrier to improvement (OFSTED, 2009: 3-18).
From my own experience in school I have witnessed examples where the practice of teaching to the test is evident. In a particular school the year 11 pupils on a C/D boarder line for mathematics are taking their GCSE in November rather than in the summer. This applied pressure on their teacher to prepare them for an early exam. In response to this the focus of many lessons was to be able to complete exam style questions on the particular topic and not to gain an understanding. When speaking to the teacher about this situation she commented that if the pupils were to get grade C’s after the exam then she would like to push them to raise their grade in the summer. However she acknowledged that the school was under substantial pressure to raise its percentage of pupils attaining 5 GCSE’s A* to C including Mathematics and English. Therefore pupils achieving a grade C in the early exam would attend booster lessons in other subjects to ensure they achieved more GCSE’s rather than further developing their mathematical knowledge. This is a key example of where assessment is preventing the opportunity of further learning and the development of mathematics within the school. Another implication of summative assessment is the effect on a pupil’s motivation. In this teach to the test culture pupils experience repeated practice tests which in some cases reinforce the low self-image of the lower-achieving students.
Another form of assessment and also a driving force to teach to the test is the publication of results and league tables of schools.
League tables give us no credit for maintaining an exciting, rich, creative and diverse curriculum... It (effect of league table) encompasses at one end, teaching to the test and cramming. At the other end, it includes bending the rules on reading test-questions aloud right through to changing answers on children's scripts. It has come about because of the pressure put on teachers by the publication of league tables’ (Strauss 2004).
This argues the negative views of publishing league tables as it puts more pressure on pupils achieving five GCSEs grade A*-C including Mathematics and English. To raise results teachers can feel compelled to teach to the test, to get the best possible results as they rely on instant recall of methods and not mathematical understanding. This is not the best solution for the pupils as previously mentioned; more focus would be given to other subjects and prevent further development in mathematics.
Taking all different methods and purposes of assessment into account overall I believe assessment does make a positive contribution towards a pupils learning when used appropriately. However there barriers caused by assessment which do hinder pupils learning. There are many occasions still in schools today where the affect of assessment in the classroom has developed a ‘teaching to the test’ culture, driven by league tables and statistics. Assessment is never going to go away as it will always be used to acknowledge learning has taken place and to certify performance, therefore it is important for teachers to maximise the advantages assessment brings to the classroom. Each class will be different so it is vital that the teacher understands the different approaches to assessment that can be taken in order to assess that class in the most efficient way.
References
Black, P. (1998) Testing: Friend or Foe? Theory and Practice of Assessment and Testing, London: Falmer Press.
Black, P. and Wiliam, D. (1998) Inside the black box: Raising standards through classroom assessment, London: GL Assessment.
Black, P. and Wiliam, D. (1996) ‘Meanings and consequences: a basis for distinguishing formative and summative functions of assessment?’, British Education Research Journal, Vol. 22, No. 5, December, pp. 537-548.
Butler, R. (1987) ‘Task-involving and ego-involving properties of evaluation: effects of different feedback conditions on motivational perceptions, interest and performance’, Journal of Educational Psychology, Vol 79, No. 4, December, pp. 474–482.
Coe, R. (1998) ‘Can feedback improve teaching? A review of the social science literature with a view to identifying the conditions under which giving feedback to teachers will result in improved performance.’ Research Papers in Education, Vol 13, No. 1, pp. 43-66.
Harlen, W. (2005) ‘Teachers’ summative practices and assessment for learning – tensions and synergies’, The Curriculum Journal, Vol 16, No. 2, June, pp. 207-223
Harlen, W. and Deakin Crick, R. (2002) A systematic review of the impact of summative assessment
and tests on students’ motivation for learning, Research Evidence in Education Library, issue 1
Locke, E.A. and Latham, G.P. (1990) A Theory of Goal Setting and Task Performance. Englewood Cliffs, NJ: Prentice Hall.
Naylor, S. And Keogh, B (2009) ‘Active Assessment’, Mathematics teaching 215, September
Strauss, P. (2004) ‘Barriers in the way of progress’, Times Education Supplement, 26 November
Wiliam D. (1999) 'Formative Assessment in Mathematics. Part 2: Feedback’. Equals: Mathematics and Special Educational Needs, Vol 5, no 3, 8-11.
Department for Children, Schools and Families (DCSF), (2009), Assessing Pupils’ Progress: Secondary mathematics guidance, Day-to-day assessment in mathematics, Nottingham: DCSF publications
Office for Standards in Education, Children’s services and Skills (OFSTED), (2009), Mathematics: Understanding the score. Improving practice in mathematics teaching at secondary level, London: OSTED publications