Assessment refers to all those activities undertaken by teachers, and by the students in assessing themselves, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged. Such assessment become ‘formative assessment’ when the evidence is actually used to adapt the teaching to meet the needs. – Black & Wiliam, 1998
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Those involved in the field of educational study and pedagogy often credit British researchers Paul Black and Dylan Wiliam for igniting global awareness and interest in the concept of formative assessment. In 1998, Black and Wiliam published two important papers – an article in which they argued that formative assessment, when properly employed in the classroom, would help students learn what was being taught to a significantly improved extent, and an in depth meta-analysis which would provide the evidence base to suggest that the benefits brought to pupils by the utilisation of formative assessment are “amongst the largest ever reported for educational interventions”.
Formative assessment is best explained by comparing it to the idea of summative assessment. Summative assessment is an unambiguous method by which one can record the progress of pupils. The assessment is carried out after a defined quantity of teaching and/or pupils’ work, usually in the form of an exam, and this information is used to inform the teacher as to what degree each pupil has understood the information that has been taught. The pupils are fed information, their understanding is reinforced through a variety of tasks and then the pupils are asked to feed this information back to the teacher so they can be assigned a grade. Formative assessment, on the other hand, doesn’t concern itself with grading an entire mass of learning, but rather focuses upon assessment throughout the learning process so that the teacher is better informed as to what choices they can make to better inform the students during the on-going feed of information. Crooks (2001) describes this idea as “assessment OF learning versus assessment FOR learning”.
In this paper, I will critically analyse how formative assessment may be used to support pupils’ learning, with particular focus upon its use in the teaching of early mathematics. The first section focuses upon the key ideas, concepts and theories associated with formative assessment and the second section concerns itself with my own personal experience of their implementation.
Formative assessment: A Critical Analysis
Formative Assessment vs Summative Assesment
Cowie and Bell (1999) refer to formative assessment as: “The process used by teachers and students to recognise and respond to student learning in order to enhance that learning, during the learning.” They allude to the idea that formative assessment is a continuous process. This idea of a constant procedure of development is one which is referred to by many theorists. Ginsburg (2009) states that “Formative assessment is generally defined as assessment for the purpose of instruction. The central idea is that assessment should not be reserved for an examination of achievement after the teacher has completed instruction. Rather, assessment should be used to gain information that can help the teacher plan effective instruction, particularly for the individual.” This refers to the fact that formative assessment should be used to inform the teacher’s ‘instruction’. This furthers this idea of a continuous process and creates the argument that formative assessment is cyclic in its nature.
One could argue that certain forms of formative assessment are no different than certain methods of summative assessment, and this raises an important issue. It could be stated that it is not the assessment that acts as the variable in the process of formative assessment, but rather it is the way in which the assessment is used. For example, one may carry out a method of assessment that upon first impression could be deemed as ‘summative’, but if the results of this measurement are then used to inform future developments in the teaching/learning process, then surely it can be concluded that this is a use of formative assessment. Crooks (1988) referred to this idea as “the formative impact of summative assessment”.
In the past, assessment in early mathematics had always been seen as a method of recording pupil attainment. Many theorists and practitioners have debated about the varying mediums of assessment, such as formal examinations and on-going coursework, because they could not agree on which form of assessment would best represent a pupil’s learning, but one aspect that was agreed upon was that assessment was “primarily about evaluating the effects of instruction.” (Wiliam, 2007). In more recent times, research began to focus more analytically at the function assessment could play in actually improving pupils’ learning rather than simply measuring it – a characteristic that has been precisely captured as “the difference between assessment for learning and assessment of learning.” (Gipps & Stobart, 1997).
“Assessment for learning is any assessment for which the first priority in its design and practice is to serve the purpose of promoting pupils’ learning. It thus differs from assessment designed primarily to serve the purposes of accountability, or of ranking, or of certifying competence. An assessment activity can help learning if it provides information to be used as feedback, by teachers, and by their pupils, in assessing themselves and each other, to modify the teaching and learning activities in which they are engaged.” – Black, 2004
Formative Assessment in Relation to Constructivism
Constructivism is a relatively new theory in explaining how humans acquire and develop knowledge. Constructivists believe that learners are better able to process, comprehend and understand information if they have had some input in the construction of this information. Constructivists believe that learning is a social advancement that involves language, real world situations, and interaction and collaboration among learners – not simply a process by which one is fed and absorbs information. The learners must be the central focus and hub of the learning process (Piaget, 1974). Constructivists believe that learning is affected by the environment the learner inhabits, their own personal opinions and beliefs and their physical and mental maturity. A learner must possess the self-motivation to want to learn in order to begin the process of doing so by selecting information, converting it to a format that they understand, formulating their own hypotheses and testing these theories and ideas by experimentation and interaction which will ultimately lead to the formulation of their own knowledge.
If a teacher is to adhere to the constructivist way of thinking, the teacher becomes a facilitator rather than simply the imparter of knowledge. It becomes their responsibility to plan, organize, guide, and direct the learner, who is held responsible for their own learning. The teacher supports the learner by suggesting ideas that are shaped from both spontaneous and planned activities, setting challenges that stimulate motivation and inspire creativity, and with the setting of tasks that encompass and promote independent thinking and new ways of learning information.
Lave (1988) stated that “traditional learning situations in which students are passive recipients of knowledge are inconsistent with the learning situations of real-life.” In the modern day classroom, research into constructivist theory has led to the introduction of ‘authentic learning experiences’. Authentic learning experiences have been implemented to bridge the gap between the content of the curriculum and real life application. In more traditional, arguably ‘outdated’, teaching methods subject knowledge was taught as a concept that simply had to be learnt for the sake of education – usually in order to pass some form of summative assessment, most often an exam. Constructivist theories argue that it is the ability to apply this subject knowledge to the real life contexts in which it would be required that holds the key to successful education (Browns, Collins & Duguid, 1989). The information is given a relevance which triggers the learner to want to obtain knowledge, rather than simply because they have been instructed to do so (Gardner, 1991). Constructivists argue that this approach creates an effective foundation for each pupil, whereby the pupil can construct knowledge by relating it in a logical way to their existing knowledge. Herrington & Oliver (2000) outline nine essential characteristics of authentic learning experiences.
1. Provide authentic contexts that reflect the way knowledge will be used in real life.
2. Provide authentic activities.
3. Provide access to expert performances and the modelling of processes.
4. Provide multiple roles and perspectives.
5. Support collaborative construction of knowledge.
6. Provide reflection to enable abstraction to be formed.
7. Provide articulation to enable tacit knowledge to be made explicit.
8. Provide coaching and scaffolding by the teacher at critical times.
9. Provide for authentic assessment of learning within the tasks.
Authentic learning experiences present pupils with an opportunity to investigate their learning and develop their own sense of understanding. Pupils are often encouraged to work within collaborative groups in order to expose them to alternative view points that can help them either form, clarify or justify their own thoughts. A constructivist stance would be that each pupil within the classroom is unique and will engage in thought processes and form interpretations of the same experience in different ways. Authentic learning experiences not only allow pupils to form their own understanding of taught concepts, but also allow them the freedom to utilise these concepts in different ways (Mims, 2003). In recent years, constructivist approaches to learning are being integrated with constantly developing forms of technology, particularly within the realms of assessment. Technology is bringing forth opportunities for pupils to engage with authentic learning tasks that would previously not have been available to them. This technology is also becomingly increasingly mobile, with the introduction of data-enabled mobile phones, tablet computers, laptops, etc., allowing pupils to now access information from a practically infinite number of locations. Technology is extremely evident within the classroom environment through various mediums such as the Interactive White Board, tablet computers, etc. allowing for game-based learning, and providing pupils with real-life contextualisation in a digital format that provides an element of interactivity that previously one could only imagine. Technology skills themselves are seen as a necessity for advancement in current and future society. By combining constructivist approaches to learning and technology, students are acquiring more than one useful skill. Assessment therefore not only assesses the curricular knowledge that created the learning goal, but the learner’s ability to apply this knowledge through the use of technology as well.
Shepard (2000) makes distinct connections between the idea of formative assessment and the constructivist movement suggesting that learning is an active process, building on previous knowledge, experience, skills, and interests and that formative assessment effectively feeds into this cycle. Giebelhaus & Bowman (2002) state that “learning is highly individualized. Constructivism recognizes that teaching must be adaptive to the context, involving complex decision-making, and requiring that a teacher draws upon a repertoire of techniques”. It is assumed by constructivist theory that information or feedback to students in provided continuously and consistently as learning progresses. Formative assessment allows for this continuous stream of feedback to be provided to the learners, allowing them to take control of their own learning and respond to the principles outlined by the constructivist theory.
The Positive Impacts of Formative Assessment
Wiliam & Thompson (2007) conducted research on how the use of formative assessment can support the learning of mathematics within the school environment. The findings suggest that the use of formative assessment had a more beneficial effect on student attainment than previously investigated variables such as an enhancement in teachers’ subject knowledge or a decrease in the number of pupils within a class. Such findings led to a monumental shift in the focus of the Education Authorities, eager to adopt the idea of formative assessment as both an academically-effective and cost-effective tool to implement. Shepard (2007) claimed that this surge led to a large number of products, schemes and other classroom materials being developed, designed to encompass the use of formative assessment, but that these were very often poorly implemented due to a lack of focus upon the necessary principles forming the foundation of formative assessment.
A wealth of research has been executed in order to identify elements that are essential to the effectiveness of formative assessment. Sadler (1989) found that the following three concepts were crucial:
Helping students to recognise clearly the desired goal (understand what is required)
Providing students with evidence about how well their work matches that goal;
Explaining ways to close the gap between the goal and their current performance.
Sadler explained that formative assessment is simply a means of bridging the gap between an individual’s current performance and their intended goal (Figure 1).
CURRENT STUDENT PERFORMANCE
Figure 1: Bridging the gap between performance and desired goal.
Wiliam & Thompson (2007) furthered this idea and concluded that three essential processes were vital to the effective use of formative assessment.
Establishing where learners are in their learning
Establishing where learners are going
Establishing how to get there
These three basic concepts would form the basis on which the government were to introduce their ‘Assessment for Learning’ strategy in 2008. The government referred to this strategy as “Assessment for learning is the process of seeking and interpreting evidence for use by learners and their teachers to decide where the learners are in their learning, where they need to go and how best to get there”.
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A study conducted by Crooks in 1988, found that effective assessment practice could have a considerable positive impact on students’ attainment and attitude. He argued that effective use of formative assessment could consolidate pupils’ learning, increase their self-motivation and teach them the fundamental learning strategies underpinning a successful education. Crooks referred to formative assessment as being “one of the most potent forces influencing education”. Crooks split his findings into two categories, outlined below in Figure 2.
Short term effects
Medium/Longer term effects
Focusing attention on the important aspects of the subject.
Giving students opportunities to practice skills and consolidate learning.
Guiding further instructional or learning activities within the course.
Influencing students’ motivation as learners and increasing their perceptions of their capabilities.
Communicating and reinforcing teaching goals, including key performance criteria and desired standards of performance.
Influencing students’ choice of learning strategies, skills and study patterns.
Influencing students’ subsequent choice of courses, activities and careers.
Figure 2: Adapted from Crooks (1988): The impact of classroom evaluation practices on students.
The table outlines the importance of the learner rather than focusing specifically on the teacher’s role and pays particular attention to how the use of formative assessment informs the learner not only of the topical information that is being fed to them, but more importantly, allows them to develop their own positive attitudes, effective skills and higher standards which allow them to become more succinct learners. Harlen & James (1996) reinforced this idea and wrote that “students have to be active in their own learning (teachers cannot learn for them) and unless they come to understand their own strengths and weaknesses, and how they might deal with them, they will not make progress.” Formative assessment relies heavily on giving feedback to the pupil, and many theorists have argued that this plays a crucial role in the process. Crooks (1988) stated that “Feedback should be specific and related to need. Simple knowledge of results should be provided consistently (directly or implicitly), with more detailed feedback only where necessary to help the student work through misconceptions or other weaknesses in performance. Praise should be used sparingly and where used should be task-specific, whereas criticism (other than simply identifying deficiencies) is usually counterproductive.”
It can be argued that formative assessment is not only a valuable commodity for the pupils involved but also for teacher. Formative assessment provides constant and consistent data to teachers regarding the progression of the individuals in their class, and from this information adjustments can be made to their teaching in order to further this progression.
The Downfalls of Formative Assessment
When adopting a pedagogical viewpoint upon the use of formative assessment, it is difficult to oppose many of the claims made about formative assessment. Formative assessment can help with planning as it allows clear learning objectives to be portrayed to the pupils, pupils become more involved with their learning and can make comments upon it, pupils are given the ability to identify their own learning and needs and to form targets based upon these and this fuels pupil motivation, empowering them with a need to actually want to progress. However, it is the lack of efficient and effective execution of such formative assessment within the education system that contributes to a more cynical picture.
Marsh (2007) produced a critical analysis of the use of formative assessment within the classroom. He reported that “it is evident that it is infrequently used in classrooms.” This echoes findings made by Black & Wiliam (1998) in which they write about a “poverty of practice”. Such findings could be explained by a number of factors. One such reason could be the teachers own experience of schooling when they were growing up – in the past, the focus within the education system was very much upon summative assessment and grading. Teachers grew up in an environment where the central focus was very much about achieving good results, via practices such as ‘rote learning’ – the teacher feeds the information to the pupil, the pupil withholds this information and regurgitates it for the sake of an examination. Even in today’s society, this idea is practically impossible to eradicate as governments and the media place great emphasis and priority on the importance of passing examinations and collating high results. One does not have to look far to observe examples of this – Statutory Assessment Tests at the end of KS1, KS2 & KS3, as well as GCSE results for school-leavers still rank highly in the priorities of many teachers. This comes as no surprise when one considers the importance the education system places upon “achieving minimum standards” within government education policies. Funding is granted and withdrawn from schools based upon the academic performance of its pupils, measured by summative testing methods (Marsh, 2007). It could therefore be fair to argue that pressure is placed upon teachers by the head teachers and local education authorities to ensure that the school-wide results of formalised testing methods are satisfactory, essentially jeopardising the focus upon formative assessment and ensuring that the needs of every child are met and developed.
Another reason for this lack of focus upon formative assessment could be attributed to the curriculum documents supposedly at the very heart of the child’s education. The National Curriculum focuses very strongly upon the key topics and knowledge that educators are to deliver to the pupils, but far less emphasis on the actual processes of learning that underpin the development of the child. Marsh (2007) wrote:
Although some emphasis is given in these documents to processes of learning, the predominant focus is upon knowledge, concepts and skills, as measured by summative examinations.
A similar argument could be made in reference to the child’s feedback of such information. Cultural influences within our society dictate that within the education system, awards and recognition should be given to pupils whom are performing well. The majority of these awards are based upon the results and grading of individuals’ summative testing. Many cultures commend pupils who achieve a high level or score, but rarely give recognition to the underlying processes involved in managing to attain such results. Marsh (2007) argues that critical thinking, diligence and self-reflection are all vital attributes in the implementation of formative assessment.
A report by Dunn & Mulvenon (2009) also criticises the growing extent of positive literature being published regarding the use of formative assessment. The research argues that Black & Wiliams report (1998) is limited in its use of data and demonstrates a profound need for more efficient research to be carried out, to provide more credible data regarding the positive impacts of formative assessment upon pupil attainment. Dunn & Mulvenon state “we do not argue that formative evaluation is unimportant, only that limited empirical evidence exists to support the “best practices” for formative evaluation. In particular, limited evidence investigates the group that may benefit the most from formative evaluation, low performing students.” This lack of concrete scientific research could be argued to detract from the integrity and reliability of cases put forward stating that formative assessment does have such a positive impact upon pupils.
Observations & Evidence
During my time training within the education sector, it has become clear that the theories and principles outlined in my report are evident within classroom practice, although to what degree they can be deemed effective varies significantly. With a focus on the teaching and learning of early mathematics, many techniques were employed by myself and the class teacher in order to utilise formative assessment.
Sadler (1989) identifies three criteria that are crucial to the effective use of formative assessment. The first key point is that “students should be helped to clearly recognise the desired goal”. The fulfilment of this criterion is constantly evident in the lessons taking place in my classroom. The first and foremost way in which this occurs is through the clear outlining of the learning objectives at the start of each lesson. These learning objectives are shared with the class in a number of ways. Firstly, the pupils are asked to write a title in their books before the directed teaching begins – this title is always in the form of a question, for example ‘Can I draw hops on a beaded line to make multiplication sentences?’. The question is deliberately phrased in the first-person to immediately involve the pupil. Selected children are then encouraged to explain the learning objective to the class, with the teacher clarifying any misconceptions. Brooks (1999) outlined the importance of children being in control of their own learning, stating that “constructivist teachers enquire about students’ understanding of concepts before sharing their own understanding of those concepts.” The learning objective is then further clarified to the pupils by being available to read on the whiteboard, with words and ideas being broken down individually. For example, in the learning objective ‘Can I draw hops on a beaded line to make multiplication sentences?’, children were asked if they could remember how to draw hops, think of other terms for ‘multiplication’, and to consider how they think they might write down a multiplication sentence. After the directed teaching, the children are set differentiated tasks according to their ability, and the teacher explains thoroughly what they are expecting the child to achieve. For example, children may be asked to the use the coins available to them on their table in order to write down their own multiplication sentences or repeated addition sentences. An expectation of the amount of work required is also made clear, based on the individual’s ability.
The second criterion identified by Sadler (1989) is that “students should be provided with evidence about how well their work matches that goal”. The most apparent example was through the marking of the children’s work. It quickly became evident to me that simply marking and grading the work was not enough. Gipps & Stobart (2007) referred to “the difference between assessment for learning and assessment of learning”. If the work was to be marked in this manner, then the pupils’ work would be being subject to summative assessment – the pupil would be made aware as to how well they had understood and performed the set task, but the value of the teacher’s feedback would end there. The feedback given by the teacher would certainly fulfil the ‘assessment of learning’ criteria, but in order to satisfy the demands of the ‘assessment for learning’ criteria, other approaches would have to be executed. This was evident through the initial stages of marking in which the child’s work was marked against the expected outcomes of the task – the child’s attention was drawn to the parts that they had carried out particularly well by the inclusion of comments and ticks, and they were subtly made aware of any failings by the exclusion of any ticks – it may be argued that the use crosses to signify errors may be detrimental to the child’s self-confidence and self-motivation that are vital to constructivist theory (Piaget, 1974). For example, one pupil had produced a high number of accurate multiplication sentences based on their work with the beaded line – however, on one multiplication sentence, they had used an addition sign in place of the multiplication sign, and this had led to an addition sentence, which whilst accurate, was not appropriate to the learning objectives of the lesson. If the teacher was to mark this with a cross, the pupil may then form a misconception that their addition sentence was incorrect, so instead, feedback is given in the form of a comment ‘Have a look at the rest of your work! What’s wrong with this one?’. The pupil is given the advice and guidance they need in order to self-correct their work, which constructivists would argue allows for a stronger basis for learning.
The final condition, and arguably the most effective within the realms of formative assessment, was that the teacher should “explain ways to close the gap between the goal and their current performance.” This was a condition that was met satisfactorily by the use of ‘next steps’. When marking the pupils’ work, ‘next steps’ are used as a clear and defined way of instructing them on how to progress their learning, and bridge the gap between their current attainment and the target they are intending to reach. These ‘next steps’ were based on the expected attainment of the individual and could serve a variety of purposes. If the child was clearly struggling, misconceptions would be clarified and further work may be given. In one instance a pupil was clearly struggling to draw arrays to match multiplication sentences, so examples were written out and explained within the pupil’s exercise book demonstrating how they various components of the number sentence could be gathered from the array. The task was then turned on its head and the pupil was asked to write multiplication sentences based on the arrays drawn for them.
‘Next steps’ could also serve as a challenge for the higher ability ‘guiding further instructional activities within the course’ and ‘influencing students’ motivation as learners and increasing their perceptions of their capabilities’ (Crooks, 1988), pushing them to explore and experiment with concepts independently. For example, one pupil had clearly understood how number bonding could be used to create addition sentences totalling 20, so they were asked to try and use larger numbers to create addition sentences that would make 40 and 60. An effective component here is that children are directing their own learning, and maintaining responsibility for their own progress. Harlen & James (1996) reinforced this idea and wrote that “students have to be active in their own learning (teachers cannot learn for them) and unless they come to understand their own strengths and weaknesses, and how they might deal with them, they will not make progress.”
Cognitive conflict (Piaget, 1985) is another tool that can be useful in the formative assessment of Mathematics (Limon, 2001). If a child encounters a problem in their written mathematics, concrete objects can be provided with which to check their work. Ginsburg (2009) found that a child is more likely to believe hard evidence in the form of ‘manipulatives’ (eg. counting blocks) than a written equation on paper. When one child in my class encountered a misconception evident through their solving of the equation ’30 – 16 = 24′, I asked them to confirm this for me by giving them counting blocks. The pupil soon discovered that by carrying out this practically, the answer was in fact ’14’ and they were able to link this knowledge to the written equation. The teacher has provided the scaffolding for allowing them to make this connection and also developed their range of problem solving skills.
Ginsburg (2009) also criticises the use of formal formative assessment methods within mathematics stating that
Teachers need assessments that give them a personally meaningful and practical ‘theory’ of the child’s performance, thinking/knowledge, learning potential, and affect/motivation. Unless it is to be merely ‘academic,’ namely something learned in the academy and usually irrelevant for practice, the theory should make sense to the teacher, and should entail concepts that the teacher can see contribute to the practical job of teaching mathematics.
Ginsburg feels that teachers should not become obsessed with the idea of pedagogical theory, but instead should approach their teaching practically, and make the necessary decisions based on the needs of their class. Ginsburg argues that it is not the results of the formative assessment itself that provides the solutions for bridging the gap between knowledge and progression, but it is how these results empower the teacher to make relevant choices that will push forward the pupils on an individual and whole class basis. This is continually evident within my own teaching practice. I have designed and begun to maintain an assessment file which maps out the progress of the pupils within my class in relation to the learning objectives of each lesson and each unit. These results are then used in conjunction with the national curriculum levels in order to ensure that I am continually aware of the academic position of each pupil. The data allows me to distinguish which areas specific pupils need more support in, and allow me to make certain informed choices regarding the planning of lessons. For example, when teaching the relationship between repeated addition and multiplication, it became apparent t
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