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Exploring Critical Incidents in a Comprehensive School

Introduction

In this study, I am going to explore two critical incidents, which took place in a large comprehensive school (School A), situated in central Birmingham in a Mathematics lesson. Behaviour management strategies and use of assessment to aid pupils’ learning are two key components, discussed in this paper. The reasons for the critical issues and how to address these issues in terms of solutions are further investigated.

Critical Incident 1

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The first incident occurred at a bottom set Year 9 class. The teaching experience of initial weeks was surrounded by the behaviour management issues. During my teaching, I found that, the students lack motivation and interest in maths. Some pupils were constantly talking, causing low level disruption and they are not following the instructions, whereas the others were getting distracted and not doing their work that is a general lack of attention. The school behaviour policy starts with non-verbal communication by using body language, cold- calling, warning, C1 (30 minutes after school) and C2 (60 minutes after school). Initially, I wasn’t following the school behaviour policy accordingly rather raising my voice, which resulted in increased negativity and impaired student-teacher relationship (Barbetta, Norona, and Bicard, 2005). I was also informed by my mentor that, there were two students in the class, who would always be disruptive in the class, no matter what you do. However, my mentor didn’t have any issues with that because she was in more control than me as a trainee teacher to tackle those students. Giallo and Little (2003) stated that, the effectiveness of the behaviour management of a student teacher would be different from an effectiveness of an established teacher. I have implemented school behaviour policy, but it didn’t seem to be working and resulted in a number of C1 and C2, given in one lesson. Moreover, detentions didn’t mean much to the students, as they became used to it. When I reflected back on my practice, I was guilty of an increased focused on negativity, criticism and derogatory feedback (Perle, 2016). The delivery of the next lesson changed the whole scene of the practice, as it was full of positivity, appreciation, encouragement and praise. Firstly, I change my speech from “Don’t” and “this is not allowed” to “you should” and “I expect”, components of positive attendance (Perle, 2016). I looked for the opportunities to target and praise the good behaviour with the accurate phrases, “praise, that is delivered contingent on the occurrence of target behaviour, can also have collateral effects” (Hester et al., 2009). The difference was noticeable straight away, as the students started responding well and excitement could be seen through their eagerness to answer the questions through the occurrence of learning (Kern and Clemens, 2007).

Reinforcing positive behaviour and praising pupils who are modelling the expectations of the classroom are essential tools to increase the likelihood of pupils consistently demonstrating similar patterns of behaviour and their recognition through teacher’s appreciation (Perle, 2016). Therefore, the teacher should avoid derogatory talk and reprimands in response to the student disruptive behaviour (Hester et al., 2009) as this will result in perpetuating the low self-esteem of pupils. According to Sabey, et al. (2018), a ratio of 5:1 of positive to negative comments from the teacher is a potential performance indicator and effective basis for evaluation.

To be able to have an efficacy of the approach, praise should be specific to the behaviour demonstrated. “Good job”, “well done” are vague phrases (Brophy, 1981). “Done well in the assignment”, “It makes me very happy that you are using nice words” are more specific examples of praise. Desired academic and social behaviour can be increased by providing specific and contingent praise and establishing classroom expectations (Simonsen et al., 2008). Furthermore, a spontaneous expression of surprise or admiration in reaction to student’s accomplishment is more reinforcing than most deliberate praise because it is based on real accomplishment and accompanied by non-verbal expressiveness that lends it credibility (Brophy, 1981, pp. 272-273). Nonetheless, an unrealistic praise can viewed as insincere and overtly faltering , therefore praise should be sincere and genuine (Hester et al., 2009).

However, differentiation in praise is another considerable aspect as some of the pupils may not like praise and attention publically, therefore it is important that, the praise is appropriate in the context and to the individual pupils as well (Burnett, 2011). Furthermore, Brophy (1981) also mentioned that, praise should be at right time and mode of speech should suit the age group addressed.

In contrast, Kohn (1995) saw praise as the aspect of behaviourism, which controls and empowers, and have opposite effects. The lack of motivation and interest in a task has also been seen in children as a result of praise in comparison to children, who were not given any feedback (kast and Connor, 1988). Moreover, Graham (1990) considered that, praise more complicated and consequently increases pressure and anxiety, implying low self-esteem among the children and discounting principle (Birch, Marlin, and Rotter, 1984).

In conclusion, praise plays a significant role in encouraging pupils to demonstrate good behaviour and stimulates motivation to develop interest in the classroom. However, praise should be constrained to be sincere, genuine and based on realistic expectations to be effective (Henderlong & Lepper, 2002).

During my practice, I have noticed that, another major factor affecting the behaviour in the Year 9 Set 7 could be the perception of being in the bottom set. To include some comments from pupils, “this is set 7 miss we know nothing”, “I don’t understand it and I can’t do it”, before even any attempt to start the task and this often lead to talking and distracting other students and causing low level disruption. A study based in the Greater London area schools, conducted by Boaler (2000), found that, the results from a survey showed that, the threshold of less than two minutes was recorded by 32% of pupils in bottom set before giving up, as compared to the pupils in higher sets, which is 7%. The notion is prejudice in nature, because if the student enters in a setting with a perceived low self-esteem and confidence, it is less likely that he/she will strive for learning. This indicates that setting has negative effects on student’s behaviour and accomplishments in mathematics. Grouping can cause pupils to feel stigmatised as failures in the subject, resulting in detached with the subject and lack of motivation. Pupils are less likely to show interest and engagement, if they perceive their ability weak (Nardi and Steward, 2003).

Furthermore, pupils believe that, they don’t have potential or ability to move to the top sets, as they need to perform exceptionally well and get high results in summative assessments (Boaler, 2000). This is the reality after speaking to my mentor and she has informed me that too. Once a pupil is allocated a group, rarely moves out of it. Therefore, initial group placement can have serious consequences for child’s life (Jackson, 1964; Barker Lunn, 1970; Neave, 1975). In the school, if students sit the similar end of term test, it is very unlikely that, they will achieve good results as the scheme of work is different for bottom sets than the higher sets and further limited to fewer concepts as compared to the higher one. The practice of “streaming” starts in year 7 and continues to year 11, the where students will be very likely sitting GCSE foundation paper for Mathematics. Boaler’s study (2000) found that, the student gave up on Mathematics, due to limits placed on them and resulted in severe disaffection. The interesting thing is that bottom sets are not the only ones affected by the “streaming system”, higher sets also have an impact where pupils struggle to keep up with the fast-pace, higher expectations and pressure to succeed and result in provoking anxiety amongst students (Boaler, 2000). The study has also revealed that, the quality of teaching is compromised teaching, where the lower sets and often unqualified teachers are assigned to the groups in which the teachers don’t tend to put much effort in delivering high quality lessons. The experienced and qualified teachers are assigned to the higher sets and this shows the ironic ethos, neglect and lack of consideration given to low ability students. Moreover, lack of belief in the ability and progress of pupils in lower sets, the pace may be slow in lessons and work too easy. Gamoran and Berends (1987) also argued that, placing pupils in particular groups lead to differential expectations regardless of actual performance and potential.

However, 62% of the students favoured setting compared to 24% preferred mixed ability groups shown as a result of Hallam and Ireson’s (2005) research of 5000 Year 9 pupil’s views and experiences of setting mixed ability classes in 45 secondary comprehensive schools. The overwhelming reason of the choice students gave for preferring setting was that, it enabled tasks and pace to be set at an appropriate level and to match the pupils’ needs, which is advantageous for both higher and lower ability groups. The evidence has also suggested that, the pupils don’t feel that there is sufficient differentiation provided in mixed ability groups hence they may struggle with the level of work and completing the activities and tasks given to them which could cause behavioural issues, therefore switching off task. More support is provided to lower ability sets in comparison to the higher ability sets and without provided that, it may lead to further low level disruption (Hallam and Ireson, 2005).

In conclusion, due to a perceived lack of interest, motivation and experiences in Maths, lessons throughout their school experience can cause inordinate amount of behavioural problems in their lessons as compared to the higher sets. To this end, mixed ability classes are considered to be more constructive as well as effective in motivating the low ability learner.

The behavioural problems are mainly caused by pupils who are disengaged and off task. This leads to lack of motivation in the lesson and dislike for the subject amongst the students. There are a numerous reasons and explanations to the point of view of these pupils and negative perception they carry for the subject. Nardi and Steward (2003) argued discussing “Elitism” that pupils perceive maths as demanding and only highly intelligent people can succeed. With this mindset, engagement is fraught with a potential risk of worsening the student’s image of their own intellectual capacity. One of the pupils in Nardi and Steward’s study(2003) stated during a lesson regarding practising algebraic and geometrical skills that, “what are we going to use them for?” and “ I am not exactly going to design fence that, you know, you have to work out a third of this to get round the whole of the circle”. These pupils could not understand the rationale of learning Mathematics in relation to real life context. Pupils lack exposure and comprehending the practical application of how learning concepts is relevant to the outside world. In one of the classes of Year 8, pupils failed to understand the use of letters in algebra and purpose of using it, when writing formulae. However, there was a shift of old curriculum to a newer GCSE Mathematics curriculum in 2014 by the government and focus has been transferred mainly on problem solving and mathematical reasoning allowing for application of skills and concepts. This new curriculum is comprehensive and helps pupils in understanding the abstract nature of Mathematics ((Department for Education, 2014).

Continually, the Nardi and Steward’s study (2003) has also highlighted that, pupils’ view of the nature of subject is isolated with limited opportunity to work collaboratively. Pupils favoured working mutually and added that, they can learn and understand from each other. Furthermore, the pupils also view that, the instrumental teaching style is prone to copying and memorising one method. Therefore, engagement and motivation is also down to the teaching, where it must be aimed at achieving Mathematical mastery rather than rote learning.

Additionally, I have also noticed that, particularly the girls in year 8 require more encouragement and prompt to start the tasks as compared to the boys. The gender differences in attitudes and experiences of Mathematics have been highlighted by research. UK Resource Centre for Women reported, in A-level Mathematics, only 40% girls opted for the subject in England in 2009 and the inequity continues into Higher Education and employment (UK Resource Centre for Women, 2009).

A research in Ireland found that girls didn’t like and enjoy Mathematics due to stress and anxiety experienced towards the subject. These factors can contribute to disengagement and disaffection hence causing behavioural issues in the classroom. According to Boaler (1998) of England based schools, the girls wanted to have conceptual and deeper understanding about Mathematics, where the methods have been probed into how and why they work. The most promising aspect of Boaler’s study (1998) was that, 99% of the girls chose “understanding” compared to only 65% of the boys opting “understanding”. 35% of the boys preferred to remember the rules as the most important. Gender based difference in Mathematics is apparent and therefore their differing experiences. Due to the very nature of gender, Boaler (1998) also observed that boys were motivated and racing through the text book exercise whereas lack of motivation, detachment and confusion was seen in girls.

In regard to gender and Mathematics, it is considered societal stereotype that female pupils having a lack of motivation and effort (Song, Zuo and Yan, 2016). However the surveys involved in the methodology measured the opinions of students solely, which is not enough to draw conclusion from and could be misleading.

However, the GCSE results from 2009 showed a different version where performance was similar for both girls and boys. The gender gap of performance has dropped between 1990 and 2007 confirmed by use of meta-analysis study of Linderberg et al. (2010). The findings of the study can be considered as accurate, because computerised databases involved large samples confirming the validity and reliability of the data, used in the study. Therefore, the girls perform as well as boys reject the idea that the factor of lack of motivation is specific to girls. Boaler (2009) stated that, over the last 20 years, gender stereotypes in Mathematics have been decreased significantly.

In conclusion, the way that maths is perceived and taught has an impact on pupils’ motivation and understanding, which is also one of the major factors, which further leads to disaffection amongst students. The culture of elitism, passive teaching method and abstract nature of Mathematics can be the root causes for negative experiences and attitudes towards the subject. Consequently, phenomenon can lead to triggering behavioural problems in the classroom and positive behaviour management is vital to deal with the problems. Mathematics teachers should adapt to the teaching styles aligned with pupils’ needs, develop confidence and motivate pupils, so that the subject is appreciated and enjoyable along with purpose of understanding it.

Critical Incident 2

The second crucial and critical incident is related to “Marking”. Ticks and crosses were the main practice, followed by myself as well as the pupils. 50% of their answers were marked as crosses in one of the homework assigned except some pupils, who got all the answers correct. Once pupils marked their work, the only things they wanted to compare that how many ticks they got as compared to each other. There was no response as well as interest shown in terms of inquiring about mistakes they made (Price, et al., 2010). The incident led me to critically reflect the practice of feedback, whether it is productive and useful for the pupils to progress in their learning. The element of understanding was missing in terms of how the students could improve their work through my feedback, because ticks and crosses were not serving the purpose of achieving the required outcome. Consequently, the format of marking should have included such a precise detail, so that the pupils could develop the understanding of their errors (Hodgen and Wiliam, 2006).

According to Hodgen and Wiliam (2006), marking system of ticks and crosses, which is not a useful form of feedback for pupils, as it doesn’t inform or guide the students about the errors that they made and how to improve on them. The idea is also supported by the investigation of Price, et al. (2010), who observed pupils attitudes towards marking by ticks and crosses only. Through this research they found that, the students viewed ticks and crosses which are an ineffective and inadequate form of feedback with no benefit. Wiliam and Black (1998) viewed assessment as the most powerful tool for effective learning and raising standards. However, the assessment has to be followed by the correct marking to achieve the goal, where pupils’ understanding on what mistakes that they have made and how to develop on them are beneficial. Moreover, Harlen and Crick (2003) believed that, assessment involving grades can cause negative impact on pupils’ learning. This is because, the marks oriented feedback can lead to a lack of understanding, therefore doesn’t define the progress route for pupils. 131 Studies have shown that, this kind of feedback has lowered the performance (Kluger and DeNisi, 1996). Furthermore, the scores can be one of the factors contributing towards demotivating low attaining pupil as well as not stretching the high ability students too (Careless, 2006). Formative assessments are seen more effective due to the fact that they set the route for development and achievement rather than stamping the success and failure. This can help improve motivation and improve confidence of low attaining pupils (Harlen and Crick, 2003).

Providing too frequent feedback containing blend of marks and written annotations is also not viewed as useful because the pupils may well be focussing mainly on the marks they have scored rather than on the written comments (Butler and Nisan, 1986). Therefore marking through explicitly written comments every two to three weeks is more beneficial as well as productive and the most effective way of feedback than stamping a tick or a cross on every piece of work (Hodgen and Wiliam , 2006).

Comments are the means of dialogue between teacher and the pupils hence can be used to aid the progression. Hodgen and Wiliam (2006) have given some examples of useful written feedback. One of the examples is to enable pupils to identify their mistakes and misconceptions, which helps to assess students’ comprehension of the concept and can be achieved by designing multiple choice options with only one correct option. Additionally, through written annotation of feedback, the teacher can motivate the students to reflect on the concept, such as evaluate and compare two non-identical methods and identify the similarities and differences between them. Extending the knowledge of pupils is another form of written feedback, where the pupils have done quite well on a task, by using the existing knowledge to stretch these pupils. For example, if the students have solved a simultaneous equation using substitution, elimination could be the mode of stretch that they could move on to. Suggesting pupils to compare and discuss their ideas with their peer, which is also a constructive strategy of feedback (Hodgen and Wiliam, 2006).

Hattie and Timperley (2007) stated that, high quality feedback has an influential impact on the students’ learning and achievement, and also it contributes towards individual student attributes. The reason for this is that it is beneficial to have formative feedback as it provides an opportunity to the students for reflecting upon their progress and therefore escort them via their learning as opposed to merely providing statistics regarding their work (Jonassen, 2004). Feedback provides a passage, where the students can take charge of their own learning and progress hence can analyse their progress and be driven in targeting their expected goals (Nicol, Macfarlane – Dick, 2006).

Nicol and Macfarlane-Dick (2006) found that, the teacher and pupil both were equally benefitted from formative assessment and feedback. The data from formative assessments could be utilised by the teacher to adjust the teaching style for improving the student’s performance. This is because teacher can track understanding through formative assessment and can also use it to develop. McNeill (2015) braced this view that the teachers valued feedback more than pupils.

However, it is vital that, the feedback is of good quality; otherwise it will lose its purpose of being effective and constructive (Price, et al., 2010). Using complex language is one of the examples of ineffective feedback which is above the ability of students to comprehend. Difficulty to understand feedback would lead to dissatisfaction amongst students, therefore it is vital to produce quality feedback to be effective (Crimmins, et al. 2016). The barrier of understanding the feedback was well explored by Crimmins, et al. (2016), where they found that, WRDF; written, reflective and dialogic feedback strategy have a positive impact therefore it enhances pupil’s learning. Following the feedback, it is critical for the students to reflect, respond and act upon feedback. This could be achieved via conversation with peers as well as reporting back to the teacher their response to the feedback (Sopina and McNeill, 2015). Three out of seven principles of feedback practise identified by Nicol and Macfaelane-Dick (2006) were facilitating self-reflection, encouraging peer dialogue and continuous motivation.

Formative assessment lesson plans were designed by the Mathematics Assessment Project in the USA, where the teachers do not assign marks to the pupils’ work rather place questions in reaction to the key components identified. The idea was to annotate the pupils work via feedback to draw them proactively with the feedback given. Consequently, it is argued that, formative assessment is useful without giving marks, rather using a questioning, as this form of feedback gives the opportunity to address students’ misconceptions and strengthen critical thinking of students (Schoenfeld, 2015).

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Feedback plays a vital part in pupils’ progression and achievement, as key areas of development can be identified and addressed. So, as a result, feedback is a source to enhance learning and therefore achieves outcomes and targets (Vollmeyer and Rheinberg, 2005). Jonassen (2004) viewed that; guiding students through their learning process can be achieved by a high quality feedback, rather than just stating facts about one piece of work.

The research of 250 studies by Black and Wiliam (1998) in relation to feedback from teacher, self and peer assessment found significant benefits in pupils learning and achievement through effective feedback. Furthermore, it is argued by Sadler (1989) that, to maximise the benefit achieved from feedback, three constraints must be met; students’ recognition of what a good performance, comprehend the relationship between their current performance and good performance and how closing the gap between current and good performance is achieved. Boud (2000) described that, to be able to satisfy these three conditions, the students need to construct on their self-assessment and evaluation skills. It is vital that, the students’ understanding of the conception of the goals and criteria on a piece of work are based on mutual understanding and aligned with the teacher, because it will have crucial impacts on the value of feedback received. Hounsell (1997) argued that, if scenario is different from this, the students will struggle to associate with the feedback. Furthermore, feedback clarifies the expected goals as well as guiding the students to achieve these goals (Sadler, 1989). This can be achieved by providing clear definitions of requirements, detail discussion of criteria prior to work being set and peer assessment, where the pupils mark according to the defined criteria and standards (Nicol and Macfaelane- Dick, 2006).

However, complexity of criteria makes it difficult to articulate and improve communicate standards through written and verbal means (Rust et al., 2003).

Self- regulating and taking control of one’s own learning are the virtues shown by the most effective learners according to research. Pintrich and Zusho (2002) described that, self-regulating is the ability to regulate individual thinking, motivation and behaviour. The individuals acquired the skill of self-regulating, are likely to be highly achieving, persistent and independent (Zimmerman and Schunk, 2001).

In conclusion, formative assessment is the most effective tool, which allows the teachers to adapt their teaching to suit the needs of pupils and therefore improve student performance (Bennett, 2011). High quality feedback is productive for the pupils in terms of their progression, understanding and written annotations, which further identifies the weaknesses of pupils’ work help in guiding and directing pupils’ learning (Sopina and McNeill, 2015).

Feedback can foster motivation, increase self-esteem as well as develop understanding and confidence amongst the pupils. However, for feedback to be effective and useful, it should be delivered at the correct time and in an easy way to comprehend (Higgins, Hartley and Skelton, 2002).

Conclusion

Assessment and behaviour management were the two areas under discussion in relation to Mathematics teaching. Both the incidents share common concern of low self-esteem and lack of motivation in the learning of this subject. However, negative attitudes and experiences can be eliminated through placing positive behaviour management strategies and by providing high quality feedback.

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