Essay on Explain How To Plan a Successful Mathematics Lesson

“Great lessons are a product of great planning” (Elliott, 2007) is a quote which exemplifies just how important planning is in the context of teaching a lesson. Teachers have to consider a wide variety of issues when planning a lesson including: differentiation, inclusion, classroom/behaviour management and ensuring all students learn successfully.

Prior to planning the lesson, a concept map of the ideas associated with the topic (linear equations) was constructed. This allowed me to attempt to make connections with different strands of the topic and identify a clear progression of ideas within the lesson. Askew (1997) stated that teachers’ beliefs are either transmission, connectionist or discovery. He also suggests that teachers with a strong connectionist orientation embody the best of both transmission and discovery in terms of their acknowledgement of the role of the teacher and pupil within the lesson. Ultimately, I tried to apply the connectionist theory within my lesson by linking the concept of function machines to the construction and solution of linear equations so pupils could have something familiar to link to. I attempted to reaffirm this connection by including a question on function machines on the worksheet used in the lesson.

My lesson objectives were differentiated by what pupils should, must and could attain (Bills and Brook, 2007). The also differentiate by what level they correspond to (National Strategies, 2008). This might allow the teacher to assess pupils in a qualitative and quantitative manner. Throughout my lesson, I tried to include many opportunities for formative assessment including close observation of written work and group work among students. To further test pupils’ knowledge, I planned to ask each pupil questions which were linked to each lesson objective. Mosston (1966) devised a framework of teaching styles, dependent on the ability of the learner: ranging from simple teacher-directed ‘command’ questions (“What number does x represent in this equation?”) for lower-ability learners to more complex ‘divergent’ questioning for more able learners (“How could check your answer was correct?”). An ability to answer these questions correctly could be an indicator of giftedness.

This style of approach may be advantageous as it gets pupils to think deeply about the methods they are using to answer a question and possibly gain a more in-depth relational understanding (Skemp, 1976) of the topic. Furthermore, keeping the lesson objectives visible on the board also gave the pupils something concrete to self-assess their understanding of a topic. DfES (2007) note that this behaviourist style of teaching will have more of an impact when lessons allow for opportunities for reflection and review and students are aware of how they can progress within the topic. My lesson attempts to facilitate this style of teaching.

Brooks (2007) suggests that formative assessment has to be active, where a pupil does something different in response to the feedback given in order to be successful. In my lesson, I tried to make this happen frequently by gently probing (and rewarding) pupils’ recognition of errors and misconceptions. Black and William (1998a as cited in Brookes, p. 116) suggest that it is important that every pupil experiences the benefits of formative assessment, being especially useful for lower-ability students. Formative assessment may be a better method of assessing pupils in mixed ability groups.

Murdock (1999, as cited in Capel and Gervis, p. 120) suggest that there is a direct correlation between how motivated a pupil is and their academic success: more motivated pupils work harder, behave well in the classroom and study accordingly. Conversely, if a pupil doesn’t feel valued or appreciated, then they will likely not value school (Fine, 1986, 1989 and Finn 1989, 1993, as cited in Capel and Gervis, 2007, p. 120) and will be consequently less successful in life. Throughout my lesson, I constantly attempted to extrinsically motivate pupils by constantly giving them praise and rewarding them for their contribution (whether correct or incorrect) and promoting errors and misconceptions. Research suggests that if teachers have high, but attainable expectations, pupils are more likely to perform and behave well (Rodgers, 1982, as cited in Capel and Whitehead, 2010, p. 116). I attempted to ensure this in the lesson by stating what I expect from the pupils at the start of the lesson: hard work and good behaviour. Pupils seemed to be more motivated to meet these expectations by stating them outright.

I included a seating plan in my lesson to encourage good behaviour but more for ensuring everyone participates in the lesson. Throughout my lesson, there are a variety of problem-solving tasks which pupils complete in pairs or in a group. DfES (2007) suggest that this social constructivist model of teaching allows learners to work collaboratively and learn from one another with the teacher providing scaffolded support to address misconceptions and errors. Vygotsky (1962) advocates pairing lower-ability pupils with those who are more able, in that the higher ability learners will ‘teach’ the lower ability learners and improve their understanding. This theme of co-operative learning is further reinforced by the ‘think-pair-share’ activity (Kagan, 1994) which could have similar advantages. This approach could be especially useful for a mixed-ability group and increase the confidence of the more hesitant and withdrawn pupils.

TES (2010) note that there are 3 different types of differentiation: outcome, support and task. I have tried to incorporate all these into my lesson in some manner. A teaching assistant is deployed to work with less able pupils throughout the lesson (support) and was appropriately briefed on the learners’ needs and requirements. This should hopefully ensure that students stay on task, with the teacher also having regular input with less able learners, thus doubling the support they have access to. In terms of the rest of the class, the teacher differentiates by the amount of support they give them depending on their ability, with higher ability learners being able to work more independently with the teacher merely having to facilitate their learning. This frees the teacher to provide support and attention to those that need it most.

I have attempted to differentiate by task by providing less able pupils with an individual, simplified plan of study which does not involve the more complex algebra being attempted by the rest of the class. This is due to these pupils not being at the required level to cope with mainstream content. Though the rest of the class have the same resources, the questions on the 2 worksheets are ordered by difficulty: ranging from more simple questions to complex one aimed at higher-ability pupils. Similarly, the homework also has an extension aimed at more able pupils which they may see as more of a challenge than previous questions. This approach should allow the learning of pupils to be reinforced and also extended them suitably.

I have tried to differentiate by outcome by including a variety of different teaching methods within my lesson. Biggs (1999) supposes that higher ability students learn best from a passive form of learning whereas lower ability pupils need to be more active in the lesson to learn well. Whilst the teacher exposition and worksheet may suit more passive learners, the group and collaborative activities suit those who prefer active learning. I have tried to make sure that each student is catered for sufficiently, but algebra is a more formal strand of mathematics which mostly requires passive learning which does leave active learners at a disadvantage. Geometry topics lend themselves better to active learning.

In conclusion, I have attempted to consider a large range of issues including inclusion, differentiation and behaviour to attempt to ensure an optimal learning experience for all pupils within the class. This has enabled me to start to meet the teaching standards:

Q10: have a knowledge and understanding of a range of teaching, learning and behaviour management strategies and know how to use and adapt them, including how to personalise learning and provide opportunities for all learners to reach their potential.

Q12: Know a range of approaches to assessment, including the use of formative assessment.

(TDA, 2008)

Reference List

Askew, M., Brown, M., Rhodes, V., William, D. and Johnson, D. (1997) Effective Teachers of Numeracy in Primary Schools: Teachers’ Beliefs, Practices and Pupils’ Learning. Paper presented at the British Educational Research Association Annual Conference.

Biggs, J. (1999) ‘What the Student does: Teaching for Enhanced Learning.’, Higher Education Research and Development, 18 (1), pp. 57-75.

Capel, S. and Gervis, M. (2005) ‘Motivating Pupils’, in Capel, S., Leask, M. and Turner, T. (eds.) Learning to teach in the Secondary School: a companion to school experience. 4^th edn.

Capel, S. and Whitehead, M. (2010) Learning to teach Physical education in the Secondary school: a companion to school experience. 3^rd edn. London: Routledge.

Elliot, P. (2007) ‘Preparing for learning’ in Brooks, V., Abbott, I. and Bills, L. (eds.) Preparing to teach in the Secondary Schools: A Student’s Guide to professional issues in secondary education. 2^nd edn.

Gager, A. (2007) ‘Adapting resources for children with specific needs’, in Drews, D. and Hansen, A. (eds). Using resources to support mathematical thinking: Primary and Early Years. Learning Matters: Exeter.

Great Britain. Department for Education (2008) Assessing Pupils Progress in Mathematics at Key Stage 3. 

Great Britain. Department for Education and Skills (2007) Pedagogy and Personalisation.

Great Britain. Training and Development Agency for Schools (2008) Professional Standards for Qualified Teacher Status and Requirements for Initial Teacher Training.

Kagan, S. (1994) Kagan Online. Available at: www.kaganonline.com (Accessed: 5 December 2014).

Mosston, M. (1966) Teaching Physical Education: From Command to Discovery. Merrill Books: Colombus, Ohio.

Skemp, R. (1977) ‘Relational Understanding and Instrumental Understanding.’, Mathematics Teaching, 77: 20-26.

TES Magazine (2010) TES New Teachers. Available at: www.newteachers.tes.co.uk (Accessed: 4 December 2014).