{"id":16305,"date":"2023-04-21T11:39:06","date_gmt":"2023-04-21T11:39:06","guid":{"rendered":"https:\/\/www.goodacademic.com\/blog\/questions\/subject-knowledge-and-pedagogy-part-2-how-are-you-applying-what-you-are-learning-about-the-best-way-to-teach-mathematics-part-3-how-are-you-developing-into-a-great-teacher-of-your-subje\/"},"modified":"2023-04-21T11:39:06","modified_gmt":"2023-04-21T11:39:06","slug":"subject-knowledge-and-pedagogy-part-2-how-are-you-applying-what-you-are-learning-about-the-best-way-to-teach-mathematics-part-3-how-are-you-developing-into-a-great-teacher-of-your-subje","status":"publish","type":"questions","link":"https:\/\/www.goodacademic.com\/blog\/questions\/subject-knowledge-and-pedagogy-part-2-how-are-you-applying-what-you-are-learning-about-the-best-way-to-teach-mathematics-part-3-how-are-you-developing-into-a-great-teacher-of-your-subje\/","title":{"rendered":"Subject Knowledge and Pedagogy\u202f – Part 2: How are you applying what you are learning about the best way to teach mathematics? Part 3: How are you developing into a great teacher of your subject \/ phase?"},"content":{"rendered":"
Module Name: What does it mean to be an effective teacher of mathematics?<\/u><\/div>\n
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Part 2 has already been written however after feedback was given things need to be changed. <\/p>\n

Part 3: How are you developing into a great teacher of mathematics? <\/div>\n
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All parts are linked to one another and must follow each other sequencly. I will upload Part 1 and Part 2 (draft) for you, so please read them carefully. <\/div>\n
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Part 2 needs to be rewritten or edited<\/div>\n
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I will upload the feedback I recieved for my part 2 for you to read through and change where necessary according to the feedback and what has been done in part 1. Remember it all has to link with one another.<\/div>\n
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I will also upload the Part 2 assignment brief for you to look at as well as the part 3.<\/div>\n
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Part 2 – 3000 words<\/i><\/div>\n
Part 3 – 2500 words <\/i><\/div>\n
Total – 5500 words<\/div>\n
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So in conclusion Part 2 and Part 3 to be done only please.<\/div>\n
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Remember that this is the English academic system so when referring to classes it will be withint secondary school. Years 7, 8, 9, 10, 11.<\/div>\n
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Part 2<\/u><\/font><\/div>\n
In this part, you will plan a series of learning episodes using your focus from part 1. You will see when you read the subject guidance that these learning episodes could be sequential, or they could \u2018leapfrog\u2019 across a unit of work. So, you might use learning episodes from lessons 1, 2, 3 and 4 or you might use learning episodes from lessons 1, 5, 7 and 10, for example. The subject guidance explains this in more detail.  <\/font><\/div>\n

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What\u2019s really important here for Level 7 writing is that you try and make links between your own experience and what you have read from the research and literature.<\/font><\/div>\n

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You might find at times that what you experience conflicts or contradicts what you have read \u2013 and that is fine, because we want you to be critical in your writing by discussing to what extent the research and literature has supported your planning and understanding about the best way to teach in mathematics.<\/font><\/div>\n

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it is really important that when writing at Level 7, you have opportunities to critically reflect on what you have planned and actually tried out in your classroom.<\/font><\/div>\n

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It can often be easier to simply describe what happened, but what makes great writing at Level 7 is your ability to make links between what you have read from the literature with what has happened in the classroom, and how you can evidence any impact in terms of your pupils\u2019 learning.<\/font><\/div>\n

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This part of the assignment gives you an opportunity as a teacher to also be a researcher, collecting a range of evidence from a range of sources. So, let\u2019s now look at exactly what we mean by this:<\/font><\/div>\n

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What do we mean by classroom research?: <\/u><\/font><\/div>\n
Classroom research provides a useful methodology for starting any type of research that helps you reflect on your own practice. Hewsen et al (1999) used research to help trainee teachers become reflective about what it means to teach for conceptual change. A useful outcome of this research showed that trainee teachers tended to focus on how pupils understood conceptions and understandings, which then supported their own teaching of conceptual changes in mathematics. <\/div>\n
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So, research can improve not only your understanding of how mathematics should be taught, but also the concepts that underpin the ideas making up the mathematics curriculum.<\/div>\n
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Research does not have to be a lengthy or laborious process; being a trainee teacher is busy enough! McGregor and Cartwright, (2011) identified the following simple stages (which have been summarised below) for carrying out any research within your classroom:<\/div>\n
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Focus on one key aspect of teaching \u2013 in this assignment you will continue to focus on your chosen topic area from Part 1.<\/div>\n
Collect information about your pupils and any barriers or assets they bring to your classroom \u2013 remember this is about your pupils and how your subject can be used to enhance their life chances.<\/div>\n
Make a change in your practice based on what you have read from the literature. <\/div>\n
Collect evidence from your classroom \u2013 remember that qualitative evidence is just as valid in research.<\/div>\n
Evaluate the impact of your teaching approach \u2013 consider how you know that your pupils have learned and made progress as opposed to simply completing the task\/activity.<\/div>\n
Change your practice moving forwards \u2013 teaching is also about you as a critically reflective learner.<\/div>\n
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What do we mean by evidence? <\/u><\/div>\n
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It is really important to understand that as a teacher there is so much evidence you can use to help you measure the impact of any of your teaching approaches in terms of your pupils\u2019 learning.<\/div>\n
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We often assume that evidence must be quantifiable data that can be plotted onto a graph, but often the data available is based on what you observe, see and hear in your classroom \u2013 so if it helps, do have a notebook with you so that you can capture some of the evidence that will take place right in front of your eyes!<\/div>\n
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Evidence might include:<\/div>\n
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Pupil responses to your questions<\/div>\n
Pupils\u2019 work<\/div>\n
Pupil feedback in formative assessment activities<\/div>\n
Reflective journals \u2013 bring a notebook into your classroom so that you can quickly note any \u2018eureka moments\u2019 by either yourself or your pupils<\/div>\n
Narratives \u2013 these can provide an insight into your teaching approaches through various lenses e.g., teaching assistants, subject mentor, SDL, PDL etc. These colleagues offer an additional pair of eyes through which you can gain perceptions of the dynamics of a classroom (Brookfield, 1995)<\/div>\n
Planning and resources \u2013 you can use these to show your thinking behind how you planned a particular learning episode and what you were hoping your learning outcomes would be.<\/div>\n

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Choose Classes and topics to focus on <\/font><\/b>– You are obviously using the same topic that you focused on in Part 1. You should choose classes that you will be teaching regularly, and ideally different classes that you will be teaching your chosen topic to. For example, you might have chosen linear equations and be teaching this to both Year 7 and Year 10 classes.<\/font><\/div>\n

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Justify, analyse and evaluate how you are developing your chosed pupils’ mathematical knowledge and understanding through you application of Literature – <\/b>In this section you will be connecting the reading you have done about misconceptions with your lesson planning. How has your understanding helped you to devise appropriate questions\/activities\/modelling that will elicit misconceptions? How has your understanding helped you to sequence the examples and tasks?In this section you will be connecting the reading you have done about misconceptions with your lesson planning. How has your understanding helped you to devise appropriate questions\/activities\/modelling that will elicit misconceptions? How has your understanding helped you to sequence the examples and tasks?<\/font><\/div>\n

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 Justify, discuss and analyse the common misconceptions that your chosen pupils have demonstated. To what extent does the literature help you to account for these? <\/b><\/font>– This is an opportunity to compare your experience with the literature. Did your pupils demonstrate the misconceptions you expected? At the same stage you expected them to? If not, was this because your teaching pre-empted them? Did they demonstrate different and \/or unexpected misconceptions? What does the literature say about this? What is important here is demonstrating your ability to link – and critically reflect on – your classroom experience with the literature.This is an opportunity to compare your experience with the literature.  <\/font><\/div>\n

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Justify, analyse and evaluate the ways effective curriculum and sequencing helps to develop disciplinary knowledge and address misconceptions of your pupuls. How have you adapted your sequencing to faciliate good progress ? – <\/b>You could address this prompt in different ways. For example, you might take a macro view of a whole topic or a micro view of the questions used in one particular lesson. You may have had no choice about your sequencing because the resources were provided by the school in which case you should discuss the rationale behind them. You may have devised your own sequence and found some aspects worked better than others. In this case you could describe how you would tweak this next time. You should explain how you are determining the progress of your pupils. You might include the use of exit tickets, quick quizzes, diagnostic questions, as well as more substantial summative assessment such as end of topic tests or ongoing online homework. <\/font><\/font><\/div>\n

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Part 3<\/b><\/u><\/font><\/div>\n
It is really important that when writing at Level 7, you have opportunities to critically reflect on what you have planned and actually tried out in your classroom. Part 3 is about you, and what you have learned about what makes great teaching in mathematics. We want you to consider what you have learned from the research and literature and position yourself based on what you have read, observed and experienced as a research informed teacher of mathematics! <\/font><\/font><\/div>\n

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You might want to use a reflective model (such as Gibbs, Kolbe, Brookfields lenses) that you have probably come across in your other strands. J. A. Moon\u2019s books on reflective practice (see the full mathematics guidance) may be particularly helpful here.<\/font><\/div>\n

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You do not have to, but sometimes a structured model is really useful.<\/font><\/div>\n

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If you choose not to use a reflective model, then just make sure that you follow the guidance in making sure that you are critically reflective in your writing for this part.<\/font><\/div>\n

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1. Can the literature and theory help you to interpret\/better understand your feelings\/experiences from your classroom ? <\/font><\/div>\n

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2. Can your experiences be used to challenge\/evaluate theory? <\/font><\/div>\n

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3. Can the literature and theory be adapted in some way to account for your experience ?<\/font><\/div>\n

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Draw upon feedback from part 2 to introduce and contectualise Part 3 – This section is the evaluation of practice and critical reflection of what it means to be a great teacher of mathematics that brings together Parts 1 and 2. It will be very personal to your own experiences, interests, strengths, and areas for development. The opportunities you have had in your setting with your classes will be unique and you should factor in some time to look back. You might find it interesting to review your emails, texts, tweets from the beginning of the programme and reflect on how your thinking about teaching mathematics has developed.<\/font><\/div>\n

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Evaluate the impact of your literature review. What impact has your research into evidence-informed practice, and engagement with professional networks and organisations, had on your professional development and pupil progress. <\/font><\/div>\n

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Evaluate the ways in which your teaching practice has developed through engagement with the research literature. What teaching activities have you engaged in tgar have the potential to be a postive influence on your professional development going forward? <\/font><\/div>\n

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At this stage of your teaching you may feel that you have not been able to connect all of your research reading to the classroom because getting to know the learners, planning, teaching and assessing has been so demanding and time consuming. You are likely to have some sense of the complexity of teaching and learning and there may be areas of your practice which you are beginning to develop that you believe (perhaps from observing others or reading about them) could become very important. Some possible issues might be (this is NOT an exhaustive list):<\/font><\/div>\n
How you have begun to craft\/use questions and tasks that elicit misconceptions<\/span><\/div>\n
How you are exploring variation in the questions you use for practise in lessons. <\/font><\/div>\n
How you have worked with manipulatives and representations e.g. algebra tiles\/bar models\/double sided counters. <\/font><\/div>\n
How your understanding of a specific mathematical concept has developed.<\/font><\/div>\n

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Reflect on your Crirical engagement with relevant literature, and on your own professional experience. What does it mean to be an effective teacher of Mathematics? <\/font><\/div>\n

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This final section is likely to be very personal to you. Whatever approach you take to structure this section you will first need to engage in some organised reflection. The books by Moon (mentioned earlier) suggest models for doing this which you may find helpful. You might consider the following: <\/font><\/div>\n

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Look back at your application to Teach First and reflect on how your thinking about teaching mathematics has developed. <\/font><\/div>\n
Make a list of ideas about teaching mathematics that you strongly agree or disagree with and reflect on how\/why you have come to these views. <\/font><\/div>\n
Think about a teacher you have got to know who you consider to be very effective and reflect on why you have come to that judgement. <\/font><\/div>\n
Think about one or two critical incidents which stand out because they caused you to change the way you thought about or understood an issue. <\/font><\/div>\n
Find a description of an effective mathematics teacher from your reading\/research and critique it.<\/font><\/div>\n","protected":false},"excerpt":{"rendered":"

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