1. How my thinking about teaching GCSE maths re-sits has changed during the course.
My thinking about teaching GCSE maths re-sits has changed in that I’m more focused on improving the learning of my students.
Simplistically, before it may have been a case of “What do they need to know?” and then relaying what the student needs to know for that particular subject, in a clear and concise manner, which may have been “got” by most students, but then they would have forgot the method shortly afterwards when it came to a formative or a summative assessment.
Now I’m more determined to help students learn in a way that is going to be enjoyable to them and help them remember what they need to for the exam. This will involve doing more kinaesthetic and visual activities as a lot of learners learn by doing.
Realistic Mathematics Education (RME) The course has introduced me to Hodder Education’s range of books called ‘Making Sense of Maths’ for KS3 and KS4 (http://www.hoddereducation.co.uk/makingsenseofmaths).
Mr Gough, a maths teacher and one of the authors of the aforementioned book(s) states the following:
“My experience of teaching GCSE Foundation Tier is that by the time they get to KS4 they’ve already covered most of the content and they’re having the same content repeated in the same way that they found difficult in the first place so my experience of using this approach is that it seemed very different to them and it reinvigorated their interest in maths and they were very positive about maths lessons again.
We’ve also taken these materials to various exam boards around the country; all of them confirm that its approach can be given credit for in terms of method marks whether the question is answered correctly or not. Indeed one chief examiner was saying that anything that promoted the students drawing things in the exam was definitely a good thing. He said that, very rarely does he see the maths being put down on paper in any form other than numbers written down, and diagrams, whether they be ratio tables or percentage bars or double number lines, anything like that will definitely help them answer the questions.
Also included in the ‘Making Sense of Maths’ scheme are exam-style questions. The questions are there for the students in the workbook. Also in the teacher resource there are worked examples showing how students would use these materials to answer exam questions using all the models that have been developed during the scheme. The books that are part of the ‘Making Sense of Maths’ scheme, together, will cover all GCSE Foundation Tier maths specifications.
Purchase resources at: http://www.mei.org.uk/rme?section=resources&page=gcsebooks:
Making Sense of Maths - Fitting In: Teacher Book Area, Pythagoras and volume
Making Sense of Maths: All Things Equal - Teacher Book Solving equations and algebraic manipulation
Making Sense of Maths: Fair Shares - Teacher Book Fractions, percentages, ratio, decimals and proportion
Making Sense of Maths: Picturing Data - Teacher Book Representing, analysing and interpreting data
Making Sense of Maths: Sorting Letters - Teacher Book Sequences, formulas, expanding and factorising
Making Sense of Maths: The Power of Number - Teacher Book Number operations, conversions, negative numbers, primes & indices 2. An example of how I have applied the strategies discussed on the course (e.g. a resource or activity I’ve used) and an evaluation of its effectiveness.
I have applied the ‘mastery’ approach because it’s a whole ethos of learning that has worked in Shanghai and one that can be easily translated to my setting without huge cost.

The key features of mastery can be applied to my setting as follows: Key features of mastery | Curriculum design | Prioritising key topics - All learners will have had initial and diagnostic assessments and from these I will know which key topics to focus on because they will indicate common gaps in understanding. | Lesson design | Carefully structured lesson to develop the detail and depth * Important that all teaching staff work together rather than in isolation to plan lessons that can be repeated – with some amendments due to students’ differentiation needs. * Lessons should be well-structured with very simple steps for the students to follow. * Shorter lessons – about half an hour long. * Encourage all students to listen carefully. * Precise, consistent mathematical language should be used throughout, repeating key words and full sentences. * Students should be able to explain why, in full sentences, using precise mathematical language, rather than just give an answer. * Have students demonstrate their working out on the white board and explain their thinking. * Students engage in a lot of talk and write very little as they are encouraged to verbalise their answers and how they achieved them. * Highlight particular efficient methods used by students and compare and contrast different methods. * Only give work to students if they have been given clear guidance and support in the concepts and strategies needed to complete the problems. * Have short worksheets of very well chosen examples to check students’ understanding. * At the end of each lesson students are expected to use the knowledge they have been taught during the session. * At the beginning of each lesson, students recap on work from previous sessions. | Pupil support | Quick intervention – Mark students work as you go along to support rapid progress and give them additional help before they fall behind. Make sure that all students understand before you move on. | Teaching resources | Carefully chosen examples and activities. | Teaching methods differentiation | Keeping the class together and aiming for depth. |

In addition, OFSTED’s recent handbook made specific reference to mastery teaching :

“The expectation is that the majority of pupils will move through the programmes of study at the same pace.”

“Decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.”

Mastery teaching could be further developed by merging it with flipped/blended learning which gets students to watch and engage with tailored videos prior to the lesson in and then, when in class, the students do maths for the entire lesson with virtually no teacher instruction to the class as a whole. In addition the videos are excellent for independent maths study and revision for maths exams.

I will incorporate the use of online videos on mathematical methodologies in the following ways as stated by Dave Ashton, Teacher, and other practitioners on the following website: https://docs.google.com/document/d/1dO063hh7INsdzT5IjaV-RNhBPw994ndrmWC1t2_lwFI/edit?pref=2&pli=1
#TheFlippedLearningGuide
The purpose of this document is to collaborate with teachers implementing or planning to implement a flipped learning environment in their classroom.

The main people I use videos from are:
Colin Hegarty - Teacher of the year WINNER (@hegartymaths) - this guy really is AMAZING the time, effort and pedagogy put into his videos is amazing, here is his YouTube Channel http://www.youtube.com/channel/UCLJnnnahpUYO2tOEcXe1mHA
Brian Arnold (@Mrarnoldsmaths) - teaching concepts in exactly the same method as me - my GCSE students and even Year 7 classes learning about Pie Charts have found him extremely useful http://www.youtube.com/feed/UCwa84m5RqSJEkP9pYdeDYnw
Corbett Maths (@Corbettmaths) - has a YouTube Channel http://www.youtube.com/corbettmaths and a directory at http://corbettmaths.com/contents/
Excellent D/C borderline help - http://www.m4ths.com/
FANTASTIC work for A level - www.examsolutions.net
This is also one of the best website that talks through EVERYTHING on flipped learning: http://www.kokuamai.com/test/flipped So you've set the video - what do you do next? Please leave your twitter name next to your idea.

1) This was the first idea I ever heard to do with flipped learning- not a huge fan of this one ... but it does work. You play the entire video again in class; this time it's on mute and you ask people at random to explain to the rest of the class what's going on in the video. Have seen some of my SEN students give the best answers and heard brilliant explanations of how to complete mathematical concepts through this method. @MrAshton_Maths
2) In pairs write a mind map on everything you found out in the video (2 mins). Feed back together as a class what you know. Any ideas you hear from other pairs that you like write on your mind map in a different colour (shows pupils how good their knowledge was). At the end of the lesson/topic you can add in a third colour anything new again - as well as adding examples and success criteria. @MrAshton_Maths
3) Write a story (individually) on everything you learnt in the video explaining to someone what they saw in the video. You can create great word clouds to help inspire students from wordle.net. @MrAshton_Maths
4) In pairs explain everything that you have learned in the video (1 min) feedback to the class (very similar to the mind map - but can be performed much quicker). I observed my student teacher use this idea and it worked really well with a Year 7 class - they were very enthusiastic and they wanted to share ideas with the class. @MrAshton_Maths
5) Groups of four: Straight into GCSE questions. I used this many times with my Year 11 and 9 classes. It worked to great effect - putting a timer on the board. Having other students explain more difficult concepts of the video to others made my teaching of the topic much easier. @MrAshton_Maths
6) A quiz - plain and simple and to the point. A clear easy way to assess exactly how much understanding each individual has learned. @MrAshton_Maths
7) Asking students to devise low/medium/high challenge assessment questions/model answers based on the video? @ukfnchelle
8) If the flip is a video, students will watch the video at home (I give them 2-5 days, depending on what is going on during that time of year) from my Weebly site. There will be a notes component to the video, where students will keep track of specific points of the lesson. After this, students will fill out the accompanying form so that I can record their completion of the assignment. Within the form, I’ll ask students to regurgitate key information or proof that they actually viewed the video. At the end, I’ll usually ask them to extend their learning or ask a question. In class the next day, following our warm-up, I’ll give students share-time to discuss what was learned from the video. I’ve already seen their responses, i.e. who has turned in the form and who hasn’t, so it’s easy for me to guide instruction. After students share in pairs, I’ll ask 2-3 students to share to the class. Following this, we get into the extension of the lesson, whatever it may be. @jstevens009
9) As Mr Stevens. I always accompany my video with a google form. It informs my planning for the lesson, as it gives an overview of how the class have grasped different elements. It also enables me to spend the starter working with a small group if they have clearly not grasped the topic. I will usually get students to then design a question for peers, answer each other’s and give feedback. This discussion allows misconceptions to surface and be challenged. My classes are really positive about the 'flip' and my AfL has massively improved from using Google forms. You can also use the link http://www.videonot.es/ to make notes on videos @olivertrussell
10) Flipping lessons means that you can completely redesign your lessons in school. I have three tasks on the board when the pupils arrive and then allow them to get on with them in whatever order they like. Empowering pupils to take responsibility in their learning means that they will work harder that they would if they are listening to you. I flip using vimeo, and that way they can watch it on their iphones. If they have not watched the video for homework they can be sent to a computer to watch in during the lesson. I get them to make notes, copy out what I have written on the video so they are engaged. With the lesson being handed over to tasks, you have a chance to walk round each of them to talk about problems they had in understanding the video, or to give them a nudge with the task they are getting on with at that moment. It works for me. @DCTeachSpeak
11) This year I had my students move at their own pace through a unit with videos and textbook problems. There were some positive points to this model, but I am looking at improving it next year. I will have the students watch the video (or use the textbook) to take notes. Then in class we will do application during class (Dr. Mazur’s Peer Instruction, Working through problem sets in teams, etc.). I am hoping to end the application with some kind of explore activity to match Ramsey Musallam’s (@ramusallam) Explore-Flip-Apply model. I am also planning on starting each unit with a Dan Meyer (@ddmeyer) 3-act-math problem.
It’s a process. Don’t feel that you have to do everything your first year. Don’t be afraid to make mistakes. I made a lot of mistakes this year and still had a great first year flipping. @mr_benlewis

12.) I usually have students discuss and share their notes in small groups after the “warm up problem”. While that is happening, I have 2-3 groups of students (2 students per group) prepare a mini-presentation on one of the homework problems which is presented to the class. If you have a warm up problem of the day, these students can work on their presentation during that time. Although every student in the class doesn’t do a presentation (I call it a homework rap) I cycle students through so that different students present on different days and everyone gets the chance to present once during a unit. @GaryJohnston1 http://teachingaheadofthecurve.blogspot.com/2013/06/turn-homework-into-presentations-with.html Another thing that I’ve liked are “entry interviews” using google forms, although there are a lot of other great student response systems out there such as socrative and infuse learning. Getting feedback helps indicate where some students may benefit from working in math stations or perfect scores may suggest enrichment or independent study.
13) I usually get my classes to watch videos I have created (see www.corbettmaths.com/contents ) for homework and they use a checklist sheet to tick off when they have completed each step. Like others have said, I ask the students to make notes into their notebooks so that (a) they have somewhere to revise it from and (b) I can ensure they have watched it.
By introducing themselves to the material independently, that means there are endless possibilities within the lesson. I usually begin with a “any questions” session on the video, then have tried some of these:
a) exercises and exam practice so that my time can be used more effectively in questioning, assessing and guiding rather than spending half the lesson ‘chalk and talking.’
b) investigations, research or open ended tasks - such as after ‘flipping’ a standard lesson on constructions, I then printed off a wide range of more complex constructions such as inscribed pentagons, or finding the centre of a circle using a book (circle theorem approach).
c) Splitting the class into 8 different groups, each doing their own flipped lesson on a particular circle theorem. They watched the video, wrote the notes and also prepared their resources for teaching the other groups in the next lesson. In the next lesson, they each had 7 minutes to explain and provide questions to the rest of the class on their circle theorem. @corbettmaths
14) As with some of the above I have been attaching a Google form for feedback ahead of the lesson. This allows me to direct students to tables as they come in (red - working with me, amber, green, electric blue). Students can work cross-table to help each other and move up tables as their understanding increases. Working well at KS4 and KS5 so far - good response from students too. Still trying out new ideas - all advice/feedback/collaboration welcome. @PhysicsEducator
15) I'm new to the flipped classroom. I think using sites such as Today's Meet, Twiducate, and KidsBlog will allow students to collaborate and share what they learned. I will also be using a lot of technology tools found on my site: www.funintegratingtechnology.blogspot.com @DreamMakersNC
16) Very basic lesson. Pupils watch video I create at www.youtube.com/hegartymaths. 2 days to do and I have explained exactly the quality of notes required for each task. Over time I have learnt that the shorter the video the better. Also try to get the key information in there that could form the basis of students discovering their own extension knowledge. At start of lesson I ask 10-15 basic questions that test the key skill from the video. In that time I go around and check everyone’s homework and 5 pupils are asked specific questions to test their understanding (these pupils change. After the more open ended questions can be put on board that were not covered in the video but that pupils in theory and with the help of each other could now work out. Perhaps an investigation at the end or presentation of what they have done. @hegartymaths
17) Pupils can flip themselves. Pupils get into groups and evaluate what make a video of mine good/bad - this is to inform them of how to make a decent video. In groups they learn a topic (from my videos/textbooks etc.) and then their aim is to make a video by the end of the lesson using explain everything app on iPad. Homework for each night of the week is to watch one of the groups video’s and the next lesson that group are the helpers in the room (at this stage I would still prepare the worksheets) @hegartymaths
18) Pupils write a commentary to a video without sound (bit like Mr Ashton) @hegartymaths
19) I split the class into groups and gave them a different video to watch ( I did it on enlargement, translation, rotation and reflection.) When they came into the lesson I set up a market place activity where they had 10 mins preparing a poster to teach from, 7 mins to go to the other stalls, 10 minutes to come back to teach the rest of their group about the stall they went to. They then had a mini test before a plenary about how effectively they worked as a group. @Bexpowell7.

20) I usually just use my playlists on my youtube channel (I know prof. flippers are saying BORING!) to flip my class-- I also love using GAFE to let students collaborate and do research creating websites and other projects. Today, I found out about Live binders as a way of organizing resources. I think it seems awesome. One of my goals is to get kids to create videos for flipping. I am not too certain about what video recording software is easiest/ best for them to use. * One of my most recent projects was The Men Who Built America Project Every unit students collaborate to create a class study guide Students also work together closely to create a Unit Wiki For this wiki specifically, the following videos would be useful.
C) The men who built America episode three * A) The men who built America episode one * B) The men who built America episode two * * D) The men who built America episode four * E) Themen who built America episode five * F) The men who built America episode six @mrlepore1

21) After setting the video as a homework, students arrive at class and can visit 3 stations: 1. Go through the idea with the teacher (front desk) 2. Practice questions 3. Practice GCSE questions (slightly harder) 4. Write own questions
@mrsturdymaths

3. Evaluation of my readiness to teach (or support) GCSE maths re-sits and how I will further develop my subject knowledge and practice.
I will develop my subject knowledge by watching MathsWatch video explanations, writing notes so the concepts and methodologies are clear in my mind and practicing the different areas. Hegarty Maths (http://mathswebsite.com/) is also very good for step-by-step explanations and simplified methodologies which reinforce conceptual understanding.