Thursday, 31 January 2013

Mathematical Concept Wall - More Examples!

Here's some more examples of my students' Mathematical Concept Wall cards - some of them are just brilliant! To see my original post on the idea see

Year 7:

The Universal Panacea: TIME (#BlogSync)

January 2013 sees the 1st month of the #blogsync initiative set up by a series of bloggers via Twitter. The #blogsync is a central hub where all blogs on a common topic are shared amongst a community of bloggers/teachers/educational gurus. To see all of the posts on the below topic click the following link ==>

The 1st topic is: "The Universal Panacea? The number one shift in UK education I wish to see in my lifetime".

Having thought about the 1 universal thing that I feel could remedy UK education there was only really one answer based on my experiences so far... TIME!

If only we, as educators, had more time.

More time to plan our lessons - not just your 'bog standard' lessons but 'all singing, all dancing' lessons. Lessons that will blow our students' minds. Lessons that will grab our students attention from the minute they step through our classroom door to the minute they have to leave. Lessons that will take into account all of the multifaceted things we, as teachers, have to take into consideration when teaching a group of 30+ students. I know that I spend far too much time at the weekend and of an evening planning lessons as best as I possibly can for my classes, but even then I still find that some lessons end up being planned within a limited time frame.

Last year, when completing my GTP, I read many books that knew full well that teaching becomes a massive prioritisation task - what needs to be done now and what can be left for later. They also knew that you can't spend hours planning each lesson as there's just not the time in the day/week/term to do so. So, the suggestions of certain books is to give each class one 'all singing, all dancing' lesson a week. However, as noble as this seems that still means the majority of your lessons that week will just be 'ordinary' and surely that is just not 'outstanding'. It may be realistic, but not 'outstanding'.

More time isn't just needed to plan lessons either. There's marking to complete. There's reports to write. Parents to ring and get the support from. Resources to create and share with colleagues. CPD to complete and reflect on. E-mails to send and answer. After school revision sessions to run. and so on and so on. If we're to do all of the things we're expected to do in the current time frame we are given to do it, it's no wonder that corners end up being cut and essentially all these jobs are just done to the level required, rather than the level possible.

So, where can this extra time come from? Can we even get it from anywhere? Unfortunately my name is neither Bernard nor do I have a magical watch to freeze time...

...imagine if we all had one of these watches. How amazing would it be to, in the middle of the lesson, stop the clock and just take 5 minutes to reflect on what is happening around us. To freeze everything around us would enable us to: look at each and every student's book to see what, exactly, they had achieved so far in the lesson, to reflect on how we had just taught what we had taught - did I do a good enough job? Have I left anything out? What do we do next, what are our next steps? Is there something happening in the room that, perhaps, I wasn't aware of whilst helping the student I was previously helping? Could my TA do with a bit of guidance as to who to support next in the lesson and how best to do this? All of these questions are things that we have to take snapshot judgements on in the flow of a lesson. I know I often forget to say certain things (mainly giving out homework). Sometimes I find time just runs out in the lesson - we get so wrapped up in what we have been doing that the bell goes and you realise you've got to let them go to their next lesson - they possibly don't want to leave, you definitely don't want the lesson to end!

However, in realism, this isn't going to happen in my lifetime. So, is there a realistic solution?
I used to teach, last year on my GTP, a year 8 class for a 'double' period. This period lasted for 1 hour and 40 mins and the students were often given a 5 min break in between the 2 periods as that was when the normal lesson changeover would be taking place. Now, initially when I took over this class I was slightly daunted by the fact I would have a double period with the class and that I'd need so much more content for my lessons. However, what I found is that we were able to do so much more given the extra time and I treated the lesson as that - a lesson. Not a double lesson but an extended lesson with a short break in between. The break allowed my students to take a breather and for me to assess where we were from the first half and where to go in the 2nd half - adapting my planning where necessary. I think this structure worked quite well and there could be something there to build on?

Alternatively, we could have an afternoon a week free. I know some schools finish early on a Friday in order to complete CPD or as extra PPA time. I feel that it would be feasible to extend the Mon-Thu school day to 4pm and then have this afternoon free to complete marking/planning, go on courses, speak to and share ideas with colleagues etc. Would it solve all my time problems, of course not - but it may give that extra bit of time needed to make a significant difference to the quality of each of the tasks a teacher is required to do?

I'd be interested to here form anyone who does have a half day one day a week for planning purposes etc. Does it make a difference?

I'm sure I'm not the only one who would like to see teachers given more time to complete the job we are employed to do, as to whether it is feasible is another question.

Monday, 21 January 2013

Mathematical Concept Wall - Examples!

My Mathematical Concept Wall is coming together nicely. I have all of my year 7 cards to put up still and my Year 10s will be introduced to this soon too.

Here are a few examples of the work my students have produced so far and an overall look at the 'wall' (a work in progress)!

 Here's how the 'wall' is taking shape!
 A few Year 8 attempts!
Here's one of my Year 9 class' Pi pictures!

For more info on my Mathematical Concepts Wall see my previous blog post here. Also, see a fellow Mathematics teachers' blog with their Mathematical Concept cards they have been doing with their classes at - you can follow Mr Cavadino on Twitter too @srcav

What to do with Mock Exam Data!?

The start of the new term brought with it the start of a new year and the chance to refocus my attention on certain classes and procedures I have in place. It also saw me finish teaching the Edexcel METHODS in Mathematics Unit 1 content to my Year 10 class.
Monday this past week I had one of my school's NQT sessions. The session was on using data effectively and what to do with the information about your classes you have at your disposal. At lot of the things discussed in this meeting I was either already doing or had done in the past but needed a timely reminder of them.
The 1st week back after the Christmas/New Year break saw my Year 10 class sit a mock Unit 1 paper. Having then marked all of these papers I started to think about what I should now do with the results from this mock and how I would best support my students improve on their results and achieve their target grades. Here's what I've been doing over the past week...

The first thing I did was to, on the front of each students paper, put a sticker (kindly given to me by my Mentor after discussing the assessments) with the students target grade and their grade from the paper itself. This made it very clear to the students how far they were off their target or whether they had achieved their target grade on the paper.
I then, taking the spreadsheet created by my mentor that she sent out to the whole department, typed in each students marks on a question by question breakdown basis. This allowed me to see, as a class, the questions that on the whole were done well and those that needed some further teaching. It also allowed me to put in a VLOOKUP formula to calculate the students' grades based on the grade boundaries for the paper. Then, in a discussion with my mentor following this analysis she recommended I work out a 'value added' column to see how far off/on/above targets the class were.
Having then completed a question breakdown analysis for each student I was able to see which questions I needed to take the class through as a whole and I did this with the class in the lesson that I gave the students their papers back. I gave them their papers with their grades, an AfL sheet which stated each question, the topic covered by that question, marks available and then a column for the students to rate their RAG for the question, write in the marks they got on each question and then a column for 'actions'. The 'actions' column was for them to think about how they are going to improve on the questions they did wrong. In addition to given them these AfL sheets I then went through with them the 2 questions on the paper that stood out as being done poorly as a class - this was the manipulating algebra questions (a lot of factorising). This made me think about how I had taught this topic originally and why the topic hadn't stuck in the students minds - was it because I hadn't taught it well enough? Was it because we covered that topic nearer the start of the school year and they'd just forgotten it?
I then told the students, for homework, to do 1 of two things. The first (following feedback from the NQT session) was to complete a survey I had set up for the class on to give their honest opinion on our lessons so far this year, their grades, what they felt needed improving, what was going well, what activities they liked best in class etc. The second was to go to my YouTube Channel (mrcollinsmaths) and watch the solution videos I had created from their mock paper for the questions they did not answer correctly.
I will then discuss with them the results of the survey (some of their responses are as useful as they are brutally honest) in our lessons next week.

However, I did not feel this feedback was effective enough and wanted to focus more individually on questions the individuals needed to work on in the class - perhaps the questions they should have got right but didn't for whatever reason. So, I went back to the spreadsheet and filtered out the results by their marks. This then put the top of the class at the top of the sheet and the bottom of the class at the bottom. From this filtering I was then able to group the students by their results.
I then aimed to do a group work lesson whereby I sat students according to their results in the mock paper. The interesting thing about doing this was that when I was grouping the students into groups of 6 (the top 6 students being in group 1, the second 6 students being in group 2 and so on) I was starting to notice patterns in the questions they got incorrect or scored low marks on. Pretty much in each 'groups' case there were one or two questions that these students all got wrong. So I decided that I would differentiate the tasks for each group based on these questions they all got incorrect. This then meant that in the 5 groups I had set up each group had 2 tasks to work on relating to 2 questions they got wrong in the mock paper. There was a clear level of increasing difficulty to the questions as you went from group 5 to 1, with a few overlaps in the groups. For example group 2 and 3 had 1 task that was the same (forming expressions and solving equations) and group 1 and 2 both had a factorisation task. I used tarsia puzzles and pre-prepared worksheets for each group so they could all support each other on the tasks.

Here's the resources I prepared and how I set up my room:

I gave each group a magic whiteboard to work on and whiteboard pens/resources were on each table at the start of the lesson. The groupings were up on the board as the students came in and my number tiles were on the tables to direct them to the appropriate group. I explained at the start of the lesson why I had set the groups up in the way I had and that my intention was that each student was able to answer 1/2 questions from the mock paper at the end of the lesson that they weren't able to in their actual assessment. As the lesson progressed the great thing I found was that the top 2 groups were, for the first part of the lesson took care of themselves and were able to get straight on with the tasks they were given. This allowed me to go straight to groups 3 and 4 initially and give them support at their table so they were able to complete their tasks. Group 5 were busy at this point cutting out their tarsia puzzles and this allowed me the time to get to the other groups. When I finished explaining to groups 2 and 3 and covered any questions they had they were then able to get on with their tasks. I sat with group 5 and checked they knew what they had to do  (HCF and LCM) before then going to group 2 and 1 and giving them my input to move them on to the harder of the tasks they were given, this for group 1 meant going through factorising quadratic equations (coefficient of the x^2 term > 1) at the IWB (I purposefully sat them at the front for this reason).
At the end of the lesson I got students to revisit their AfL tracker sheets from the lesson before and fill in whether they felt more confident on their RAG scale and whether they now knew how to do the tasks they were set. I could see progress in the lesson as the groups had either completed their tarsia puzzles or completed their w/sheets, moved on to other tasks given at the IWB etc.

Here's a pic of group 5's completed tarsia on Prime Factor Decomposition (their 2nd task)...

The class worked well throughout the lesson and I feel had I not done this differentiated group work lesson that the students wouldn't have had sufficient feedback from their mock paper and wouldn't have known where they went wrong with at least a few of the questions. This also meant that they would now, if taking the paper again, would pick up more marks than they originally did, therefore improving their score.

The final thing I have thought about doing is, again after discussing the class with my mentor, set up a 'focus group' of those students who are significantly below their target grade. I already have students in a seating plan according to their target grades - in the hope that students on similar targets support each other achieve their similar goals, but also need to focus some more of my attention on 3-5 of the students that need an extra boost to achieve their targets.
I have informed the class of extra support sessions from me after school that are available and will be discussing this week with those students that are in this new 'focus group' about attending these sessions and will also aim to get their parents involved as I know they are supportive and will encourage them to attend the sessions.
I will blog more about this class in the future, after I have fed back the survey results, had a few of the after school sessions and thought more about how I can revisit some of the unit 1 topics whilst teaching the unit 2 content of the METHODS in Mathematics.

Sunday, 20 January 2013

Rule Book

Last week I did a bit of private tutoring with one of my tutees I haven't seen in a while. She's currently revising for her Mathematics GCSE exam that she has in March (well the 1st paper is 28th February)! After we had gone over lower and upper bounds, direct and indirect proportion, bearings and a few other things she showed me the 'rule book' that she had been keeping over the past month or so to revise more effectively.
Now, as I used to work in the school in which my tutee is studying I know of one of the Mathematics teachers there that uses these 'rule books' with all of his classes in KS4 as an effective way of them keeping revision notes and examples of questions. Each week he'd check these books to see that the students were using these. However, my tutee doesn't have this teacher for Mathematics and so I was massively impressed that she had decided to do one off her own back.

In the book she had a separate page for each topic/different type of question, all pages were numbered and at the back of her 'rule book' she had an index to easily find certain topics to revise from. I thought this was brilliant and I am now wondering as to how I could introduce this in class and whether or not students would use it as well as she is? Would it be something that I'd have to check on a weekly basis? Would these checks and the compulsory nature of me insisting the students kept these books then have a negative affect on them wanting to keep them? Should they be something that the students themselves would have to WANT to be keeping rather than something I would be telling them to do? All questions I'd have to consider and I may well contact my previous colleague to see how best he uses them with his classes?!

Here's my tutees' rule book...(I don't know who Sam is - maybe he appears throughout the book to explain concepts etc?)

 Here's some of the notes she's made inside - looks like Pythagoras' Theorem in 3D!

Here's the index pages - notice how she's almost made 100 pages already!!

The only thing I asked her was if anybody had checked the notes/examples she had written in her book. She said that they hadn't so far as it was just something she had been keeping to help her revise! I thought that this may need to be done so that she was certain that everything in there was accurate (I'm sure it would have been). If introduced in class these would, at some point, need marking or at least looking over by me. I could see these being used in conjunction with a class exercise book. The 'rule book' would be used for students to take down notes at the start of the lesson - just one example, key formulae/definitions etc, and then exercise books could be used for practise questions, workings out, homeworks etc. Mark the homeworks as they are given and completed and then mark the 'rule books' once a week/fortnight?

I'd be interested to hear if any Mathematics teachers are using anything similar in class and how best they have been implemented? Do the students take to these well? Do they use them proactively? Tweet me @mrprcollins or reply below!


Last week, just before the school day started, I was setting up my lessons for the day and getting all of my resources printed off and cut up etc when my HoF came into the room to ask to borrow one of my Year 9 books to show my topic trackers in the subject leaders meeting. After we spoke about these and how I use them he happened to notice one of the resources I was planning to use that day - the DfE Standards Unit S2 resource on evaluating probability statements. Having recently taught the same lesson to his year 8 class he suggested that I use the socrative resource he had used and set up for his class.

Now, at this point I hadn't used or heard of socrative before and so he explained what it was and how it worked to me in the 10 mins before the bell was due to ring. The website is a site where teachers can set up quizzes for their students to answer in class using their mobile devices. The resource by HoF had set up was the S2 Standards Unit lesson. There were 11 questions all exactly the same as those in the resource and all required students to answer true or false to the statements (there was also 1 question asking for their name). How socrative works is once you have an account (free to sign up) you get a 'room number'. When students access the site on their mobiles, by going to they are asked to type in the 'room number'. This then goes to the teachers live quizzes once set from the teacher account. At this point the teacher is able to see all results live as they are completed by the students. So, after my brief tutorial, my HoF very kindly allowed me access to his quiz by sharing it to my account and my lesson was ready to go.

In the lesson, the socrative quiz worked really well. I had the website up on the board where I was logged in and the live results were appearing on screen as the students were doing the quiz and entering their true or false answers to the statements they were given. The added bonus of this is that I was able to see who was getting them right/wrong and the 'room number' was displayed clearly for students to see. As I hadn't prepared students for the task they were excited about being able to use their mobile devices and were highly engaged in the task. However, as they weren't told about the task prior to the lesson not every student had access to a mobile device that could access the Internet. This, would probably be the case anyway even had I told the students they would be using their devices next lesson so, how I got around it was by asking students to, once they had completed the quiz themselves to share their devices with their partners or other students that didn't have one with them. Most of the students obliged and it wasn't long before all students had completed the task.
We had a few problems with some devices not being able to connect to the Internet or not being able to load up the socrative page, but all students managed to complete the quiz eventually.
Once all students had completed the task the results were there to see on the board, with all the students names and their scores out of 10 on the board. This created a healthy bit of competition across the class as they attempted to get the highest score in the class, or higher than their friends' scores.

After all students had entered their results I then fed back to the class the answers by entering my results on the IWB just as they had done on their mobile devices. I went through each statement and discussed with the students any misconceptions that they may have had on the questions before choosing the correct answer and going to the next question. It was interesting to see which questions caused the most misconceptions with the class and those that caused little confusion.

What I liked about socrative is that when I closed the quiz it then gave me an option to receive an e-mailed report of the class' results - this for future reference was great to have to hand.

I will definitely use the socrative website in the future with students as I feel the kids really bought into it, they were excited about using their mobiles, they were using their mobiles in a productive learning environment, we were able to get instant feedback of their results and analyse these together addressing misconceptions the students may have had and it was really easy to use given that it only took me and my HoF 10 mins to set up an account with me and 'train' me how to use it!

Saturday, 5 January 2013

2 0 1 3 challenge

Last year, whilst on my GTP, I put up a '4 fours challenge' in my classroom for students to do over the course of a couple of weeks until all of the numbers from 1-100 were made using 4 fours. This display (made from using some of my Magic Whiteboards) created a good amount of interest from my students, and indeed other students from classes that also used my classroom (this included an A-level Biology class that had one particular student who completed a few of them).
What I like about this activity is that in encourages students to solve a problem in their own time as well as in class as a starter activity. Classes would come in to my lessons looking at the display wondering how many had been done since their last lesson, and what target numbers where left to do.

Here is the finished '4 fours challenge' display from last year...

So, due to the success of the display/activity last year I have decided to do a similar one this year. Seen as it is the very start of 2013 I will use the digits 2, 0, 1 and 3 with the same rules as before in the 4 fours challenge.

I will put up another set of Magic Whiteboard sheets and write onto it the numbers 1-100 and then write up the rules next to it:

using the digits 2, 0, 1 and 3 try an make all the numbers from 1-100
you may use any mathematical symbol/operation (x, +, -, divide, square root, square, cube etc)
you must use all of the digits, 2, 0, 1 and 3
you can combine numbers i.e. you can make 20 from the 2 and the 0 so 20 + 1 + 3 is fine to make 24
remember BODMAS
(I may start off the display with a few examples)

I'm not yet sure that all 100 numbers can be reached, but that (I guess) is the beauty of this activity as it will be student centered in that they will be the ones doing the work, and I will just verify each. I will also award VIVOs to those that manage to complete any of the numbers 1-100 and use this to provide a bit of an added incentive to give them a go.
I will post a picture of the display when I get it up on Monday!

Mathematical Concepts Wall (for want of a better name)

On Thursday I ventured into London with @kutrahmoore. We had different things to do whilst up there; I was attending a focus group meeting at the Manga High offices and she was off to a few galleries that she was intending to go to.
I thoroughly enjoyed the time spent at the Manga High offices and taking part in the focus group was a great experience having not done anything like this before. When we met back up to head home I was shown pictures of all the things @kutrahmoore had seen in the galleries and looked through the various handouts she acquired.

One of the best things I was shown was the 'Forum' wall at the Wellcome Collection in Euston. You can see their website here. The wall was made from loads of cards that were handed out to visitors to the collection. The cards were double sided, on one side there was a list of words and on the back a simple sentence on the bottom asking visitors to take one or two of the words on the reverse of the card and then to write/draw about them. The cards were then displayed on the wall in little boxes. Here's what the cards looked like...


Here are few pictures of some of the cards that were on display on the wall...


The cards were all centered around medicine I believe?

And here's an over view of the entire wall itself in the gallery...


I thought that this would work great in my classroom and that I could create something similar around the existing display board at the back of my classroom. So, I have created a Mathematics version of the idea above. I have taken key Mathematical words/concepts/ideas/topics from the topics I will be teaching my classes this term and have created a similar card as to the one that was used in the Wellcome collection. On the back of the card I've left plenty of space for my students to draw/write about the topic and then space for their name and year group. I plan to give my classes these cards at some point in the first few weeks, I'll also leave some spare cards at the back of the room on my bookcase (my students have a habit of fiddling with anything on the top of this and so are bound to notice them and then ask questions).
Here's the card that I have created...

I will plan to give one of my classes a card each to do as part of one of our lessons (maybe as a starter activity or end of lesson activity) and then this way it will 'get the ball rolling'.
As much as I'd love to have a similar 'box' style to the display, for now it may just be easier for me to blu-tack the cards to the wall!

I'll post some pictures of my 'Mathematical Concepts Wall' once it is in full this space.