Ok so we’ve been working on this for a while now and I’m aware that it all went a little quiet for about 3 or 4 months.  The motivation factor of using the DS’s in class wore a little thin – or rather the class got used to them and started finding ways to ensure they managed just enough work to be allowed them.  The game became more of a toy than a learning tool and I had run out of ways to use the results of our races with the tennis stars so they were locked away in the cupboard for a time.

Very slowly our charts began to fill up as individuals were allowed to play games as a treat or reward.  We also made it through 2 sets of assessments, Christmas mayhem, a whole school evacuation – not a drill – and several snow days.  It was now the middle of winter term and time to ditch the project or resurrect it.  3M7 have a lot to thank my PLN and Twitter for because it was comments from you guys that moved me forward.

As I mentioned our class races had come to a natural end.  Looking forward I wanted to use the information that we had collected in the individual races.  From the beginning we had been writing down the total time for the race and the fastest lap for each game.  This in itself proved to be a learning  experience as some struggled to identify the best lap and most struggled with the format of the time.

First task was to get the information onto something more usable in the classroom than the posters that were being completed on the wall.  So we had a class discussion about the format of the times and then split into pairs.  Each pair was allocated a character and given 4 coloured cards – one for each of the cups.  They wrote their character name on each card and moved around the classroom completing the race times on the cards, working together to ensure the format was indeed correct.

Race Cards

Finding Times

Next we collected all of the character’s cards for each cup together, split into 4 groups and used them as an ordering game – fastest to slowest.  After this was completed and the misconception that the highest number was the fastest had been shot down by the pupils and confirmed in a less confrontational manner by me we did the exercise again using 2 sets of cards.  When we put the Orange and Green cups together we found an overlap in the fastest lap for one and the slowest for another which raised a good discussion about why.  Perhaps one was longer than the other, or harder, or the drivers on the slower race were just rubbish!  Regardless of the reason or ensuing argument it was the project and the pupils’ own work which prompted the discussion and not a contrived exercise for which they had no passion or interest.

Sorting Race Times

Are you sure?

Moving on we met the trickier topic of Speed Distance and Time.  I was determined to use the race cards again.  The class is only expected to complete distance calculations given the speed and time.

We discussed the average speed of a journey from home to Inverness (30m/s) and the fastest average speed recorded for a grand prix win. (67m/s – from F1technical.com)  I had calculated both in metres per second for them to give some context and to simplify calculations but keep them realistic.  From this the class decided that our Karts probably had an average speed of 40m/s.  Their responses had a very wide range due to their perception of “kart”.  Some expected the karts to be much slower than cars and I was pleased that none suggested anything close to the speed of the F1 car.  I had to persuade them up to 40m/s to ensure the next part offered some challenge.

I explained that we would assume the average speed of 40m/s and use this to calculate distance for each driver in each race. “But, miss, the race is the same length for each driver!” Thank goodness. I heartily agreed and said we were going to estimate the actual length by using averages and the information we did have.

Back to the problem of the format of the times – a quick revision on rounding to the nearest whole number and the cards were split up again.  I handed out worksheets to help the pupils organise their work and we split into groups around the 4 different cups.  We moved around the class writing down all of the fastest laps rounded to the nearest second.  Once they were all completed we calculated the distance.  Working together they managed to solve the problem of multiplying by 40 without my input and they flew through close to 32 calculations complete with working in minutes.

Calculating distance.

Still working...

From here we will do calculations to find the mean distance and time.  I hope this will prove some of our earlier discussions about some courses being longer or more difficult than others.

There are still gaps in the scoreboard which leaves more room for discussion and opportunities to reward pupils.

Moving forward I am looking forward to completing a similar exercise with the power car.  I would like to use this to calculate speed using the distance we know from work already done.

In a real life context we are far more likely to know the distance and time or the distance and speed – I am going to try something similar to extend the course, it can’t possibly be considered a waste of time even if it is not defined in the SQA arrangements.

This is a project that the whole class are involved in.  As long as I can continue to move it forward then they will probably remain engaged.  All the better if I can keep it linked to work that is prescribed by the curriculum.

For now, the motivation to play games may well have dwindled but Mario continues to keep them hooked for all the right reasons.

The Longest Journey Starts With A Single Step

I am spending some time working my way through my rather neglected Google Reader feeds. Each and every one included has value in education and has been added by me because they have provided an insight or an idea that I have been grateful for.

Reading them is not a chore, fitting the time in has become a problem. But only because I spend too much of that trying to plan what to do with it!

So, first step to taking control of my time and information flow – Reader will be checked every morning. Instead of watching adverts and personal stories of variable quality on TV over breakfast I will open up Google and have a quick flick through what’s new.

Time found!

I’m doing a presentation on Tuesday and one of the key phrases that I am going to say out loud is that assessment is not the million dollar solution to Curriculum for Excellence that we are waiting for.  Now, I’m going to wear my waterproofs to protect me from the rotten fruit and veg bound to head my way but nothing’s going to stop the glares and looks of absolute disbelief.

The great thing is though:

I finally believe it’s true.

For a long time I have wanted to believe that the abolishment of external, final exams is the right thing to do.  I have always felt that it is fundamentally wrong to test pupil’s knowledge and 12 years of learning with 1 hour summative assessment.  On the flip side I have been unable to conjure any idea of what assessment should look like.  To be honest I’m still struggling with that but I can now look forward to the challenge because I finally understand my own role.

School curricula for too long has focussed on the goal being to pass as many exams as possible, the elite head to uni, the middle to college or apprenticeships and the bottom plough through and hope for the best from their handful of foundation grades.  Great improvements have been made with the continued implementation of vocational and practical courses.  The emphasis, however, has remained on channelling as many as possible down an academic route and adding extras for other learners.  Curriculum for Excellence goes one step further and asks teachers to provide learning suitable to every learner.

How do we know what to teach if there is no final goal?  A war cry from those, and until recently me, who need assessment to be fixed so that they know “what” to teach.  This is my real revelation to date because I have realised that:

 I know what to teach regardless of the final assessment. 

Nobody has ever suggested that we should be changing the content of our courses.  Indeed it would be difficult to create a brand new maths syllabus, the nuts and bolts of number, algebra and geometry are not changing and are essential to future learning.  Each step leads logically to the next and the extent of learning is now limited only by the ability of the pupils.  I agree that a structure must be imposed to learning to ensure that pupils are gaining a breadth of learning and that records of achievement for each pupil are essential and I’m not sure how that will look either but I am now confident that I have the tools and resources to move forward.

In my toolbox I have textbooks, worksheets and schemes of work, all of which offer comprehensive structure to suit learning maths through relevant age and stage levels in an ordered manner which builds upon previous learning and provides essential numeracy and mathematical skills.  In addition I have a plethora of ICT and interactive tools including games, concrete apparatus and links to real life.  Add to all that co-operative learning and formative assessment strategies and chuck in a bit of investigation, outdoor learning and fun and I reckon I might just make it through.

If I use all the tools that I have and maintain the pace and challenge I now believe that I can ensure that the learners in my classroom will be ready for whatever the National Assessment Resource can throw at them.

My first foray into using the video camera to engage pupils in mathematics.

image from http://www.flipcamera.co.uk/

My department recently purchased a Flip video camera from Amazon at my request.  My head is full of ideas about self evaluation, presentations, pupil interviews, screencasting, etc – the trouble as always for me is where to start.

So here’s what I’m going to do first.
The main aim is to engage pupils in their learning by making them believe that maths is all around us and truly important to our everyday lives.  My target audience is S1-S3.

The plan is to video various scenes in and around Thurso and set the pupils discussion tasks to answer the title question.

I’m going to start with the obvious;

• Retail displays including offers, discounts and deals.
• In the supermarket I’m heading for the fruit and veg aisle for weights, budgets, conversions, ratio.
• Off to the estate agent window for rent and mortgage info which I will follow up with household bills.
• The bank will provide some negative numbers, personal finance and some complicated percentage calculations in the form of compound interest and APR.
• Off down the river for an introduction to vectors which I learned about teaching the cadets last month.
• A wander in the park to look at Fibonacci, the golden ratio and maths in nature courtesy of Marcus du Sautoy and Teacher’s TV.
• Finish with a closer look at some of the buildings and architecture in Caithness – this may well be worth a trip to Dounreay to get the dome close up.

The more I think about this, the more excited I get – again, it’s an idea that has been bubbling around for a while.
If all goes well, I’d like to then send the pupils on a mission to record their own videos – around the school to begin with and then further afield.

What have I missed?  Your ideas to enrich this project would be more than welcome.

Many thanks to Tom Barrett and his amazing Interesting Things series.

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As a teacher and a volunteer at a youth organisation I am in the enviable position of being able to learn alongside young people.

Just because I am older does not make me the expert. In many ways I have a better capacity to interpret new knowledge because I am often more aware of my own learning preferences and I have many more experiences with which to associate and compare new situation. In many ways I am at a disadvantage, previous misconceptions need to be overcome, it is often difficult to find a place for new information and I find it difficult to learn new practical skills.

Together my S3 class and I learned how to play Mario Kart – on Wednesday they beat me soundly – again!
Tonight I learned how an Air Speed Indicator works collaboratively with a group of cadets – although I’m not sure any of us know exactly what the Pitot tube is I know that they could offer explanations regarding pressure differences as well as me now.

Tonight I feel privileged to work with these people and tomorrow when they anger me I will try to remember writing this!

The idea has been bubbling away nicely all summer and last week my thoughts finally pulled together into a feasible learning experience.

Based on discussions with the class, the restrictions of hardware and software, advice from my PLN and the curriculum restraints this is what I have chosen to trial this term.

There will be 2 leagues.

The first is a competitive league where 8 pupils at a time will race their tennis stars in a classroom battle.

How?  I have set aside 8 of the DS devices which I am hoping I will be allowed to retain in my classroom solely for the use of the project until at least Easter.  The pupils have chosen to name the consoles after tennis players (yes, Wimbledon was on at the time).  The league has been drawn up on a point basis.  The game will work out winners and points and the pupils will record these.  For now I will keep the info in a Google spreadsheet with a view to possibly getting the pupils to duplicate the worksheet in an ICT lab.

What learning outcomes am I addressing here?

• reading tables, graphs and charts
• draw conclusions and explain them from data
• take an organised approach to solving problems

We will have 2 races each session, hopefully 6 sessions this term.
2 each time to ensure the whole class has the opportunity to play.

This will leave us time in the last week to draw our conclusions.

The second tournament will be a time trial competition.

Within the game there are 8 characters who each have 2 cars and 4 cups which each have 4 tracks.
This leaves a lot of space for trial and improvement of the project.

So we’re going to attack the first track in each cup with each player’s 2 cars – that’s 64 races – that’s more than enough for 1 term.  This is an individual game so I’ll have to be careful about who’s getting to play.  The pupils will be able to choose which character, car and cup to race until all of the blanks in the posters are filled in.

Each time trial gives overall time and best lap data which will both be recorded.  The times are given in minutes, seconds and then decimal up to 1/1000 of a second.  This will set up learning outcomes about time beyond expectations of the course.  Extending easily into time calculations, we can also consider rounding, averages and further organisation skills.

So let the races begin!

Your feedback as always would be greatly appreciated.

I found this document while looking for more recent ramblings about the transition work I am currently involved in and am pleased that it gives me a foundation to build on.  As a department we are working hard to develop strategies to ease the Primary/Secondary transition process to enable pupils to continue to achieve, maintain their confidence in maths and progress in their learning.  Maths should, after all, be considered as a continuous subject – there is no difference between the skills and knowledge or the methods of delivery that can be employed.

I am pleased that I have managed to follow through on most of the promises I made to improve my practice – the walls are, indeed, covered with S1 work and I have continued to embed AiFL strategies, discussion and formative assessment into lessons.  With the impending timetable change looming it is good to remember the pledges I made a year ago and re-draft them for this year.  Many are useful for all years, not only S1.

I had intended to blog about our department’s transition project this evening but that will have to wait now.  I’m going to focus my attention on the classes coming in Tuesday and how I can do my best for them instead.

Primary – Secondary Liaison Report 2007/08.

Stephanie Disbury – Mathematics Teacher – Thurso High School.

Aim – to discuss the similarities and differences between mathematics learning and teaching between primary and secondary school and evaluate strategies to reduce barriers in the transition process.

The more I consider the difference between primary and secondary mathematics teaching and learning the more I am convinced that the fundamental difference is in our overall objective. Drawing on classroom observations, discussion with colleagues, various in-service training courses and educational literature it has become clear to me that in secondary school the emphasis in our classrooms is on attainment, in primary it is on learning.

There is pressure on the teacher and pupil at every stage to prepare for assessments but in secondary it becomes imperative that the child is challenged to achieve the best possible results whilst completing the 5-14 curriculum so that they can go on and achieve best results in Standard Grade. Why? The time constraints involved in SQA examinations require secondary courses to constantly push forward so the more they can cover before S3 the better chance the pupil has of recalling facts for the external exam! A primary teacher has the responsibility of assessing pupils individually and setting realistic assessment dates allowing time for learning to take place at the pupils’ pace and for consolidation of skills. The courses I teach in secondary aim to maximise learning capacity for every pupil in a structured timetable of prescribed topics. If I deviate from this configuration I risk the progress of the pupils by not allowing enough time to complete the course, therefore, lowering attainment in assessments and ultimately lowering their potential for of success in the SQA exams.

I have found it easy to get carried away in a wave of exam frenzy. Approaching the assessments in November I pre-warned classes of the imminent evaluation of their learning so far this year by carefully explaining the amount of work that we still had to cover, not to mention the revision exercises and homework which had to be completed in lieu of the pending test. Pupils in S1 should not immediately recognise this as exam pressure because of the nature of their assessment in primary school and yet most still understood the importance of their placing in school as the result of rigorous testing. This self imposed anxiety to succeed causes many of them to under-perform. At what point do the pupils become aware that test results are the most important means of assessment in secondary mathematics education? I must work harder to reduce exam pressure by ensuring that assessments are part of standard classroom routine.

At the lower end of the ability spectrum the pressure to perform well can act as a barrier to learning and as a catalyst for poor behaviour. Misbehaviour acts as a distraction from the lack of understanding, pupils preferring to be the class clown than admit their difficulties.

In terms of AiFL strategies I feel that both primary and secondary teachers are committed to incorporating best practice. Continuous assessment including show me activities, peer assessment and self evaluation are commonplace in both. In particular, the secondary schools use assessment as learning by employing a variety of strategies for evaluating exam performance in order to improve future attainment. With many primary classrooms including groups at different 5-14 levels and completing work on different topics it appeared essential to use peer assessment as a tool to evaluate understanding. The pupils I witnessed implementing this were honestly critical of each other’s work and were keen to produce quality work to avoid the disapproval of their peers.

With setting key in secondary mathematics all pupils are completing the same work with little differentiation required. It is very easy to set an independent task and collate the work to check or mark. Setting up effective pairs or group work requires more preparation and careful moderation in secondary but if I continue to employ a range of peer assessment strategies and provide more opportunities for pupils to practice the skills in pairs and group work which they learned in primary it will remain the norm instead of being considered a treat. Thus the excitement and novelty factor will not be allowed to develop to the stage where pupils are unproductive. All of my research indicates that allowing pupils to talk about their work will help them to understand but like all skills, interpersonal ones must be practiced to ensure they do not degenerate. I must identify more chances for pupils to discuss their work with each other by using co-operative learning strategies and providing clear focus and learning intentions for discussions.

Both primary and secondary have efficient homework policies in place. All pupils are expected to produce work regularly and meet completion deadlines. This consistent approach should be maintained at all levels.

Moving around different classrooms is one of the fundamental changes for pupils moving up to secondary. Whilst standard rules are uniform throughout the secondary, simple conventions such as whether to use a pen or pencil, protocols for leaving the classroom and routines for collecting equipment can vary considerably.

Secondary pupils no longer have ownership of their own space. Many education writers consider a person’s environment to be vital for effective learning. Pupils must feel safe and in control of their own accountability so my own rules and expectations must be made very clear. It is also considered essential to have a sense of belonging to any group in which they are working. Again the organisation of primary has the advantage. Every pupil must be given the opportunity to contribute to the class and displaying work can be a useful tool to help pupils accept each classroom as their own place of work in secondary. My current S1 class made the number line which is displayed in the classroom and are delighted when I tell them that other classes often make use of it. I must make more time to update displays with new work from all classes.

Interactive work is critical at some levels in mathematical learning. Pupils in S1 and beyond are often not physically ready to accept or understand abstract concepts without concrete materials to aide them. The primary classes I visited were utilising various resources including ICT, games and puzzles to consolidate and introduce topics on a regular basis. Pupils are familiar with using these resources as a tool to develop mathematical skills such as logic, patterns and basic numeracy and as an opportunity to converse using mathematical language. Numerous resources are available at secondary level. Although many require customisation to suit the requirements of courses and classes the only barrier is finding time for effective preparation and evaluation of success. I will continue looking for effective resources and use a range of activities which meet the requirements of the class and course.

There are fundamental issues in the transition process which cannot be addressed as a single teacher or department within the school such as school rules, moving around classes, personal organisational skills which must be acquired and the inevitable social changes. With so much to cope with already I hope that I have identified some areas in which I can help to ease the transition process within my own classroom. Time will tell!

Thanks to Dan Meyer’s blog post My Lesson Plan: The Door Lock for this!
I read Dan’s post initially from a twitter link but my memory is dreadful so I’m afraid I can’t tell you who brought it to my attention.

However, I got myself into a conversation about problem solving strategies with my second year class this morning and used this as a trigger for discussion.  With the picture on the board I asked simply “what is the combination?”.

The discussion that ensued was based around what further information was needed to answer the problem because the maths required to state the number of possible solutions is beyond their capabilities for now.

The class came up with a single questions that they wanted answersed before they would go any further. 

How many numbers are in the code?

I only told them when they told me that they would normally find the answer to this in the question itself and what strategy they were going to try when they found out.  Some sort of ordered list seemed to be the favourite and armed now with the fact there were 3 consecutive numbers in the code they continued.

Conversation and debate followed about what consectutive could mean, whether or not they could be consecutive in decreasing order and whether 0 could follow 9.

We got it down to 14 options and everyone agreed they needed more information.  The code must be divisible by 2, the first number must be greater than the last and and the sum of the digits is fifteen elimiated all but one and brought us to a conclusion.

The important lesson today was not the maths – I know that my class can divide by 2, add to 15 and use number order.  What was beneficial was to look for the questions that had to be answered because the answers to these normally lie in the text of the question itself if they would just remember to go looking for it!

A fantastic resource and a lesson that the pupils can direct and to some degree structure themselves with the questions their own questions.  I see more potential every time I look at this and also remember that sometimes the simplest resources and ideas can provide the richest tasks.

My last post uncovered a road to Curriculum for Excellence which could keep a class engaged for a whole term, if not longer, with the arms and legs that could be developed from the initial idea.  This concept feels much more controlled.  Reading other comments on Dan’s original blog I can understand the different levels that could be investigated but for my class this was an ideal single lesson activity which empowered them to take control without me losing it.  I had a class agenda from the outset, to explore problem solving strategies, and was able to deliver my message without simply telling them.

After I’ve caught up on all the soaps, Lost and the new series of Red Dwarf I’ll have to think about what to be aiming for this term.

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My only firm plan at the moment is that it must be ICT related.
I’ve started a couple of draft posts which need more work and could relate well to the EPICT course I’m doing.  This, in turn, would suggest that the work should improve my own teaching practice.  Some ideas I have contemplated are;

1. The use of social networking as an educational tool
2. Internet security – copyright and access issues
3. VLEs – research and general implementation for a secondary maths course
4. Adding value to the department’s teaching and learning strategies and plans using the website
5. Blogging – any use for maths?
6. Podcasting problems and solutions, tools to use, making it appealing to our target audience – terror teenagers
7. Finding teacher-led resources to ehance teaching and learning of a maths and numeracy curriculum that pupils want to engage with outside the classroom.

I have to remember that I can’t assume access to computer facilities or internet with my own pupils.  Mostly outwith my control.  Not enough access at school and often unreliable.  Easy to suggest local library but many of the kids can’t get into town to manage even that.

It’s far too easy to forget the target and get carried away with applications that look good.  Do the pupils engage more with visually attractive chalk and talk lessons than good old written notes and diagrams.  Perhaps this is where I will start?  I suggested during ICT presentations last year that one of the main benefits of the IWB was the drawing tools which provide a clearer visual for the pupils but I often have to sketch a freehand example on the other board to help the pupils to illustrate notes and to allow me to explain details.

The biggest benefit of blogging is the opportunity to free-type, let your thoughts flow and talk yourself into a conclusion.  Lots of research to begin it is then.  Let’s consider in a professional and academic manner how much impact the visual aspect of lessons has on learning and teaching without an interactive element.  Is talk and chalk as good as talk and fancy illustrations?

Watch this space.

Consider the boy in my class who cannot read.  He cannot communicate in writing.  He can write by copying symbols but cannot make sense of them after they are drawn.  He can write his first name because he is familiar with what it should look like.

Then consider a site which will give him oral instructions, explain questions out loud whilst highlighting the same question on screen and finally gives him the opportunity to say the answer out loud.  This site will congratulate him when he is correct, learn his weaknesses and help him to move forward.  If anyone knows of such a site with a focus on maths I would appreciate the URL.  I already use some which learn the users and help them to consolidate work which they find difficult, some which use oral commands and I have heard of voice recognition programmes which I am sure will be developed in the near future.  This is my ideal programme though – if it is available I haven’t seen it, if it isn’t then perhaps it’s not too far off.

Now consider the girl in my class who was convinced that 5+1 = 51.  She logged on to www.worldmathsday.com on Friday and answered 10 mental maths questions correctly in 1 minute.  She was 13 (in a UK S1 class normally aged 12 at this time of year) and entered as an 11 year old to participate in this worldwide challenge but she was unaware of this.  She was so delighted that it took me a while to pull her back down from the ceiling.  Her maths is no more accomplished now than ever before but she will enter my classroom on Monday with a positive attitude, thinking that she is now good at maths and that will make learning so much easier for her.

This has nothing to with the girl’s learning style but the work on the computer in just one day has increased her confidence more than any good exam mark could have done.

So let’s look at my S5 class.  I’ve spent many long hours on www.edu20.org creating a VLE for my fifth year class.  The topic I chose to cover as my experiment was spreadsheets, a very small part of their course but one which I felt they would recognise as a benefit to them in the world of work.  I told them about the site 3 days before we got near a computer in school - 3 out of 14 had logged on before we got there.  Now is not the time or place to discuss the motivations of the class but I can tell you I was impressed by this.  When we did all get logged on together the pupils worked away without question or quarrel.  I have no doubt that the dynamic nature of the work, the instant feedback, the ownership of their online profiles all contributed to their enthusiasm that day.  Time will tell if their good will persists – about a week in fact which is when I have set their assignment due. 

In short, the VLE can provide a more personal learning experience.  If the pupil want audio instructions, they can go find them.  If they need a demonstration they just need to find the correct keywords to search.  As a class teaching presenting a lesson I can only try to suit every different learning style and hope I am at least touching on them all. 

Technology can meet the needs of specific learning styles more effectively that a classroom teacher meeting the requirements of a class of 20 but we’re not quite there yet.

Consider the work involved to tailor VLE’s to every course at every level – I find it impossible to imagine how much time that would take.  Would it be worth it?  If that boy can take one more step to understand his maths or if that girl can win one more competition then my answer is a resounding – Yes!