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.

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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I’ve put this presentation together as an introduction to using a SMART Board in the classroom.

It is my intention that users will be able to use this as a guide and work through the excellent material already available online.

I would appreciate any comments that you have.

Many Thanks in advance.

.

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.

This idea has been bubbling around me for a while now.

I’ve been reading a lot about ICT in the classroom with a particular interest in games based learning and then Adam Stevens, (@ahstevens) a contact I have made through Twitter mentioned that he had dabbled with Mario Kart and other racing games in the classroom to present some basics of distance/speed/time theory in physics.  Derek Robertson (@derekrobertson) and Ollie Bray (@olliebray) have provided further inspiration by sharing their own experiences of games based learning success.  Both are now working to spread good practice and I am pleased that they have offered me their support, albeit from the back of the car on the way home from the first Edu2020 (@edu2020) meeting in Duffies!

The pedagogy behind games based learning must lie in motivating pupils to learn by engaging them in the work being done through ensuring a common interest is found and utilised.   A great opportunity has presented itself for the new school year. I will be working with a Foundation Level maths class through 3rd and 4th year to formal assessment in May 2011.

The Standard Grade course will offer plenty of challenges to the pupils with the work covered but also many opportunities to relate work to real life scenarios and situations.  In addition it will allow me time to incorporate games based learning and the curriculum for excellence principles into our lessons.  My main learning intentions will focus on time problems, number, organisation, simple statistics and problem solving.  In addition the project will be designed to meet the 4 capacities of Curriculum for Excellence.  Although not strictly necessary for pupils at this age and stage in secondary school it will provide a richer learning experience at this level of work and anyway, it’s good practice for what’s coming!  Having had a quick glance through the arrangements these are the current outcomes I believe I can meet with Mario Kart.

• reading tables, graphs and charts
• line graph trends
• communication of data through tables, graphs and charts
• numeracy – add/subtract/multiply/divide calculations in context
• mean, median, mode
• check solutions
• experiment
• draw conclusions and explain them from data
• take an organised approach to solving problems

At this point I need to put out a prezi alert.  My planning has been done on a Prezi following a comment on Twitter from John Johnston (@johnjohnston) who mentioned that he had never considered using it as a planning tool until he saw a previous post by me – well, I had never considered it either until he said it!  I had been waiting for a flash of motivation and 10 minutes in front of my SMARTboard to plot my ideas into writing – indeed I had even started the Notebook file.

Anyway, the prezi is attached here.

So far, this project is a triumph of Twitter and my new and ever reliable personal learning network.  Since joining Twitter and joining in the chat I have found contacts, received support and criticism and, perhaps most importantly, been provided the ideas and reading which will realise this project in my classroom.

As the title of the post suggests, this is just the beginning – I have a long track to get around to see this project through with many questions about management, ownership, assessment and evaluation still to answer.  But I’m excited about pitching this idea to the class and hearing their ideas about how to proceed – am I already half way to a good outcome?

We have known from school records across the country, for a long time now that pupils can falter as they enter S1 from primary school.  Of course the kids are all different; some thrive on the new challenges of a large comprehensive secondary school, some simply don’t manage to progress much in the first few months and some unfortunate souls find the transition so hard that they can fall behind in their classwork because every ounce of effort they can muster goes into survival.

As a school we have certainly not been sitting back and watching this happen.  We have, and many of you will be familiar with these strategies I’m sure, tried to ease the transition process in ways which I have blogged about before.

This year we are trialling a project which all of our P7 catchment pupils will start in primary and continue in secondary school.  To get us started we held meetings with primary and secondary school teachers to discuss a suitable topic which could be used.

Time and measure was chosen in relation to the pupils’ journeys to school.  We are situated in a large rural area covering approximately 100 square miles.  Up to 10 primary schools feed into Thurso High School.  These primaries range fr0m large town schools to very small country schools.  The majority of the pupils attend their most local school and experience very similar journeys as their peers.  On arrival at secondary the pupils are set into maths classes according to the 5-14 Level which they have achieved (or are working towards) with pupils from all primaries.

View Thurso High School Feeder Primaries in a larger map

We have chosen to maintain flexibility for teaching staff to approach the topic in a way which suits individual classes at this very busy time.  It is, therefore, inevitable that the pupils coming will all have different learning experiences in primary school and will have varied prior knowledge and skills. The only set criteria for each pupil’s portfolio is that it should contain the following information:

1. What their mode of transport will be.
2. The distance of the new journey.
3. The time the new journey will take.

At primary school today I enjoyed the first half of this project being put into action.  Pupils have all been given a cover sheet, designed at the secondary school and including all of the school logos, which will be attached to the work they are currently completing.  They will bring this with them to high school when they attend transition days next week.  During their visit to secondary the pupils will follow their new timetables with their new classmates for 2 days.

While the pupils are with us in the maths department we will look at the question:

How does my journey to school compare to my new classmates?

We have designed a single class chart to show all pupils’ modes of transport – every pupil will make a contribution to this and it will then be displayed on the classroom wall.  Once again, individual class teachers are left the option of what other information to help them answer the question above with their classes.  As all classes are set by ability it will allow us to choose appropriate topics within the CfE experiences and outcomes to suit the learning needs of our new pupils.  Some classes may focus on collecting and displaying data about  distance and time of journeys whilst others may progress to consider the relationship of speed, distance and time.  Any work completed will be kept for them to continue after the summer.

With this project we hope to create an immediate sense of belonging within each class, an ethos of contribution, team work and relevance.  We must remember that the transition process is the main focus and not the mathematical knowledge at this stage.  Our aim is to provide a continuous learning experience to minimise, or at least reduce, any anxiety about secondary school maths.

The pupils are visiting next week – watch this space and I’ll try to let you know how it goes.

PS – at the beginning of all this I wrote a Prezi to try to piece my thoughts together.  Please feel free to have a look if it doesn’t make you queasy!

http://prezi.com/69297/

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!

I often feel a little overwhelmed by the amount of technology leads I receive and consider.  To begin with I found it difficult to evaluate resources without trying them out with a class.  It’s often hard to imagine how a class will react to different methods – I guess the daily surprises are why I enjoy teaching quite so much.  Now I’m finding it easier to place tools appropriately but finding it harder to keep track of the good ones.  So I’ve gone back to basics and had another look at what I use every day – the Interactive Whiteboard.

I have a SMARTboard in the classroom, running with Notebook 10 and the full gallery of resources download.  All the latest software is available from the website including a free student download which enables pupils to open and amend Notebook files and access most of the tools.  Use of the interactive features of these boards is highly encouraged to engage pupils – I’m not bad at this but there is a lot more I’m sure I could be doing.  I worry too little about sticky fingerprints on the actual board.  Next year I want to see more.

OK – where do I start?

Last week I dug out an old email from a colleague in the Physics department – it was a link to  José Picardo‘s video:

Top five tips for creating resources for the interactive whiteboard

I watched it again, understanding more than last time and tried out some more of the ideas including the magic pen for magnifying and highlighting small chunks of work and the word reveal tricks.

It occurred to me that even the board can offer so much potential that I have not yet realised, without me learning new ICT skills or finding new software.  All this was going to take was a little effort.

Next port of call is the Gallery – it really is about time I found time to rake through all of the resources instead of just searching for something which suits a lesson plan.  It’s rather convenient then that I had an unexpected 4 hour train journey yesterday.  The train to Thurso thankfully has first class seats and no first class tickets which means that anyone can make use of the free plugs as long as you embark quick enough!

I’m pleased to report that I came across a lot of tools that I have used before but here are the ones that I promise to use this year.

Clocks – An assortment of clock face resources which can be used for show me activities, a teacher led lesson or as an interactive tool with pupils creating the questions.

Unit circles – Radians, degrees or both – you decide – precise accurate and much more visually stimulating than anything I could draw.

Dice – 10 sided dice that the pupils can roll and race.  Or dice that speak in foreign languages for a little cross curricular work – there’s even one where you can choose what goes on each side – or rather  the pupils can!

Symmetry – 2 Flash activities that pupils can use alone if you’ve got the ICT access or as a class – ready made reflection and rotation resources.  You can achieve this using the flip tools but this looks more professional.

Algebraic Fractions – A brief lesson, more suitable as a consolidation lesson than an introduction because the quiz is a stormer.

Quadratics and Straight Lines and Trig graphs – There are plenty of online resources and maths packages which will create these graphs and allow you to change the variables showing the transformation of the graphs but why look elsewhere when the gallery holds them anyway.  These simulations are clear and easy to manipulate.

Nets – A quick movie showing different 3D shapes being opened out and closed up – supplements physical practice without getting covered in prit stick at the front of the class.

Indices – the first tool I found allowed you to enter an integer value and a power – can be used to show square, cube numbers to lower ages/abilities and patterns involved with higher orders further up the school.  Followed by a smashing game of snap where you have to think quick to simplify indices and surds and spot the correct equality from a choice of changing cards.  Great starter for a higher set.

Interactive Ruler – and finally….you can move this ruler around the page just like the standard one but in addition you can set the arrows to do the measuring for you.  Pupils can read the scale then check their answers interactively.

So my pledge is to use these tools and I would urge you to give them a try too.  iwb-ideas