Derivative of sin(x)

Desmos applet to introduce derivative of sin(x).
Also includes an opportunity to compare subsequent derivatives, as per Marc Renault’s resources (here).

Remote teaching

In the current climate of school closures, I was recently asked to share my experience of teaching from home. My plan was to maintain a little bit of lesson routine and student interaction, rather than create a ‘how to’ video for each topic – as there are plenty of these videos around.

What I use when recording videos

I usually utilise a combination of the following:

    • PowerPoint to display pre-prepared questions, and sometimes answers
    • Visualiser to model methods and demonstrate solutions
    • Screen sharing – e.g. to demonstrate maths graphing software, or similar

These are all uploaded to my school youtube account, via OBS.

Live vs. Recorded

When it was announced schools would close, I informed students of exactly when I would set them work (twice per week), to help them establish a routine. I originally planned to record videos, but the lack of ‘live feedback’ from students, not being able to respond to their questions and not knowing how well they were understanding my explanations, quickly prompted me to try livestreaming. The fact that we were already working towards a routine helped me here.

However, I did not want students to be in a position where ‘attendance’ of the video (live or recorded) was compulsory – I just hoped that it would ‘sell itself’ and students would choose to engage. The setup I opted for (i.e. hosting on youtube) allows students to revisit these videos at any time they choose.

Assessing students’ understanding

I was conscious from the outset that I did not want a two-way video. I did not want students to be further disadvantaged due to issues with technology, nor did I wish to see into their home environments. I do, however, make much use of the live (text) chat alongside the video in the following ways:

    • It is an opportunity for me to assess students’ understanding
    • Students will ask questions when they don’t understand something
    • It is also an opportunity for students to ask general questions, as they would in the corridors of school

I need to be mindful that (in this format) I am only responding to the students who are ‘present’ at the time – which is typically those who are more diligent. For this reason, and in line with the rest of the Department, it remains the case that the Hegarty tasks (for Yrs 7-10 and equivalent for Yr 12) are the only compulsory tasks for all students – as I can see clearly what students have done (and understand), and can feedback through these platforms.


Alongside this, I have given all of my students a weekly questionnaire. They know that recording videos is new to me, and I have welcomed their feedback – which has helped my own development.

I have also chosen to only record live videos for the classes who I feel would make the greatest use of this – Year 9 top set, and Year 12. I continue to record, and upload, videos for my other classes, but these are not live.

Pros and cons

The benefits that I have found are:

    • Students definitely appreciate ‘live’ teaching – and the fact it is responsive (and reactive) to their needs.
    • Students also appreciate the fact that these videos are available to view later and they do not need to attend live.
    • Alongside the questionnaires that I have sent, Google Classroom and my responding to students’ questions/comments, I feel this has helped me to maintain some sort of relationship with many students – and will hopefully help when we eventually return to the classroom (whatever form that may take).

However, the drawbacks are:

    • In the very beginning, I spent a lot of time (hours) setting up for one video. This did not remain the case – and I currently spend as much time planning as I would do normally.
    • It probably took me about 4-5 videos to start producing something I was more comfortable with.
    • I am quite happy using technology, but those less so may struggle – my advice would be to practise first, and it is possible to practise privately.
      • My live videos seem to be ‘laggy’ and I have still not managed to resolve this. This is not an issue with the prerecorded videos.
    • If students watch live, I do not know if they watch all of the video. I also do not know which students have viewed the videos at a later stage.
      • It is highly likely that some students have not engaged with the videos. I am conscious that these students must not be disadvantaged further than necessary – hence I must be mindful about the content that is included.

A sample live video is available to view here and a recorded video here.

I welcome comments, advice, or questions, on any of this.


Responding to a tweet from Dani Quinn:

My preferred introduction would be to show the following frequency table, and subsequently ask students to represent this information in a diagram.

Age Frequency
5 ≤ age < 15 10
15 ≤ age < 20 10
20 ≤ age < 30 10
30 ≤ age < 60 10

Specifically, the frequencies are equal, while the class widths vary.

Students develop an understanding of the limitations of a frequency diagram, and we have a gradual discussion, using the following as a guide:

Histograms have a number of uses relating to visually indicating the distribution of the data (e.g. skewnewss). However, they are not the best tool for other tasks (e.g. identifying frequencies).

Students have rarely (conciously) encountered them at the point that they are first introduced in the classroom, and often struggle to underhstand their purpose.

To me, it is very much one of Dan Meyer’s:

If [x] is aspirin, then how do I create the headache?

With histograms being the [x] to the headache that is an appropriate visual representation of the frequency table.

The toys and the pram

I don’t usually describe my training runs in this much detail, but tonight’s went something like this:

I started off wanting to throw all of my toys out of the pram. I was lining them up, and they were teetering on the edge, but none had been projected at this stage.

I began discussing the reasons why, while JN listened carefully and reminded me that if I threw my toys out of the pram, I would only have to go and pick them up myself. Not wanting to do that, he helped me move them to a much safer position where there was a much smaller chance of them falling.

As the run progressed, one of the toys seemed to stand out from the crowd. It was somehow better than the rest; I probably wouldn’t mind picking it up.

So we spent the remainder of the session discussing the best strategies for throwing it. How far should I throw it? Where? When?

I knew the answer once the run was complete*.

So, if you want free fish and chips for lunch tomorrow (Saturday) and/or Chinese takeaway for dinner, let me know asap**. Seriously, I don’t like to see food go to waste.


*Thanks JN
**I’m only paying for one (it’s the rules), so am operating on a strictly first-come, first-served basis.


Why d’you have to lie? Should’ve realised that you should’ve told the truth.
– John Lydon (Johnny Rotten, Sex Pistols), 1977

Here are some of my early thoughts regarding the first part of Lance Armstrong’s interview with Oprah*. However, first of all, you might like to view this montage of his greatest doping denials, courtesy of msn now.


Video has since been removed.

He has now publicly admitted to deliberately taking performance enhancing drugs since before his cancer diagnosis. Aside from the usual implications that this might have, there are more concerns in this instance due to the amount of success Lance has had – i.e. 7 consecutive Tour de France wins.

Indications suggest that these drugs could have caused (or at least enhanced the seriousness of) his cancer, which nullifies the fairytale of a cancer defeating Tour de France champion. Whatever the good that comes from the Livestrong charity, its origins are now tainted.

Lance refers to his current predicament (the ‘truth’ being unravelled) as being ‘out of his control’. The only other time he claims to have felt like this was when he had cancer, stating that he knew he was going to win the Tours. Surely part of the excitement of sport is in not knowing the outcome, and he would have been better applying his determination to succeed somewhere else, in business perhaps.

When asked about Betsy Andreu (former team-mate Frankie Andreu’s wife), who claims to have heard a confession in 1996, Lance refuses to answer. He also limits his comments regarding Michele Ferrari (the Doctor who supposedly helped facilitate the drugs and transfusions). There is still too much that he is controlling about what we know.

When asked about his donation to the UCI, he states that they were low on money, so approached him for help. While this seems possible (if the amount of speculation surrounding corruption in the UCI is true), it requires further investigation as it is certainly not a satisfactory response.

To gain the trust of someone who has lied will always be difficult and this instance is no different. There are currently a number of theories circulating, such as WADA reducing his lifetime ban to 8 years… and he has said the last time he doped was in 2005 (do the maths). I just hope that his genuine motive is for the long-term good of the sport.

This all needs resolving so that the sport can potentially move forward. No sport is without any controversy, but the UCI needs to ensure that the entire truth regarding this matter is discovered, so that people can regain their trust in cycling as a whole. Complete honesty (without secrets) from all parties is the only way this can happen.

However, I am also concerned that there is fairness. While Lance was the one who cheated most successfully, with the biggest rewards, he was not the only one to have cheated. Please do not reward Lance, or any of the teammates who testified against him, or anyone else associated with this mess, as it will not discourage similar behaviours. Giving some of those teammates 6 month bans during the winter is nonsensical. This is the only way that sport can become clean in the future.

*My comments are based upon the transcript from the bbc, having not yet seen the interview.

Sitting over here on Parchmann Farm

It was a typical Saturday morning, with a 6.30am rise for the scheduled long run. For the last six years*, the significant majority of the long runs have been completed in an area that is labelled as Thetford Forest on some maps, but is actually much closer to Swaffham. There are many different routes that can be run here, and it is possible to go for well over three hours without covering the same ground twice while being on the (tarmac) road for less than five minutes. Perfect marathon training.

Today’s run was the same as it had been for the last couple of weeks; a straightforward 90 minute route that forms the core part of the longer runs when the duration approaches 3 hours.

I had run off ahead of the group with CP and emerged from a wooded area to join a section of gravelled track. The track ‘dog-legs’ left but, as we joined it, I noticed a Land Rover parked up facing directly towards us. We turned left about 100m ahead of the vehicle and noticed that it had begun to move in our direction. Fortunately myself and CP are not the slowest of runners but, despite unfavourable driving conditions, we are both unable to outrun a vehicle.

Its path changed as we turned the corner and there was now no question that it was heading for us. Our heart-rates increased together with the speed of the accelerating driver. It felt like a cross between Duel** and a game of ‘chicken’. Realising that aiming for us was naïve (just ask Zeno), it made a beeline for our path and tried to intercept our run.

The vehicle stopped sharply a couple of metres from us. A young farmer wound down the window and started shouting “You’re not allowed to run here. It’s private. The signs say ‘keep out’. I saw you here the last few weeks. And there were some others too.”

I figured we weren’t going to win this argument at this moment and we couldn’t realistically continue, so I played dumb.

“Oh, sorry” I said “where should we have gone?”

A brief dialogue soon established where he wanted us to go; as far away from his game shoot as possible.

A quick retrace of our steps to inform the rest of the party that continuing along that route was unwise (for today) and that we should find an alternative. But not before I carefully examined his signage hypothesis.

There was not one sign from the direction we had run. All along the route he had described, there were no signs. Paths leading back to the track had no signs. The devil in me proceeded to investigate the far side of the track, where there was a single hand-made sign that read “private road”. There was not a single other reference elsewhere. And nothing implied the “keep out” that the farmer had suggested.

I look forward to running there again soon to see if the signs have changed. I suspect I will be disappointed, but at least I will have more ammunition for a future argument.

*more than 150 runs since summer 2007
**Steven Spielberg’s early film is highly recommended

2012 annual report

These images represent my year of running in 2012.

Distance Speed


Following my graphical analysis for the last two years (see 2010 and 2011), I have repeated the procedure for 2012.

Some key features that are not apparent from the graphics:

  • I recorded 19 days ill or injured (19 days were also recorded in 2011)
  • Each running day* averaged just over 10 miles (10m in 2011) at an average of 7 minutes 42 seconds per mile (8mins in 2011)

The year was relatively quiet, but I was particularly pleased with a two month period (22ndApril until 23rd June) when I raced three marathons and completed a 50 mile run – the furthest distance I have ever run in one go.

The data suggests that I achieved all of the targets I set myself last year (see targets), which basically focused on an overall increase of speed.

One aspect I would change would be to start marathon training at a later stage. I trained hard through the summer (July and August), but seemed to lose motivation through September. I therefore plan on starting training for my next marathon closer to the race date.

I have already entered four marathons for 2013 and am thinking about entering more, particularly mountain marathons. These are therefore my targets for the year ahead:

  • Increase the amount of hill training that I do (including races on the hills)
  • Try to make one session of each regular training week (excluding the long run) mountain or marathon related – e.g. hills, tempo, long intervals or similar
  • Make recovery a more focused part of my training – i.e. make a concerted effort to improve my eating and sleeping habits [I expect this to be harder than it sounds and am not yet sure how I quantify improved eating – all suggestions are appreciated]

Here goes…

*I ran twice a day on seven occasions

Endurance workshop

I recently attended a marathon training seminar held by Nick Anderson (NA), a level 4 UKA coach and nutritionist. He has worked with a number of elite athletes from 800m through to marathon distances. Here are some of his comments that caught my attention.

Training triangle

Training triangle

A successful training regime requires patience, planning and progression. However, consideration must also be given to rest and nutrition.

Food should be eaten regularly, before becoming hungry and, where necessary, by snacking. Becoming hungry and thirsty (signs of dehydration) can have a negative impact on training for the subsequent two days.

Between 7 and 9 hours of sleep each night were recommended, but certainly more than 6. Professional athletes may sleep for more than 12 hours in any given day.

If rest or nutrition are inadequate, improving these will have a greater benefit on performance than changing a training regime. These can also be significant causes of illness, which will have an even greater impact on training – through an inability to do so.


The usefulness of training diaries was emphasised. My own training diary has evolved over time, and documents approximate distance, time, effort, trainers and ‘notes’. I don’t record all variables, such as weather, unless they had a particular impact on that run (e.g. blizzard conditions). I have kept this in Microsoft Excel for almost 10 years and it has been hosted online since 2011. Download it (from if you are interested and adapt it as you require*.

Heart rate

Regularly monitoring heart rate can help detect the imminent onset of illness so that adjustments can be made to my training. A slight increase (a couple of beats per minute, bpm) might be evidence of a hard training session, but a few bpm is more significant and a rest day would be advised. Adding this to my training diary is on my to-do list.

Wearing a heart rate monitor (HRM) would allow this to be monitored while training. I choose to compare my training to the large bank of similar previous runs, but a HRM would certainly make detecting performance changes more responsive (and provide me with more data).


In any marathon training schedule, the really crucial time period is between 9 and 4 weeks before the race. It takes about 10 days for a training session to have any impact**, but longer (4-6 weeks) for a sustained program to have a noticeable impact. These six weeks are where the training counts and must be marathon specific. I have been thinking about this fact for the last couple of years, after showing signs of fatigue (mental and physical), by trying to train ‘ahead of the curve’. Consequently I have been planning to adjust my training accordingly – by starting to focus from early February, rather than mid December.

Training should be done before breakfast where possible. If NA’s nutritional advice has been followed, enough food should have been eaten the day before, so a 90 minute run should be achievable. This has the benefit of training the body to burn fat, the reserves which the body has to use during a marathon, as opposed to glycogen, which is in short supply during endurance events.

I wonder if a variety of training times are preferable – before breakfast, after breakfast, or at other times. I wouldn’t dream of running a race without breakfast, so wouldn’t want running after breakfast to surprise my body.

Reference was made to Moses Kiptanui (past 3k, steeplechase and 5k World Record holder) who always trained to be in personal best (pb) shape for a 10 mile race. This would approximately replicate threshold pace, and an intention to be able to run well at around lactic threshold.

More specific training advice was in line with previous beliefs. This includes having three key marathon orientated training sessions per week. Sacrifice the club run if it’s not specific enough – adapt it to make it more suitable, or be selfish and avoid it altogether. Have an easy week every three or four weeks; a tapering week before a race counts as an easy week. Run a few strides at the end of a session to focus on maintaining form and technique when tired.

Cross train if injury prone. Work on core stability. Good basic exercises include 1-leg squats, press-ups and seated row.


Reference was made to current technique advice resulting in a reduced difference between heel and toe heights in trainers (towards barefoot technology). Lean forwards, so weight is on the middle of the foot (rather than the heel). This should result the foot landing underneath the body and not in front.


NA suggested that carbo-loading was unnecessary if his nutrition was adhered to… but he does have a product to sell.

*All suggestions and improvements are appreciated
**Nothing can be done to improve marathon performance in the last 10 days before a race

Thanks to HM for saving me from taking notes

Buying what I’m told

It is difficult for me to write about my next challenge at present.

The short story is I have been denied permission to take part. The long story is that obstacles are there to be overcome.

The somewhat longer story is that the details behind the significantly abridged versions make discussing the nature of the obstacle and the challenge itself rather difficult – some might suggest a challenge of its own.

Furthermore, I know that I will regret any excuse that I make in order to not take part. To this end, I have my first run specifically with the event in mind. It will give me opportunity to run in the hills, carrying kit and navigating.

Thanks in advance go to CV who will be supporting me on this.

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