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Tutoring in your own home, at your own convenience

Today's schooling typically doesn't allow any room for individual learning, which means that students who don't suit the pace of the whole class can fall between the cracks. If students aren't achieving at the level they are capable of, their learning can stall, leading to boredom and frustration. Their confidence can suffer and they won't enjoy school as much as they should.

I can help. I offer personal tutoring in a range of subjects for NCEA and Cambridge International Exams, and can provide students with the skills and confidence they need to achieve their potential.

I'm based in Auckland and will come to your home at a time that suits you, for maximum convenience and maximum learning. Because the home is a familiar environment, it's where the student is the most comfortable – this is an important part of enjoying learning.

With regard to the October 2021 vaccination directive for home-based educators, I am fully vaccinated and have had a second booster.

Ian Mander.





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Treasure Hunt

After twelve and a half years the treasure remains unfound.



28 July 2022 – Five "and"s in a row

It's an old question: How can you have five "and"s in a row in a sentence that makes sense (semantically and syntactically)?

See News page for solution.

I covered it with a student yesterday, and we started looking at the sequence of numbers that can be formed by recursively performing the same action (or making the same mistake) required to make the sentence. The numbers increase quite rapidly: 1, 5, 21, 85, ...

I figured out how consecutive terms are related to each other (Tn = 4Tn-1 + 1) – in the process confirming I had 85 correct – then looked it up in The On-Line Encyclopedia of Integer Sequences. It's sequence A002450. I note the number of "and"s in sentences is not listed as one of the applications of the sequence.

22-02-2022 – Present situation

Sorry, my schedule is now reasonably full, so I'm somewhat unlikely to be able to accept new students. However, I do have a waiting list which every so often I manage to whittle back a bit, so enquiries are still welcome.


31 July 2021 – the first international vaccination campaign

In 1803 the first international vaccination campaign was launched (literally – they used a ship) by a Spanish physician, Francisco Javier de Balmis, using cowpox to vaccinate against the deadly smallpox virus spreading in Central and South America.

Smallpox was highly contagious and had up to a 52% fatality rate, which is bad enough, but diseases don't just kill. In 18th century Europe, smallpox killed an estimated 400,000 people a year, and caused a third of all cases of blindness. Survivers were left badly scarred.

The vaccination technique discovered a few years earlier by Edward Jenner was effective, but cowpox only lasts in a test tube for 12 days, and there was a big ocean to cross.

To transport the cowpox virus to South America, de Balmis took 22 orphan boys, aged 3 to 10, selected by their carer and nurse Isabel Zendal, who insisted on accompanying them. (She also took her 9 year old son, so maybe only 21 of the boys were orphans.) The children were used as live incubators of the cowpox virus. Every ten days during the voyage, the virus was transferred from the pustules of two infected children to two healthy children, thus maintaining an unbroken strain across the Atlantic Ocean, visiting the Canary Islands, Puerto Rico, and Cuba on the way.

This may seem a somewhat barbaric way to transport a virus, but it was certainly the most practical method at the time. Cowpox was not life threatening, smallpox was.

The boys were left in Mexico, and from that country in 1806 a further 26 boys, aged 4 to 14, were collected for de Balmis' onward trip across the Pacific Ocean to Macau, Canton in China, and the Philippines. Meanwhile, José Salvany, deputy surgeon of the expedition, had gone south to what is now Venezuela, Panama, Colombia, Ecuador, Peru, Chile, and Bolivia. The vaccine was also carried north as far as Texas.

On his return journey to Spain in 1806 de Balmis offered the vaccine to the British in Saint Helena, in the middle of the Anglo-Spanish War (1804-1808).

As this article explains, "By the end of the campaign, about 300,000 people ... had received the vaccine for free." The mission was a success, and an extraordinary achievement.

Smallpox was officially declared to be globally eradicated in 1980. As for vaccines, we have it much easier now. Vaccines can be transported internationally without using orphans, they are safer than they've ever been, and it's easy to get a vaccine. Vaccines work.

By the way, Edward Jenner coined the words "vaccine" and "vaccination" in 1796 from the Latin for "of the cow". Isabel Zendal was recognised by the WHO in 1950 as the first nurse to take part in an international mission.

More News

See the News page.

Believing in God costs you nothing if you're wrong, and wins you everything if you're right.
– Blaise Pascal (paraphrased, known as Pascal's Wager), who aged 12 studied geometry secretly because his father had forbidden it.