Tag Archives: Mathematics

Probability problem of the day

Fantastic probability problem – as told by a genius colleague!

100 patient people are standing in line waiting to get on a plane. All of them have their tickets – except the first person, who has left theirs at home. They board the plane in the order in which they have lined up.

The first person boards the plane, and since they don’t know which seat is theirs, they choose any seat. There are exactly 100 seats, so they have a 1/100 chance of getting their own seat.

The next person boards the plane, and if the first person is sitting in their seat, they randomly choose another seat. The person after that boards the plane, and if their seat is already taken, they also choose another seat.

When the final person boards the plane, what is the probability that they will be sitting in their own seat as assigned to them on their ticket?

Think about it…then give it to your maths classes!

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Yes I still want to be a maths teacher

I know maths is not the most popular subject in the universe.  However, I have decided that I am completely determined to become eligible to teach it as a second teaching area.  Why?  There are a few reasons…

I was very lucky at the beginning of high school to have a wonderful maths teacher.  I don’t think I recognised it at the time, but I did recognise the calming effect she had on me, mostly due to the absolute control she had in the classroom.  It was the way she did it that was the most influential – I don’t remember her ever raising her voice, but she managed to command respect from her students, and communicate the high standard of behaviour that she expected of us – along with the high standard of mathematics!  The fact that this was in a country high school in a very small town (which has had a declining population for many years as well as a high proportion of Indigenous students) I think speaks for the quality of teachers that can be found not only in public schools, but the quality of education that can be found outside the major cities.  But that is another topic.

My history with maths is not great.  I think that is true for a lot of us though – we all go through life with a little bit of ‘math anxiety’ and this even translates into the classroom (which is my point!) – I have seen teachers so absolutely petrified of maths they refuse to teach it casually, or cover a maths class if a teacher is away sick.  I know their fear of maths is not their fault, however don’t you think that as teachers, we are best equipped to try and overcome what is essentially our own fear of learning(!), and think about the effect math anxiety in a teacher would have on their students in the classroom!

I was held back at the end of primary school.  The reason I was given at the time was that my mother couldn’t decide where to send me to high school.  But in retrospect, it was a very bad decision.  I think the teachers that were involved in my education at the time should have tried to make more of an impact on my mothers’ decision, and in fact my father told me years later that only a couple of weeks in to my second round of final year of primary school it became blatantly obvious to him and everyone else that I should have been in high school.  Through that repeated year, I borrowed a high school maths text and began working my way through it.  My teacher discouraged me from doing so, saying ‘but you’ll get bored next year when you’ve already covered the work’.  There are many things I have to say about that particular attitude, however I won’t – only that it is one that I won’t be having!  But she was right though – I did get to high school and DID get bored with maths, coming first in the year with little to no effort (I did the work, but it didn’t stretch my brain!).  Acceleration was talked about, but the school was very resistant I’m disappointed to say, so things remained as they were, for a while.

I got halfway through high school and my mother once again had an idea.  She decided that in order for me to make up the lost time from repeating a year, she would find a school that would skip me a year.  In an important year of high school.  Great – it wasn’t an issue in any subject except MATHS.  As you can imagine, by the time I got through most of high school it wasn’t the content that was bothering me, it was the fact that I needed the background knowledge in order to move on to the next topic with ease.  Revolutionary thought, right??  So I entered my final years of high school having skipped a year of content, and all it did was confuse me and make me miserable.

So after almost a year, my dad enrolled me back in my former school, and I spent the rest of the year trying to catch up in just one subject – maths.  I did the best I could, and by the time I did my final years (again), things were starting to make sense for me.  So I began to enjoy maths more.  Says a lot for teaching appropriate content, checking prior knowledge, and targeting the zone of proximal development, doesn’t it!

It was during this time that I saw my first high school maths teacher again, for the last time.  Out of the kindness of her heart she helped me catch up during the holidays.  It was then that I found out that her content knowledge wasn’t as great as I thought it was – it was her pedagogy that was outstanding.  She was able to teach things in a way that aided understanding, and gave students confidence.  Or maybe that was just me.  Anyway, that was the last time I saw her.  I found out during my time at uni that she had passed away with cancer.  I am extremely upset that I didn’t get the chance to say goodbye.

What have I learnt from this?  I think the best teachers are sometimes the ones who may have struggled with the content themselves, as they are more able to identify with the students who are also struggling, and are hence able to explain the content better.  Being a genius is certainly not a prerequisite for being a teacher.  Knowing how to teach the content effectively is.

What else?  Maths is not and should not be an all male domain.  Women have much to contribute.  Some women just need a little time to develop the confidence needed.

I have enrolled in a postgraduate diploma starting next year to get the maths subjects I need to be an accredited maths teacher, as well as music.  I have tried university level maths before, and failed.  I am doing this for myself as much as I am for my future students, but I think we will all be better off because of that.