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> Maths teaching

<< 8 / 2007 10 / 2007 >>

The Monty Hall problem

2007-09-22 11:46:00

My white board, with decision trees.

For one of my school assignments I was asked to write three class openings for the subject of statistics. The object of a class opening is to draw in the students, to capture their attention and to motivate them.

The opening I presented at school involved the McNuggets problem (aka the Frobenius problem). It was well received, though most of my class mates thought it better suitable for a class on analytical math. I tend to agree with them now.

One of the other openings I've designed involves the famous Monty Hall problem. The one that involves a gameshow, three doors, two goats and a car. Ring a bell?

Because this problem is so counter-intuitive it tends to throw a lot of people off. Their gut instinct tells them that the chance of winning a car (after revealing one of the goats) should be 50%. They are unfortunately incorrect.

Before we continue, some of you may enjoy a snippet from the TV show Numb3rs. The character of Charlie Eppes doesn't explain the solution very clearly, but does make a nice job of explaining the problem.

Numb3rs-MontyHall.mov

I tried to come to the proper solution by myself by using a decision tree (boom diagram in dutch). It took me a while, but I got there :) My tree looks a bit different from the one Wikipedia shows (linked above), but that's because I use two trees instead of combining them into one.

Going from left to right:

* The original tree, unconstrained, given that you get two choices.

* The gameshow host takes away one of the goats. He asks you whether you want to switch doors.

* The decision tree, should you stay with the door you chose.

* The decision tree, should you decide to switch doors.

The red X-es show the option taken away by the host. The purple X-es show the option taken away by your own choice.

Yes, it's counter-intuitive, but switching doors after having one goat revealed IMPROVES your chances. Instead of having a 1:3 chance, you now have 2:3! Nice!

And this is why I think this problem would make a nice opener for a high school course on statistics. It stumps the kids, makes them curious and them amazes them :)


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College curricula are -also- mixed bag

2007-09-19 07:35:00

About a week ago I remarked how college books are mixed bag. Some of them seem really good, though others are almost crap.

Well, the whole mixed bag deal also goes for the course curricula themselves apparently. On Monday a big discussion broke out during SLB1 about the courses' contents. Marjan thought there was too little theory, Karin though teaching by examples is great, Wouter though the maths was too easy, Badegul thought the maths were too complicated. And here I was, loving all of college, thinking everything's just right. (transcription)

The points me and Hans tried to make were these:

* College has to cater to the lowest, common denominator. During their first year they have to take a whole bunch of -very- different people and ready them for the following years. You simply can't be very specific in your teachings during the first year.

* Isn't college about going out and finding the answers for yourself? If an assignment uses terms that you don't understand, shouldn't you go investigate? Or at least talk to the docent?

At least it's good to know that I'm not the only one still adjusting to college :D


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Course books: they're a mixed bag

2007-09-11 19:33:00

How is it possible for one book to be both highly educational and (IMNSHO) absolutely craptacular at the same time? Case in point: Lesgeven en zelfstandig leren by Geerlings and Van Der Veen.

This course book covers basic didactics of teaching at the high school level. It covers all kinds of interesting subjects and I feel that there's a lot for me to learn.

Unfortunately the book's laced with three things that irk me.

1. To me it seems that the authors often skim over stuff that could be very interesting. Instead of taking an analytical, or academic approach, they fill chapters with examples and stories. There's nothing wrong with examples, but neither is there with pure psychology.

2. The book feels outdated and like it was written by cuddly-fluffy psychologists. The kind who want to pamper kids and feel that they should be let free to explore their youth and possibilities. *cue Care Bear song* Seriously, I'm all for letting kids discover what they can and can't do, but I believe that in the end kids also need structure and hierarchy. Besides, the original print was written in the eighties D:

3. Their writing is atrocious at times. At the beginning of chapter five there's a sentence that runs for a full -ten- lines! It runs a hundred and thirty words in length! What the fsck were they thinking?

And then there's pure genius like this:

In reality, assessing the beginning situation [of a student] is done based on 'experience'. This is a conglomerate of pedagogic-didactical knowledge and intuition.

/me shakes head

/me goes back to studying


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What? I've already got school results and grades?

2007-09-11 12:49:00

A modded screenshot of Osiris

Well, that was a surprise! I was dicking around in Osiris, the online student management toolset at HU. Enrolling in a few classes, signing up for tests and term papers, just generally looking around and exploring.

After clicking the Results button I was greeted with a big list. But how is it possible that I already have grades?! I just started school a week ago!

Then I took a closer look at the dates. Apparently my student number isn't the only thing that carried over to my new college enrollment ^_^


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Slugging through my homework

2007-09-08 19:10:00

Wow, this is a lot of work :)

Yesterday I raced through a large part of my first dossier assignment for Statistics 1. The didactical part of the course, that is. I'm about halfway through that assignment, though what remains will take more effort than what I did yesterday.

How do I know this? Because the second part of that assignment requires that I work through each maths assignment that I picked for my report. And judging by today's progress through the other part of Statistics 1 (the real maths), I'm going to need a long while.

My homework for Monday said that I'd need to study paragraphs 1.0-1.3 and 1.4-1.6. Sounds rather simple right? Well, it looks it too, since each paragraph is only two pages. However, looks can be deceiving since so far I've needed about an hour-and-a-half per paragraph! Ouch!

Talk about underestimating the workload! Tonight's gonna be an all-nighter.

Luckily, productivity blog LifeHacker provided me with something useful today! They posted about the why and how behind power naps. I took one this afternoon before studying and I'll take another one around 20:00.

EDIT:

Meanwhile, the cat's asleep on her pillow. She's actually snoring! That's so cute! <3


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Getting my Canon scanner to work (n650u on Mac OS X)

2007-09-05 21:45:00

Please let the record state that Canon are a bunch of f-ing toolboxes when it comes to their scanners. More specifically, when it comes to using their scanners in Mac OS X. Some of their older models are completely unusable, although there are tricks, rituals and voodoo that may get you varying results.

I've fought a few times to get my N650u to work.

I need to scan some stuff for school. Since I cannot drag along my Powermac (which runs the Classic Canon tools) I've fought my Macbook for an hour or so tonight. I tried all the crap that's out there, but Canon's software's crap. So I caved in and bought Vue Scan. Thankfully it's come down in price since the last time I wrote about it.

At least I can use the bill for VueScan to get a tax write-off, since it was a purchase made for school. *sigh*


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Holy shit! That's a lot of work!

2007-09-04 22:14:00

A screenshot from Schoolhouse 2

Holy crap! I just entered all of my homework and such for the following few weeks. The screenshot to the left is my current ToDo list in Schoolhouse 2. You probably can't see it very clearly, but it boils down to the following.

Due in one week -> Read about five chapters, make all relevant assignments.

Due in two weeks -> Read about six chapters, make all relevant assingments. WRITE FIVE REPORTS!

Crickey!

Now I'm off to bed. For now I'll stick to a regimen where I do schoolwork both before and after my normal, sysadmin work. So there's a bit in the early morning and the rest is between 1900 and 2200.

Like I said earlier today: I've good reason to be nervous!


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What a day! My first day at school

2007-09-04 10:34:00

Satelite view of my school

Wow! I'm feeling exhilarated! This whole going-back-to-school thing rocks ^_^

Yesterday was my first day at Instituut Archimedes, following classes from 12:00 until 21:45. As I mentioned earlier, this semester's roster entails four classes: Statistics 1 (math and didactics), Study Guidance and Math didactics 2. I'm very lucky to have a break between 18:00 and 20:00, giving me time to get started on homework and have some dinner.

The folks at school all seem quite nice. The teachers are cool and usually in their thirties. My classmates range between 21 and 56, though there's one daunting thing about them: over 80% of them are already in education. O_O

So yea, that's a little intimidating. Being one of the few who have no teaching experience whatsoever and who don't currently hold a teaching position. That second part is really important for classes that need me to do project in a teaching environment. Where the heck am I going to find a bunch of thirteen year olds, just to try some teaching methods on them?!

Aside from the exhilaration, there's also nervousness. I'd already mentioned it before, but it's still there. The feeling that I -know- that I can fail at what I'm doing here. The feeling that I'm treading completely new ground. The feeling that I'm getting in over my head. Mind you, I'm still loving it, but that doesn't mean I don't feel the fear :)

About the workload... I was prepared for (and expected) a lot of work. However, it seems that I underestimated things a little. Aside from working 32 hours a week for Snow I will also need to spend about 40 hours per week to earn my ten credits this semester. The basic math: 1 ECT equals about 28 hours of work. Three of my courses are good for hard credits: 10 ECTS in total. So in about seven weeks I'll have to shift 280 hours of work. Ouch! Goodbye social life! :)

Ah well... First, let's see how hard things really are.

In the meantime Marli is a great value to me, giving me loadses of support! The fact that she's so proud of me and has faith in me really means a lot!


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Well, today's the first day of school!

2007-09-03 07:27:00

Wow! Today's the first day of school and it already feels rather different! I went to bed around 2130, read for an hour, then slept like a brick. And I woke around 0700, instead of the usual 0600 on workdays. This actually feels rather nice! Combine that with yesterday and I'm feeling rather relaxed!

You see, yesterday I was feeling really worked up because I hadn't studied yet, nor done any of my maths revision like I said I would. Too much time had gone into this site's redesign and after that I was just too busy socially. Of course, getting worked up in this case was counter productive: how much could I do in just a few hours?

So instead I decided to follow the sage advice of my wiffums and some of my friends: I relaxed. After taking Marli to work I went back to bed, read a lot, slept a bit and chomped away half a tube of Pringles. So yea, it may have been a "horrible" evening, but IMHO it was "great".

I'm sorry that I had to blow of Peter's invitation for a walk though. He was reaching out to me, but I didn't go. I'll go and visit them this week...


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