Notes on Starting Teaching – Week 3

This week I got my first dose of the immense, crushing kind of feeling you get when you realize that your class have little to no idea of what you’re talking about – I gave them a quiz. I bet my students had the same kind of feeling as well – none of them managed to answer the fairly easy questions, poor things.

After two weeks of dealing with a fairly passive class, and having little to no feedback of their understanding of my classes, I decided to embark on some continuous assessment. I’m also trying finding out if students more willing to participate if there are marks at stake. I designed three activities, one individual, one small group and one whole class discussion. I ran out of time to do the small group activity, but we did the other two.

Individual Activity

Anyways here’s the sequence of events:

1. Announced in class and in our online learning system that there’s going to be a quiz during the next class on sampling distribution.
2. Generated 200 random 9-digit numbers (random.org) and counted the number of numbers with a digit recurring beside itself (976511234 has ‘1’ recurring beside itself) – there are 112 out of 200 of these. (56%) Got the basic idea for the recurring digit test from a book.
3. In class, discussed briefly if computers and humans are capable of generating truly random numbers by themselves. (These are IT students at foundation level.)
4. Asked each student to, as randomly as possible, write down a 9 digit number. Out of 74 students, 9 wrote numbers with a recurring digit. (12.2%)
5. Explained how random.org uses atmospheric parameters to generate random data to affect its random number generation in order to be truly random, and showed them the numbers generated earlier.
6. Asked them three questions as a quiz:

Propose which statistic we have discussed can most accurately be assumed to describe the proportion of all truly random numbers that have a digit appearing beside itself. Why?

Using your proposal above, what is the probability that in a sample of random numbers, you will find the class’ proportion of random numbers generated that have a digit appearing beside itself or less?

Based on the discussion and the result of your calculation above, can humans accurately ‘behave’ randomly? Why?

To help them:

• I circled in bright red the only two statistics we discussed.
• They were free to open their textbook (or anything else, for that matter).
• I told them the page of the chapter (sampling distribution) that have samples of this question.
• They were free to discuss it among themselves.

Two out of 74 students decided that 56% most closely describes the percentage of random numbers with a recurring digit. TWO. No one figured out that they could’ve just filled in p=56%, p(hat)=12.2% and n=74 into the equation in the suggested chapter to get the probability. Half of the students answered 12.2% as the answer to question 2, showing that although they get what proportions are for, they cannot yet extrapolate it to the concept of sampling distributions. And a lot of them reasoned at length for the third question without basing it on the results of their calculation.

I’m guessing the problem here is a combination of these:

• I covered sampling distribution before a 1 1/2 weeks pause for CNY – they’ve forgotten it.
• They’re waiting until the mid-trimester examinations to study the topic.
• I’m not making enough sense in class.

I’m going to try switching it around a bit – doing a quiz-like activity immediately at the end of a topic to see if they improve any.

Class Activity

I got the whole class to discuss about gathering height and salary information from lecturers to do a local survey similar to the one found here. Purposely chose this topic since that they have to deal with how to obtain sensitive information, and naturally leads to discussions about anonymity, privacy and so on.

The idea is to give them an immensely easy way to score – the whole class gets the same score, if they cover the 8 things important to running surveys and gathering data in their discussion. I prompt them from the side of course. They picked up 5 out of the 8 matters. About 10 students participated actively, they rest stared into space. Yep – even when there’s marks at stake. Suffice to say, not going to do this again. Heh.

Assessment

At the end of the day, I find that my wish to innovate my teaching methodology for the course is severely limited by the assessment method, which is out of my control – 70% mid-trimester and final examinations. The usual sit down, closed book affair. Even the 20% assignments are more exam-oriented questions that they are to do and submit. It seems to be common practice in math courses, from my own experience. The only purpose of giving an assignment of this kind, it seems to me, is to ensure that a few dedicated students actually do the questions, and that the rest copy it. Does copying solutions constitute learning? (Maybe it helps one memorize the format of specific math solutions?)

The overt pressure I feel as the lecturer for this subject seems to be to teach them how to solve these examination questions. In a way, their final examinations is both a test for them, as well as myself. Individually if they score well they get a good grade. Collectively if they score well, it is taken as an indication that I have taught them well. And at that point, what would I have taught them exactly?

The individual activity I did above is an example of an ‘unnecessary’ activity for the purpose of teaching them how to answer examination questions. That activity involved a little bit of analysis and even synthesis, whereas they only need knowledge, comprehension and application to answer examination questions. To teach the latter three, all I would’ve done is to present the question, “Given that 56% of all random numbers have a recurring digit, calculate the probability that a random sample of 74 numbers have only 9 numbers with recurring digits,” and given them the solution. It takes only 20 seconds to come up with, and the chances of them answering it correctly in a quiz with an open book is significantly higher.

The activity I conducted in class on the other hand took a few hours to prepare – finding the idea, generating the numbers, counting them, coming up with a good way to phrase the questions etc. Yet the easy one – examination questions – is what both I and they will be assessed on at the end of the semester. Why then, should I bother teaching them the former? Not that I didn’t realize all this before, but this is the first time I’m experiencing it for myself.

It is frustrating because statistics is such an interesting subject. Imagine if we harnessed the power of our statistics undergraduate students in mini studies and projects for the past ten years, we would have correlated thousands of pairs of statistics in the university by now!

In a limited-circulation piece I wrote some time ago, I said:

What our undergraduates are actually picking up in the vast majority of subjects is a form of lexical analysis and pattern recognition – they are studying the forms examination questions usually take, and they practice the solution to these questions in order to later answer their examination papers. Every chapter becomes the source of a few possible examination question types, instead of a slice of knowledge.

Even now as a lecturer, recognizing this, I feel that I am helpless to change it.

For now.

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