November 21, 2011

Report on peer–teaching of statistics

I opted to "torture" a previous university classmate (whom I shall give the cognomen "Alberto") with the main points of our previous session on statistics for summative assessment. Naturally, consent was garnered beforehand! I could see no fault in how Steve had structured the session and so I decided to take the same organisational approach to my mini-session (which was carried out through Skype). Although Alberto (God, I'm regretting using that name already!) had heard of the majority of the terms, he explained how he was no longer in tune with what they meant. Out of sheer laziness, when explaining functionalities of box & whisker plots, I used those in Steve's PPT presentation. Alberto demonstrated an accomplishment of the subject and appeared to take in the concepts of frequency diagrams, grouped frequency distribution charts, and cumulative frequency tables and graphs with reative ease. The notion of standard deviation and how to calculate it also seemed to be no difficult tasks for Alberto (much to my delight, as my throat was getting a bit dry at this stage!).

Upon completion of the lesson, I took the liberty of conducting a short oral summative assessment (I say "summative assessment" whereby one could interpret it as formative assessment since the "student" received immediate feedback from me as to whether a particular answer was correct and, if not, why). Alberto made only one mistake on differentiating between the mean and the median, but scored perfectly on all other questions.

This exercise was useful for me in that it refreshed my memory of the contents covered in Steve's session on statistics. Alberto also expressed pleasure in regaining knowledge of some of the core concepts within general maths, but admitted he was happy to leave for dinner!


November 16, 2011

Impacts of Summative Assessment (hw for session on Nov 19)

This comes very last-minute, as I've been devoting all my available time outside of my personal life (which has been somewhat in turmoil recently) to another assignment. Consequently, the following contributions are not particularly academic in that they are personal accounts (in particular the first one) rather than discussions of themes, concepts and articles already established in the literature. I apologise for this shortcoming. Without further ado, then...


Entry 1: Impact of Summative Assessment on Motivation

My first account takes me back to 1998, just before I graduated from the American high school I was attending in Dubai. I had taken the SAT (a standardised test for university admission in the U.S.A.) and scored 960 points (on a 1600-point scale). I suppose you might say it was (and is) used for formative purposes in that it gauges high school students' scholastic aptitude as a means to predict how challenging an academic environment they need or are able to endure. However, it is, by and large, used as a summative assessment, primarily for the reason that it is not and cannot be used for AfL - the greatest amount of detail I can see are the section scores, but not which questions I answered incorrectly nor why they were wrong. Anyway, the general minimum for entry into an American university is (or at least was at that time) 1000 points. At that time, at school, I had an average score of around 90%, so I naturally felt shortchanged when I received my SAT results and couldn't see how the score I had received represented ("summarised") my level of academic achievement. This "motivated" me (motivation generally carries a positive connotation, hence my conscious use of quotation marks) to resit the test. This I did and scored only 20 points higher. So, obviously, the test was very reliable (I hadn't done any additional revision beforehand, which I perhaps should have), but not - so I now believe - very valid. I, thus, sent off my university applications and ended up still managing to get accepted into 6 out of 8 institutions, one of which being Cornell University. If you haven't heard of it, then, so as to avoid seeming to want to brag, I'll just say it's a good university. Anyway, suffice it to say, I didn't go there (one of my biggest regrets) and went to study at a less prestigious university. So, the obvious outcome of my test scores was that they had a detrimental effect on my motivation and on my self-image. And so, it could be said that, instead of (accurately) reflecting my true ability, the SAT, in effect, determined it. I felt I must not be such a capable student after all and wouldn't be able to survive the much higher academic expectations of a more prestigious university. Such pigeonholing undoubtedly occurs every day and people (not just students) who have potential to achieve so much more, are led onto and down another path.


Entry 2: Impact of Summative Assessment on Learning

Summative assessment having an impact on learning appears to be somewhat of a paradox to me, which is why I chose this topic for my second entry. By definition, summative assessment is not for learning; if it were, it would be termed as formative assessment. That's not to say that summatice assessment doesn't and can't have an impact as such; it, as I described above, very much can and does. However, summative assessment, as it is typically discussed in the literature, is a cul-de-sac of sorts in that in that it is an end in itself. As soon as the word "impact" is brought into the equation, it is implied that the road goes on and that learning is in some way shaped or influenced by the assessment, in which case, again, it would evolve into formative assessment. I suppose some of you reading this (if, indeed, there is anyone reading this) will scoff and reject the relevance of this point on the basis that it is only a question of semantics. But, semantics are intrinsic to a discussion on any subject which involves an analysis of the different elements within that subject. For example, there isn't just assessment; there are both different methods and different purposes of assessment. Therefore, drawing a distinction between summative and formative assessment is important. The question in this case is: Can we really draw a clean line between summative and formative assessment? You might retort: well, yes, of course - a case of a quantification of learning is an example of summative assessment while a quantification for learning is an example of formative assessment. But - a point which, I believe, had already been brought up before in one of our workshops - a formative assessment can mutate into a summative assessment and vice versa. Psychology and the effects of assessment on students' perceptions and attitudes play a very central role in such situations. For example, have you ever felt like a correction, a piece of advice or feedback you received on an assignment intended only for guidance and improvement seemed like a "dooming" statement of your overall capability? Similarly, did your A-level results indicate to you which subjects you were better or worse at than others, and thus determine which track you would take later on in your academic and, eventually, professional career? I think many would answer "yes" to both questions. Hence, in a situation where the intention was summative assessment, it ended up having a formative effect; or while the intention was formative assessment, it ended up having a summative effect. Therefore, it would appear to me that, when we are speaking of differentiating between summative and formative assessment, we should not only keep in mind the purpose, but also the impact.


October 13, 2011

Chocolate, anyone?

Cathie, this one's for you:

On Chocolate, Phenomenological Existentialism and Assessment: A quiet brain-fart

From the series "Food for Thought"

Chocolate is chocolate, or is it? Does it have an essence or do we merely perceive it as being chocolate? Or, perhaps, instead of a chocolate-or-no-chocolate dichotomy, we may employ a scale on which to assess an extent of "chocolateyness."

If we could shut off all our senses and if we were to then, without our knowing more than the fact that we would simply be given an item of food, be fed a piece of chocolate, would we (be able to) perceive that which we were consuming as chocolate? Most likely not, but would that fact make that piece of chocolate any less a piece of chocolate? If, by divine intervention or a freak physics accident carried out hundreds of thousands of years afterwards by a crazy scientist (with, it must be said, a distinct dislike of chocolate) tinkering with a new wormhole technology, a Neanderthal had come across a piece of chocolate and thought it was simply a nice-tasting (albeit rather oddly-shaped and -textured) turd, would it inherently still be a piece of chocolate or only become a piece of chocolate once we identified it as being so?

Some may argue that chocolate does not have an essence in the first place, as, firstly, it is not sentient (though I refuse to believe that chocolate stains are purely an accident!) and, secondly, because it is formed of several different inanimate components or ingredients. In other words, we are "in ourselves;" we have a transcendental Selbst, but chocolate does not. But, is this necessarily the case? Are we, too, not also a conglomeration of different components that very conveniently act together to enable us to perceive and palatably interact with a given square of chocolate? Perhaps so, but a piece of chocolate cannot define or transform itself while we, on the other hand and according to existentialist holdings, can; we can choose what is that makes us essentially human.

Or can we? Humanists would beg to differ. They would argue that essence precedes existence, i.e. that we are innately X, Y and Z and that is those attributes which make us quintessentially human. But, consider a Mowgli'esque figure (who, I'm sure would have loved to have chowed down on a nice, big bar of Cadbury's Dairy Milk Caramel chocolate) who had wolves as parents and the wild forest as a home, entirely divorced - geographically, socially and linguistically - of the outside human world. While, at least by most, he would still be considered as a member of the human species, would he still be considered human? Is it our human traits which make us human or are we essentially human? Is it the characteristics of a piece of chocolate that make it a piece of chocolate or is it essentially a piece of chocolate? If the former is true, is there a presupposition of the existence of a sentient being of some sort which can perceive and interact with a given object before that object can, in fact, be uniquely identified? Does existence presuppose perception?

We divide objects and aspects of reality (or what we perceive to be reality) into discreet categories. We all know what we mean when we say "chocolate" and we would all be able to give a similar definition of chocolate or identify certain "sacrosanct" characteristics, much like German beer, for example. But, the further we move away from those characteristics, the less familiar that object becomes. If we added caviar and Brussels sprouts (both of which, incidentally, I hate with a passion!) into the chocolate mixture, would the end product still be chocolate? Some may say "good grief, of course not!" while others would contend that it would simply be a very foul-tasting example of chocolate, but chocolate nonetheless.


Perhaps assessment (or "Assessmentology") holds the answer. Assessment may generally be defined as the evaluation of the nature, quality or ability of someone or something. Whenever we are confronted with an object (such as...oh, I don't know, chocolate!) and perceive it, we automatically assess it - a process which normally only lasts a few milliseconds. If the object has a familiar shape, texture, taste, etc. which correlates with a previously-learned image and/or description in our mind, then we identify that object in a particular way. Although I'm not a scientist and have neither research nor references to back this up, I think we can assume that this process is neither direct nor instantaneous - there is another stage juxtapositioning existence and essence or noumena and phenomena: assessment. "Chocolate" is an assessment because we must first decide whether what we have in front of us is, in fact, a piece of chocolate. And, as assessment goes, it does not have to be dyadic either. We can make an assessment as to the level of "purity" of a particular object, i.e. to what extent that object conforms to the definition of the object it appears or is supposed to be - a particular object may be a piece of chocolate or it may be a turd, OR it may be a bit of both and thus, either a very foul-tasting piece of chocolate or a very nice-tasting turd.

The dilemma we are left with is the criteria on which we base a conclusion as to the nature of a particular object. To some, a particular object may be more closely related to what it's supposed to be than to others. Normally, this is not a problem. Can you imagine two old ladies chatting over an afternoon snack, commenting on how "tea'ish" the tea is or how "scone'ish" the scones are? However, in the case of educational assessment, this is very much an issue. Most students are neither good nor bad; they may sit anywhere on the spectrum between those two poles, and it is the job of educational assessors to evaluate them and reach a conclusion as to where exactly on that spectrum they sit. The same applies to, for instance, professional food tasters. One such person may be asked to judge the quality of a piece of chocolate, i.e. how closely it equates to that person's preconception of what a (good) piece of chocolate should taste like, but not whether or not it is a piece of chocolate.

And so, it seems that, what exactly something is or purported to be, is not important. I would gladly eat a turd if it had the appearance, smell, taste and texture of what I have commonly experienced to be chocolate. Now, if you'll excuse me, I'm going to go and raid the sweets cupboard and hopefully find something which says "chocolate" on it!


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