Is there a role for rote learning?

So here we are, then, back to work here in Maynooth for the last week of teaching. Or, to be precise, the last four days – yesterday was a Bank Holiday. With university and school examinations looming, it is no surprise to find an article griping about the Irish Leaving Certificate examinations and the fact that teachers seem to encourage students to approach them by by rote learning. This is something I’ve complained about before in the context of British A-levels and indeed the system of university examinations.

Over my lifetime the ratio of assessment to education has risen sharply, with the undeniable result that academic standards have fallen – especially in my own discipline of physics. The modular system encourages students to think of modules as little bit-sized bits of education to be consumed and then forgotten. Instead of learning to rely on their brains to solve problems, students tend to approach learning by memorizing chunks of their notes and regurgitating them in the exam. I find it very sad when students ask me what derivations they should memorize to prepare for examinations because that seems to imply that they think their brain is no more than a memory device. It has become very clear to me over the years that school education in the UK does not do enough to encourage students to develop their all-round intellectual potential, which means that very few have confidence in their ability to do anything other than remember things. It seems the same malaise affects the Irish system too.

On the other hand, there’s no question in my mind that a good memory is undoubtedly an extremely important asset in its own right. I went to a traditional Grammar school that I feel provided me with a very good education in which rote learning played a significant part. Learning vocabulary and grammar was an essential part of their approach to foreign languages, for example. How can one learn Latin without knowing the correct declensions for nouns and conjugations for verbs? But although these basic elements are necessary, they are not sufficient. You need other aspects of your mental capacity to comprehend, translate or compose meaningful pieces of text. I’m sure this applies to many other subjects. No doubt a good memory is a great benefit to a budding lawyer, for example,  but the ability to reason logically must surely be necessary too.

The same considerations apply to STEM disciplines. It is important to have a basic knowledge of the essential elements of mathematics and physics as a grounding, but you also need to develop the skill to apply these in unusual settings. I also think it’s simplistic to think of memory and creative intelligence as entirely separate things. I seems to me that the latter feeds off the former in a very complex way. A good memory does give you rapid access to information, which means you can do many things more quickly than if you had to keep looking stuff up, but I think there’s a lot more to it than that. Our memories are an essential part of the overall functioning of our brain, which is not  compartmentalized in  a simple way.  For example, one aspect of problem-solving skill relies on the ability to see hidden connections; the brain’s own filing system plays a key role in this.

Recognizing the importance of memory is not to say that rote learning is necessarily the best way to develop the relevant skills. My own powers of recall are not great – and are certainly not improving with age – but I find I can remember things much better if I find them interesting and/or if I can see the point of remembering them. Remembering things because they’re memorably is far easier than remembering because you need to remember them to pass an examination!

But while rote learning has a role, it should not be all there is and my worry is that the teaching-to-the-test approach is diminishing the ability of educators to develop other aspects of intelligence. There has to be a better way to encourage the development of the creative imagination, especially in the context of problem-solving. Future generations are going to have to face many extremely serious problems in the very near future, and they won’t be able to solve them simply by remembering the past.

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Age, Memory and Learning

Today’s a big day for prospective students at Irish universities. It’s the day when the Central Applications Office (CAO, the equivalent of the UK’s UCAS) makes offers of places to students based the Leaving Certificate results that were announced last week. Thus begins the process by which universities find out how many students we will have for entry next month. Lectures here at Maynooth start on 24th September, with an induction week before that, so there promises to be quite a rush to get everything sorted out.

The first thing that struck me thinking ahead to this year’s new entry of students was that the majority of students starting this autumn either here in Ireland or in the UK were born in the year 2000. That means that I’ve been a Professor (at four different universities: Nottingham, Cardiff, Sussex and Maynooth) all the time they have been alive! Yikes I feel old!

The other thing that struck me among all the press coverage of the Leaving Certificate in Ireland is the significant amount of griping about how these examinations are basically just memory tests and the system encourages rote learning. This is something I’ve complained about before in the context of British A-levels and indeed the system of university examinations.

Over my lifetime the ratio of assessment to education has risen sharply, with the undeniable result that academic standards have fallen especially in my own discipline of physics. The modular system encourages students to think of modules as little bit-sized bits of education to be consumed and then forgotten. Instead of learning to rely on their brains to solve problems, students tend to approach learning by memorizing chunks of their notes and regurgitating them in the exam. I find it very sad when students ask me what derivations they should memorize to prepare for examinations because that seems to imply that they think their brain is no more than a memory device. It has become very clear to me over the years that school education in the UK does not do enough to encourage students to develop their all-round intellectual potential, which means that very few have confidence in their ability to do anything other than remember things. It seems the same malaise affects the Irish system too.

On the other hand, as a number of people have pointed out in opinion pieces (e.g. here) and letters (here and here), a good memory is undoubtedly an extremely important asset in its own right.

I went to a traditional Grammar school that I feel provided me with a very good education in which rote learning played a significant part. Learning vocabulary and grammar was an essential part of their approach to foreign languages, for example. How can one learn Latin without knowing the correct declensions for nouns and conjugations for verbs? But although these basic elements are necessary, however, they are not sufficient. You other aspects of your mental capacity to comprehend, translate or compose meaningful pieces of text.

The same considerations apply to STEM disciplines. It is important to have a basic knowledge of the essential elements of mathematics and physics as a grounding, but you also need to develop the skill to apply these in unusual settings. I also think it’s simplistic to think of memory and creative intelligence as entirely separate things. I seems to me that the latter feeds off the former in a very complex way. A good memory does give you rapid access to information, which means you can do many things more quickly than if you had to keep looking stuff up, but I think there’s a lot more to it than that. Our memories are an essential part of the overall functioning of our brain, which is not  compartmentalized in such a simple way.  For example, one aspect of problem-solving skill relies on the ability to see hidden connections; the brain’s own filing system plays a key role in this.

Recognizing the importance of memory is not to say that rote learning is necessarily the best way to develop the relevant skills. My own powers of recall are not great – and are certainly not improving with age – but I find I can remember things much better if I find them interesting and/or if I can see the point of remembering them. Remembering things because they’re memorably is far easier than remembering because you need to remember them to pass an examination!

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Results Day Advice!

Today’s the day in Ireland that students get the results of their school Leaving Certificate examinations and, over the other side of the Irish Sea, tomorrow is when A-level results come out. For many there will be joy at their success, and I particularly look forward to meeting those who made their grades to get into Maynooth University shortly.

Others will no doubt receive some disappointing news.

For those of you who didn’t get the grades you needed or expected, I have one piece of very clear advice:

In particular, if you didn’t get the Leaving Certificate points you needed for entry to your first University in Ireland or the A-levels needed to do likewise in the United Kingdom, do not despair. There are always options.

For example, in Ireland, you could try looking at alternative choices on the Available Courses, where any places remaining unfilled in particular courses after all offers have been made and the waiting lists of applicants meeting minimum entry requirements have been exhausted, will be advertised.

In the United Kingdom the Clearing system will kick into operation this week. It’s very well organized and student-friendly, so give it a go if you didn’t make your offer.

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Trees, Graphs and the Leaving Certificate

I’m starting to get the hang of some of the differences between things here in Ireland and the United Kingdom, both domestically and in the world of work.

One of the most important points of variation that concerns academic life is the school system students go through before going to University. In the system operating in England and Wales the standard qualification for entry is the GCE A-level. Most students take A-levels in three subjects, which gives them a relatively narrow focus although the range of subjects to choose from is rather large. In Ireland the standard qualification is the Leaving Certificate, which comprises a minimum of six subjects, giving students a broader range of knowledge at the sacrifice (perhaps) of a certain amount of depth; it has been decreed for entry into this system that an Irish Leaving Certificate counts as about 2/3 of an A-level for admissions purposes, so Irish students do the equivalent of at least four A-levels, and many do more than this.

There’s a lot to be said for the increased breadth of subjects undertaken for the leaving certificate, but I have no direct experience of teaching first-year university students here yet so I can’t comment on their level of preparedness.

Coincidentally, though, one of the first emails I received this week referred to a consultation about proposed changes to the Leaving Certificate in Applied Mathematics. Not knowing much about the old syllabus, I didn’t feel there was much I could add but I had a look at the new one and was surprised to see a whole `Strand’, on Mathematical Modelling with netwworks and graphs.

The introductory blurb reads:

In this strand students learn about networks or graphs as mathematical models which can be used to investigate a wide range of real-world problems. They learn about graphs and adjacency matrices and how useful these are in solving problems. They are given further opportunity to consolidate their understanding that mathematical ideas can be represented in multiple ways. They are introduced to dynamic programming as a quantitative analysis technique used to solve large, complex problems that involve the need to make a sequence of decisions. As they progress in their understanding they will explore and appreciate the use of algorithms in problem solving as well as considering some of the wider issues involved with the use of such techniques.

 

Among the specific topics listed you will find:

• Minimal Spanning trees applied to problems involving optimising networks and algorithms associated with finding these (Kruskal, Prim);  
• Bellman’s Optimality Principal to find the shortest paths in a weighted directed network, and to be able to formulate the process algebraically;
•  Dijkstra’s algorithm to find shortest paths in a weighted directed network; etc.

 

For the record I should say that I’ve actually used Minimal Spanning Trees in a research context (see, e.g., this paper) and have read (and still have) a number of books on graph theory, which I find a truly fascinating subject. It seems to me that the topics all listed above  are all interesting and they’re all useful in a range of contexts, but they do seem rather advanced topics to me for a pre-university student and will be unfamiliar to a great many potential teachers of Applied Mathematics too. It may turn out, therefore, that the students will end up getting a very superficial knowledge of this very trendy subject, when they would actually be better off getting a more solid basis in more traditional mathematical methods  so I wonder what the reaction will be to this proposal!