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Tailgating is a very popular activity associated with American college football games. Tailgating typically involves food and alcoholic beverages served from the backs of parked vehicles or associated equipment at or near athletic events. At large universities with Division I football programs, the football stadiums may hold upwards of 100,000 fans, sometimes with thousands of additional fans

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By Lara Alcock

Two contrasting experiences stick in mind from my first year at university.

First, I spent a lot of time in lectures that I did not understand. I don’t mean lectures in which I got the general gist but didn’t quite follow the technical details. I mean lectures in which I understood not one thing from the beginning to the end. I still went to all the lectures and wrote everything down – I was a dutiful sort of student – but this was hardly the ideal learning experience.

Second, at the end of the year, I was awarded first class marks. The best thing about this was that later that evening, a friend came up to me in the bar and said, “Hey Lara, I hear you got a first!” and I was rapidly surrounded by other friends offering enthusiastic congratulations. This was a revelation. I had attended the kind of school at which students who did well were derided rather than congratulated. I was delighted to find myself in a place where success was celebrated.

Looking back, I think that the interesting thing about these two experiences is the relationship between the two. How could I have done so well when I understood so little of so many lectures?

I don’t think that there was a problem with me. I didn’t come out at the very top, but obviously I had the ability and dedication to get to grips with the mathematics. Nor do I think that there was a problem with the lecturers. Like the vast majority of the mathematicians I have met since, my lecturers cared about their courses and put considerable effort into giving a logically coherent presentation. Not all were natural entertainers, but there was nothing fundamentally wrong with their teaching.

I now think that the problems were more subtle, and related to two issues in particular.

First, there was a communication gap: the lecturers and I did not understand mathematics in the same way. Mathematicians understand mathematics as a network of axioms, definitions, examples, algorithms, theorems, proofs, and applications.  They present and explain these, hoping that students will appreciate the logic of the ideas and will think about the ways in which they can be combined. I didn’t really know how to learn effectively from lectures on abstract material, and research indicates that I was pretty typical in this respect.

Students arrive at university with a set of expectations about what it means to ‘do mathematics’ – about what kind of information teachers will provide and about what students are supposed to do with it. Some of these expectations work well at school but not at university. Many students need to learn, for instance, to treat definitions as stipulative rather than descriptive, to generate and check their own examples, to interpret logical language in a strict, mathematical way rather than a more flexible, context-influenced way, and to infer logical relationships within and across mathematical proofs. These things are expected, but often they are not explicitly taught.

My second problem was that I didn’t have very good study skills. I wasn’t terrible – I wasn’t lazy, or arrogant, or easily distracted, or unwilling to put in the hours. But I wasn’t very effective in deciding how to spend my study time. In fact, I don’t remember making many conscious decisions about it at all. I would try a question, find it difficult, stare out of the window, become worried, attempt to study some section of my lecture notes instead, fail at that too, and end up discouraged. Again, many students are like this. I have met a few who probably should have postponed university until they were ready to exercise some self-discipline, but most do want to learn.

What they lack is a set of strategies for managing their learning – for deciding how to distribute their time when no-one is checking what they’ve done from one class to the next, and for maintaining momentum when things get difficult. Many could improve their effectiveness by doing simple things like systematically prioritizing study tasks, and developing a routine in which they study particular subjects in particular gaps between lectures.  Again, the responsibility for learning these skills lies primarily with the student.

Personally, I never got to a point where I understood every lecture. But I learned how to make sense of abstract material, I developed strategies for studying effectively, and I maintained my first class marks. What I would now say to current students is this: take charge. Find out what lecturers and tutors are expecting, and take opportunities to learn about good study habits. Students who do that should find, like I did, that undergraduate mathematics is challenging, but a pleasure to learn.

Lara Alcock is a Senior Lecturer in the Mathematics Education Centre at Loughborough University. She has taught both mathematics and mathematics education to undergraduates and postgraduates in the UK and the US. She conducts research on the ways in which undergraduates and mathematicians learn and think about mathematics, and she was recently awarded the Selden Prize for Research in Undergraduate Mathematics Education. She is the author of How to Study for a Mathematics Degree (2012, UK) and How to Study as a Mathematics Major (2013, US).

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It was the birthday this week of Edward Thomas, a quitessentially English poet. This is one of the many poems he wrote in the short period of poetic creativity that came upon him before he was killed in the First World War:


Lights Out

I have come to the borders of sleep,
The unfathomable deep
Forest where all must lose
Their way, however straight,
Or winding, soon or late;
They cannot choose.

Many a road and track
That, since the dawn's first crack,
Up to the forest brink,
Deceived the travellers,
Suddenly now blurs,
And in they sink.

Here love ends,
Despair, ambition ends,
All pleasure and all trouble,
Although most sweet or bitter,
Here ends in sleep that is sweeter
Than tasks most noble.

There is not any book
Or face of dearest look
That I would not turn from now
To go into the unknown
I must enter and leave alone
I know not how.

The tall forest towers;
Its cloudy foliage lowers
Ahead, shelf above shelf;
Its silence I hear and obey
That I may lose my way
And myself.


Thomas' was the first poetry by a FWW poet that I ever read, many many years ago: I was 16 and a friend recited from memory his poem But These Things Also Are Spring's, which impressed itself upon my brain that I sought out a copy of Thomas' poems later that same morning.

Today is the anniversary of the first publication in 1923 of Robert Frost's well-loved poem:

Stopping By Woods On A Snowy Evening

Whose woods these are I think I know.
His house is in the village though;
He will not see me stopping here
To watch his woods fill up with snow.
My little horse must think it queer
To stop without a farmhouse near
Between the woods and frozen lake
The darkest evening of the year.
He gives his harness bells a shake
To ask if there is some mistake.
The only other sound's the sweep
Of easy wind and downy flake.
The woods are lovely, dark and deep.
But I have promises to keep,
And miles to go before I sleep,
And miles to go before I sleep.

Note that both men, who were very great friends for a few years before Thomas' death, wrote of woods and sleep.

The Poetry Friday round-up this week is over at The Simple and The Ordinary.

The annual Glastonbury Music Festival and Wimbledon are both approaching, sure guarantees of rain arriving on these shores, and this morning I woke to a leak in my attic roof, so I'm feeling rather rain obsessed at the moment !


Rain

Rain, midnight rain, nothing but the wild rain
On this bleak hut, and solitude, and me
Remembering again that I shall die
And neither hear the rain nor give it thanks
For washing me cleaner than I have been
Since I was born into this solitude.
Blessed are the dead that the rain rains upon:
But here I pray that none whom once I loved
Is dying tonight or lying still awake
Solitary, listening to the rain,
Either in pain or thus in sympathy
Helpless among the living and the dead,
Like a cold water among broken reeds,
Myriads of broken reeds all still and stiff,
Like me who have no love which this wild rain
Has not dissolved except the love of death,
If love it be for what is perfect and
Cannot, the tempest tells me,
disappoint.

Edward Thomas' poem "Rain" was written on January 7, 1916 - for those familiar with poetry of the WW1 period, the images of rain and mud are probably the strongest ones.


The other thing I'm obsessed about, of course, is "Doctor Who" - the season finale is only 8 days away. Last week's episode (which I will review on my Spoiler Zone Blog at some point in the next two days) was called "Utopia", although there was no sign of Utopia in the episode, but it got me thinking about Utopia and Dystopia, and of course, then I went looking for some poetry, and found this:

Utopia

Island where all becomes clear.

Solid ground beneath your feet.

The only roads are those that offer access.

Bushes bend beneath the weight of proofs.

The Tree of Valid Supposition grows here
with branches disentangled since time immemorial.

The Tree of Understanding, dazzlingly straight and simple,
sprouts by the spring called Now I Get It.

The thicker the woods, the vaster the vista:
the Valley of Obviously.

You can read the rest of Wislawa Szymborska's poem here. I confess to being completely unfamiliar with Szymborska's work until Elaine of Wild Rose Reader and Blue Rose Girls posted "The Joy of Writing" for an April Poetry Friday offering. You can find a biography of this Polish poet here; Szymborska won the "Nobel Prize in Literature" in 1996 and you can read her Nobel Prize lecture here.


This week's poetry round-up is hosted by cloudscome of A Wrung Sponge.

I first discovered the poems of Edward Thomas (1878-1917) as a child in my now out of print copy of All Day Long: An Anthology of Poetry for Children, compiled by Pamela Whitlock (Oxford University). Thmas wrote beautifully of the English countryside and the seasons. Later, in high school, I learned that he was also one of the World War I poets. And several years ago, I came across some of his