The Cost of Learning

A situation

At the end of the academic year 2016/17, in the UK, 70.8% of 414305 undergraduate students achieved an upper second or above (the figure is a little higher if one only looks at first time students).  19.2% achieved a lower second; and, 4.6% achieved a third.  This left 5.4% unclassified. Figure 1 gives the total data in terms of percentage allocation across 155 UK Higher Education Institutions (HEIs) for that year.

Figure 1: Percentage allocation of degree classifications across 155 UK HEIs for 2016/17 (data source:[1]).  This gives the proportionality of awards at first, upper, lower, third and unclassified levels within each HEI.  HEIs are rank ordered by the percentage of first class honours degrees awarded.  The names of the HEIs have been removed.

A linear regression analysis using the raw data shows that only the number of upper second class degrees positively and significantly predicts the number of firsts (F4,150=335.736, p<0.0001; Adjusted R2=0.897; Standardized-β=1.014, SE=0.028) when all classifications are entered as a block.  Figure 1 makes clear why this might be, as upper second-class degrees dominate the space (see Table 1).  

Table 1: Descriptive statistics for percentage first and upper second-class honours degrees across 155 UK HEIs in the academic year 2016-17.  The kurtosis value for first class degrees is most likely due to some extreme performance in a few institutions (see Figure 1).

				95% CI		Outliers
	Mean	Median	Standard Deviation	Lower bound	Upper bound	Kurtosis	SE
First	23.976	23.746	7.454	22.793	25.159	9.351	0.387
Upper	46.262	47.143	8.431	44.924	47.600	1.895	0.387

Policy makers and commentators look at this data in more or less this way and draw various conclusions.  Some worry about grade inflation, driven by the pressures of teaching quality audits, whilst others discuss improved standards of educational practice in schools and universities, leading to better prepared students [2].  Given that the average UK tuition fee has been £9250 per annum for the three years these students were pursuing their qualifications, there is a clear obligation to make sure this huge investment is well spent.  This investment is, of course, made by the students themselves and so represents 414305 such decisions; but it is also a decision that impacts upon the student loan book and one that is therefore made by HM Government.

How should behavioural scientists begin to think about this situation?


Optimality

In the 1970s microeconomic models began to be applied beyond economics.  A key area of this application was foraging and the decisions organisms made when seeking and choosing food items [3,4].  The fundamental substrate of this approach was evolutionary theory, with a clear focus on fitness maximization.  Natural selection was the rational actor in this microeconomic approach, building behavioural adaptations that would, on average, maximize average lifetime inclusive fitness.  Within foraging theory calorie gain was used as a proxy of fitness.  The argument was straightforward – calories sustained life and could be converted into new life via reproduction: collecting calories therefore enabled survival and reproduction.  Later work took account of the current state of organisms during a behavioural bout as well as life history details, such as longevity, reproductive strategies etc. [5,6] in order to derive more sophisticated models.

Microeconomic models of foraging sought optimal solutions to foraging problems.  This meant deriving general cost-benefit relations applicable across a wide range of circumstances.  For example, a standard issue of prey choice (which food item to choose) could be captured in terms of a trade-off between energy gained and handling time (the time and, by extension, energy expended processing a food item – think of the effort to extract the kernel of a nut, for example).  An array of prey could be rank ordered in terms of their profitability using this simple ratio and the assumption would be that the most profitable would be chosen, whilst the least would be rejected.  This simple model was readily tested in the field and laboratory, but was also extended theoretically to include other important variables including the abundance of prey items enabling predictions to be made about when an organism would shift between specialist and generalist predation strategies [7,8].

Danchin and colleagues argue that the hard sciences aim to discover general laws, whereas the soft sciences look to account for a sequence of particular events in historical terms [9].  Optimality modelling is a hard scientific approach, but the use of real organisms, often in the field, adds a soft scientific element.  The model reduces the noise, allowing the empirical work to gain a greater perspective on that noise.  For example, in the patch foraging literature it has been found that animals typically stay longer than they should in a diminishing resource patch, operating at a suboptimal rate of gain.  The discovery of this has enabled researchers to begin thinking about other key variables such as predation risk during patch transition [10].

Optimal foraging strategies have been explored in human behaviours that are related to food acquisition [11,12] and those that are not [13,14].  The latter work assumes that foraging for information is a formally similar problem to that of foraging for food.  Thus, information is not evenly distributed in the world, some information is relatively difficult to extract, and information can be ordered in terms of value. Most pertinently, information is something to be maximized.

This approach may be of value to those trying to make sense of student choices within the current higher education ecology.  Perhaps students should be seen as striving to find optimal methods for the acquisition of benefits within a set of search spaces?  A student needs to decide upon at least three things: 1) what to learn; 2) where to learn; and, 3) what options to pursue once 1 and 2 are decided.  At each point one would anticipate a focus upon costs and benefits, and it is this that I wish to discuss in this essay.  I will describe aspects of the current situation facing students in order to sketch the early stages of a model of student decision-making based on foraging theory.  It is presented in the hope that readers of this magazine will begin to think about the ecology of universities from the perspective of the behavioural sciences.  It is also presented in order to encourage a more formal modelling approach to these issues.  The trend in higher education practice is to dwell upon soft scientific, historical trends that can only narrate what might have happened when done in isolation – we need an explanatory framework to marshal these trends.


A beginning

Let us put to one side the choice of subject and move directly to the decision about where to learn.  This decision is a patch choice; but we can model this as a one-shot patch choice as students mostly stay put at the university they enter.  To this end the patch choice problem is equivalent to a prey choice problem.  This means that reward and effort should be considered.  The student should be looking for a patch (a university) with a good rate of return on effort.

Figure 1 provides information for this decision because it can be interpreted as a diagram of the whole higher education reward space.  Whilst the size of any reward will be related to effort made, this space represents 414305 labouring individuals across 155 patches.  The data show that the average effort realized by this large population yields a good reward.  A student could have yet more confidence if she knew how many individuals came into the overall space in 2014/15 (the first year for this cohort).  In fact, 6.2% of first time entrants dropped out in their first year in 2014/15 [15], which amounts to 27384 individuals.

Using more detailed first year dropout data for 2016/17 and benchmark dropout data for the same year to predict the percentage of good degree classifications (firsts and upper seconds) in 2016/17 only actual dropout data predicts degree performance (F2,149=15.427, p<0.0001; Adjusted R2=0.160; Standardized-β=-0.444, SE=0.398).  Benchmark data adds nothing to the analysis.  This result tells us that some patches within the overall reward space are more difficult to establish oneself in.  Put another way, the larger the number of early leavers the less likely one is to gain a good degree.  These results are a useful indicator of patch quality; but as we have noted all the patches are basically good (Figure 1; Table 1).

It is perhaps the case that patches with higher dropout rates are patches that require slightly greater than the average effort to attain a good reward.  However, we should note that entry to patches is controlled and this control is effectively a state-dependent control.  To get into a patch a potential student has to have accrued some costs through prior learning and/or experience and their outcome state after that process is used to permit entry.  That state is a result of individual differences in ability and effort.  Patches can have a uniform entry demand, which can be high, medium or low value, or they can be more variable.

Patches that vary their demands may present a risky choice for students with low entry qualifications, not least because it is difficult to assess the weighting given to ability versus effort.  If average effort is met with a structured patch that maximizes reward likelihood that would make such a patch a good choice.  But if the patch requires high level skills to extract reward, irrespective of average effort, then choosing that patch may lead to a poor outcome.  It is also possible that a more mixed ability cohort will make competition in the patch more difficult.  By competition I mean the scramble to access limited resources such as tutor time, library books and so forth.  If one is a high entry qualification student, choosing a variable patch would be a bad idea as one runs the risk of extracting less value for any level of effort, in part due to the costs of competition.  This carries implications for those wishing to engineer a patch in order to attract students.

These last reflections indicate that the data from Figure 1 are perhaps insufficient for a student to make a final, state-based decision.  None the less, the distribution of reward in the search space makes it very likely that choosing any random HEI and engaging in the mean effort, or greater, will yield a good (first or upper second) outcome.  Achieving a poor outcome (third or unclassified) is difficult.  The odds of a good outcome can be marginally improved by processing the dropout rate data as this might indicate patch quality.  What none of this tells us is what a model student will do once at university.


Life in the patch

A key innovation in foraging theory was the introduction of risk modelling.  The basic idea was that whilst organisms may act to achieve a reward, there was always uncertainty associated with that outcome.  As uncertainty, or probability varied, so should behaviour [16].  Risk clearly relates to delay, such that the longer the delay to the reward the more opportunity there is for something to impede its delivery.  Immediate reward may be preferable to a delayed one, dependent upon the value of the reward and the rate that value diminishes over time, or the probability that it will [17,18].  

The final degree outcome for a student is at least three years into the future beyond the final choice of university.  Given the average age of first year undergraduates this is a considerable offset, a sixth of a lived life. From the preceding comments I have suggested that the risk associated with patch choice is reasonably even.  Given this one might predict that student decisions about which university to attend are in fact driven by concerns pertaining to immediately accessible assets and costs associated with a university, such as its location, cost of living in that area, extra-curricula opportunities etc.  Again, this may lead to particular conclusions for those seeking to engineer student choice.  The structure of a degree programme may well feature in this set.

Degrees are for the most part modular in structure.  This presents a series of shorter-term opportunities to accrue reward across three years.  It is well documented that animal models present preferences for variable delays in food reward.  This is thought to be because shorter delays sometimes occur and the animal can get to the reward quicker.  There is also a preference for variable delays over fixed; and for unpredictably variable over predictably variable delays [19].  This might be relevant to the reward schedules for students.  The underlying issue is that of temporal discounting (under an assumption of hyperbolic discount rate - such that the more distant the pay-off the less value is attached to it).  Modular structures enable the total reward to be built in stages, thus offsetting the risk associated with delay.  To that end, the search space is again fairly homogenous as most programmes do this.  However, the assessment regimes associated with modules are less similar.  For example, an overall degree programme might be organized such that one simply has to pass year 1, then year 2 is a 40% contribution and year 3 a 60% contribution to a final award.  Alternatively all three years may make various contributions to the final reward, or everything could rest on the final year alone.

Within each year assessments may fall within the terms or at the end of the year.  Exam based modules may well all be assessed in May/June even if taught within the first semester.  Non-exam based modules will be assessed at a variety of points during the course of the module.  Some modules have mixed strategies.  But all of these strategies are predictable due to the constraints of university timetables: students will know when they are to submit work.  And students will be able to make calculations about risk.  For example, a module that is assessed later in the academic year, at some distance from the teaching, introduces the possibility of greater forgetting as well as other, unforeseen obstacles impeding progression.

Anselme and Gunturkun note that that a smaller effort and a shorter delay are preferred in some animal models and that there is evidence to suggest that shorter durations are preferred over reward size, such that variable delay to reward ratios are favoured even when pay-offs are less sizeable.  This makes particular sense in certain foraging situations where near constant feeding is needed due to high metabolic costs and high predation rates:  the animal needs energy but needs to move too. Assessment regimes that operate a short duration after the relevant teaching, perhaps looking to build structured skills across time, and that make available only small proportions of the overall module mark at each point of assessment may well be preferred.  If those assessments are done in class, and without announcement, the variable structure might also be appealing; especially to students who have to avoid financial predation by working.


Risk and uncertainty

In the classic work on risk sensitive foraging the state of the organism was crucial.  If under starvation and faced with a variable reward or a certain reward set at the mean value of the overall variable pay out, the argument was that the variable pay out should be preferable as it could pay out big [20].  In other words, under starvation animals should be riskier.  This finding has not been well replicated and has been criticized conceptually for assuming that animals had perfect information about the probabilities associated with the experiment, or more importantly, it is clear that animals do not have perfect information about probability of reward in nature [16].  Kacelnick and El Mouden note that there is a distinction between risk, where probabilities are known, and uncertainty, where they are not.  Life is, for the most part, uncertain and natural selection will have had to deal with this differently.  Their paper, as with Anselme and Gunturkun’s, focuses upon possible proximate behavioural mechanisms for solving these issues of unpredictability; and this work will likely be of great interest to pedagogical scholars. 

I have suggested that students are in receipt of perfect information about risk, as a consequence of curriculum design and timetabling constraints.  Thus I have assumed that the classic work has something to offer when modelling student behaviour, and I have run risk and uncertainty together as synonyms.  But I have only focused upon decisions about where to study and, to some extent, my argument also applies to module choices within a degree programme.  What I have not considered are the truly uncertain aspects of life.

All readers will be aware that students’ lived lives can have a huge impact upon their studies and universities go to great lengths to offer support where appropriate.  However, the prior experiences of uncertainty will undoubtedly influence how students make choices even at times of stability, as particular discounting responses will likely be entrained due to prior life-history calibration [21,22].  This again is something of relevance to patch engineers.  More strongly put, less investment in post hoc support and more in upfront design of programmes would probably enable students better.  But this will take a strong stomach, as a stress response will be an integral part of the engineering and most university administrators run shy of these behaviours.


References:

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