KIwwledqe. . . u n dl e rsta ;id i ng (mind the gap!) by R. F. Jinks

The hiatus that all too often exists between knowledge and understanding is illustrated in this article by two separate case studies. The author begins with an overview ofthe problem. The substance ofthe case studies is then slot out to demonstifate how scholastic discernment Wac used in recent coursework,/examination solutions to gauge depth o f student understanding.

eachers take a great deal of satisfaction when student:; in their charge show a depth of understanding. It is very gratifying when a student develops from a mere recipient or

accumulator of facts to the stage where they actively display, via the quality of their course work, exaniina- tion solutions and oral argument, that they, too, under- stand the nuances of a particular subject.

In simple te rm the primary ambition of-teachers of engineering is ‘to give each student in their charge opportunities to assimilate a series of known facts into an understanding of a particular subject.

The acquisition of knowledge is the first step in the hierarchical learning chain. Indeed, it is noted that the measurement of learning begins via an investigation of knowledge, defined as ‘information which has been niemorised’’ , and culminates in a determination of understanding, defined as ‘the capacity to use concepts/knowledge creatively in the pehrmance of complex activities’’.

Needless to say different tutors often use different methods to achieve the common goal of cultivating understanding. Equally different subject material will also requirdchctate differing techniques in this pursuit. of better understanding. However, the general principles by which a person learns remain much the same irrespective of subject matte?. Deeper learning

involves important aspects to which a student must be conumtted. In essence these are:

studying subject material for its perceivable merits having a personal interest in the subject material being able to develop an overview of the subject material being able to develop structural interrelationshps between different parts ‘of the subject: material being able to interpret material against background experience.

Teachers who manage to inculcate these noted learning characteristics in their students can and should look forward to seeing developnient of .understanding. Yet the analysis of understanding is not as easy as one might think. For instance, it is not always apparent that a student exhibits understanding unless questions are designed to seek it out. And although. the approach taken in assessing knowledge is often blatant, that taken in establishing understanding becomes subtly inore testing of a student’s ability to synthesise knowledge. The synthesis of facts from different sources must create a composite which in fbirin is much more than an amalgam of facts.

Frequently it is the role o f the teacher to set in place an assessment mechanism which directly tests the general subject knowledge while at the same time circuitously examining the student’s real depth of understanding. It is the s n i d but significant differences in individual responses to a set examination question or a coursework problem that often separate knowledge from understanding.

The following case studies illuctrate sonic instancev over the last year in which it was contrived to analyse that often elusive strand which offers evidence of learning, i.e. understanding.

ENGINEERING SCIENCE AND EDUCATION JOURNAL OCTOBER 1996

227

Fig. 1 Electrical circuit experiment

Case Study 1: Circuit analysis

The intention of this case study was to look at the typical experimental method and interpretation of results in part of the electrical circuit experiment shown in Fig. 1. The objective of this element of the experiment was simply to vary the applied frequency until the phase shift between the circuit input and output became 45". No general instruction relating to how to conduct the experiment was given, the purpose of the experiment being both to review taught theory and to introduce these students to some of the more basic areas of electrical engineering experimentation.

Synposis Outwardly the objectives dld not look very dfficult

to achieve. Indeed it was found that the majority of the students, having gained an appreciation of the functionality of the oscilloscope, the digital voltmeter and the signal generator, became quite adept at varying the 6equency of the generator in order to make a measurement of the frequency at which a 45" phase shift occurred.

Initially the preferred measurement of phase shift was via an examination of waveforms presented on the oscilloscope. However it was not the intention of the originator of the experiment to deliberately deny students the opportunity of adopting a different phase measuring technique if they recognised its worth. Therefore before proceeding to the next part of this experiment each student was asked to record in their

shifi occurred and the circuit potentials at this phase point, i.e. V,,, l/;,d and Vres. In this way a hint was given to those students who had not recognised the merit of comparing the oscilloscope phase measure- ment method with alternative phase measurement techniques. No further hints or suggestions were given as to the relationships that should exist between the circuit potentials at the 45" phase point. It was left entirely to the students to see whether they could use prior knowledge creatively. Some saw the association,

logbook both the frequency at which the 45' phase

some did not. Those who &d invariably found a discrepancy between the apparent 45" measurement via the oscilloscope and the voltmeter method, i.e. q n d & lies. Subsequently it was found that these students repeated this part of the experiment until the results of the two methods of phase measurement coincided.

Thus this seemingly innocuous phase measurement activity set the stage for an examination of under- standing. In the subsequent analysis part of the experiment students were required to plot a phasor hagram. The significance of this was that those who had incorrectly measured the point at which the phase shift occurred would find that the resultant angle on their diagrams was not 45"! Additionally a calculation had to be made in order to determine the frequency at which the 45' phase shift occurred. Again this was included in order to draw attention towards the v&&ty or invahdlty of the measurement.

Subsequent analysis of the 30 student reports received revealed the following:

Those showing understanding: 9 of the students demonstrated a full understanding ofboth principles of phase measurement. Their experimental and theoretical results were very close. Those showing knowledge: 13 students questioned the correctness of their experimental approach when they found the resultant phase angle in the phasor magram did not equal or approximate to 45'. Most of these students demonstrated an a b h y to use circuit formulae.

students made no comment about the dlsparity between the angle plotted in the phasor diagram and the experimental result.

Those showing lack of knowledge: The remaining 8

Case Study 2: Telecommunications examination question

The second case study investigated general under- standmg of noise prevention methods in a specific type of telecommunication system. The mode of

ENGINEERING SCIENCE AND EDUCATION JOURNAL OCTOBER 1996

228

Fig. 2 Two-stage amplifier

investigation was based upon a fairly standard two-part examination question:

(U) You are asked to implement the design of an antenna/downlink/RF amplifier receiver system. If the radm frequency signal to be received originates fiom a distant VHF transmitter, specify features that you would incorporate into your system in order that the effects of noise would be minimised.

(b) The two stage amplifier system shown in Fig. 2 operates at 20°C. If the bandwidth of the thermal noise developed by resistor R1 is 200 x lo5 Hz determine:

(i) the input thermal noise voltage, G:, (ii) the input thermal noise power (iii) the noise power at the output (assuming both

amplifiers are noiseless (iv) the noise factor (in ratio form) of the system (v) the actual output noise power dssipated across

the 30Cl !2 resistor.

Synopsis Of the 29 students takmg the examination 27 opted

to answer this question. The average mark for the question was found to be 57%. A standard deviation of 21% (the highest and lowest marks scored being 85% and 1596, respectively) indicated that a wide spread of marks existed around the mean. Further investigation of studlent responses to parts U and b provided the information shown in Figs. 3 and 4 on the performance of the students.

In view of the evidence provided by the histograms in the Figures it is apparent that few students managed to provide a reasonable discussion of the problems associated with noise in telecommunication systems, but a much higher proportion of the 27 found answering part b far less complicated.

The results for part U shown in Fig. 3 unveiled the gap that all too often exists between knowledge and understandmg. Indeed, in reference to the definitions

of ‘deeper learning’ given earlier it was anticipated that students would only do well in part a if they engaged in the learning activities described. The relative shallowness of many of tlie replies typified the innate tendency towards acquiring knowledge at the expense ofunderstanding. It was apparent that few students had read the recommended course text^^,^ or had any real understandmg of the noise irnmunity factors that would have to be considered.

In some instances students seemed to be at a complete loss to explain themselves. Many of these merely advocated improving the signal-to-noise ratio

A 0 C D E F A VHF band frequency limits Use of bandpass filter in this

range in order to limit wide-band noise power B Matching all parts of system, antenna/downlink/amplifier

together C Use of high-gain directiorial antenna and

antenna mounted htghlpointing towards t D Use of low-noise amplifier at receiver inp E Use of low-loss good-quality coaxial downlin F Use of a masthead amplifier

Fig. 3 Numbers of students giving a reasonable explanation of noted noise reduction methods (A to F) in part a of the examination question

ENGINEERING SCIENCE AND EDUCATION JOURNAL OCTOIB ER 1996

229

16

I

~

23

ii

17

111

21

Fig. 4 each component of part b of the examination question

Numbers of students making correct calculation in

at the receiver. Others opted to ‘turn up the power at the transmitter’ or ‘scrap the system entirely’, replacing it with optical fibre.

On a more positive note nearly all those who answered part a well also achieved high marks in part b.

Scholastic discernment

Measuring understandmg is a difficult task in compari- son with that of quantifying knowledge. The strategy employed in each of the case studies was simply to recognise that ‘knowledge precedes understanding’. Iiiiplicit in this approach is the need to include the asressment of both in any coursework or examination in ordcr to be fair.

The two case studies also illustrate that coursework promotes the development of understanding, e.g. a ytudent missing the important point about the significance of the potentials measured across the circuit components in the laboratory does have a second chance to gain an understanding, whereas in the examination question no deferred learning oppor- tunity exists.

Clearly, given these factors there was a need to structure each piece of educational work in order that a discernnient of understanding could take place. The approach in the laboratory exercise involved intro- ducing an element of uncertainty relating to the vahdity of the initial phase measurement technique and then monitoring the student’s reaction to the problem.

The examination approach was that of intentionally dividmg the question between part a, testing under- standing, and part b, testing knowledge, and then encouraging the display of understanding via a series of ‘ladders and bridges’. For example, the calculation of the thermal noise power at the input of amplifier A1 required use of the formula Pfi = kTB. The use of this stratagem for discriminating between knowledge and understanding revealed that 85% of the students had the knowledge to coniplete the numerical calculation correctly whereas only 30% displayed a written under- standing of the topic.

Simdarly the case for minimising the noise factor of the amplifiers produced separate numerical results for knowledge and understandmg.

It might reasonably have been argued that if parts a and b of the question had been transposed then students might have provided a better written discussion. How- ever this idea was considered and then lsmissed due to the lack of subtlety of approach.

Summary

Unfortunately initial appraisal of assessment is all too often far less erudte than one would like. A pass rate in excess of 70% seems to be the criterion of success nowadays. But what is the real ‘added value’ if a large majority of those who pass an examination possess ‘poor understanding’?

The gap that exists between mediocrity and excellence is one that must be continually held under close scrutiny. Sindarly the gap between understanding and knowledge is an eternal problem for educators, irrespective of field. It would be far too simplistic to aspire here to the ideal in saying that the development of understanding of a particular subject is the primary objective of a teacher. Neither would it be fair to say that the impetus of a teacher is often largely restrained to development of knowledge because of mitigating factors, e.g. class size. Unquestionably it must be the intention of a teacher to steer towards the promotion of undevstanding irrespective of the circunistances in which they find themselves.

References

I MATTHEW, R. G. S., and HUGHES, D. C.: ‘Getting at deep learning: a problem-based approach’, Erg. Sci. G Educ. J , October 1994, 3, (5), pp.234-240

2 BIGGS, J. B.: ‘Approaches to the enhancement of tertiary teaching’, HE Educutional Reseuvrh G Developwit , 1989, (8),

3 MILLER, G. M.: ‘Modern electronic communications’

4 COUCH, L. W: ‘Modern com~ii~nicatio~i syrteinr’

pp.7-25

(Prentice-Hall, 1993, 4th edn.)

(Prentice-Hall, 1995)

0 IEE. 1996

The author IS a Senior Lecturer in the School of Engineering, Coventry University, Priory Street, Coventry CV1 SFB, U K

ENGINEERING SCIENCE AND EDUCATION JOURNAL OCTOBER 1996

230