A case of hybrid research design?

When is "a case study" not a case study? Perhaps when it is (nearly) an experiment?

Keith S. Taber

I read this interesting study exploring learners shifting conceptions of the particulate nature of gases.

Key features:

• Science curriculum context: the particulate nature of matter in the gaseous phase
• Educational context: Grade 4 students in South Africa
• Pedagogic context: Teacher-initiated inquiry approach (compared to a 'lecture' condition/treatment)
• Methodology: "qualitative pre-test/post-test case study design" – or possibly a quasi-experiment?
• Population/sample: the sample comprised 116 students from four grade four classes, two from each of two schools

This study offers some interesting data, providing evidence of how students represent their conceptions of the particulate nature of gases. What most intrigued me about the study was its research design, which seemed to reflect an unusual hybrid of quite distinct methodologies.

In this post I look at whether the study is indeed a case study as the authors suggest, or perhaps a kind of experiment. I also make some comments about the teaching model of the states of matter presented to the learners, and raise the question of whether the comparison condition (lecturing 8-9 year old children about an abstract scientific model) is appropriate, and indeed ethical.

Learners' conceptions of the particulate nature of matter

This paper is well worth reading for anyone who is not familiar with existing research (such as that cited in the paper) describing how children make sense of the particulate nature of matter, something that many find counter-intuitive. As a taster for this, I reproduce here two figures from the paper (which is published open access under a creative common license* that allows sharing and adaption of copyright material with due acknowledgement).

Figures © 2020 by the authors of the cited paper *

Conceptions are internal, and only directly available to the epistemic subject, the person holding the conception. (Indeed, some conceptions may be considered implicit, and so not even available to direct introspection.) In research, participants are asked to represent their understandings in the external 'public space' – often in talk, here by drawing (Taber, 2013). The drawings have to be interpreted by the researchers (during data analysis). In this study the researchers also collected data from group work during learning (in the enquiry condition) and by interviewing students.

What kind of research design is this?

Mamombe and colleagues describe their study as "a qualitative pre-test/post-test case study design with qualitative content analysis to provide more insight into learners' ideas of matter in the gaseous phase" (p. 3), yet it has many features of an experimental study.

The study was

"conducted to explore the influence of inquiry-based education in eliciting learners' understanding of the particulate nature of matter in the gaseous phase"

p.1

The experiment compared two pedagogical treatments :

• "inquiry-based teaching…teacher-guided inquiry method" (p.3) guided by "inquiry-based instruction as conceptualized in the 5Es instructional model" (p.5)
• "direct instruction…the lecture method" (p.3)

These pedagogic approaches were described:

"In the inquiry lessons learners were given a lot of materials and equipment to work with in various activities to determine answers to the questions about matter in the gaseous phase. The learners in the inquiry lessons made use of their observations and made their own representations of air in different contexts."

"the teacher gave probing questions to learners who worked in groups and constructed different models of their conceptions of matter in the gaseous phase. The learners engaged in discussion and asked the teacher many questions during their group activities. Each group of learners reported their understanding of matter in the gaseous phase to the class"

p.5, p.1

"In the lecture lessons learners did not do any activities. They were taught in a lecturing style and given all the notes and all the necessary drawings.

In the lecture classes the learners were exposed to lecture method which constituted mainly of the teacher telling the learners all they needed to know about the topic PNM [particulate nature of matter]. …During the lecture classes the learners wrote a lot of notes and copied a lot of drawings. Learners were instructed to paste some of the drawings in their books."

pp.5-6

The authors report that,

"The learners were given clear and neat drawings which represent particles in the gaseous, liquid and solid states…The following drawing was copied by learners from the chalkboard."

p.6

A teaching model of the states of matter

This figure shows increasing separation between particles moving from solid to liquid to gas. It is not a canonical figure, in that the spacing in a liquid is not substantially greater than in a solid (indeed, in ice floating on water the spacing is greater in the solid), whereas the difference in spacing in the two fluid states is under-represented.

Such figures do not show the very important dynamic aspect: that in a solid particles can usually only oscillate around a fixed position (a very low rate of diffusion not withstanding), where in a liquid particles can move around, but movement is restricted by the close arrangement of (and intermolecular forces between) the particles, where in a gas there is a significant mean free path between collisions where particles move with virtually constant velocity. A static figure like this, then, does not show the critical differences in particle interactions which are core to the basic scientific model

Perhaps even more significant, figure 2 suggests there is the same level of order in the three states, whereas the difference in ordering between a solid and liquid is much more significant than any change in particle spacing.

In teaching, choices have to be made about how to represent science (through teaching models) to learners who are usually not ready to take on board the full details and complexity of scientific knowledge. Here, Figure 2 represents a teaching model where it has been decided to emphasise one aspect of the scientific model (particle spacing) by distorting the canonical model, and to neglect other key features of the basic scientific account (particle movement and arrangement).

External teachers taught the classes

The teaching was undertaken by two university lecturers

"Two experienced teachers who are university lecturers and well experienced in teacher education taught the two classes during the intervention. Each experienced teacher taught using the lecture method in one school and using the teacher-guided inquiry method in the other school."

p.3

So, in each school there was one class taught by each approach (enquiry/lecture) by a different visiting teacher, and the teachers 'swapped' the teaching approaches between schools (a sensible measure to balance possible differences between the skills/styles of the two teachers).

An experiment; or a case study?

Although the study compared progression in learning across two teaching treatments using an analysis of learner diagrams, the study also included interviews, as well as learners' "notes during class activities" (which one would expect would be fairly uniform within each class in the 'lecture' treatment).

The outcome

The authors do not consider their study to be an experiment, despite setting up two conditions for teaching, and comparing outcomes between the two conditions, and drawing conclusions accordingly:

"The results of the inquiry classes of the current study revealed a considerable improvement in the learners' drawings…The results of the lecture group were however, contrary to those of the inquiry group. Most learners in the lecture group showed continuous model in their post-intervention results just as they did before the intervention…only a slight improvement was observed in the drawings of the lecture group as compared to their pre-intervention results"

pp.8-9

These statements can be read in two ways – either

• a description of events (it just happened that with these particular classes the researchers found better outcomes in the enquiry condition), or
• as the basis for a generalised inference.

An experiment would be designed to test a hypothesis (this study does not seem to have an explicit hypothesis, nor explicit research questions). Participants would be assigned randomly to conditions (Taber, 2019), or, at least, classes would be randomly assigned (although then strictly each class should be considered as a single unit of analysis offering much less basis for statistical comparisons). No information is given in the paper on how it was decided which classes would be taught by which treatment.

Representativeness

A study could be carried out with the participation of a complete population of interest (e.g., all of the science teachers in one secondary school), but more commonly a sample is selected from a population of interest. In a true experiment, the sample has to be selected randomly from the population (Taber, 2019) which is seldom possible in educational studies.

In Mamombe and colleagues' study the sample is described. However, there is no explicit reference to the population from which the sample is drawn. Yet the use of the term 'sample' (rather than just, say, 'participants') implies that they did have a population in mind.

The aim of the study is given as to "to explore the influence of inquiry-based education in eliciting learners' understanding of the particulate nature of matter in the gaseous phase" (p.1) which could be considered to imply that the population is 'learners'. The title of the paper could be taken to suggest the population of interests is more specific: "grade four learners". However, the authors make no attempt to argue that their sample is representative of any particular population, and therefore have no basis for statistical generalisation beyond the sample (whether to learners, or to grade four learners, or to grade four learners in RSA, or to grade four learners in farm schools in RSA, or…).

Indeed only descriptive statistics are presented: there is no attempt to use tests of statistical significance to infer whether the difference in outcomes between conditions found in the sample would probably have also been found in the wider population.

(That is inferential stats. are commonly used to suggest 'we found a statistically significant better outcome in one condition in our sample, so in the hypothetical situation that we had been able to include the entire population in out study we would probably have found better mean outcomes in that same condition'.)

This may be one reason why Mamombe and colleagues do not consider their study to be an experiment. The authors acknowledge limitations in their study (as there always are in any study) including that "the sample was limited to two schools and two science education specialists as instructors; the results should therefore not be generalized" (p.9).

Yet, of course, if the results cannot be generalised beyond these four classes in two schools, this undermines the usefulness of the study (and the grounds for the recommendations the authors make for teaching based on their findings in the specific research contexts).

If considered as an experiment, the study suffers from other inherent limitations (Taber, 2019). There were likely novelty effects, and even though there was no explicit hypothesis, it is clear that the authors expected enquiry to be a productive approach, so expectancy effects may have been operating.

Analytical framework

In an experiment is it important to have an objective means to measure outcomes, and this should be determined before data are collected. (Read about 'Analysis' in research studies.). In this study methods used in previous published work were adopted, and the authors tell us that "A coding scheme was developed based on the findings of previous research…and used during the coding process in the current research" (p.6).

But they then go on to report,

"Learners' drawings during the pre-test and post-test, their notes during class activities and their responses during interviews were all analysed using the coding scheme developed. This study used a combination of deductive and inductive content analysis where new conceptions were allowed to emerge from the data in addition to the ones previously identified in the literature"

p.6

An emerging analytical frame is perfectly appropriate in 'discovery' research where a pre-determined conceptualisation of how data is to be understood is not employed. However in 'confirmatory' research, testing a specific idea, the analysis is operationalised prior to collecting data. The use of qualitative data does not exclude a hypothesis-testing, confirmatory study, as qualitative data can be analysed quantitatively (as is done in this study), but using codes that link back to a hypothesis being tested, rather than emergent codes. (Read about 'Approaches to qualitative data analysis'.)

Much of Mamombe and colleagues' description of their work aligns with an exploratory discovery approach to enquiry, yet the gist of the study is to compare student representations in relation to a model of correct/acceptable or alternative conceptions to test the relative effectiveness of two pedagogic treatments (i.e., an experiment). That is a 'nomothetic' approach that assumed standard categories of response.

Overall, the author's account of how they collected and analysed data seem to suggest a hybrid approach, with elements of both a confirmatory approach (suitable for an experiment) and elements of a discovery approach (more suitable for case study). It might seem this is a kind of mixed methods study with both confirmatory/nomothetic and discovery/idiographic aspects – responding to two different types of research question the same study.

Yet there do not actually seem (**) to be two complementary strands to the research (one exploring the richness of student's ideas, the other comparing variables – i.e., type of teaching versus degree of learning), but rather an attempt to hybridise distinct approaches based on incongruent fundamental (paradigmatic) assumptions about research. (** Having explicit research questions stated in the paper could have clarified this issue for a reader.)

So, do we have a case study?

Mamombe and colleagues may have chosen to frame their study as a kind of case study because of the issues raised above in regard to considering it an experiment. However, it is hard to see how it qualifies as case study (even if the editor and peer reviewers of the EURASIA Journal of Mathematics, Science and Technology Education presumably felt this description was appropriate).

Mamombe and colleagues do use multiple data sources, which is a common feature of case study. However, in other ways the study does not meet the usual criteria for case study. (Read more about 'Case study'.)

For one thing, case study is naturalistic. The method is used to study a complex phenomena (e.g., a teacher teaching a class) that is embedded in a wider context (e.g., a particular school, timetable, cultural context, etc.) such that it cannot be excised for clinical examination (e.g., moving the lesson to a university campus for easy observation) without changing it. Here, there was an intervention, imposed from the outside, with external agents acting as the class teachers.

Even more fundamentally – what is the 'case'?

A case has to have a recognisable ('natural') boundary, albeit one that has some permeability in relation to its context. A classroom, class, year group, teacher, school, school district, etcetera, can be the subject of a case study. Two different classes in one school, combined with two other classes from another school, does not seem to make a bounded case.

In case study, the case has to be defined (not so in this study); and it should be clear it is a naturally occurring unit (not so here); and the case report should provide 'thick description' (not provided here) of the case in its context. Mamombe and colleagues' study is simply not a case study as usually understood: not a "qualitative pre-test/post-test case study design" or any other kind of case study.

That kind of mislabelling does not in itself does not invalidate research – but may indicate some confusion in the basic paradigmatic underpinnings of a study. That seems to be the case [sic] here, as suggested above.

Suitability of the comparison condition: lecturing

A final issue of note about the methodology in this study is the nature of one of the two conditions used as a pedagogic treatment. In a true experiment, this condition (against which the enquiry condition was contrasted) would be referred to as the control condition. In a quasi-experiment (where randomisation of participants to conditions is not carried out) this would usually be referred to as the comparison condition.

At one point Mamombe and colleagues refer to this pedagogic treatment as 'direct instruction' (p.3), although this term has become ambiguous as it has been shown to mean quite different things to different authors. This is also referred to in the paper as the lecture condition.

Is the comparison condition ethical?

Parental consent was given for students contributing data for analysis in the study, but parents would likely trust the professional judgement of the researchers to ensure their children were taught appropriately. Readers are informed that "the learners whose parents had not given consent also participated in all the activities together with the rest of the class" (p.3) so it seems some children in the lecture treatment were subject to the inferior teaching approach despite this lack of consent, as they were studying "a prescribed topic in the syllabus of the learners" (p.3).

I have been very critical of a certain kind of 'rhetorical' research (Taber, 2019) report which

• begins by extolling the virtues of some kind of active / learner-centred / progressive / constructivist pedagogy; explaining why it would be expected to provide effective teaching; and citing numerous studies that show its proven superiority across diverse teaching contexts;
• then compares this with passive modes of learning, based on the teacher talking and giving students notes to copy, which is often characterised as 'traditional' but is said to be ineffective in supporting student learning;
• then describes how authors set up an experiment to test the (superior) pedagogy in some specific context, using as a comparison condition the very passive learning approach they have already criticised as being ineffective as supporting learning.

My argument is that such research is unethical

• It is not genuine science as the researchers are not testing a genuine hypothesis, but rather looking to demonstrate something they are already convinced of (which does not mean they could not be wrong, but in research we are trying to develop new knowledge).
• It is not a proper test of the effectiveness of the progressive pedagogy as it is being compared against a teaching approach the authors have already established is sub-standard.

Most critically, young people are subjected to teaching that the researchers already believe they know will disadvantage them, just for the sake of their 'research', to generate data for reporting in a research journal. Sadly, such rhetorical studies are still often accepted for publication despite their methodological weaknesses and ethical flaws.

I am not suggesting that Mamombe, Mathabathe and Gaigher have carried out such a rhetorical study (i.e., one that poses a pseudo-question where from the outset only one outcome is considered feasible). They do not make strong criticisms of the lecturing approach, and even note that it produces some learning in their study:

"Similar to the inquiry group, the drawings of the learners were also clearer and easier to classify after teaching"

"although the inquiry method was more effective than the lecture method in eliciting improved particulate conception and reducing continuous conception, there was also improvement in the lecture group"

p.9, p.10

I have no experience of the South African education context, so I do not know what is typical pedagogy in primary schools there, nor the range of teaching approaches that grade 4 students there might normally experience (in the absence of external interventions such as reported in this study).

It is for the "two experienced teachers who are university lecturers and well experienced in teacher education" (p.3) to have judged whether a lecture approach based on teacher telling, children making notes and copying drawings, but with no student activities, can be considered an effective way of teaching 8-9 year old children a highly counter-intuitive, abstract, science topic. If they consider this good teaching practice (i.e., if it is the kind of approach they would recommend in their teacher education roles) then it is quite reasonable for them to have employed this comparison condition.

However, if these experienced teachers and teacher educators, and the researchers designing the study, considered that this was poor pedagogy, then there is a real question for them to address as to why they thought it was appropriate to implement it, rather than compare the enquiry condition with an alternative teaching approach that they would have expected to be effective.

Sources cited:

• Mamombe, C., Mathabathe, K. C., & Gaigher, E. (2020). The influence of an inquiry-based approach on grade four learners' understanding of the particulate nature of matter in the gaseous phase: a case study. EURASIA Journal of Mathematics, Science and Technology Education, 16(1), 1-11. doi:10.29333/ejmste/110391
• Taber, K. S. (2013). Modelling Learners and Learning in Science Education: Developing representations of concepts, conceptual structure and conceptual change to inform teaching and research. Dordrecht: Springer.
• Taber, K. S. (2019). Experimental research into teaching innovations: responding to methodological and ethical challenges. Studies in Science Education, 55(1), 69-119. doi:10.1080/03057267.2019.1658058

* Material reproduced from Mamombe, Mathabathe & Gaigher, 2020 is © 2020 licensee Modestum Ltd., UK. That article is an open access article distributed under the terms and conditions of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) [This post, excepting that material, is © 2020, Keith S. Taber.]