Book review of "Approaches to Qualitative Research in Mathematics Education by A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.)"

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Proulx, J., & Maheux, J.-F. (2016) Approaches to qualitative research in mathematics education

by A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Mathematical Thinking and

Learning, 18(2), 142-150.

DOI: 10.1080/10986065.2016.1151294

Cet article est disponible au :

This article is available at:

https://www.tandfonline.com/doi/full/10.1080/10986065.2016.1151294

What follows is the pre-print. It might differ (significantly) from the final published version.

Ce qui suit est le pre-print. Il peut être (très) différent de la version finale publiée.

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Methodological And Research Developments Endeavours : Engaging with and

Going beyond Mathematics Education Research

A.Bikner-Ahsbahs, C.Knipping, & N.Presmeg (Eds.). Approaches to Qualitative Research in

Mathematics Education, Springer, 592 pages

Reviewed by

Jérôme Proulx and Jean-François Maheux

Université du Québec à Montréal, Canada

"Five h undred p ages– the truth c an't be that long!"

G. Benn on Karl Jaspers's book Von der Wahrheit [About truth]

The above epigraph, used by Heinrich Bauersfeld for his review of the 1992 Handbook of

research on mathematics teaching and learning (Bauersfeld, 1992), felt quite appropriate when

we first saw copies of the book we were invited to review arriving on our desks this summer.

Bikner-Ahsbahs, Knipping, and Presmeg's edited book is huge! Not being experts on the topic of

research methodologies, we found it interesting to look at the challenge of reviewing such a piece

with intrigued eyes: do we know that much about qualitative research in mathematics education?

Following Hazlitt (1822), we did not want to position ourselves as critics:

A critic does nothing nowadays who does not try to torture the most obvious expression into a

thousand meanings, and enter into a circuitous explanation of all that can be urged for or against

its being in the best or worst style possible. His object indeed is not to do justice to his author,

whom he treats with very little ceremony, but to do himself homage, and to show his acquaintance

with all the topics and resources of criticism.

Reading the Preface and Final Considerations (Chap.19 in the book), we also realized that our

review was not necessarily about presenting the book (its organization, the content of its chapters,

the links between them) because this had already been well done. So we decided to adopt Kelle &

Buchholtz's (Chap.12) suggestion about aiming for productive debate. Our review would have to

be a "new look" (re-view) at the work, our take on some of the presented ideas, which meant that

we would have to engage with those ideas, play with them, and take them further to see where,

beyond our current state, the book could lead us as a community.

First, let's get something out of the way: Should one read this book? Our answer is yes, but

maybe not cover to cover. As some authors themselves mention, these chapters are meant to get

one started, to gain a sense of and some examples about various approaches. It is more of a

reference book; and for us, one to be used as a stepping-stone to push ideas further. For us, the

book serves a driving objective: to give an overview for those who, almost as neophytes, would

like to start learning about such and such approach.

However, to appreciate its publication in Springer's Advances in Mathematics Education series,

we also need to see how those 600 pages of information from researchers all over the world can

help us to move forward as a community. This leads us to the next set of questions: What do we

do with this? Where do we go from there? How is the future? Addressing these questions is the

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core intention of our review. To tackle them, we enter into epistemological issues and

dimensions: a productive way to carry on the conversation/debate in a new direction. New? As

the saying goes, "the proof of the pudding is in the eating", and reading the book proved to us

how we have not engaged in epistemological issues enough. Epistemological issues are rarely

present in the book explicitly, timid exceptions being chapters by Teppo (Chap.1), Mayring

(Chap.13), Kelle & Buchholtz (Chap.12), and Mok & Clarke (Chap.15). In relation to

mathematics education research approaches, epistemological concerns can be taken up in (at

least) two ways: 1) regarding methodology and the research process, and 2) in relation to

mathematics itself. Our review of Bikner-Ahsbahs, Knipping, and Presmeg's edited book treats

both concerns. Moreover, it attempts to bridge epistemological reflections about methodology

and the research process per se with issues about mathematics as a specific field of study, and

thus mathematics education as a specific field of study in itself.

In the following sections, we raise eight epistemological issues relative to the book and where it

can lead us. Why eight? Let us call it a lack of space, because there was a great deal more to

address in this enriching book.

Point 1: Varieties in epistemological cultures

With all its chapters on a variety of qualitative methodologies well traced and explained, the book

shows clearly that we are now at the point where we can advance our field by attempting to make

some of these methodologies interact. By this we think less of the current trend of networking

and bridging methodologies for, among other things, attaining deeper understandings of the

phenomenon under study, but mainly to engage in differences and rationales in variety of

"positionings", of means of conducting research. Such interactions could lead epistemological

issues to come to the fore and to be addressed. We are well served to do so with this book. For

example, we could ask how the perspective of Grounded Theory methods presented by Teppo

(Chap.1) and Vollsted (Chap.2) can be engaged with Content Analysis methods presented by

Mayring (Chap.13) and Schwarz (Chap.14). Or how can Mok & Clarke's (Chap.15) viewpoint on

Triangulation and Kelle & Buchholtz's (Chap.12) Mixed Methods perspective be articulated to

discuss Kidron & Bikner-Ahsbahs's (Chap.9,10) Networking of Theories? They seem to stand on

similar epistemological grounds concerning views of knowledge production, of research, and of

science, but do they?

Another way to raise such (healthy) debates in and for mathematics education could be by

examining how a number of similar or even at times identically formulated concepts are used

throughout the book, often with different meanings. There is value in attempting to contrast these

varied concepts and formulations and scrutinize their signification in the varied approaches,

grasping insights about methodological and epistemological orientations through these

similarities and differences. An example is the Abstraction in Context presented in Dreyfus,

Hershkowitz & Schwarz (Chap.8), and mentioned again in Kidron & Bikner-Ahsbahs (Chap.10):

Do both use the words/concept in the same ways with the same purpose or meaning? What are

differences, insistences, and so forth? Similarly, we could question the notion of Triangulation

found in Mok & Clarke's (Chap.15), directed toward exploiting difference and revealing

diversity, with the implicit or explicit idea of triangulating data (e.g. Kelle & Buchholtz,

Chap.12). Similarly, epistemological cultures could also be debated with regard to notions such

as a priori and a posteriori analysis, used quite differently by Dreyfus, Hershkowitz & Schwarz

(Chap.8) and Artigue (Chap.17). It seems to us fundamental and healthy to evoke such

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epistemological oppositions in a field of study that aims to continue growing, expending, and

deepening. And, this book is rich in occasions to do so.

Point 2: Interrelations of methodology and theory

Most contributors to the book maintain that there are strong links between methodological

considerations/approaches and theoretical frames (as discussed also by Cobb, 2007 and Silver &

Herbst, 2007). These links are so prevalent in the first ten chapters or so that one doubts the two

can be disentangled: methodologies are often strongly grounded, intertwined, or even arising

from particular theories (foregrounded or not, cf. Bakker & van Eerde, Chap.16). Also, these

links are even more developed when some authors assert, like Radford & Sabena (Chap.7) or

Teppo (Chap.1), that research is (perceived as) a theory production endeavour. The blurring of

methodology and theory is augmented when methodology in some chapters is collapsed with data

analysis procedures. This leads to important questions for a field of study: Does data analysis

count as methodology? Are there differences between an analytical framework for analyzing data

and a theoretical framework that grounds the study? Krummheuer's (Chap.3) work raises

significant issues about the meaning of qualitative research methods: Is it about data gathering? Is

it about data analysis? Is it about theorization? And above all, is there a need to disentangle these

issues or an advantage of working on them simultaneously?

The notion of methodology also seems to need to be enlarged in order to accommodate the

strategies undertaken for Networking of Theories (Chap.9,10). Such accommodation might,

however, lead to conceive methodology more as (a series of) techniques undertaken for

conducting studies. And, it is not clear if such an orientation might be compatible with the

distinction made by the philosopher Edgar Morin (1990) between methodology and method,

echoed in Radford & Sabena's (Chap.7) assertion that:

A method is rather a reflexive and critical endeavour–a philosophical practice. As such a method

conveys a worldview that provides ideas about the entities or phenomena that can be investigated

and how they can be investigated. (pp. 178-179)

Although other social sciences have addressed questions of methodology and theory, reading this

book makes one realize that these questions are still alive and salient in our field, and need to be

tackled in our own ways and on our own ground, that is, with/in mathematics education research.

The book makes it clear that these questions have to be raised from within our own research

community, as we further discuss below. .

Point 3: Methodologies produced with/in our own field

The methodological approaches reported in the book are essentially borrowed from or inspired by

other fields of research (mostly from other social sciences disciplines), with the exception of

three chapters in Part XI (Bakker & van Eerde [Chap.16], Artigue [Chap.17] and Henrick, Cobb

& Jackson [Chap.18]). Simply said, most methodologies presented in the book are not specific to

mathematics education research. Teppo [Chap.1] even mentions that the Grounded Theory

approaches that she reports on "do not fully meet the needs of mathematics education research, in

which mathematics, the subject matter, should be an integral part of any research study" (p. 18).

On the other hand, mathematics education research is what mathematics education researchers do

(Sierpinska & Kilpatrick, 1998).Hence, even when methodologies are "borrowed" from other

fields, they are made specific to mathematics education research through their uses and highlight

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concerns and intentions of developing methodologies for/of mathematics education research in

the first place. What progress have we made on this since Sierpinska and Kilpatrick's (1998)

conclusions? Might a shortage in epistemologically driven debates explain why, following the

book, we seem to advance little since Piaget's remarks about the methodological development for

mathematics education research (didactics) away from psychology?

There is a necessity to constitute a special study of didactics that is both supported by psychology

and distinct from it […] adapting to a classroom is really different than doing psychology with

students of the same age. It is absolutely excluded that one can directly draw didactics lessons

from psychology. For example I think of teaching arithmetic, where things can be represented in

many ways. The psychologist cannot tell you in advance that this way is better than that way.

There needs to be didactical experiments, and not psychological experiments, didactical

experiments that are obviously much more tedious (because of the time they require). It is thus a

science that seems to me necessary to develop, but much more sensitive than psychology, much

more costly because it takes much more time and requires greater efforts. ( Piaget, in Morf, 1971,

pp. 4-6, our translation).

There are, of course, methodologies more directly related to and developed in mathematics

education research, for example, didactical engineering described by Artigue (Chap.15) or the

design-based research described by Bakker & van Eerde (Chap.16) and by Henrick, Cobb &

Jackson (Chap.18). We could also mention Steffe's teaching experiment methodology (e.g.,

Steffe's 1983; Steffe & Thompson, 2000), briefly discussed in Bakker & van Eerde's and

Henrick et al.'s chapters. But the point is that this book made us realize there is room for debate

about where our methodologies come from and what they do, especially from an epistemological

perspective. These are worthwhile debates for understanding our field better for ourselves, and

positioning it in relation to natural sciences or social sciences, a position that is not obvious, as

Radford & Sabena (Chap.7) explain.

Point 4: On methodologies for the collective

Another theme that emerges from reading this book is the significance of the study of classroom

collectives. In many of the chapters and the studies reported, data are often collected from

classroom collective situations. It is, however, striking and highly interesting that the scrutiny of

the classroom collective seems always to be done with tools and intentions that address

individual learners or individual cognition/achievement. Thus the study of the collective

classroom is never done for the collective classroom itself, but for the individual learner (with

potential exceptions alluded to in Saxe, et al. (Chap.11), and Dreyfus, Hershkowitz & Schwarz

(Chap.8, p. 215).

This situation is surprising because many theories adoped by mathematics education research

bring out issues of collectivities or social and cultural aspects recognizing the role of social

aspects. However, as Lave (1988, 1991) argues, this social turn is often at best used only to

consider the presence or impact of the social aspects on individual cognition. Despite recurrent

interest in them, we rarely aim for the social aspects in themselves, perhaps in part because we

lack the means to do so. The move back to the individual learner seems understandable in a field

that has strong interest and ties to schooling, which is typically seen as individually focused (with

its assessment, plans, organisations, etc.). But this orientation may also prevails because we do

not know enough about how to look at classroom collectives, even from a research perspective.

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What could the study of the collective means for mathematics education research? What specific

methodologies might help bring out this collective phenomenon? It is our contention--and we

must acknowledge the numerous discussions that we have had with colleagues on these issues

(see McGarvey et al., 2015)--that bringing out the collective requires an epistemological shift

allowing us to zoom in on a collective phenomenon (e.g. learning) without reverting to individual

markers or dimensions (see Simmt, 2015). This also leads us back to one of our earlier

observations about the interrelation between methodology and theory: developing methodologies

for studying collective phenomena requires at the same time theorizing about these collective

phenomena themselves, and vice versa.

Point 5: The researcher as observer

Krummheuer's (Chap.3) work on processes of argumentation raises methodological issues and

questions about gathering data, and data analysis procedures producing data. It thus highlight the

presence and impact of the researcher in the data, as well as the influence of the frames used for

giving meaning to the research. Epistemologically speaking, issues about the objective separation

between the researcher and the researched (the in vitro approach) are long overdue. Among other

things, we have to consider the difference between data-gathering and data analysis, or whether

any difference between them simply collapses. For example, in Krummheuer's work, one might

wonder if Toulmin's frame is used to describe argumentative processes or to reconstruct events,

or even if it is used to produce interactions as argumentative processes. Or is it all the same?

Many chapters could also be read with similar questions in mind.

Even if as researchers we reject the position that "the phenomenon being observed" tis

independent of the observer and can be decontextualized from the observational act, we often,

nevertheless, take this position implicitly by how we report our findings (Barwell, 2009). That is,

even if we agree that we cannot account for what really happens, research is still being reported

(and maybe even conceived) as if this were the case. What would research look like if we were to

behave differently and avoid presenting what we report as a report of "what really happened"?

More than anything else, research would have to consider always how the observer is central to

any account of any given phenomenon, for "everything said is said by an observer to another

observer that could be himself or herself" (Maturana, 1988, p. 27). If the researcher accepts that

one does not describe what is being observed, but constructs one's own account of one's own

perceptions (Barwell, 2009), the stakes of analyzing data rest no longer in their truth or validity,

but in what they offer to oneself and others. From this perspective, the issue of "accurate

account" fades into meaninglessness: one becomes geared toward the development, as

Schrodinger (1992/1951) asserted, of what is likely to be true 1 (something we refer to as the

development of propositions, e.g., in Proulx, 2015). What would this mean for our field of

mathematics education research? What sense would we make of data in this context? What sense

can we make of earlier research results that were conceived along what Barwell critiques as a

decontextualized-separated-independent results? Those are significant epistemological questions

relative to the role of the researcher in the research endeavour.

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1 This is our translation of the French "susceptible d'être vrai" (1992, pp. 41-43).

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Point 6: Developing our own "science"

The above issues culminate in raising questions about the scientific character of our own research

field. In similar ways that Cobb (2007) and Lave (1988) assert, as a community we seem to be

hanging onto a romanticized/idealized view of science. What many of the chapters highlight is

not the question of whether our research field is scientific or not, but our own understandings of

what science is, what it represents, and what role we attribute to it. Radford & Sabena (Chap.7)

emphasize, in their argumentation about the differences between natural and social sciences, that

there is a clear need to rethink our view of what science is.

Thus, questions concerning replicability, for example, which Radford & Sabena (Chap.7)

question as a valid distinction between natural and social sciences, have been initiated by

researchers in our own field such as Mason (2009), who writes:

If it is either impossible or not necessary to be able to replicate the conditions of a study, what

is it that we are gaining by reporting on our studies? My radical response to such a question is

that what matters most is educating awareness by alerting me to something worth noticing

because it then opens the way to choosing to respond rather than react with a more creative

action than would otherwise be the case. I don't need all sorts of detailed data, because the

more precise and fine-grained the detail, the less likely I am to pay attention to the over all

phenomenon being instantiated, and so the less likely I am to recognise it again in the future

and so choose to act differently. (p.12)

As a research field, we are thus at a point where we can go beyond romanticized/idealized views

of (doing) science. This book shows us that, as a community, we have to develop our own

"standards", our own ways of doing. If reflecting on these matters is no simple task, it can have

important outcomes for our own field, starting with a major shift from truth-seeking to ideas

generating (to use Valero & Vithal's, 1998, expression). Mok & Clarke's (Chap.15) arguments

about embracing differences, contrasts, incoherencies and variabilities in order to reveal

complexity rather than concealing it is certainly a step in that direction. Such perspective can be

linked to (debatable?) epistemological views on the progress of science advocated by Dewey

(1910):

The conviction persists, though history shows it to be a hallucination, that all the questions that

the human mind has asked are questions that can be answered in terms of the alternatives that the

questions themselves present. But, in fact, intellectual progress usually occurs through sheer

abandonment of questions together w ith both of the alternatives they assume – an abandonment

that results from their decreasing vitality and a change of urgent interest. We do not solve them:

we get over them. Old questions are solved by disappearing, evaporating, while new questions

corresponding to the changed attitude of endeavor and preference take their place (pp. 18- 19)

Point 7: On rigor in qualitative research

Issues of scientificity also lead one to question the "scientific criteria" used to qualify "rigorous"

mathematics education research, criteria such as validity, reliability, and causality. Yet, this book

does not always make it obvious how we stand as a community on such matters of "scientific

rigor", despite the well-known debates (a few decades ago) between quantitative and qualitative

research (see e.g., Guba & Lincoln, 1982, 1985; or more recently Kemp, 2012). We were

surprised, for example, when we read Bakker & van Eerde's (Chap.15) assertion that "All

qualitative research approaches face this challenge of drawing causal claims" (p. 434). One might

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wonder whether we should not already be beyond this view about causality and rigor, knowing

how little mathematics education research "findings" actually affect teachers' and students'

everyday lives (Kilpatrick, 1981). Questions of a similar nature could be raised about notions of

saturation (Teppo, Chap.1) or generalizability (Kelle & Buchholtz, Chap.12); on the other hand,

we have Artigue's (Chap.16) reported work, which is not lodged in this kind of causal paradigm.

Inspired by the work of Jardine (1994) on fecund cases, or simply from Wolcott's (1994) or

Geertz's (1967) ethnomethodological work, rooted in qualitative paradigms, might we not engage

more deeply in developing similar alternatives to traditional scientific rigor, but again within our

field, attuned to mathematics and mathematical activity in educational settings? These

considerations might lead us far beyond the usual accounts, or to use Mok & Clarke (Chap.15)

expression, toward post-positivist views about rigor, causality, and generalization. We see such

reflections about research and the meaning of research findings as part of our future

(epistemological) challenges as a research field.

Point 8: Writing research

Finally, it is always surprising to us how rarely our community considers modes of writing

research. In qualitative paradigms, the importance of how research is presented to our colleagues

immediately comes to the fore. But as researchers we still seem to write papers as if they were

merely "transcriptions" of well-formed research questions and analysis, simple "descriptions" of

research settings and classroom events, unproblematic presentations of conclusions, and so forth.

Barthes (1986) associates this with a certain view on method: "everything had been put into the

method, nothing remains for the writing" (p. 318). Throughout the book, the (actual) challenges

of researching in mathematics education are continually vanishing in the smoothness of polished

arguments and well-chosen examples; and among these struggles are the labour of writing

research and its role as actually producing research.

In the Preface, the authors make reference to Roth's (2005) analysis on how participating in

research "helps students to understand methodologies in a much better way than general how-to-

do descriptions are able to achieve". As an alternative to how-to books, Bikner-Ahsbahs,

Knipping, and Presmeg's edited book wants to offer the "detailed descriptions on how

methodologies are substantiated in a specific project, how they are implemented to investigate a

research question, and how they are used to capture the research objects" (p. v). However, if we

want our student to "participate" in research through reading (about) research, additional issues

appear in need to be addressed. In Roth's view, it is not (only) examples of research that provide

students with incomparable learning opportunities, but also the inherent arduousness that come

when actually living it. Epistemologically speaking, there is still an enormous difference between

first-hand experience and illustrative accounts of one's action (see e.g., Roth, 2015).

What, then, would it mean to develop research (writing) practices in which the complexity of

researching mathematics education could become salient, so that readers would be brought closer

to how research unfolds, and observe, reflexively the relationship between research and writing

stressed by scholars in various fields of social research (e.g. Derrida, 1976; van Manen, 1989;

Ivanič , 1998)? What if in the future qualitative research in mathematics education were to

consider seriously how writing research is not simply the transmission of findings? What kinds of

"methodologies" of/for writing research might we develop? How might these connect with our

larger epistemological positions on students' or teachers' mathematical activity, and with our

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own activity as researchers and analysts? These are, for us, fascinating questions that emerge

from this voluminous reading.!

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Closing remarks

One of our main points in this review is that we can now think of and develop methodologies

specific to mathematics education, for example, those that focus on collectivities related to

classrooms. These discussions in our field would not be about these methodologies per se, but

mainly about their presence as methodologies in /for mathematics education research. It would be

mathematics education research, as our science, which acts as a grounding reference point in our

discussions and arguments; other social sciences fields (sociology, psychology, anthropology,

etc.) or any other research domain may inspire our methodologies but not ground them. For

methodologies to be specific to mathematics education not only entails that they are produced

with/in and for mathematics education research, but also that their understandings and rationales

be grounded in mathematics education research (as are Steffe's teaching experiment or Artigue's

didactical engineering).

The second main point concerns our way of conceiving the place and role of the researcher.

Specifically, our community would gain from considering: (1) how this impacts one's view of

what research is and how it influences one's work; and what it says about (2) causality (and, in

that connection, what it says about quantitative and qualitative research, their differences and

similarities); (3) data analysis procedures; (4) the writing/producing process; and (5) the

combining of methodologies. We think it is time that questions raised by Sierpinska and

Kilpatrick's (1998) Mathematics Education as a Research Domain: A Search for Identity to be

revived, and debates need to be initiated about where we see ourselves going, and standing, and

why.

So let us close with this: the ball is in our camp, as a community, to tackle (or not) these

epistemological questions and issues. To paraphrase Kelle & Buchholtz's (Chap.12)

characterization of the paradigmatic wars concerning mixed methods, some of us will prefer to

keep a pragmatic profile, whereas others will dig into epistemological questions. We have argued

in the past for the necessity, in our research field, to keep epistemological issues alive, and above

all things (Proulx & Maheux, 2012). We obviously greatly hope that this challenge be taken up

by the community by building on what we currently have, as done in this volume on qualitative

approaches in mathematics education research, and going beyond our current methodological and

research development endeavours.

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  • Helena Roos Helena Roos

This article presents a reflection on what the qualitative interview method conducted with students can provide to (mathematics) education research in terms of in-depth knowledge and what critical methodological points should be taken into consideration. Repeated interviews with the same students in relation to research quality is considered. The argument is that repeated interviews can provide in-depth knowledge and a grasp of students' understandings. Critical points to consider when gaining in-depth knowledge are person-dependency, process ethics, connections between repeated interviews as a method and the aim, and the re-interview effect. These are important to discuss and reflect on throughout the research process, as they can function as quality criteria when producing in-depth knowledge in qualitative research with repeated interviews.

  • Jérôme Proulx Jérôme Proulx

Influenced by Bauersfeld's above proposal, it is my contention that the role of mathematics education researchers is not to follow and answer society's or practice's problems and needs, but to attempt to bring them forward by hurrying ahead, by aiming to participate in and push the continually evolving dynamic of society and practices. In my view, the role of the researcher is at its core (1) to conduct thought experiments on ideas, through (2) developing distinctions for thinking about and understanding mathematics teaching, learning, and practices, and thus (3) to generate ideas to bring practices and society forward. The researcher's role is to generate, using Bateson's (2000) words, differences that make a difference or, following St-Exupéry, to "mettre des forces en mouvement". In short, research is not geared toward truth-seeking, but the generation of ideas.

La recherche, disait Dewey, avance au rythme des questions qu'elle se pose. La mort toute récente d'Ernst von Glasersfeld, un des « pères » des théories constructivistes, nous conduit à réfléchir à certaines questions épistémologiques qui ont été posées au démarrage contemporain de la recherche en didactique des mathématiques, et que nous souhaitons ici re-lancer. Ces questions, qui concernent l'apprentissage et la nature des connaissances, méritent selon nous d'être reprises aujourd'hui pour examiner leur apport en didactique des mathématiques, mais aussi la manière dont elles sont traitées de ce point de vue. En particulier, nous pensons aux notions constructivistes de viabilité , d'erreur en tant que connaissance et de subjectivité des interprétations. Issues de la pensée mise en avant par von Glasersfeld, nous suggérons que ces questions d'ordre épistémologique ont agi comme moteur de réflexion en didactique des mathématiques et que ce type de réflexion peut donc contribuer de manière importante au développement de notre domaine de recherche.

  • Sandra J. Kemp

context: Ernst von Glasersfeld's radical constructivism has been very influential in education, particularly in mathematics and science education. > Problem: There is limited guidance available for educational researchers who wish to design research that is consistent with constructivist thinking. Von Glasersfeld's radical constructivism, together with the theoretical perspectives outlined by constructivist educational researchers such as Guba and Lincoln, can be considered as a source of guidance. > method: The paper outlines a constructivist knowledge framework that could be adopted for educational research. The discussion considers how judgement of what counts as knowledge could be made, and how the set of procedures chosen could enable the researcher to represent the findings of the inquiry as knowledge. > Results: An argument is made for researchers to explicate the criteria for judging an inquiry. Each criterion can then be linked to the standards to be reached and the techniques for generating data. The joint satisfaction of criteria and techniques for a constructivist inquiry creates conditions that indicate the "trustworthiness" or "authenticity" of an educational research study. > implications: The illustration of how a constructivist inquiry could be judged recognises how the contribution of von Glasersfeld's radical constructivism can be used to inform the practice of educational research. > constructivist content: The argument presented in the paper links to radical constructivism and suggests ways in which it can be applied in the context of educational research.