Writing an Empirical Research Report in Mathematics Education: Understanding the Genre and Its Registers

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Patricio Herbst University of Michigan

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As I prepare to leave the position of editor-in-chief of JRME, I am thinking about the unique opportunities the job has afforded me. The usual activities of researcher, instructor, and mentor, or the service to the field and the university that I did as a faculty member, had allowed me to peer into possibilities that might come with the editor’s role and attracted me to it. But only being in the role, and being willing to commit to it, provided me with the opportunity to learn and grow in ways that made these almost-6 years a memorable, joyful period of my professional life. In this last year of editorials, I wish to reflect on what the position has afforded me, starting from some of what I have learned about writing for publication and that I can convey to authors. A salient set of learnings has to do with what I have gleaned about scholarly writing in our field from reflecting on my work with authors of manuscripts that have been accepted for publication to produce a final copy. I write this editorial with the hope of helping authors and reviewers relate to the research report genre as they prepare or review potential contributions to the journal.

Teaching Scholarly Writing in Mathematics Education

This editorial is about scholarly writing in mathematics education, a small attempt at making explicit what one might call the writing curriculum for mathematics education scholars. As I write this, I cannot ignore images of my own former self growing up in the field and of receiving my writing (always printed) profusely marked up (in pencil) by my mentor Jeremy Kilpatrick. At the time, I sometimes resented that Jeremy paid so much attention to detail in the writing that it was not clear to me whether he cared about the overall ideas I wanted to convey. I saw him reacting like an editor and wondered whether that had become his modus operandi after having been JRME editor (a decade before I arrived in Athens). What I ignored at the time, and I learned over the ensuing years, is that the line-by-line attention to detail Jeremy exercised was a tactic to teach me (and his other students) about writing, and particularly about addressing the reader.

The tactic of teaching writing by engaging line by line with the author’s text involves reacting contextually to the author’s writing—asking for clarifications, saying back what the reader understood or how the reader was left, proposing alternative phrasings, quibbling with word choice or tone, questioning images and metaphors, enforcing style, and more. As editor, working with manuscripts accepted pending minor revisions, I have proceeded similarly. Authors of those manuscripts probably share the experience of having to wait a bit to hear from me after they have sent their revised manuscript and quite often receiving back a heavily marked-up document. It takes me a long time to work through their manuscripts—an hour for 10 pages of manuscript, at best. But, on the basis of my own experience learning from Jeremy’s editing, I have the hope that as we interact this way, editor and author accomplish more than improving the text—we teach and learn writing to each other.

But therein lies the question. Whereas one has the sense that editor and author are respectively (and reciprocally) teaching and learning about writing, the explicit content taught and learned remains very much tied to the context of what is being written and may, at times, seem arbitrary, platitudinous, or minor. But if we look at the whole experience, I would think that what gets learned may fall under the larger heading of dispositional or aesthetical, and these are no small things—we learn a taste for writing that helps us build our identity not only as writers or intellectuals but more specifically as denizens of the field of mathematics education research, people who share a common culture with a common way of interacting through text. As I develop the theme of the writing curriculum in this editorial, I bring in some discussion of language and culture that help me name and organize my editorial practice into a budding writing curriculum of sorts. In doing that, I hope I can frame the experience of writing for publication, especially for novice researchers.1

Learning the Genres and Registers of Mathematics Education Scholarship

I want to frame the experience of writing for publication, including interacting with reviewers and editors, as offering the author an opportunity to learn about genres and registers of scholarly writing in mathematics education. In my experience, it is the rare manuscript that goes through production without some substantial reworking of language. If we also think about rejected manuscripts, issues with written expression are many. These are not generic language issues tied to whether authors are native English speakers because even authors whose native language is English sometimes receive reviewers’ suggestions of having a native English speaker edit the text. These are not generic academic writing skills either because reviewers may also criticize the language use (e.g., word choices, assumptions made about the reader’s knowledge, or lack of details) in manuscripts written by authors trained in other fields (e.g., educational psychology, mathematics). I believe the suggestion that language competence or academic writing skills need development is too unspecific to be helpful. Indeed, what is at issue is much more specific than English language or academic writing: it is competence with the genres and registers we use in mathematics education scholarship.

In suggesting that the experience of writing for publication in our field should be framed as an opportunity to learn the genres and registers of our field, I am taking issue specifically with an alternative framing that I think is often present as a default and that we can caricaturize by the idea that writing for publication is an individual’s attempt to express themselves in spite of or against the pet peeves and small-mindedness of editors and the laziness or ignorance of reviewers. That caricature exhibits an approach to writing that is individualistic and sees the editorial process as bureaucratic or even authoritarian. I surmise that all of us have at some time felt that way—I certainly did, early in my career: I felt so entitled that I expected reviewers and readers to work hard to understand my prose and was not thankful enough for what they were doing to help me improve my text. Over the years, I have come to realize that the experience of writing for publication in mathematics education should not be framed with respect to individual expression, and the review and editing process should not be thought of as merely a set of hoops to jump through to be allowed to express oneself.

Indeed, even those who practice writing as an art—essayists, playwrights, poets, and storytellers—express themselves within and against the norms of writing in their field. In the writing arts, where originality in the use of language is the coin of the realm, authors still need to know their genres to be able to successfully negotiate the reception of their originality. However, in the communication of scholarship, originality in the use of language is not the coin of the realm. Rather, we trade in the complexity of ideas, in the novelty of information, and in the rigor of arguments. In JRME, reviewers assess the value of a manuscript by looking at its contribution to the field of research in mathematics education and consider this contribution with respect to theory, methodology, or findings. To fulfill those goals, authors sometimes need to innovate in language: For example, some authors coin new words or expressions, whereas others propose restricting the meanings allocated to current words or expressions. But, as authors, we should do that innovation in language while recognizing that we work with and against uses of language that are normative in our field (even though such norms are only partially explicit in the American Psychological Association [APA] style guide). I invite readers to think of such normativity as associated with the genres and registers to be learned and used and not as reducible to the arbitrary preferences of powerful position holders.2

Because this journal’s central focus is empirical articles, this is the genre that our authors have the chance to learn the most about when they work on an article for JRME. But often, the reactions from editor or reviewers will also provide glimpses of other genres that have currency in our field, including the Research Commentary, a genre that we are constructing as we keep publishing instances of it, or the practitioner’s article, for which other outlets are available, such as the other journals published by the National Council of Teachers of Mathematics (NCTM), Mathematics Teacher Educator and Mathematics Teacher: Learning and Teaching PK–12. In what follows, I first address genres and registers at some level of generality, with the goal of providing some framing that can, on the one hand, help authors face the writing they work on with the expectation that it be an educative experience and, on the other hand, help reviewers fine-tune their comments about language so as to make the experience educative.

Genre and Register in Systemic Functional Linguistics

Readers may recognize the word “genre” from its uses in ordinary discourse—novel, short story, biography, and poetry, for example, are among the literary genres. The word “register” is less common in ordinary parlance, but some mathematics education scholars (e.g., Duval, 2020) have used it to refer to underlying differences among symbolic, geometric, graphic, and linguistic representations in mathematical discourse. More relevant to our present discussion are Pimm’s (1987) and Morgan’s (2002) uses of Halliday’s (1978) notion of the mathematical register. I raise these existing examples of the use of “genre” and “register” to evoke some common ground but also to suggest the need for a bit more precision when applying these terms to describe mathematics education scholarly writing (in contrast with classroom language). In what follows, I present an interpretation of how systemic functional linguistics (SFL) treats the semiotic concepts of genre and register that I believe can be helpful as we consider various kinds of scholarly writing in our field.

SFL is a theory of language proposed by Michael Halliday that considers language as a social semiotic system, that is, as an organized set of signs that people use to make meanings in the context of sociocultural activity. Key in this consideration is that language participates in the constitution of much sociocultural activity (e.g., purchasing goods and services, getting married, or entertaining). The communication of research is an activity partially accomplished through the use of language. Thus, the relationships between language and culture and between texts3 and social situations are at the center of the theory, and this makes the theory useful to us.

According to SFL, genre is a construct that describes the types of texts associated with different types of activity in the world where those types of texts play a role—thus, one can speak of the genre of farmers’ market purchases, of doctor’s visits, or of parent-teacher conferences. All these activities are accomplished not only through singular actions (e.g., transportation to the doctor’s office) but also through semiosis, or the use of signs (language, in particular). The type of semiosis that participates in accomplishing the activity is a genre. Thus, social purpose is key to genre: The type of text needs to contribute to the effectiveness of the activity. According to Martin and Rose (2008), genres are manifestations of the different social purposes for which we use language and can be modeled by sequences of obligatory and optional stages in which language and actions interact to fulfill those purposes.

Here, I apply this conception of genre to empirical research reports in mathematics education. This genre plays a role in the activity of communicating the research work and findings of a research team to its audience, which includes as a core the mathematics education scholarly community.4 This genre, like other academic genres, is constituted through the use of written language, symbols, and visuals. The purpose of the empirical research report reveals itself in stages, which are key sections of an empirical research report, such as Title, Abstract, presentation of the problem, Literature Review, and so on. But though the aggregate of sections constitutes the article as an example of the genre, the sections themselves can be distinguished in their uses of signs—as happens in other genres (e.g., a doctor’s visit in the U.S. usually includes speaking with an intake technician before speaking with the doctor, and patients speak differently about their conditions with the technician than with the doctor). The presence of combinations of language and visuals, for example, is one difference across sections of an article (for example, abstracts do not include figures or tables). However, more important differences across sections of the article are better described with respect to the registers that each section employs.

The construct of register was introduced by Halliday (1978) initially to describe variations of natural language according to use. He exemplified this with the mathematical register; one might also consider a medical register and a cookery register as examples—specializations of natural language for particular uses. Vocabulary is one place where register differences can be recognized: The word “center,” for example, has a special meaning and use in geometry that is different from its use in printing—the first one is usually a noun and refers to a point that has some properties (e.g., “A is the center of a circle”), the second one is a verb used to describe aspects of page layout (e.g., “center the title”). However, register differences go beyond vocabulary.

When defining register, Halliday coined the terms Field, Tenor, and Mode to name the ways in which register variation is realized. These are context variables: Field alludes to the ways a register specializes language to address particular ideas and experiences in the world (e.g., mathematical concepts). Tenor alludes to the ways register choices support the development of particular kinds of relationships between communicants (e.g., author and reader of a mathematics education research article). Mode alludes to the language resources that organize the flow of information in a text, instantiating particular kinds of social interaction (e.g., by defining new constructs and potentially marking them typographically before using them in technical ways).

Register and genre are related concepts insofar as both of them refer to variations in language use. Genre pays attention to the realized types of text in relation to specific social purposes. Genres are then instantiated through configurations of language choices that realize the Field, Tenor, and Mode of the context of the situation. Along those lines, the realization of different stages of a genre (the accomplishment of different aspects of the social activity) might appeal to different registers or different combinations of registers. Within this interpretation of register, one can say that register choices realize the social purposes of a genre in particular ways that allow for variation (see Matthiessen et al., 2010, p. 22). To accomplish an example of a genre (i.e., to write an empirical research article), an author makes use of a variety of registers, with different stages of the genre being realized by possibly different combinations of different registers.

Next, I use this interpretation of genre and register to describe the empirical research article as a genre. Needless to say, this being an editorial and not an expository text, I mention registers that I claim could be characterized with respect to Field, Tenor, and Mode but do not quite do that characterization here. Instead, I allude to selected register variables I have found salient in my work with manuscripts as I briefly consider the sections of an empirical research report. These comments are not meant to be exhaustive or definitive.

The Empirical Research Report Genre

As noted earlier, the stages of the genre of empirical research report can be assimilated into the usual sections of such an article: Title, Abstract, Introduction or presentation of the problem, Literature Review, Theoretical Framework, Research Questions, Methods, Findings or Results, Discussion, Implications, and Conclusion. In what follows, I briefly describe those sections with respect to their social purposes and the registers that they usually employ and include some observations of how submissions sometimes breach those expectations to their detriment.

Title

Our field’s article titles differ substantially from mathematics research articles, which often allude only to the mathematical ideas being discussed. Articles in mathematics education research tend to instantiate a combination of two registers: the register of practice (either classroom mathematics or mathematics teacher education) and an educated but not technical register of education scholarship. The pattern X:Y is common in title making, where X is an idiosyncratic, even specific, expression in the register of practice, using vocabulary and even interactional language that evokes that context, and Y is an elaboration of the issue instantiated by X in the register of education scholarship. The X:Y pattern is not the only one and it may be worn out, but authors who want to innovate could consider what the pattern achieves with respect to both appealing for engagement and informing about content.

Introduction and Conclusion

The APA style guide says that articles should not have an explicit heading called “Introduction,” but I suggest that they do still need to introduce their study to the reader or present a problem. Authors of empirical articles often do that in the first section of an article by making observations of a common experience they share with the reader, such as having read results of high-profile assessments (e.g., the executive summary of TIMSS), desiderata from policy documents (e.g., Principles to Actions [NCTM, 2014]), or prominent discussions on topics that bear on policy and practice (e.g., the report on educational equity by the National Academies of Sciences, Engineering, and Medicine, 2019). Authors use such common ground to identify one or more relevant concepts that connect to the study. As an example of Mode, the Introduction usually gives a definition or some precision on the concept in terms general enough for an educated reader to assess face validity, even when those terms come from policy or other technical contexts.

The Introduction also names a problem or poses a question about the concept that avowedly contributes to the larger issue in which the concept participates and that will be addressed through the empirical study being offered. This problem or question is posed in terms that an educated reader can understand. In doing this, and as an example of the interrelations between Field and Tenor, the author orients the reader to an experiential reality that they assume to be shared but to which the author may assume the reader’s attention is not yet focused. To accomplish this, authors may use the present and present perfect verb tenses to relate what has been done to the existing situation, as well as vocabulary that could be shared by any reader sufficiently familiar with educational policy and practice. The goal of the Introduction is usually to develop the interest of the reader to follow the path the author has used to explore the question stated about the concept named. The register of the Introduction thus draws on the register of mathematics education policy and practice.

The Conclusion of an empirical article (or the last paragraph of a Discussion section) needs to come back to the same register as the Introduction, expressing in those terms how the findings of the study have contributed to changing the description of the shared experiential reality described in the Introduction. Note that the reality itself may not have changed, but the way this reality is described may have. For example, the study may have provided some understanding of issues that contribute to the state of affairs described, including possibly new concepts. The Tenor of the register used in the Introduction and Conclusion is welcoming and inclusive, inviting people on a journey and emphasizing the shared aspects of experience despite expected differences in expertise between author and reader.

Literature Review

The goal of a Literature Review is to describe how prior research has addressed the terrain in which the question posed is located and to identify a gap in the research literature that the present study will fill. The first goal, mapping the terrain, can be accomplished in a rather synthetic way—for example, by naming areas of the terrain and associating those with studies that have addressed them. In doing this, the Tenor may be different than in the Introduction, inasmuch as the audience of the Literature Review more likely comprises researchers in mathematics education who will evaluate how the manuscript relies on and potentially adds to the research literature.

The Field of this register includes the issue and problem introduced conceptually in the Introduction, but now it relates it to the ideational terrain that surrounds the issue. The author describes to the researcher-reader how our field has investigated the issue in the past. Sometimes the mathematics education research community has not done much work on that issue yet, especially in the ways that the issue has been described in the Introduction. In that case, the author needs to take on the responsibility to use the research record in our field to demonstrate that the issue named earlier is part of a larger whole that our field has begun to examine or at least has staked a claim on. In doing so, the author needs to present the research field as still active and open for more contributions that address the issue. For this purpose, the use of verbs is often in the present perfect tense when describing active lines of work while reserving the simple past and past perfect tenses for pieces that may have been seminal to the terrain, though their approaches have been overcome by newer ones. The Field mapped in the Literature Review is rendered in more specific language than the issue alluded to in the Introduction: It may name theoretical perspectives that have been used in studying the issue (as elements of the Field), but the way this mapping is realized through language, the Mode of this register, will not be strongly shaped by theoretical language. Rather, the author will use the register of policy and practice to introduce a deeper level of conceptual distinctions, combining it with the register of education research methods to deepen the description of the central issue in relation to its terrain.

The second goal of the Literature Review, identifying a gap in the existing research, uses a different Tenor than the first one (mapping the terrain). In mapping the terrain, the author may want to join the company of fellow travelers, but the identification of the gap in the literature serves to distinguish the author as an informed critic of that company. Field differences are noticeable, too: Mapping the terrain is an exercise in research synthesis, in which a shared experience is described, whereas the identification of the research gap is an exercise in analysis, revealing ideas that were hidden until unearthed by the author. This gap can be one of information (i.e., something that has not been investigated yet), theory (i.e., the way the issue has been conceived ignores alternative ways of framing the problem), method (i.e., the ways in which the issue has been investigated do not permit the sort of conclusions that would be desirable), or data sources or research design (i.e., limitations in the sample or design of prior studies do not permit validly making desirable conclusions).

To construe the relationship between author and reader in ways that distinguish the author from the reader (Tenor), literature that addresses the concept under study may need to be represented in ways that compel the reader to acquiesce that a gap exists. This means that in addition to describing pieces in terms that cohere with how the pieces describe themselves, the author may have to interpret or assess the pieces in ways that are serviceable for the identification of a gap in the literature. This requires drawing from the register that researchers in mathematics education active in this area would use. The use of verb tenses can switch from the present perfect to the simple past because the goal is no longer to indicate that the field is working on a general topic but to report on and critique the specific works that have been done. Each of those works constitutes an event in the past, and reporting about them may take advantage of this past nature to represent the current work as a contribution.

Theoretical ideas may start making an entrance in the Literature Review, especially when theoretical distinctions serve the description of what different studies have aimed for. Still, empirical research in mathematics education (unlike research in educational psychology; see Matthews, 2024) is also likely to have a separate section on theory or the theoretical framework.

Theoretical Framework

Though this has not always been the case, the norm in mathematics education research has become for articles to have a Theoretical Framework section—a development that attests to the theoretical pluralism of our field. This theoretical pluralism concerns not only different theories for different research topics (e.g., theories of mathematical cognition and theories of mathematics teaching practice) but also different theories within research topics (e.g., different theories of mathematical cognition). Because researchers in our field use a variety of theories to frame their work, an author aiming to publish in journals directed to a general audience of mathematics education researchers (such as JRME) must make an explicit effort to explain such frameworks in enough detail for readers to understand how the researcher is processing the question asked in the Introduction and the gap in literature found in the Literature Review into more specific, operationalizable research questions. Those goals are not easy to meet (especially considering word-count requirements), but even so, register considerations also need to be made.

Specifically, the author, as someone whose work uses or contributes to a theoretical framework, cannot merely position themselves in such a framework. Instead, the manuscript needs to render the framework in ways that show the author as knowledgeable of the framework and that make a reasonable effort at informing the reader about aspects of the framework that will be key in the posing of research questions, making methodological decisions, and interpreting results. The theoretical framework is one of the domains of expertise that editors are likely to seek experts on for the review process, but some reviewers will probably not be experts in the framework. Instead, some reviewers are very likely to be learning about the framework as they review the manuscript (because the expertise on whose basis their review was solicited is a different one—e.g., they know the literature on the topic or they are an expert user of the methods). These two kinds of reviewers are two modal readers that the author needs to keep in mind: the expert who will expect a user of the framework to demonstrate sufficient understanding and the highly educated researcher who, although not expert on the framework, expects to learn something from reading the paper. Those two modal readers suggest two registers that may need to be combined in the writing of the Theoretical Framework section.

How the author personally relates to the theory (e.g., whether the author is a senior contributor to the theory or a more detached user of the theory) may matter in how they demonstrate their expertise in relating to reviewers who are experts in the theory. Regardless, the author will also have to inform nonexpert readers about the theory. One way to see how difficult it can be to strike the right balance between addressing those two audiences is by considering two typical Tenors for the writing of the Theoretical Framework section that, in my view, must be avoided: On the one hand, the relationship with the theoretical expert could default to one in which the author is a student of the theory being assessed by the expert as assessor; on the other hand, the relationship with the highly educated reader who is not an expert on the theory could default to one in which the author is a teacher and the reader a student. Though these default relationships serve to distinguish both goals of demonstrating competence and affording understanding, they cannot be simultaneously constructed in an article. Authors need to steer away from making their article read like a student paper (one whose avowed goal is to demonstrate competence in the theory through its use) as well as from making their paper read like a textbook on the theory (one in which the avowed goal is to explain the theory to someone who does not know it).

In the register of the Theoretical Framework section, the Field is formed by the ideas of the theory. In realizing this Field, language choices need to support both (a) the connections between the world of ideas of the theory and the real-world beings the theory accounts for (e.g., when identifying things in the world and giving them names) and (b) the connections within the world of ideas of the theory (e.g., when presenting claims that rely on theoretical constructs and that are background for the study). In this task, and particularly because of the theoretical pluralism of our field, the relationship with a reader who needs to be informed must take precedence over that with a reader who is an expert on the theory. Whereas theory experts may prefer simple relational and existential clauses to describe the theory (e.g., “learning consists of the adaptation of schemes”), nonexperts will expect the language to reflect more awareness of the distance between the real world and the world of the theory (e.g., “Piagetian theory models learning as the adaptation of schemes”).

The Tenor of informing an educated reader should also orient authors to consider carefully what interpersonal messages are conveyed as details of the theory are exposed. In mathematics, avoiding excessive details in writing is commonplace, lest it come across as an insult to the reader’s intelligence—the author tends to omit what the reader can think on their own. Writing in social research in the U.S. is not quite like that, but authors still need to discern which and how many details need to be given: More is not necessarily better. Some detail may be needed to bring the theory to connect to the research questions, and this detail may be very useful for experts to assess the use of the theory where it matters most. Selection of appropriate details is also important when more than one theory is networked into a complex theoretical framework—the literature on networking theories is a good resource to describe how different theories are gathered into a common framework (i.e., comparing, contrasting, coordinating, unifying, etc.; see Bikner-Ashbahs & Prediger, 2014). This may also be helpful for the nonexpert reader to understand the relevance of the theory for the topic explored. Yet, providing the same amount of detail across the whole exposition of a theory may convey the sense that the author is not being purposeful in what they are asking the reader to consider for the sake of understanding the research being communicated.

This relates to Mode and Tenor in one distinct way: Despite the fact that the author is informing readers who may not know about the theory and despite the fact that asking questions is integral to research, the exposition of a theoretical framework should not use interrogative sentences because their presence articulating the text of a theory may appear didactic and hence patronizing to nonexpert readers. Also related to Mode, a well-written Theoretical Framework section will strive to refer to primary sources or book studies of a theoretical perspective rather than commentaries or textbooks.

Research Questions

The Theoretical Framework section often converges to the statement of research questions. Locating the Research Questions section after both the Literature Review and the Theoretical Framework allows the author to use those resources to state the questions. However, the problem or layperson’s question posed at the beginning is also available, and the reader needs to know how the author translates it into the research questions. Thus, rather than just state the research questions, I recommend that an author use the Research Questions section to describe how the Literature Review and Theoretical Framework support the translation.

Methods

Like in the Theoretical Framework section, the Methods section pursues the social purposes of demonstrating competence to experts and informing others about method, but this section also narrates the execution of method to all. The register choices in this section need to support those three purposes.

The Field of this register includes concepts and procedures from social research methods that the author uses to report on the research design, instrument and sample design, data curation, and analytic methods they employed. Being a reader of the journal and keeping abreast of methods used in the field (and how other authors write about methods) is essential to determine how much detail is needed about which aspects of method.

But Field in the Methods section also includes the actual experiences of using the methods. The distinction I am making here concerns how language supports the aspect of ideational content because the communication of experiences of the use of method is less standardized than the description of method itself. Unlike in the Theoretical Framework, in which the Field of the register includes ideas and things in the world, the Methods section reports on actions that researchers took in the world of participants, educational activities, information, and technologies. Not only will those actions require different choices in describing them (e.g., using verbs that denote action rather than verbs that describe relationships as in the Theoretical Framework), but these linguistic choices also intervene in the relationship between author and reader: As they write the Methods section, the author has already done the actions being reported, and all readers are positioned as recipients of historical information. Though readers have the chance to disagree with descriptions of ideas in the Theoretical Framework section and dispute the accuracy of those descriptions, readers do not have the same affordances when reading about the application of methods. Their options are to evaluate and, when possible, suggest alternative courses of action that may lead to revisions or identification of limitations.

In anticipation of this, the author should be candid about their application of method, particularly when these applications show some differences from what methods textbooks would offer as canonical examples. A Methods section in which the author describes the methods used formulaically, without any narration of the experience of applying them, may encourage suspicions on the part of attentive readers. Conversely, when an author reports their experience applying methods in realistic detail, they contribute to the building of a research practice in our field that can document how methodical rigor, methodological ambition, and the practical conditions on the ground relate to one another. The use of hedging in the Methods section seems much more warranted than in the Theoretical Framework section. Here, it supports the Tenor between an author who gives information candidly and a reader who listens compassionately as they consider whether what has been done is, in spite of its limitations, worth communicating. Hedging, either through the use of modal auxiliaries or projecting clauses (e.g., “We suggest that . . .”) can go a long way to convincing experts, in particular, that the author recognizes potential limitations in the application of method.

Findings or Results

The Findings section is probably the one in which the author is the least constrained by the social relationships they support through writing. Both experts and nonexpert readers in either theory or method can be thought of as receivers of information on what the author found. In doing that exposition, the author needs to consider not only the alignment between what they said they did in the Methods section and what they actually found when they collected the data but also what standard reporting practice is in the journal. Because of this purpose, this section should optimize the ways it presents information (e.g., using multiple semiotic modalities) and maintain coherence while doing so.

The Field in this register includes the observations made in the data and derived from its analysis, whereas the connections between those and the ideas in the presentation of the problem, Literature Review, and Theoretical Framework have already been translated into the language of the data through the statement of research questions and the description of methods. In writing the Findings section, therefore, authors should stay close to the data and set aside most connections that they may want to make back to the Theoretical Framework, Literature Review, or Introduction, leaving those for the Discussion section.

The Findings section should instead report on the author’s experience traversing the data set using the constructs under study as operationalized in the Methods section. This traversal could be a report on the execution of a series of analytic steps and the reporting of results as the steps are taken. Alternatively, it could be the deployment of an argument grounded in observations afforded by a coded data set, the successive narration of case studies, or something else. In any of these, however, the author needs to claim an authoritative voice not only in reporting what they did and observed but also in highlighting what they notice in data displays, what they interpret it to mean in the context of the data set, and how they see such observations as contributing to answer the research questions—all in preparation for the Discussion.

The Field of this register is the specific operationalization of the theoretical framework and the data set, coded according to such operationalization and gathered and analyzed with the described methods; the author is the expert in all this, and they need to display this expertise by informing the reader on what they make of it. The author’s traversal of the data set, regardless of how transparently narrated it is, will allow much to be seen and may let the reader’s mind wander. The author can help structure the reader’s attention by stressing the aspects of the findings that readers need to remember as they move from Findings to Discussion.

As far as Mode, the Findings section is where various modalities (e.g., print and various kinds of visuals) are used to present results. Ensuring the cohesion among texts in those different semiotic modalities is important. Making references to figures and tables is a requirement in APA style, but authors can go further by indicating in the text how to read figures or what to look for in tables. This intersemiotic cohesion can contribute to impress on the reader that tables and figures need to be looked at to understand the content.

Discussion

The Discussion section is the place where the author connects the Findings to the introduction of the problem, the Literature Review, the Theoretical Framework, and the Methods. The registers employed in all those sections need to be integrated to distill what the findings mean with respect to theory, method, contributions to the literature, and contributions to the issue on which the article has been introduced. The article may or may not offer a strong contribution to all those possible features, but it should address those features and emphasize how it contributes to the field. Reviewers of journals like JRME will expect a strong Discussion that goes beyond a summary of findings to instead pitch the findings at a higher level.

Usually, an empirical research article published in JRME contributes to filling a salient gap in the literature, offering new benchmarks in the application of method or providing new insights on theory. If the contribution is methodological, tying the Findings to the Methods and to the Literature Review can help argue that our research field should consider this new method because of its valuable capacity to reproduce known information or to provide information that complements what is known. A theoretical contribution can make a similar case. Here, because the findings are now translated into a Field of concepts and issues that belong in the reader’s experiential world, the authoritative voice of the author needs to recede a bit to construct a relationship with the reader as a vicarious participant of the research experience, one who may no longer just listen but also agree or object.

Two common pitfalls in Discussion sections submitted to JRME are worth considering specifically. Each of these highlights interrelations between Field and Tenor of the register in the Discussion. The first is the presumed expectation that an author should offer implications for practice. I think this instinct is grounded in the correct assumption that some readers of JRME are practitioners or policymakers who read articles looking for what they can use. If an article’s findings connect to the issues addressed in ways that provide warrantable implications for practice, stating those is important. But few articles can do that. Reviewers can often tell when some purported implications are overreaching: The various elements of Field (data, observations, literature connections, theory, etc.) cannot be organized logically to make an argument for what should be done.

Therefore, as an author ponders their desire to give implications for practice, they should consider the relationship they want to foster with their reader: If the proposed implications are sustained by a faulty argument, practitioners and policymakers will not increase their trust in the author. But perhaps appropriately hedged statements of implications will allow the author to lay out the recommendations they are building toward while being forthcoming about their tentativeness or their reliance on assumptions. However, as editor, I am not bothered by the lack of recommendations for practice because, in my opinion, articles that review research in an area are in a better position to produce warrantable implications for policy or practice using the aggregate findings from many studies. Empirical articles5 do plenty when they contribute to fill a gap in the literature, to increase our methodological arsenal, or to reveal the value of theoretical considerations.

The second pitfall I notice in Discussion sections is when an author does not take the opportunity to pose new research questions that our research field could undertake next. This connects to Field in the sense that a research study usually opens opportunities for new distinctions to be made, and as those distinctions enter the ideational world of the article, their juxtaposition with the prior ideas affords new questions to be asked. These new questions are part of the contribution of the article, and they are potentially valuable to the whole field rather than just to the author. The author may have ideas of what to do next, sometimes even with the same data set. But readers can benefit from reading what the field could do next with data like those the author has analyzed. The writing of those recommendations for future research, using modal auxiliaries to indicate potential avenues (e.g., “Future research could investigate . . .”) contributes positively to the relationship between author and reader, revealing the author as generous and inclusive. I usually encourage authors of accepted manuscripts to take the opportunity to suggest future research—to cultivate our field’s taste for what studies are worth doing, as well as to connect people with similar interests.

In Conclusion

Man-o-man, this editorial has gotten long for a change! What can I say? Writing is pretty hard and before getting into this linguistic stuff, learning to write had seemed to me very much an osmotic process.6 In the past, my best advice for learning to write had been to read, write, get feedback, revise, repeat, submit, read reviews, and repeat. No substitution exists for that experience. You get better at writing by writing a lot and by discarding a lot of the drafts and half-baked ideas you write.

That said, the role of JRME editor has given me the opportunity to use what I presently know of linguistics to think about and see patterns in the feedback I give. By reflecting on patterns in my reactions to uses of verb tense, vocabulary, and hedging in different sections of manuscripts, I have come to think of different registers as a way to organize those reactions. And this has led me to think that the notions of genre and register are useful explicit elements of linguistic theory that can help us organize how we undertake scholarly writing. Though this editorial barely scratches the surface, I hope it will serve to help authors of articles for JRME (as well as other journals) think about their writing as a contribution to a social situation and to see the different sections as instances of interactions with particular audiences.

Footnotes

1

Many of these ideas were discussed in the talk “Géneros y registros en la escritura científica en educación matemática” [Genres and registers in scholarly writing in mathematics education] given on the occasion of the 2023 Summer School in Braganza, Portugal, jointly organized by the Spanish Society for Research in Mathematics Education and the Portuguese Society for Research in Mathematics Education.

2

Clearly, I am not disavowing this default framing under the presumption that it is always false, because it is not always false. Some authors do experience their attempts to publish as repressive and discouraging. What I am suggesting is that authors framing their experience this way is not helpful, and framing it instead as an enculturation experience will have better ends, regardless of the intentions of editors or reviewers.

3

“Text” alludes to any specific language production, regardless of modality (written, spoken, signed).

4

Mathematics education scholars might be involved in other genres: school mathematics textbooks, presentations at a research conference, teaching a doctoral level course, school practitioner articles, and more. Each of these genres is amenable to a similar treatment as that which I am giving to the empirical research article.

5

Of course, reviews of the literature (including meta-analyses and metasyntheses) are empirical articles too, though here I am referring to all other kinds of empirical research studies.

6

You surely noted the change in register I illustrated here. What did it do for you as a reader?

References

  • Bikner-Ahsbahs, A., & Prediger, S. (Eds.). (2014). Networking of theories as a research practice in mathematics education. Springer. https://doi.org/10.1007/978-3-319-05389-9

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  • Duval, R. (2020). Registers of semiotic representation. In S. Lerman (Ed.), Encyclopedia of mathematics education (2nd ed., pp. 724727). Springer. https://doi.org/10.1007/978-3-030-15789-0_100033

    • Search Google Scholar
    • Export Citation
  • Halliday, M. A. K. (1978). Language as social semiotic: The social interpretation of language and meaning. University Park Press.

  • Martin, J. R., & Rose, D. (2008). Genre relations: Mapping culture. Equinox.

  • Matthews, P. G. (2024). Reflecting from the border between mathematics education research and cognitive psychology. Journal for Research in Mathematics Education, 55(2), 6875. https://doi.org/10.5951/jresematheduc-2023-0229

    • Search Google Scholar
    • Export Citation
  • Matthiessen, C. M. I. M., Teruya, K., & Lam, M. (2010). Key terms in systemic functional linguistics. Continuum.

  • Morgan, C. (2002). Writing mathematically: The discourse of investigation. Routledge. https://doi.org/10.4324/9780203017715

  • National Academies of Sciences, Engineering, and Medicine. (2019). Monitoring educational equity. National Academies Press. https://doi.org/10.17226/25389

    • Search Google Scholar
    • Export Citation
  • National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. https://www.nctm.org/PtA/

    • Search Google Scholar
    • Export Citation
  • Pimm, D. (1987). Speaking mathematically: Communication in mathematics classrooms. Routledge.

Footnotes

I appreciate comments on an earlier draft by Dan Chazan, Sandra Crespo, Karl Kosko, Erin Lichtenstein, Vilma Mesa, Mary Schleppegrell, and Bill Zahner.

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Journal for Research in Mathematics Education
  • Bikner-Ahsbahs, A., & Prediger, S. (Eds.). (2014). Networking of theories as a research practice in mathematics education. Springer. https://doi.org/10.1007/978-3-319-05389-9

    • Search Google Scholar
    • Export Citation
  • Duval, R. (2020). Registers of semiotic representation. In S. Lerman (Ed.), Encyclopedia of mathematics education (2nd ed., pp. 724727). Springer. https://doi.org/10.1007/978-3-030-15789-0_100033

    • Search Google Scholar
    • Export Citation
  • Halliday, M. A. K. (1978). Language as social semiotic: The social interpretation of language and meaning. University Park Press.

  • Martin, J. R., & Rose, D. (2008). Genre relations: Mapping culture. Equinox.

  • Matthews, P. G. (2024). Reflecting from the border between mathematics education research and cognitive psychology. Journal for Research in Mathematics Education, 55(2), 6875. https://doi.org/10.5951/jresematheduc-2023-0229

    • Search Google Scholar
    • Export Citation
  • Matthiessen, C. M. I. M., Teruya, K., & Lam, M. (2010). Key terms in systemic functional linguistics. Continuum.

  • Morgan, C. (2002). Writing mathematically: The discourse of investigation. Routledge. https://doi.org/10.4324/9780203017715

  • National Academies of Sciences, Engineering, and Medicine. (2019). Monitoring educational equity. National Academies Press. https://doi.org/10.17226/25389

    • Search Google Scholar
    • Export Citation
  • National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. https://www.nctm.org/PtA/

    • Search Google Scholar
    • Export Citation
  • Pimm, D. (1987). Speaking mathematically: Communication in mathematics classrooms. Routledge.

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