Towards Article Acceptance: Avoiding Common Pitfalls in Submissions to Mathematical Thinking and Learning

This chapter examines core aspects of quality publishing in mathematics education journals, with a particular focus on the journal, Mathematical Thinking and Learning: An International Journal ([MTL] https://www.tandfonline.com/loi/hmtl20). Following an introduction to MTL, I provide recommendations for writing and submitting a research journal article, from both a general perspective and from that of MTL. I give consideration to core components of a journal article and offer suggestions for maximising one’s chances of final publication acceptance. Next, I examine journal reviewing processes from the perspectives of a journal editor, an author, and reviewer. MTL serves to illustrate key points in the reviewing processes.

are encouraged to make contact. The most recent special issue (volume 20, issue 1) comprised articles that explored computational thinking and mathematics learning.
As the title implies, MTL publishes scholarly articles that primarily address mathematical thinking, reasoning, and learning. Articles can draw upon a number of theoretical domains including the various fields of psychology, sociology, philosophy, anthropology, and information technology. In addition to receiving articles that report on research studies conducted, the journal invites articles that present theoretical and philosophical analyses of pertinent issues. Specifically, MTL seeks articles that address one or more of the following: • Interdisciplinary studies on mathematical learning, reasoning or thinking, and their developments at all ages; • Technological advances and their impact on mathematical thinking and learning; • Studies that explore the diverse processes of mathematical reasoning; • New insights into how mathematical understandings develop across the life span, including significant transitional periods; • Changing perspectives on the nature of mathematics and their impact on mathematical thinking and learning in both formal and informal contexts; • Studies that explore the internationalization of mathematics education, together with other cross-cultural studies of mathematical thinking and learning; and • Studies of innovative instructional practices that foster mathematical learning, thinking, and development.

Choosing a Potential Research Journal
The scope of articles that a journal publishes should be one of the first aspects a potential author should check. As MTL editor, I receive several submissions that do not meet the aims and scope of articles published in MTL. In these cases, I have to reject the paper outright and sometimes suggest an alternative journal such as one in the field of educational psychology. When scoping a journal for a potential submission, it is important to note the range of articles and reports it publishes. In addition to regular research articles, several mathematics education journals including MTL publish special issues, book reviews, and shorter research reports. Short Reports for MTL might report on larger, more comprehensive studies that might be documented elsewhere in non-journal format (e.g., doctoral dissertations). Short Reports might also address introductory or pilot studies, with proposals included for further research. Theoretical pieces that address significant and timely issues on mathematical thinking and learning could likewise form a Short Report. Such reports typically comprise around 15 manuscript pages. Other types of submissions considered by MTL, although rarely received, include an occasional discourse section comprising timely dialogue among researchers on significant issues pertaining to mathematical thinking and learning. Letters to the editor and more extensive critical commentaries on published articles are welcomed. These should comprise critical, timely, and responsible comment on issues of significance to mathematical thinking and learning. Once the aims and scope of a particular journal have been checked, it is worth reading a range of articles published in the journal to obtain a sense of their nature. Prior to writing an intended article for submission, a journal's style guidelines should be studied. These include features such as the nature of section headings, the line spacing, font type, referencing format, table and figure requirements, and word/ page length. It is easy for a journal editor to gauge whether an author has studied these guidelines, especially if several key points have not been followed. Editors will often return a submission prior to sending for external review if these guidelines are not adhered to, in particular, if a journal's page or word limits are exceeded (if this criterion applies). For MTL, authors are to follow the style guidelines described in the current edition of the Publication Manual of the American Psychological Association (6th edn. 2013, [APA]). Taylor & Francis advises authors to consult Merriam-Webster's Collegiate Dictionary (11th ed.) for spelling.
In the remaining Sections I give consideration to some key issues that potential authors for MTL should keep in mind. For example, sometimes an MTL submission suffers from a number of weaknesses that need to be addressed before it can be sent for external review. These include a limited or outdated literature background, a lack of a theoretical or conceptual framework, poor expression, and other scholarly attributes a submission should display. Ensuring that a submitted paper adheres to the requirements of a scholarly research publication can be difficult, especially when there are limited resources that can assist a beginning researcher. A few valuable resources include the American Educational Research Association (AERA 2006), the Journal for Research in Mathematics Education (JRME 2015), and the Publication Manual of the American Psychological Association (APA 6th edn. 2013). The APA is a foundational reference that applies to many journals.

Creating an Appropriate Title and Abstract
Article titles and abstracts provide a window into a study and thus need to be clear, concise, and accurately represent its contents, both for the reader and for electronic indexing purposes (Saracho 2013). Overly long titles are not recommended, as they can detract from the overall appeal of the article and can also be misleading for indexing (APA 6th edn. 2013). When I receive submissions to MTL, I find very long titles off-putting; likewise, some submissions have titles that would be more appropriate for a professional journal than a research journal.
Writing abstracts is not a simple matter and can take considerably longer than anticipated. Abstracts should convey within 150-250 words (depending on the journal) the study's purpose, methodology, key findings, and conclusions or implications. As Saracho (2013) emphasises, an abstract should provide a "complete but concise description of the study" as well as incorporate key words that can be used for indexing and data bases (p. 48). The advice of Bol and Hacker (2014) is worth citing here: A poorly written abstract creates a poor first impression that could set a negative tone for the remainder of the manuscript. Do not lose your audience in the first few words. One sure way to do this is to write an abstract that omits important details of one or more components of your research so that there is no easy way for the reader to judge your research as worth reading. (p. 41) Reviewers who devote substantial time to a submission need to be "captured" by an article's abstract and be motivated to read the paper. As can be seen in the excerpt below, this reviewer had to alert the author to the importance of detailing clearly and concisely the key components of a study.
The abstract is currently written in vague language that does not communicate a summary of findings, assertions, or implications very clearly or precisely. Since many readers only look at the abstract, it is essential that it be written in a way that clearly communicates key details about the study. In a revision, it would be useful to clearly state 1-2 key findings, 1-2 central assertions about how/why the findings happened, and 1-2 conclusions or implications about what these findings mean for scholarship and for practice.

Setting the Scene: The Many Facets of the Literature Review
Literature reviews fulfil many roles. Importantly, they should highlight the existing gaps in the topic area and how the reported study is targeting these missing aspects and thus is advancing the field. Literature reviews need to go beyond simply reporting; rather, the existing literature requires critical analysis to identify areas that remain under-researched and in need of attention. One of the more frequent concerns of MTL reviewers is the author's failure to indicate the significance of the problem being investigated and how the study is advancing the field. This concern is compounded by articles that do not convey a clear statement of the problem, with the result that reviewers are uncertain of exactly what is being studied. A submission without a clear problem statement and/or a limited review of the literature is unlikely to receive favourable reviews. A poor literature review might be characterized by brevity, omission of important studies in the field and/or inappropriate/irrelevant studies, dated literature that does not convey the current state of play, literature that is confined to just one nation (for international journals), and a literature review that does not highlight the importance of the topic of investigation. As can be seen in the following example of one reviewer's feedback, the authors did not argue adequately the case for their study (words have been omitted to avoid any possible identification): The authors need to provide more background on the value and importance of X activities as established in the mathematics research literature and field. Why is this approach so critical to developing students' mathematical knowledge and skills, and that of their teachers? The authors need more description of the current research in order to build the argument for their study…. Why is it so important to determine how Y abilities develop? What impact does this development have on teaching and learning in mathematics? In what ways has the current research on X activities informed the field and what areas remain to be investigated? The authors provide brief treatment of this topic on p x, but more depth is needed. It is not clear why the study purpose, Z, is critical to enhancing the current mathematics knowledge base. Literature reviews also provide the basis for a study's theoretical or conceptual framework. This framework is important in potentially advancing the field, guiding the research questions or hypotheses, the subsequent conduct of the study, and the data collected and analysis performed. The framework further guides the discussion of results, which in turn, might reveal extensions or modifications to the framework. Submissions that lack such a conceptual or theoretical framing are likely to have reduced impact, with reviewer requests to address this omission. It is also worth mentioning that if parts of a study, such as key components of the theoretical framework, have been reported in another research outlet, the unique contributions of the new, submitted article must be clearly indicated. In addition, readers should not be expected to search for authors' publications for required information; a submission should stand alone. Reviewers might source the author's other articles that have emanated from the same study and question how the new submission differs from previously published works, if this has not been made clear in the submitted article. On the other hand, reviewers might choose to locate an author's cited publications out of interest in the research. It is thus important that all references are correctly cited. Considerable time is lost and frustration experienced by reviewers and readers when a reference is listed incorrectly.
Many of the foregoing points regarding a literature review apply also to articles that present theoretical and philosophical analyses of pertinent issues. Such articles can be difficult as they need to present timely, well-argued ideas that flow logically and cohesively. The concepts need to be not only well grounded in the literature but also significantly advance the field. MTL does not receive many articles of this type. Unfortunately, to judge by those that have been submitted, they are not often accepted for publication primarily because they might not extend existing work, might not offer new insights into, say, a vexing issue or an emerging topic of importance, draw on a limited range of research, and might lack coherence. Articles that suffer from one or more of these weaknesses can of course, be substantially revised and resubmitted for further review. In essence, theoretical and philosophical articles need to stimulate the interested reader with thought-provoking ideas, which might prompt possible further exploration and application to existing research.

Explaining and Justifying the Design and Methodology
For articles that report on research studies undertaken, the research design and methodology need to contain sufficient detail and be appropriate for answering the research questions. With many journals having strict length limits, giving adequate attention to design and methodology can be difficult. Nevertheless, required information generally includes the nature, number, and background of the participants, the population from which they were drawn, and how they were chosen for study. Describing the instruments developed or sourced, how they were administered, their appropriateness for addressing the research questions, their reliability for yielding the required data, and samples of items (or the entire instrument) should be included in the methodology, where appropriate. When authors omit aspects or all of this information, it is difficult for readers to determine the validity of the results and any subsequent claims made. For experimental studies, control of variables is essential if causal inferences are to be made. As Bol and Hacker (2014) point out, reviewers will look for potential confounding factors and possible competing hypotheses. For both experimental and qualitative studies, any methodological limitations should be noted in the discussion section or in a separate section towards the end of an article. Another important methodological component, with respect to studies that report on treatments or classroom interventions, is that sufficient detail should be provided so that their key features can be determined and applied in interpreting the results (AERA 2006). The types of approaches adopted, examples of instructional materials or treatments implemented, and the duration and frequency of implementation or administration should also be indicated. The nature of the intervention should be guided/supported by the theoretical framework, which enables the reader to see how the study emanated from its conceptual foundation/s. It is not uncommon for an author to advocate a particular perspective (e.g., constructivism) but then describe a study that does not reflect its core philosophy or ideas. Reviewers invariably question this failing, as can be seen in a sample review below (some words have been omitted to avoid any author/reviewer identification): The authors start Sect. 24.3 by claiming that they "employed a teaching experiment approach (Cobb and Steffe 1983;Simon 1990) to explore the potential …. Neither of the references named in this sentence were included in the reference section, nor did the paper do a thorough job of explaining the purpose and process of a teaching experiment. In readings I did myself to re-familiarize myself with the teaching experiment methodology, I found that what the authors did does not fit this methodology and there isn't a match between the authors' goals and the goals of a teaching experiment.
Articles that omit or have inadequate information on how a study's data were obtained and analysed, including justification for the data analysis methods used, will be questioned by a reviewer. As emphasized by AERA (2006), data analysis procedures should be: precisely and transparently described from the beginning of the study through presentation of the outcomes. Reporting should make clear how the analysis procedures address the research question or problem and lead to the outcomes reported. The relevance of the analysis procedures to the problem formulation should be made clear (p. 37).

Results
In reporting the results of data analysis, it is important to keep in mind the research questions being investigated. It should be made clear how the analysis addresses the research questions and leads to the outcomes (AERA 2006; Bol and Hacker 2014). As expressed succinctly by Bol and Hacker (2014), "The whole point of the research can be lost if the analyses are improperly and inadequately conducted and do not clearly provide the answers to the research questions" (p. 43).
It is not uncommon for a submitted MTL article to overlook the questions posed and to report on results that address other issues. One approach to avoiding this problem is to organize the results according to each research question, that is, revisit each question in turn (assuming there is more than one question). Only those results that actually answer the questions should be included. If other relevant findings emerge from the data analysis, they could be incorporated within the discussion and cited as unanticipated outcomes. Such results could serve as one area for further research.
Ensuring that all claims and conclusions made are supported by the data is especially important (AERA 2006) and is an aspect that can be easily overlooked even by experienced researchers. Making claims or generalisations that are not supported by evidence will be picked up by reviewers, as is frequently the case with MTL submissions. The reader needs to be able to trust the claims made. A number of approaches to providing such a warrant are cited by AERA (2006), including triangulation of data, having data coded by other researchers, and a critical examination of how the researchers' pre-existing perspectives or beliefs might have impacted on the data collection and analysis. Triangulation is frequently used in mathematics education research, such as including examples of specific participant responses from classroom or group discussions to support quantitative data. If, for example, a claim is made that students were engaging in metacognitive activity, then specific, concrete examples of students' actions in this regard can further support the claim from the reported data.
In documenting data outcomes, it is recommended that tables should be used only when they clarify or summarise outcomes involving multiple data points (Saracho 2013). The APA (6th edn. 2013) provides examples of appropriate table layouts. It is generally recommended that the fewer tables the better, as too many tables can detract from a paper and extend its length, especially for those journals that have a strict page limit. While tables should be readily interpreted, the messages they convey need to be summarised in the associated text. One of the problems with several of the manuscripts submitted to MTL is their overuse of tables and figures. Furthermore, sometimes these tables and figures, especially figures, can be so dense and have such small font size, that they are barely legible and more importantly, will not reproduce well in the printed journal issue. The use of colour is also problematic for printed issues of journals (but not the online format), as colour is costly for the publisher (and the author). If authors require colour then they will have to cover the costs. Problems can arise when colour is essential for some graphs or other figures where it is used as a distinguishing feature. In this instance, the use of shading or other such effects will need to serve as a substitute.

Developing an In-Depth and Insightful Discussion
There are a number of approaches to the discussion section but typically these include a summary of the outcomes, together with an "interpretive commentary" (AERA 2006, p. 38) providing a more in-depth understanding of the claims made. Such a commentary would indicate how each research question was addressed, offer possible reasons for how and why particular outcomes occurred, the context/s in which the outcomes took place, how they support or challenge existing theory and previous research results, and possible alternative interpretations. Importantly, the discussion should indicate how the outcomes and conclusions drawn from the study connect to and support (or perhaps challenge) the study's theoretical framework. Implications that follow from the study might refer to theoretical, practical, or methodological considerations (AERA 2006), but importantly, any claims and recommendations made in the discussion section must be backed up by data from the study (Bol and Hacker 2014;Robinson et al. 2013). An interesting recommendation by Robinson et al. (2013) is that authors should limit their discussion and conclusions to their study's data and not offer recommendations regarding educational practice or educational policy. Such a recommendation was proposed to maintain a "separation between evidence and opinion concerning the legitimate warrants of empirical research" (p. 291). Although educational implications from mathematics education studies are valuable and indeed usually expected, maintaining a clear distinction between evidence and opinion is nevertheless essential.
One of the drawbacks I frequently see in submissions to MTL is a failure to revisit the study's conceptual framework in light of the findings. Limited reference, if at all, to existing research in discussing the study outcomes is also present in some submissions. It is important that researchers indicate how their study has extended current work in the field, thus advancing the existing knowledge base. One of the more common reasons for a reviewer to reject a paper is that it does not make a significant contribution to the field, rather, it simply reinforces well-established research; the reviewer thus comes away questioning why the study did not progress beyond this point. Although studies that duplicate the findings of earlier research can still make a contribution, the nature of any such contribution should be well argued with implications for further studies clearly indicated, such as how a task or context variation might generate new insights.

Acknowledging Limitations and Drawing Conclusions
The inclusion of a concluding section is not always followed in mathematics education journal articles but can provide a valuable summation statement. Conclusions are normally brief and succinct, with Saracho (2013) recommending that they include a clear statement on the key outcomes and justification for their significance with reference to related studies, and a few core conclusions from the study results. Recommendations for future research are sometimes included in this section. Acknowledging the limitations of a study is an aspect that can also be overlooked by authors. Suggestions for reducing these limitations should be indicated, such as the need for a larger sample or interviewing participants to obtain greater insights into their thinking.

Checking References, Structure, and Readability
As for each journal, the MTL website contains instructions for authors (https:// www.tandfonline.com/action/authorSubmission?show=instructions&journalCode= hmtl20). MTL follows the APA (6th edn. 2013) guidelines in overall layout including how references should be cited. Common mistakes made by authors who fail to check the MTL guidelines include using non-blinded submissions (reviewers become concerned when this is the case), numbered instead of non-numbered section headings, single instead of double line spacing, inappropriate referencing, and the inclusion of figures and tables within the body of the paper (MTL does accept these as separate files). Checking that all references cited within the text also appear in the reference list and vice versa is important. Although authors are usually aware of this standard requirement, it is easy to miss some references. Appendices are valuable for including important information that can be distracting or difficult to incorporate within the text, such as questionnaires and tests administered, or excerpts from these. The APA (6th edn. 2013) guidelines provide detailed instructions on the inclusion of appendices together with other supplementary materials, which might be included in the electronic version of an article.
On completion of an article, undertaking a review of its overall structure and readability is essential. In structuring an MTL submission, it is recommended that the following order be adhered to: title page, abstract, text, quotations, acknowledgments, references, appendices, footnotes, tables and figures. It is paramount that an article reads well and flows smoothly. A submission should be cohesive, address the required components, and be free of typographical errors and awkward expression. This last aspect can be difficult when English is not an author's primary language; in this case, some editorial assistance will need to be sought prior to submission. One of the many obstacles to achieving journal publication is to submit a paper that is not 'reader-friendly'. Undertaking a review of a journal article is time consuming for busy scholars; trying to interpret an article for meaning, prior to undertaking a review of its contents, adds an extra layer of unwelcome work.

Being Aware of the Review Processes for MTL
Manuscript review processes vary across mathematics education journals. For MTL, all submissions are rigorously reviewed by three reviewers, occasionally four if needed. As noted on the journal website: Taylor & Francis is committed to peer-review integrity and upholding the highest standards of review. Once your paper has been assessed for suitability by the editor, it will then be double blind peer-reviewed by expert referees. (https://www.tandfonline.com/action/ authorSubmission?journalCode=hmtl20&page=instructions) The Author Services section of Taylor & Francis provides an outline of "What to expect during peer review." Within a week or less on receipt of a new submission (submitted via Editorial Manager, http://www.edmgr.com/mtl/default.aspx), my editorial assistant and I commence the review process. As MTL editor, I reject outright those submissions that are unsuitable for the journal and should be submitted to a more appropriate outlet. Other submissions might meet the journal's aims and scope but suffer from one or more problematic issues, as addressed in this chapter. In these instances, I provide feedback to the author on some of these issues and indicate that the submission cannot be sent for external review as it stands. For submissions that appear borderline or problematic, I might seek the advice of the associate editors. For all other submissions, I identify up to a dozen scholars to invite as potential reviewers, in the hope of securing three. These reviewers are chosen from the Editorial Board as well as from external sources, such as authors whose work has been cited. Many scholars refuse to review for various reasons, while some will never review for the journal. It is not uncommon for over half of potential reviewers to decline, which makes the task of securing reviewers extra difficult. Although disappointing, such a decline rate is understandable given that undertaking insightful and helpful reviews of a journal article is time consuming; there has also been a substantial increase in mathematics education journals in the past decade, all seeking reviewers.
Reviewers are allowed up to six weeks to complete their review, which appears to be a considerably longer period than permitted by many other journals. Even then, we have to chase late reviews and often need to send at least two reminders. Together with reviewers who agree to review but then never submit a review, these delays in reviewer feedback naturally cause problems for both the editor and author.
In submitting their review, reviewers are to make one of four recommendations: accept, accept with revisions, revise and resubmit, and reject. It is rare for a final editorial decision to be a complete acceptance on an article's first submission; most submissions are to be revised, sometimes substantially, and then resubmitted for further review. Authors receive a letter from me usually within two weeks of my receipt of reviews, where I summarise the key points raised by the reviewers. Authors are advised to submit their revised paper within a six-weeks window but are permitted extra time if needed. To enable us to keep track of all submitted articles and to enable a resubmission on the Editorial Manager system, we request that authors inform us of their intention to revise, or their wish to withdraw their submission. For the former, we then send a standard letter from the Editorial Manager system to notify authors that they can revise and resubmit their paper. If authors do not inform us of their intention to revise and resubmit, the Editorial Manager system will not enable a revised paper to be submitted.
For resubmitted MTL manuscripts, we try to include at least one of the original reviewers. This is not always possible, however, as some reviewers decline or are reviewing another MTL submission. For manuscripts that are borderline between reject outright, and revise and resubmit, it might be necessary to seek three new reviewers, depending on the nature of the original reviewer feedback. For example, a reviewer who provided limited commentary on the original submission would probably not be more forthcoming on a resubmission. The difficult aspect of revising and resubmitting a paper is that there is no guarantee that a revised version will be accepted. As both an author and editor I appreciate this difficulty, and to reject a paper after revision is not a decision I enjoy conveying to an author. I know what it is like being in such a situation as an author. When a submission has to be revised and resubmitted, it is not uncommon for two or more revisions to be requested.
New reviewers for a resubmitted MTL paper have access to the previous reviews when considering the revisions an author has made. An author should respond to reviewers' feedback in a detailed and easy-to-follow manner; this is essential for both the reviewer and editor. Authors who simply indicate that a reviewer's points were addressed on pages x, y, and z, or were not followed up because the author considered the reviewer to have different or inappropriate viewpoints, do not do their revised paper justice. On the other hand, sometimes a reviewer might suggest a change that the author does not deem suitable for the paper. It is acceptable to indicate why the change was not made (e.g., some suggested research that does not align with the direction of the submission). Bol and Hacker's (2014) words of advice are worth citing here: You not only need to make nearly all of the revisions suggested but describe the revisions made and how they were responsive to the reviewers. Your chances of acceptance in the next round greatly decrease if you refuse to make many of the changes and claim the reviewers did not know what they were talking about. Vague and broad responses, such as ''the manuscript is now much improved,'' won't cut it either. Your responses need to be very specific and thorough. Consider presenting your responses to reviewers in table format. (p. 47)

A Few Final Points
MTL strives to maintain a high standard of scholarship. It is to be hoped that the points presented in this chapter assist authors who are interested in submitting their papers to the journal. The advice included here is by no means exhaustive. Queries regarding the suitability of an article prior to submission are always welcome. We encourage a range of submissions that address the aims and scope of the journal, and that adhere to the journal guidelines. As we almost never receive commentaries on published MTL articles, we encourage interested readers to submit their thoughts on issues raised. Submissions for special issues are also appreciated.
It is important to keep in mind that MTL is an international journal, and as such, has readers and submissions from many nations. Authors who only cite research or curriculum development in their own country need to also consider what is happening elsewhere.
Submissions from beginning researchers are always welcomed, and we try to offer as much support as we can. Likewise, we welcome young researchers as reviewers and even recommend that competent doctoral students undertake reviews under the guidance of their advisor or supervisor. Some of the better reviews I have received for MTL submissions have come from young researchers and doctoral students nearing completion of their studies.
Lastly, as founding editor, I wish to thank and acknowledge the valuable contributions from a range of authors and reviewers, over two decades. Without such support the journal would not be where it is today. The assistance from the journal publishers, Taylor & Francis, is also appreciated.
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