When Research Ends Without a Paper: One Story

Today’s post belongs to the “unfinished article (or written-but-never-to-be-published)” category. I believe every researcher has a secret stash of half-written manuscripts. Sometimes you start writing and stop for various reasons. Sometimes you go all the way—submit to journals—but still never manage to publish. I have several such pieces. Today, I want to tell the story of one of them.

The topic may seem a bit niche, and probably only of interest to those working in numerical cognition. But it raises questions I still think are worth asking.

How It Began: Transcoding Between Symbolic Formats

We started this project long before COVID. We were intrigued by the process of transcoding between different symbolic formats of number representation. According to the well-known triple-code model (Dehaene, 1992), numbers can be represented in three formats:

·       two symbolic formats: visual (digits) and verbal (number words), and

·       one nonsymbolic format: analog magnitude.

Symbolic representations, unlike nonsymbolic ones, are culturally acquired and uniquely human.

Both children and adults frequently convert numbers between these symbolic formats. For instance, reading a table aloud requires converting digits into number words. Conversely, solving a spoken math problem requires turning number words into digits. This process—transcoding—is an essential part of everyday numerical tasks.

Many studies have shown that symbolic numerosity representations are related to math performance. But surprisingly few have explored the process of transcoding between symbolic formats, perhaps because theoretical models are inconsistent and tasks used to measure transcoding vary considerably. Most studies rely on number dictation or recognition tasks, often in auditory format, or magnitude comparison tasks using spoken number words. But we wanted to use written number words in a magnitude comparison task. (Yes, I know—who the hell uses written number words? But that was part of our point. And it were easier to collect data).

Study Design: Cross-Format Magnitude Comparison

We wanted to test whether transcoding skills in both directions (visual-to-verbal and verbal-to-visual) predict math performance in first graders.

We designed a cross-format magnitude comparison task with four types of item pairs:

·       "4 eight" — digit followed by word (verbal-to-visual transcoding),

·       "eight 4" — word followed by digit (visual-to-verbal),

·       "4 8" — digit-digit,

·       "eight five" — word-word.

Children had to choose the larger number in each pair as quickly and accurately as possible.

From this task, we computed Rate Correct Scores (RCS) for each trial type. To isolate transcoding skills, we estimated two regression models, using the RCS for the cross-format conditions (“digit–word” and “word–digit”) as outcomes, and RCS for the within-format conditions (“digit–digit” and “word–word”) as predictors. The standardized residuals from these models were used as measures of transcoding:

·       visual-to-verbal transcoding: “word–digit” condition,

·       verbal-to-visual transcoding: “digit–word” condition.

We also administered:

·       a math achievement test (two waves: math achievement in Wave 1 was a predictor, math performance in Wave 2 was an outcome),

·       a phonological awareness task,

·       a digit span task, and

·       a nonsymbolic numerosity comparison test.

The Findings

What we found was interesting. The two directions of transcoding seem asymmetrical. Only visual-to-verbal transcoding (e.g., “eight 4”) predicted math performance after controlling for all other factors. The reverse (verbal-to-visual) did not

In other words, the direction of transcoding matters. This may reflect how children learn math in school: they are taught to read and write digits, while number words become less central over time. So, processing digits may become more automatic, while converting number words into digits remains more effortful.

We hypothesized that this asymmetry supports Multiple Representation Models, and challenges simplified views that symbolic formats are interchangeable

Revise, Resubmit, Repeat… and Then Let Go

We submitted this paper to more than 10 journals (subsequently, of cause, after receiving rejection from previous one). In about half of the cases, we received rejections from reviewers, sometime from editors (usually they explained rejection by the lack of theoretical novelty). The title of the paper changed several times (though not in any fundamental way). A couple of times we even reached the revise-and-resubmit stage. The last time, we received quite positive reviews with only a few minor suggestions. After responding to the comments and making small edits, we were feeling hopeful.

But unexpectedly, we received a rejection—without any substantial explanation. Considering it was April 2022, the timing made it hard to keep caring about the paper.

So, we gave up.

Although I still think the study was interesting, I now clearly see the mistakes we made in the research design. The tasks should have been structured differently. The overall design should have been better. And now, there’s nothing we can fix in the data—we’d have to collect new data entirely. But I’m no longer sure I’ll ever do that. I’m not even sure the original research question is worth it anymore.

That said, there is an interesting angle I’ve been thinking about here in Serbia—one that brings the focus back to the verbal format of number representation, specifically written number words. As many people know, Serbia uses two alphabets: Cyrillic and Latin. I started wondering whether there's any difference in how children process numerical information written in these two scripts. It would be fascinating to explore. But it would also require resources I currently don’t have.

So that’s the story—a lot of work that ultimately led nowhere. But this is a common experience for researchers (at least in the social sciences). Am I disappointed? A little. Do I regret spending so much time on it, even though it didn’t result in a publication? Maybe a little. But I still believe the lessons I learned along the way were valuable.

And this isn’t the only case. I have quite a few stories and half-forgotten papers like this—so I’ll probably be sharing more of them from time to time. Every researcher I know has at least one project like this. If you’re reading this and nodding—you’re not alone.

Would I return to this topic? Maybe. But for now, this story stays here—in this post—and I’m moving forward.