Teaching K–3 Multi-Digit Arithmetic Computation to Students with Slow Language Processing

Round 1

Reviewer 1 Report (Previous Reviewer 3)

Comments and Suggestions for Authors

 

This new version of the article is an improved version of the previous article and it is more organized and focused, making it easier to follow.

In this new version I begin by focusing on abstract. The abstract should give a clear idea of the article. So I propose that the first paragraph of the section 1 Introduction (lines 27-30) (which explains the purpose of the article) must be moved (or to put the same idea) to the beginning of the abstract. Or else, introduce the same  idea of that paragraph. I'd also suggest removing the references (the abstract doesn't usually include references). Where the author appears, e.g. line 14, you could instead of, write "It was developed a paper and pencil ......".

Each study presents methods and results quite described.

The ideas presented in the final discussions of each study as well the final discussion should not only be supported by empirical data but also framed by theoretical references, in particular those presented in the literature reviewed (item 1).

Thank you for the adjustments realized.

Author Response

Thank you for praising the improved version of the article.

As per your request, I used the first sentence of the article as the introduction to the abstract. I then cut sentences and some of the computation to cut down on the number of words in the abstract. I also eliminated the reference in the abstract.

I must admit that I should have inquired earlier about the meaning of the comment that seems to have a word or phrase missing: “Each study presents methods quite described.”  On my original reading I had taken this to mean “Each study presents method quite well described.”  Which is probably wishful thinking.

As per the comment requesting that the results section should go beyond empirical data analysis to bring back the foundational theories behind the study. Thus I made sure to bring back the concepts of learning trajectories and subtization that suggest that students must master facts and computation to the point of subitization before moving onto the next learning trajectory. And that individualized instruction would have been worthwhile in Study C where the Urban General Education students did far better on speed and accuracy than the Urban General Education students in Studies A and B, but some were shy of mastering the material before moving on to either the next chapter of addition and/or to the topic of subtraction and multiplication.

Author Response File: Author Response.docx

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

I found your topic fascinating in comparing the way addition is taught. I have been in education for 29 years, focusing on math, and as a math interventionist,  I never would have considered this strategy. I always took the concrete/ manipulative approach until students were ready to move on.

In reading your results, it was disappointing to read that some of the original groups ended up not finishing the programs for your research, but you took what you gained from the results and you made important comparisons. I enjoyed reading your research.

Author Response

Response to reviewer two:

Thank you for your positive comments. I’m glad that you enjoyed the article.

 

Author Response File: Author Response.docx

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper I have received for peer review does not meet the standards of scientific publication. From the abstract alone, it is not possible to see what the research problem is. Furthermore, it can be seen that the author is presenting the results of three studies that are unrelated to each other and are presented as a collage of three different parts. In short, I advise the authors to first read the literature on scientific writing, read scientific articles in the field of didactics of mathematics and then approach publishing with their new knowledge. I cannot even give a detailed review, because the article should not even have been submitted for review.

Author Response

Reply to Reviewer One from Author1,

 

When putting together the original article I was trying to tie together my three avenues of research. In retrospect, this was a mistake.

For my revision I focused the article on the three related studies to developing and test-piloting the Blended Arithmetic Curriculum. In the revised article these are designated a Study A, Study B, and Study C, and tried to clarify how each one led to the next study, and how these three studies relate to the special issue of Computation. In the process, I needed to eliminate my co-author since she participated in the research and writing of the other portions of the paper, but not in the interrelated Studies A, B, and C.

As an added benefit, the article has been shortened by almost one half in page count, number of words, and number of figures. 

Additionally, I reformatted the figures, tables, and references to the style of the MDPI journal standards as opposed to the APA standards that I had used in the originally submitted draft.

I’ll let you decide whether the revision better approximate what you expect out of an article submitted to the journal Computation.

Reviewer 2 Report

Comments and Suggestions for Authors

The title of the paper is too long. The abstract is not satisfactory. There are too many unnecessary graphical representations in the paper. Some references used in the paper are not listed in the bibliography.

Author Response

Reply to Reviewer Two from Author1,

 

As you noted in your review, the title of the paper was too long. Consequently, I have shortened the title to a more succinct “Teaching K-3 Multi-Digit Arithmetic Computation to Students with Slow Language Processing.”

 

Thank you for your review.

I believe the long title reflected one of the key problems with the whole paper—which was the paper wasn’t focused enough on the three stages of the multi-year research study on K-3 computation instruction that is most pertinent to the special issue of the journal Computation to which it is submitted. In the process, I needed to eliminate my co-author since she participated in the research and writing of the other portions of the paper, but not in the interrelated Studies A, B, and C.

You also noted the abstract of the paper is not satisfactory. I’ve tried to make it more concise and more focused. I hope it is more satisfactory to you.

Next, you pointed out that there were too many graphical representations in the paper. By refocusing the paper, not only have I been I’ve been able to reduce the number of graphical representations by half.  Additionally, I’ve tried to make the graphical representations more stripped down and cleaner. Furthermore, I’ve cut the number of words, pages, and sections of the paper.

Finally, you pointed out that some of the references in the paper are not listed in the bibliography. Not only I did check to make sure that each reference in the paper matched up with a listing in the bibliography, I reformatted the references from APA to the style expected in MDPI journal articles.

Overall, I hope that you find the rewritten article a better article.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

 

General comments: This is an important paper because it focuses on a pertinent topic related to elementary computation and specific learning disabilities.  However, the writing in the manuscript is a little confused and literature in the area should be reinforced.  As it reports on three of studies carried out over time by the authors, it would be clearer for the reader organize the text into another way instead of 13 sections there would only be 6.

1.     Introduction

2.     Theoretical Background/Literature review

3.     Study 1a&1b

4.     Study 2

5.     Study 3a&3bcd

6.     Overall Dsicussion

 

Title. Very long title. Change to a shorter title with the essential that should identify the content of the study expressed in the manuscript.

 

Abstract: Very long abstract. This should have a total of about 200 words maximum. Don't specify with examples, but with the essential ideas following the: Background; Methods; Resul ; Conclusions.

 

Introduction: The introduction should be rewritten. First, briefly present the pertinence and relevance of what will be presented (e.g. elementary computation and specific learning disabilities). Then the aim of the paper. Finally summarize the 3 studies. For example, you shouldn't present study results in this section if you're going to describe them later. The next item (Theoretical Foundation of Blended Arithmetic Curriculum) should appear outside the Introduction but in a new section 2, which should be called Theoretical Background/Literature review. This new point should be more developed, as it lacks a theoretical discussion to support the studies presented later.

 

Materials, Methods Results: Each study presents methods and results quite described. We suggest revising the figures and tables as they are not uniform.

 

Discussion: the final discussion (13) should be reinforced grounded on literature and

presenting some contributions for teachers/school actions carry out

Author Response

Reply to Reviewer Three from Author1,

 

First off, Thank you very much for reviewing our manuscript and stating “This is an important paper because it focuses on a pertinent topic related to elementary computation and specific learning disabilities.”

 

I’ve tried to make the manuscript less confused by directly reporting on the three interrelated studies focusing on K-3 computation so that the article fits the Special Issue topic. In the article, I call these Study A, Study B, and Study C.

 

This contrasts with your outline containing Study 1a&b, Study 2, and Study 3a, b, c, & d. What I have done is eliminate my discussion of Studies 1a&b and Study 2, except to present them as the theoretical foundation for Study 3’s a,b, & d.

 

I cut out Study 3c in this draft because I realized it was a bit too confusing to fit it in and the study had very little data of its own that I could present. The only real purpose of study 3c was that it showed me the researcher, my boss, the principals, the teachers, and ultimately convinced the U.S. Department of Education’s Special Ed division to fund our project because we were getting urban students to subitize their facts and complete their 2-digit addition worksheets quickly and accurately and this led to their doing well on their year end proficiency exams. Which we could then more easily demonstrate in Study 3d (which in this study becomes labeled as Study C) when every student in every class was taking the 42-problem worksheets as well as taking the district’s proficiency exams that contained both a math and science component and in which we tripled the passage wide jump in math and science passage rates.

 

Ultimately, I did reformat the paper into pretty much the 6 sections you present, though one section focuses on the theoretical underpinnings of the Blended Arithmetic Curriculum which includes the large n study of visual processing and slow language processing that Author2 had helped me with when I was teaching future teachers K-3 Phonics & Word study, K-3 Literacy Assessment, and K-12 Content Literature. Unfortunately, since I was only presenting some the key results of that paper in this one , and Author2 had nothing to do with Studies A, B, and C, Author2 was eliminated from authorship of this manuscript.

 

Nonetheless, when I was doing a final revision, I noticed that MDPI expects section 6 to focus on patents—which we probably could have gotten for the online conceptual games we developed if the urban school district had signed onto the follow-up level 2 grant. I would argue that their design was ahead of its time in anticipating tablets with touchscreens that would allow students to use their finger to write in numbers and move objects around the screen.  

 

Hopefully, by following your reformatting suggestions, I hope this draft of the manuscript is a little less confused and that the literature review does cover the content of this penultimate draft.

Author Response File: Author Response.docx