I wrote a 20 pages 10K words chapter “Demodeling Calculus from Deriving Functions to Adding Per-numbers” to a coming Springer Nature book “New trends in teaching and learning of calculus” published in the book series “Research in Mathematics Education”.
The chapter points out that calculus is needed in grade one to add the bundle-numbers with units that children bring to school, e.g., ‘2 3s + 4 5s = ? 8s’, i.e., if you want to teach mathematics instead of ‘mathematism’ claiming that 1+1 = 2 despite 1week+1day = 8 days.
However, it was rejected based on two peer reviews. I gladly accept quality reviews, but in this case I think they may deserve the label ‘Poor Peer Review’.
And frankly, I am a little tired of Poor Peer reviews, so I have prosed to Springer to write a book with examples of Poor Peer Reviews and a Journal called ‘Preventing Poor Peer Review’.
You find the two reviews below as well as an extract from the paper.
An extended extract is published on LinkedIn.
The full paper may be seen here until the end of February 2025.
Review 01.
The proposed work is new and original, and it also has interesting historical and philosophical aspects. However, its connection with the teaching and learning of Calculus is minimal , so it does not seem to be the appropriate book for this work. On the other hand, the proposal is not truly a research work , since it lacks a methodological section, field work, results, etc.
In summary, I do not recommend the publication of this work for the book “New Trends in Teaching and Learning of Calculus” and I would suggest the author to send it to a publication more appropriate to his subject matter.
Review 02.
The proposed chapter presents a number of difficulties that, given my expertise, I believe require a detailed examination, particularly in relation to the intended audience.
One of my first observations is that throughout the text several shortcomings in its structuring are identified. In several sections , the relevance of sustainable development is mentioned (e.g. the goal By 2030, ensure that all youth and a substantial proportion of adults, both men and women, achieve literacy and numeracy), but this idea is presented in a superficial way , without a clear link to school reality and the description of the objectives of the 2030 Agenda. In my opinion, the author takes only the title of this agenda and develops his own interpretation , without going deeper into the subject.
During the reading, doubt arises about the target audience of the proposal , and although it is mentioned in a general way that it should be implemented in primary education, it is not made explicit in such a clear way.
Another important aspect is the lack of empirical studies to support the proposal, which would demonstrate its relevance for teaching and learning of calculus. Instead, the approach seems more like a personal intention of the author . While this approach is not necessarily negative, in the context of a book aimed at the teaching and learning of calculus , it is not appropriate, or at least not at this stage of development.
As a specialist in mathematics didactics, I am concerned about the implementation of this proposal in primary school students. In a relatively recent history (around 1960), the ‘New Math’ trend generated significant problems in teaching by prioritising mathematical formality over students’ cognitive readiness to understand these concepts. This chapter reminds me, to some extent, of that trend, so I would pay attention to it.
Now, in mathematical terms, the proposal is interesting, but I think it would be more suitable for students training to be teachers or mathematicians. This approach would allow them to visualise and explore mathematics from another perspective, as well as to work on demodeling processes, an aspect that I also find valuable on the part of the author.
In conclusion, I consider that the proposal needs a thorough restructuring . This includes clearly defining the target audience , conducting a more detailed analysis of the school curriculum (including a review of educational reforms in mathematics teaching), and supporting the proposal with empirical studies that demonstrate its relevance .