The Promise of AI Object-Recognition in Learning Mathematics: An Explorative Study of 6-Year-Old Children’s Interactions with Cuisenaire Rods and the Blockplay.ai App

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

 

 

This paper describes the development of an AI based application that speaks the lengths of Cuisenaire rods and describes two six year olds interacting with the app, trying to get the app to say the two times table.

 

I think the conclusion could be improved significantly. I read the conclusion first and didn't get any sense of what happened in the paper, nor what it was the authors learned, even though they state that they learned something. There are statements such as “we believe”, “we view”, but I suggest being more specific and more focused on what you learned and not what you think, which seems to be the same as what you might have thought before the study (this was confirmed later after I read the paper). As I was reading the introduction, line 62 suggests that there will be a discussion of implications and future research, but I didn’t see it in the conclusion, nor earlier.

 

Overall, the paper is a little challenging to follow. My first criticism would be that the whole notion of abstract is very unclear. I suggest a more rigorous description of abstract is given. The word abstract seems to me to be used as a placeholder for something the authors are not clear about, which is problematic since the paper is making a few claims about abstract. Without any sense of how the notion of abstract is being used in this paper, it obscures the message. For example, in line 186, why is the inscription of dots on a cube suggest now that the cube is an abstract artifact? What is it about the dots that are abstract? Is the abstraction in the dots, or in the child’s minds? I believe this matters since the conclusion of the paper is that children may see number as length in which case it seems the abstraction is in the child’s minds.

 

I suggest that lines 185 to 196 to be much, much clearer. Line 202 to 203 is clear, I think that sentence is fair. But now the argument needs to be to be made as to why abstract is being introduced. I think I'm convinced the things that are being called abstract are symbols, but still not sure what abstract is. Btw, the Shvartz et al. quote which suggests abstract is “a transformation of perception” doesn’t help much since both transformation and perception are not taken up.

 

Going back to the introduction, it touches on the idea of moving from the concrete to the abstract to the new concrete but not only should this be clearer in the introduction but it should be taken up again in the conclusion (which other than one sentence, it is not).

 

I think the introduction needs to be clear that the section that follows is very long and describes the development of the app. In fact, the introduction might be better spent on describing the structure of the paper and the stance of the authors since it is not a standard paper. For example, there is no research question nor any empirical conclusions. This is fine but it should be noted in the introduction in some form or another.

 

 

Section 2.1 (I think it should be 3.1) doesn’t follow from the previous sections so it needs an introduction of sorts. And also tell the reader why “attractor” is being introduced. You're asking the reader to commit to this section, but it doesn't follow naturally from the previous section. In fact the whole section needs clarity. It’s very hard to follow. Simondon is given two sentences, how is that helpful? Assume most people haven’t read Simondon in which case it is the author’s role to clarify.

 

Single points:

Line 55, why chaotic?

Line 65 introduces Michael, but maybe position Michael in a way that when we read his name it means something other than a name.

Line 238 typo

Author Response

Dear Editors and Reviewers

Many thanks for the insightful comments. We have really appreciated working with the challenge of your reflections and we feel the paper is much stronger as a result – we hope you agree!

With thanks

Reviewer 1
I think the conclusion could be improved significantly. I read the conclusion first and didn't get any sense of what happened in the paper, nor what it was the authors learned, even though they state that they learned something. There are statements such as “we believe”, “we view”, but I suggest being more specific and more focused on what you learned and not what you think, which seems to be the same as what you might have thought before the study (this was confirmed later after I read the paper). As I was reading the introduction, line 62 suggests that there will be a discussion of implications and future research, but I didn’t see it in the conclusion, nor earlier.	Thank you – we have re-worked the conclusion to pull out more explicitly our learning. We have been prompted to focus on the study as one example of what we see as the key contribution of our work – which is pointing to the potential for object-recognition in learning mathematics.
My first criticism would be that the whole notion of abstract is very unclear. I suggest a more rigorous description of abstract is given. The word abstract seems to me to be used as a placeholder for something the authors are not clear about, which is problematic since the paper is making a few claims about abstract. Without any sense of how the notion of abstract is being used in this paper, it obscures the message. For example, in line 186, why is the inscription of dots on a cube suggest now that the cube is an abstract artifact? What is it about the dots that are abstract? Is the abstraction in the dots, or in the child’s minds? I believe this matters since the conclusion of the paper is that children may see number as length in which case it seems the abstraction is in the child’s minds.   I suggest that lines 185 to 196 to be much, much clearer. Line 202 to 203 is clear, I think that sentence is fair. But now the argument needs to be to be made as to why abstract is being introduced. I think I'm convinced the things that are being called abstract are symbols, but still not sure what abstract is. Btw, the Shvartz et al. quote which suggests abstract is “a transformation of perception” doesn’t help much since both transformation and perception are not taken up.   Going back to the introduction, it touches on the idea of moving from the concrete to the abstract to the new concrete but not only should this be clearer in the introduction but it should be taken up again in the conclusion (which other than one sentence, it is not).	Thank you – we agree that we were not entirely clear about how we were taking up the notions of concrete and abstract.   We have worked on section 3 and hopefully clarified these meanings, including removing the Shvarts et al. quotation.   We have also re-worked the introduction, to make it more of a forward-marker of the structure of the paper.   We believe we have become much clearer about the concrete-abstract-new concrete move being used.
I think the introduction needs to be clear that the section that follows is very long and describes the development of the app. In fact, the introduction might be better spent on describing the structure of the paper and the stance of the authors since it is not a standard paper. For example, there is no research question nor any empirical conclusions. This is fine but it should be noted in the introduction in some form or another.	Thank you we have re-worked the introduction to focus more on the structure of the paper and to warn the reader that our research is not driven by specific questions yet.
Section 3.1 doesn’t follow from the previous sections so it needs an introduction of sorts. And also tell the reader why “attractor” is being introduced. You're asking the reader to commit to this section, but it doesn't follow naturally from the previous section. In fact the whole section needs clarity. It’s very hard to follow. Simondon is given two sentences, how is that helpful? Assume most people haven’t read Simondon in which case it is the author’s role to clarify.	Thank you. We have moved section 3.1 to the start of section 3 and elaborated in more detail about what we mean by attractor. We have removed reference to Simondon, which we agree, would need more space to make meaningful.
Single points: Line 55, why chaotic? Line 65 introduces Michael, but maybe position Michael in a way that when we read his name it means something other than a name.	We have removed the line 55 reference to “chaotic”.

 

 

Reviewer 2 Report

Comments and Suggestions for Authors

The article describes the experimentation of an AI-based image recognition application with 5-6 year-old students in an English school. The experimentation is situated within Davydov’s theory, which describes learning as a process in which abstract thinking moves towards concrete practice by offering a lens with which to perceive and act on concrete objects in new ways. A part from the fact that the theoretical framework could be more up-to-date, drawing from this, the concrete objects (Cuisenaire rods) proposed to the students during the activity can be read, in the authors’ view, through the concepts of number-as-counting and number-as-measure.

Firstly, the decision to utilise Cuisenaire rods as a teaching tool is problematic in itself. This concrete model is in fact ambiguous, confusing numerosity and metrics. What didactic intent was intended? It is not clear whether one wants to work on number from the point of view of cardinality or number as length. A Cuisenaire rod is an object that does not show units of measurement (e.g. those five cubes in Fig. 4 cannot be seen), so pupils do not see units of measurement to compare lengths, but unique objects. The proposed use of Cuisenaire rod is precisely what is not recommended in mathematics education, as it conveys the misconception that cardinality depends on metrics. Considering also the age of the young pupils involved (5-6 years old), it would be didactically more valid to have an application that says 3 if you have three objects, as cardinality, and not a single object of volume three times a cube.

Summing up, this methodological choice recalls a tool that is currently regarded as outdated by research in the field, conveys misconceptions and considerably reduce the significancy of the teaching activity presented.

The idea of the app and the path that led to its realisation are interesting, but the use of the technology here is totally overstated compared to the activity. In other words, what is the meaning/value of such a sophisticated training of the device if the didactic significancy of the teaching example is low?

It is advisable to experiment with a use of the app in which this sophisticated device is used for real didactic needs, with the aim of showing what this technology brings over the practical activity. What is the added value of the technology here?

In this sense, it is questionable whether the application developed has any particular teaching potential; rather, it seems that other contexts, e.g. interaction with a teacher, would have been equally effective for the proposed teaching activity. In general, application and AI prove to be constraints on the teaching experience, preventing its educational potential from being appreciated. The use of coloured Cuisenaire rods, for example, due to software design constraints, is actually a teaching obstacle, as the student may tend to recognise the colour rather than the number. There are also numerous technical difficulties related to the operation and usability of the software, as the authors themselves have acknowledged.

The authors claim that during the experimentation, the tensions between the child’s actions and perceptions, generated by the interaction with the app, led one of the students to switch from the number-as-counting attractor to the number-as-measure attractor in order to solve the task. The authors therefore argue that the app could have educational potential in generating meaningful attractors during a student-task interaction activity.

Here, another weaknesses emerge concerning the authors’ conclusions: it is unclear how the students’ prior knowledge might have influenced one of them to adopt a number-as-measure conception. Did they know the number sequence in the same way? The child understands the logic behind the request but what did they understand about the number?

In conclusion, for the critical aspects mentioned above, the paper does not appear eligible for publication.

Author Response

Dear Editors and Reviewers

Many thanks for the insightful comments. We have really appreciated working with the challenge of your reflections and we feel the paper is much stronger as a result – we hope you agree!

With thanks

 

Reviewer 2
Firstly, the decision to utilise Cuisenaire rods as a teaching tool is problematic in itself. This concrete model is in fact ambiguous, confusing numerosity and metrics. What didactic intent was intended? It is not clear whether one wants to work on number from the point of view of cardinality or number as length. A Cuisenaire rod is an object that does not show units of measurement (e.g. those five cubes in Fig. 4 cannot be seen), so pupils do not see units of measurement to compare lengths, but unique objects. The proposed use of Cuisenaire rod is precisely what is not recommended in mathematics education, as it conveys the misconception that cardinality depends on metrics. Considering also the age of the young pupils involved (5-6 years old), it would be didactically more valid to have an application that says 3 if you have three objects, as cardinality, and not a single object of volume three times a cube. Summing up, this methodological choice recalls a tool that is currently regarded as outdated by research in the field, conveys misconceptions and considerably reduce the significancy of the teaching activity presented.	We respectfully disagree with this reviewer that Cuisenaire rods are outdated. We note, for example, the recent proposal by Hyman Bass in his 2024 book “Mathematical Neighbourhoods of School Mathematics” to derive a coherent basis of mathematics, taking number as length (as the Cuisenaire rods do). We also note the on-going interest and use of Davydov’s curriculum insights (e.g., a recent special issue of Educational Studies in Mathematics), based on introducing number as measure, which is entirely consistent with the use of Cuisenaire rods. Davydov and Gattegno both argued for the teaching of algebra before arithmetic, which is our ultimate intention also.   We are grateful for these comments, as they have prompted us to be more explicit about the ideas above in the introduction.
Here, another weaknesses emerge concerning the authors’ conclusions: it is unclear how the students’ prior knowledge might have influenced one of them to adopt a number-as-measure conception. Did they know the number sequence in the same way? The child understands the logic behind the request but what did they understand about the number?	We have found this a helpful comment to work with. This has prompted us to make more explicit that our aim in this paper is to show the potential for object-recognition as a novel technology for teaching and learning. Our study – with all its limitations – is there to point to future possibilities. We have made this more explicit in the title, introduction and conclusion.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have taken into consideration the suggestions concerning the expansion of the bibliographical references, the methodology and the analysis of the processes implemented by the pupils: the changes made in this respect have made it possible to improve the contribution and clarified the added value of technology in this experiment.

The more recent references added are appreciated, even though the basic criticalities pointed out in the first reference on the choice of rods and the possible confusion between number as a quantity and number as a measure for 6-year-old pupils who are constructing a sense of number remain, in my opinion. However, the changes made may allow for deeper reflection and discussion.

Author Response

Thank you again for your comments - please see our responses attached.

Author Response File: Author Response.pdf