Open reviewing process

Living Mathematics

Living Mathematics

by Brian Williamson -
Number of replies: 30

Hi All,

Please find attached a draft of my article 'Living Statistics'. 

I hope it is of interest. 

Please see my attempts to address the Editorial Boards original comments shown in red. 

Looking forward to hearing from you in due course.

With thanks and best wishes

Brian

In reply to Brian Williamson

Re: Living Statistics

by Jocelyn Demirbag -
Hi Brian,

You have presented a fascinating topic; I have enjoyed thinking about the application of concepts we usually reserve for human beings to numbers. That would be one way to think about it. I suppose what you are arguing is more like the application of your values to working with numbers. I think this is a worthy course of investigation.

The difficulty I am experiencing as I read your paper as it is posted here is that it seems to be trying to do so much. I think it could be much more impactful if you were to show how your values could cause you to look at numbers/statistics differently. However, it would also help me if you listed which values you were focusing on early in the paper. It would also help if the number of values you were focusing on were no more than 3.

I think if you focus on one main point you would be able to organize the paper so that it is fully fleshed out. As it stands you have the idea of applying your values to numbers, the idea of helping students understand statistics through art and values, how you came to some of your previous work, and the whole section at the end in red that I am unsure about what it is demonstrating.

Now granted, I am not a mathematician or a statistician and you might be able to say that I don't understand your paper because I am not strong in these topics. However, I do think that the points you are making are interesting and could be presented much more effectively and persuasively if they were more focused. Perhaps you have 2-3 papers embedded here.

I will post your paper that shows some of the comments I made as I was reading. At this point, I do not think the paper is ready for publication.

Looking forward to learning more,
Jocelyn
In reply to Jocelyn Demirbag

Re: Living Statistics

by Brian Williamson -
Hi Jocelyn,

Thank you for thinking about my submission and for your appreciation of the fun idea of personifying numbers.
I understand that the paper is a bit complicated (!) and am grateful for your comments because I believe they will help me to clarify and edit the messages. My values and beliefs are identified in my 2015 paper where they were used as ‘living axioms’ to support the progression of a taxonomy of learning interactions. I also talk, in the article, of surmised values and believes that could have been held by others (i.e. students, researchers in the past or even characters in a comic strip); and in my 2015 paper, these ‘unlived’ values and beliefs were referred to as ‘toy’.

An explanation at the start of how my values could have caused me to look at numbers/statistics differently would frame the account I agree, and I should cite the values and beliefs identified with Pip. Would this be something that needs adding for the next iteration?

The section at the end in red (as an applied science researcher who uses statistics) cites my lived experience when working on my 2015 paper; and compares the representation of a living theory using mathematics to a situation in which an existing established piece of mathematics can cause a living contradiction in a practitioner, that is, when a researcher is supposed to apply a model that is contrary to their values and beliefs.

I hope that my writing will communicate my living theory that is growing around the values and beliefs I hold about the application of statistics without the reader needing to be a mathematician or statistician. However, it is hard because it is so tempting to include an equation, when after all it is the equation that caused so much angst and sits at the core of my living theory in the first place! Should I write more about my feelings towards these equations?

Yes, perhaps I do need to slow things down and become more focused. The article seems to divide naturally into two parts ‘Living Statistics: my I as a statistics teacher’, and ‘Living Statistics: my I as a statistics researcher’. Do you think this would help?

Thanks for your comments in the text. I will use them when preparing the next iteration(s) along with the feedback from Stephen and Pete.

Looking forward to learning more,
Brian
In reply to Brian Williamson

Re: Living Statistics

by Peter Mellett -
Good afternoon Brian

Following my previous posting, I started to work my way through your main text (as intended) and adding comments in the margin as I felt the need arose. Meeting with Jack and Marie this morning, I understand that the production process at this stage does not permit the luxury of the time required to complete this job. Therefore, I have attached to this posting just the first part of your paper (reformatted to single-line spacing) for which I have completed the process.

It is likely that further annotations would simply be variations on the theme of my current overall reservations. It would perhaps be better for me to be more directive from my point of view . . . . I think that the paper is complete. You have said what you wish to say. The major point now for me is the order in which you state the major elements of your argument and the clarity of the vocabulary that you use.

Suggestion: After 18 years as a secondary school chemistry teacher, I worked as an editor for the rest of my time – initially with science textbooks and then with distance learning MSc teaching and learning materials. My core task in both cases was to remove ambiguity and to ensure that a text had a developmental structure. Reorganisation of the elements in an argument was often the key to producing the final copy-edit. My stratagem when in extremis was to print out the author’s text, tape the sheets together and pin the entire artefact (sometimes one or more square metres in extent) to the wall. I would stand back, ponder, and then advance on this composite with coloured pens in my hand. Blocks of text would be circled and repositioned with an arrow; others would have queries highlighted . . . etc. Then I would return to the word processor and restructure according to this ‘map’ and then complete the process by ’papering over the cracks’.

Were you to do this with your paper at this stage, then your reordering might be partly in response to the questions that have arisen during my repeated readings – as follows.

1. Have I given my readers sufficient initial information to hold an outline (a map) of the journey on which I intend to take them?

2. Have I given my readers sufficient information about the subject-specific vocabulary I shall use, especially terms that are used in common speech to which I attribute more complex meanings?

3. Does each section of my text contain sufficient ‘signposts’ so that my readers know (a) the stage they are at in the argument (as outlined in 1. above) and (b) where this stage is leading?

4. Have I eliminated discontinuities from the text, where the reader might feel they have abruptly been transported off ‘the beaten track’ and onto unexpected territory?

I could write more . . . but Marie has asked me to post to you today!

Best wishes

Peter Mellett
In reply to Jocelyn Demirbag

Re: Living Statistics

by Brian Williamson -
Hi Peter, Jocelyn and Stephen,

Thank you all very much for your feedback and comments on my article. I am going to sit down now and collect all the information and prepare the next iteration for you to consider, hopefully before the end of this month.

Love
Brian
In reply to Brian Williamson

Re: Living Statistics

by Brian Williamson -
Dear Peter, Jocelyn, and Stephen,

Please find attached the second iteration of my paper. I apologise for the delay and hope that you will find the arguments here more coherent. Thank you for your support and work so far.

Love
Brian
In reply to Brian Williamson

Re: Living Statistics

by Jocelyn Demirbag -
Brian, I wrote a response earlier but do not see it here so am assuming I made a posting error and will submit again.

Thank you for working on this once again. It is such a worthwhile topic, and I find the paper much easier to work with now. At this point I would suggest enhancing the signposts as to where you are going and what you are arguing as referred to earlier.

1) What is the connection between the two pathways mentioned at the beginning?
2) Why have you segmented some of the paragraphs in the discussion section? Consider introducing the explanation.
3) Why have you segmented the sections starting p. 16? Again, be explicit about what you are thinking.

And finally, I find myself distracted by some of the writing mechanics, particularly the use of commas and semi-colons. See the attachment in a separate reply where I highlight examples in the first half of the paper.

Again, mahalo for persevering and coming so far.

Aloha,
Jocelyn
In reply to Brian Williamson

Re: Living Statistics

by Peter Mellett -
Brian -

Thirty years ago, I chanced upon the following assertion by Spengler (in Bloor 1983) that:

"... if we appreciate each culture in its individuality we will realise that the unshakable truths and convictions of its members are but expressions of one specific existence and one only ... [for example] Mathematics is not a universal thing; there is not, and cannot be, number as such. There are different number worlds and the character of a piece of mathematics depends wholly on the culture in which it is rooted, the sort of mankind it is that ponders it ..."

Bloor, D. (1983) Wittgenstein: a social theory of knowledge. Columbia: Columbia University Press.

Thirty years later, through reading the current iteration of your paper - and grasping (for example) the significance of Figure 4 - I finally understand what Spengler was talking about. Thank you.

While it is not a standard ‘EJOLTS’ account of a living theory research enquiry, for me, your paper ‘works’ - but within its own frame of reference. This is where I have an area of concern. The Abstract states – “This article sets out to investigate the relationship between Living Theory and mathematics”. The Keywords section includes ‘Mathematics’ and ‘Living Educational Theory’. However, a word search for ‘living’ within the main text highlights: ‘Living Mathematics’; ‘Living Values’; Living Contradiction; ‘Living Visual Taxonomy’; ‘Living Narrative’. By contrast, there are just four instances of the term ‘living [educational] theory’. i.e.

1. This is suggesting that living [educational] theories can be built on the top of a mathematical form.

2. I believe that using a mathematical lens to gain an awareness of the world outside of myself, for example, the learning interactions of others or of quantitative genetics, can be made more beneficial by the living theory methodology.

3. Integrative education: I can suggest ways in which art and my living educational theories can support the ST∑@M (Science Technology Engineering Art and Mathematics) integrative education movement (Yakman, 2008) potentially empowering learners to engage with mathematics communicating their lived experiences through the integration of a range of artistic medium …

4. Reverse-engineering: … concepts that are traditionally mathematically sophisticated may be more clearly understood, unravelled and demystified, using the living theory approach.

None of these references engages directly with the “… relationship between Living Theory and mathematics” as stated in the Abstract.

The conclusion states: “This article has argued that a collaboration between living theory, applied statistics and mathematics may enrich the applicability, validity and purposefulness of mathematical models as a creative medium and an organic tool.” The main text uses the terms ‘Living Mathematics’, ‘Living Values’, Living Contradiction, ‘Living Visual Taxonomy’ and ‘Living Narrative’ - I would like to see a firmer connection with your own living-educational-theory or with the overarching Living Educational Theory per se. This firmer connection could be achieved with the help of just four additions to the quotations 1-4 above to make these oblique references to living theory explicit to your practice.

In short, my question is: What makes this paper a living theory research paper? Apart from this lingering question - I like it; I think that it ticks all the review criteria . . . but in a round-about sort of way. Can you make it more head-on?

Best wishes

- Pete
In reply to Brian Williamson

Re: Living Statistics

by Stephen Bigger -
Hi Brian, Your paper has moved on since last time. I am attaching a page of comments and your paper with my corrections in comments. I hope you find some meat there (as a veggie I prob need a different metaphor) for further consideration. Please try to update by focusing more on things published within the last two decades. I will say in general I am in tune with your general direction.
In reply to Jocelyn Demirbag

Re: Living Statistics

by Peter Mellett -

Good afternoon Brian

First of all - please accept my apologies for having taken so long to reply to the posting of your latest draft. I realised early on that it required more than just reading through - I had to live with it for a while, making repeated readings and then returning to certain paragraphs. My approach to a hard copy is to use a highlighter pen as I read, marking out the phrases and words that especially strike me at the point of reading.  I then review the highlights and question whether I was struck by YES!! or by WHAT?? at the time. I then add comments in the margin from me to the author. I have similarly highlighted the attached pdf copy of your text and added comments; I have also added at the end a summary of the highlights that I think represent the structure and development of the paper. Is this the main path? Have I missed something pertinent / important? Am I 'correctly' (there's that word again!) reading what you have written?

Having gone through this process, I think that I can claim to understand your Living Mathematics and the claims that it is making with respect to Living Educational Theory. I have not found it an easy read but I conclude that it is worth the effort. I suspect that many will not be able to move beyond their fixed concept of what mathematics is and will conclude that Living Mathematics  does not offer any insights for the improvement of their own practice.

Having said all this, I reckon that the draft as it stands meets the criteria for publishing. There are typos, some dodgy grammar and a couple of doubtful words that need attention but that's just part of the next step.

Best wishes

Peter



In reply to Peter Mellett

Re: Living Statistics

by Brian Williamson -
Hello Peter,

Thank you. No need to apologizes about the delay, I work in a very similar way.

I was really happy to read that you believe that these ideas are worth the effort. I know that there is a communication challenge ahead and hope that the 4th iteration will make a start.

The summary you placed at the end just about sums up what I am trying to say which gives me heart.

I was very pleased to read that you consider the 3rd iteration to be at publishable standard!

Your support is really welcomed.

All good wishes
Brian

P. S. I will upload the 4th iteration after replying to Stephen shortly.
In reply to Brian Williamson

Re: Living Statistics

by Peter Mellett -

Good afternoon Brian -

Jocelyn has already added pertinent questions and comments at several points within your draft paper. I do not wish to repeat in different ways what has already been eloquently said. The following is offered as my personal experience as I set out to read and review your draft, holding in mind, as I usually do, the four review criteria that are central to this exercise i.e.

4. Is there sufficient evidence to support all the claims that are made?

5. Are there sufficient details of how the author has validated their claims?

6. Is the normative background of the author and their work clear?

8.  Are the author's' explanatory principles and living standards of judgment clear in this paper?

However, before I started reading the body of your paper, the title itself gave me cause to stop in my tracks. With the banner of the Educational Journal of Living Theories at the head of the page, I immediately read the first word of your title – Living – as a matter concerned with value; and the second word – Statistics – as a matter concerned with facts.

Now thinking of David Hume and his A Treatise of Human Nature, the phrase came to my mind – whether written by Hume himself or a subsequent commentator I know not – that matters of fact and matters of value constitute separate realms of logical discourse. From the very outset, therefore, it appeared to me that your paper intends to demonstrate the merging of incommensurable paradigms – which, implicit in the definition of incommensurable paradigms, is not possible.

Reading on: in the abstract you state your intention to ...

"... explore the relationship between my lived experience and my understanding, communication and application of statistical ideas".

You speak here of the application of statistical ideas and not just the application of statistics. For me, there is a distinction. As a parallel example, I would be comfortable with a values-based living-theory account of an inquiry into the structural design of a housing estate in a rural area; I would not be comfortable if that account centred on a stress analysis of roof trusses.

In the abstract you go on to claim that you ...

"... can build my living educational theory based on my lived experience of a statistical model; enabling me to present statistical ideas to undergraduate mathematicians and colleagues using a value-based approach ...".  

This process is then reversed, where you say that you will show ...

"... how I, as an applied science researcher who uses statistics, can build a statistical model based on my living educational theory; calling up my lived experiences and capturing and representing them in a mathematical form".

In these two latter extracts you speak of a statistical model, which now joins statistical ideas and statistics from earlier text. What is the relationship between the three – or are they one entity / concept? (I ask this question as one who has zero knowledge of the subject).

Whatever the distinctions between these three terms may or may not be, I understand you to be claiming that 'Statistics' and 'Living Theory' share a common "... set of concepts or thought patterns, including theories, research methods, postulates, and standards for what constitutes legitimate contributions to a field" (stolen from the Wikipedia definition of 'Paradigm'). Can statistics itself – rather than the process of using it in a context – be shown to have a quality of value?

These were the initial thoughts that I held as a 'knee jerk' response to the first page of your paper. I am stuck with this 'horizon of expectation' that emerged from a close look at your title and abstract. I am hoping that, in the course of reading the main text, the concerns I have raised will be addressed (or dismissed) and that we shall achieve a 'fusion of horizons'. (I'm a non-academic amateur in all this and so may have completely mis-represented Hume, Kuhn and Gadamer.)

Best wishes

Peter Mellett



In reply to Brian Williamson

Re: Living Statistics

by Stephen Bigger -
Living Statistics Brian Williamson
An interesting topic, Brian.
First a serious point to attend to – many, maybe most – of the titles in your References are not referred to in the text. That misses the point of references. Either find a way to discuss them or cut them out. Some are old and even very old. Your argument should address the academic climate of 2019, not four decades ago.
Elections in UK and USA is a good time to talk of statistics, and in particular the problematic (fallible) nature of statistics. At the moment, pseudo-stats are being debunked daily. At the start of your paper I felt that interesting things might emerge. I am not a statistician but deal in pedagogy in which the human side of the curriculum through examples and case studies helps understanding. So Living Statistics is a worthy title, exploring how statistics helps (or hinders) understanding of life. Discussion of what statistics mean is crucial, especially whether they mean what their promoters claim they mean. I am a statistic within dozens of categories. None of these occurrences say anything about who or what I am. They are therefore meaningless.
Questions on methodology are therefore crucial. The data comes from somewhere, questionnaires, electronic data sets etc. There is a rubbish in rubbish out argument, which is why I set high validity/credibility tests for stats, especially how the data is obtained and where it comes from. An education which challenges statistics in these ways will set the pupils up for life, critical of claims made in adverts and by politicians. This is what I would hope Living Statistics to embody.
Humanistic statistics is full of uncertainty. I never fill in questionnaires because the questions and options are nonsense. But many do and people make money from their data (and indeed from data unknowing collected on social media). There has never been a more important time to talk about real life statistics.
You mention ‘living contradiction’ as the gap between the subject and your deep values. This is a good place to develop. The things above are somewhere in that gap. The values that you highlight are part of the journey.
Stephen Bigger 8/11/19
In reply to Brian Williamson

Re: Living Statistics - 3rd iteration posted 270420

by Marie Huxtable -

I am posting this for Brian because he is having IT issues

This is this third iteration developed with reviewers responses

In reply to Marie Huxtable

Re: Living Statistics - 3rd iteration posted 270420

by Jocelyn Demirbag -
Dear Brian,

Thank you for your persistence in rewriting this. It is definitely much smoother and feels like there is good direction. You are significantly closer to publication quality. I can now look at your actual concepts more closely and respond to them.

1--I don't believe that Kline's 4 worlds of knowledge strengthens your paper. If you took out that whole section at the beginning and again in the discussion where you refer to it, I do not believe your paper would lose value. In fact, your paper would be clearer without them because it appears difficult to talk about these worlds without sounding confusing. Further, you are only really dealing with the first world. If you felt that first world was important, you could just mention the first world and not the rest.

2--You make some really interesting points in your discussion section (I have highlighted them in the attachment). I believe that you need to develop them further with a couple of sentences each (that would be my preference since they seem to be at the heart of why you are writing this) or I don't think they should be mentioned. I think if you were to just add a couple of sentences fleshing out those points, your paper would be strengthened.

While the paper's mechanics are also cleaner, there are still too many to be published as is. I have commented on these areas in the attachment. The comma/semicolon issue is better but still present but there are also quite a few sentence fragments. Citations also must still be cleaned up, both within the document and in the reference section. I have not marked each of these but as an example, in the reference section, you need a period at the end and quite a few don't have them. It may be worth having a good editor review the document for and with you.

Further, the 2nd examplar section did not come through. I think a figure is blocking some of the text so I am unsure of what you are talking about and what I have missed. As it is, exemplars 2 and 4 are not pointed out as 1 and 3 are. Please also look at the figures as some of them are blurry. I am not a technical person so don't know why that is.

Brian, you are almost there!!! This is worthy of continuing as it is such an intriguing concept. Please let me know if you have any questions.

Aloha,
Jocelyn

(Edited by Marie Huxtable - original submission Wednesday, 29 April 2020, 2:38 AM)

In reply to Jocelyn Demirbag

Re: Living Statistics - 3rd iteration posted 270420

by Brian Williamson -
Dear Jocelyn,

Thank you for you message and encouragement. Your comments have helped me to dig deeper.

The 4 worlds I write about do not belong to Kline they are part of my living theory. I think I mislead the reader by placing it next to the quote from Kline's book. I use my 4 worlds visualisation to frame Living Mathematics and therefore my living mathematics.

I have deleted some parts that seem off topic and too technical and hope this cleared some of the dead wood. I would be keen to flesh out anything more.

I hope that the images are in the right places in this iteration. I have continued to correct references and syntax and feel that this is a weak spot for me.

Thanks for your support with this idea.

I will upload the 4th iteration after replying to Stephen and Peter.

All good wishes
Brian
In reply to Marie Huxtable

Re: Living Statistics - 3rd iteration posted 270420

by Stephen Bigger -
Brian, Third iteration. You are making progress, following the conversation through. I agree with Jocelyn that there is a considerable amount of housekeeping to do, with typos, punctuation issues etc. I have struggled and am struggling with working out exactly what you are trying so say within the complexity and business of the text. There may be choices needing to be made to free up the argument a bit. At the moment I don't really 'get' your thread. I thought I did earlier but the mix of cartoons, drama and genetics is defeating me a little. I thought you drift was away from getting sums right, to encouraging pupils to become mathematicians and playing with the ideas and concept of mathematics to reach more creative solutions, understandings and processes. If so your argument needs to be sharpened and some clutter removed, perhaps with a bit of commentary to show how things fit with your argument. If I have read your intention right, it is a worthwhile enterprise as it could get pupils away from the sense of failure that sometimes inhibits progress. Please note, I am not a mathematician so you will need to focus things as you see fit. Best wishes and keep safe, Stephen
In reply to Stephen Bigger

Re: Living Statistics - 3rd iteration posted 270420

by Brian Williamson -
Hi Stephen,

Thank you for your comments which have given me food for thought.

I hope you will agree that there is less dead wood in the 4th iteration. I have decided to cut out the more technical parts (were hand holding would have become necessary) and hope that this has emphasised the thread.

Yes I thank you for making the point about cartoons and genetics and I agree that there is a danger that the whole thing becomes too outlandish! I am struggling to connect seemingly unconnectable ideas using my living educational theory called my living mathematics.

I hope you feel that the 4th iteration is a step in the right direction.

Best wishes and keep safe.

Brian
In reply to Brian Williamson

Re: Living Statistics - Pete M response to 4th iteration 140520

by Marie Huxtable -
In reply to Marie Huxtable

Re: Living Statistics - Pete M response to 4th iteration 140520

by Jocelyn Demirbag -
Hi Brian,

The paper gets cleaner and cleaner as an argument with each iteration. It is truly a process, isn't it? Thank you for working the process for this worthy theory.

At this point, I still cannot support publication because I do not believe you have met publishing criteria 9 and 10. Number 9 says that the paper "is written in English of a standard appropriate for an international academic journal, has been thoroughly checked to ensure that English spelling and grammar has been used throughout, and all references are correct in both the txt and references list." There is a substantial list of errors with punctuation, specifically the comma, semi-colon, and the colon; not all of your lists are parallel; spelling errors are present that will not be caught by spell check but only by someone reading for context (my vs may, Twin vs Twain, pros vs prose, etc); there are many sentence fragments; and your references are not cited consistently in the end. These are errors that an editor can make for you if you don't have the time or inclination to work on them. The paper cannot be considered scholarly otherwise, nor of a publishable quality.

I believe your paper would be stronger if you spent less time on worlds 2-4 in your introduction since your paper focuses on world 1. It becomes too confusing and is a bit off-point because that is not what you are focusing on. I also believe your paper would be stronger if you used the term "I argue" very sparingly--maybe once or twice in the whole paper. However, I would not block publication if you did not take these suggestions.

You have left me with much to think about and I would imagine that some students would respond much more positively to being taught Mathematics with a Living Mathematics approach. Thank you!

Aloha,
Jocelyn
In reply to Jocelyn Demirbag

Re: Living Statistics - Pete M response to 4th iteration 140520

by Brian Williamson -
Hi Jocelyn,

Thank you for you feedback. I feel very positive about the open review process. It seems like everyone gains.

Thank you for the time you have spent finding errors with missing commas, fragments and formating. I realise that there is quite a lot of work to be done in this area before the paper is OK.

I Need to mention my four worlds for completeness (one of my values). I have added to the World Two text to justify this more. Less time has been spent discussing Worlds Three and Four, especially Four - 'I believe that there is still more but it is hidden'.

I found 5 'I argues' and have reduced this to 2 'I argues' . Thanks for making me aware of this.

I hope this work will be used and that the 5th iteration to be uploaded soon is more readable.

Best wishes and thanks very much

Brian
In reply to Marie Huxtable

Re: Living Statistics - Pete M response to 4th iteration 140520

by Brian Williamson -
Dear Peter,

Thank you for your guidance and comments on my paper.

I have been working on iteration 5 and hope that you notice some improvements. A hierarchy of headings is now in place and linking sentences.

The introduction is now bounded! It introduces Living Theory and gives some examples of how a values based approach could interact with mathematical forms. I hope this helps to move your 'ahh' feeling closer to the start.

I have tweeked the text in several places in response to your comments.

1.Kline: I do belong to the world.
2. Emotive applications
3. I have tried to redefine language
4. Yes, I was extrapolating from the source
5. Yes this approach is applicable to older learners
6. I have tried to move the 'ahh'
7. The pathways are not the same. This reflects my lived experience - relatable not generalisable
8. Thanks for the Midwife Toad and for using the phrase 'Academic double-dealing'
9. Yes. The teaching and research case studies are dealt with differently. The research one is more intense. They both focus on my narrative so perhaps my living mathematics can be in both but differently.

I hope your IT gremlins have now been defeated!!

All best wishes
Brian
In reply to Brian Williamson

Re: Living Mathematics - 5th Iteration

by Brian Williamson -

Hi Peter, Jocelyn and Stephen,

Please find attached the 5th iteration of Living Mathematics. 

Best wishes 

Brian 

In reply to Brian Williamson

Re: Living Mathematics - 5th Iteration

by Brian Williamson -
Please find attached a pdf version of the 5th iteration.

Best wishes
Brian
In reply to Brian Williamson

Re: Living Mathematics - 5th Iteration

by Peter Mellett -
Brian

This current iteration of your paper now speaks to me with a firmer and more authoritative voice than previously (or is it that I’m starting to learn the text by heart?) As stated in my previous postings, I (still) regard this paper as not an easy one to ‘get into’ - perhaps because I am the sort of reader that likes to see a contents list and section headings so that I can note where I am in the development of an author’s overall argument. That said, I think your paper now makes a distinctive, if unorthodox, contribution to Living Educational Theory, which together might “… enrich the applicability, validity and purposefulness of mathematical models as a creative medium and an organic tool”. (p.24)

When the typos, references, syntax etc. are all sorted out, I think it will be ready to proceed through to publishing.

Residual points from my latest read-through are below.

Best wishes

Pete

———————————

Page 4
I understand the use of the word ‘axiom’ within general speech but am not sure if it has a specialised meaning within mathematics - also the term ’living axiom’ that derives from it.

Page 7
Key Actions are first introduced here. Not clear that they are the four steps in each of the Teaching Pathway and the Research Pathway.

Page 8
Key Action 1 - I could do with a reminder about what this term means, rather than having to refer back. See also Page 12, final paragraph, in which Key Actions 1, 2 and 3 all appear in quick succession.

Page 14
“Engaging with (1) …”. Not sure what (1) refers to: please make that all such references are clear.
In reply to Peter Mellett

Re: Living Mathematics - 5th Iteration

by Brian Williamson -
Dear Pete,

Thank you for your feedback and residual points.
I may try to make an 'ideas map' or contents page for the paper.
Marie has asked me to prepare a carefully edited version of the paper for consideration by the Editorial Board so this will be my next job.
It has been quite a journey. Thank you for your support along the way.

Thanks and best wishes

Brian
In reply to Brian Williamson

Re: Living Statistics - 3rd iteration posted 270420

by Stephen Bigger -

Hi Brian, Comments on the 4th iteration are on stickies in the attached. Most are in the references, a few in the text. I don't need to see it again, just sort out the typos and corrections. Keep safe,  Stephen 

In reply to Stephen Bigger

Re: Living Statistics - 3rd iteration posted 270420

by Brian Williamson -
Hi Stephen,

Thank you that is great and much appreciated. I will go though the comments and make the changes.

All best wishes
Brian