![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
Inglis, M., & Foster, C. (2018). Five decades of mathematics education research. Journal for Research in Mathematics Education, 49(4), 462-500.
http://www.foster77.co.uk/JRME2018-07-462.pdf
In this remarkable paper, the authors look at almost five decades of publications in Educational Studies in Mathematics and the Journal for Research in Mathematics Education to see whether the field of mathematics education research has changed over this period and, if so, how. They are particularly interested in looking at evidence of the “social turn” in maths education research noticed by Lerman in 2000; is this “social turn” still apparent?
In order to see what has changed, there first needs to be some way of clustering papers or categorizing them and then to see how those clusters have altered in prominence (measured how?) over the years. The authors decide to use Lakatos’s notion of scientific research programmes. Within this methodology, “the base descriptive unit of research” (p. 464) is a research programme. A programme is a connected set of theories sharing
To illustrate this model of a research programme, the authors give constructivism as an example where radical constructivism and social constructivism can be seen as part of the protective belt of the hard core of constructivism, whereas sociocultural theory has a different hard core to any type of constructivism (although sharing parts of its heuristic with social constructivism) and therefore is a different research programme entirely. There are progressing programmes and degenerating programmes, based on how these deal with and accommodate anomalies.
The paper’s methodology was to download every article from ESM and JRME from their first publications, to remove words that are topic independent (such as the and a) and then to use the computational method called topic modeling to identify words that co-occur. An optimum number of 35 topics was pre-chosen as the best fit (the paper discusses reducing “perplexity” offset against maintaining interpretability). The results of the analysis finally included 28 usable topics, the others being related to journal administration and to foreign language articles. The authors contemplated each topic’s cluster of co-occurring words as determined by the automated computational process and thereafter assigned a descriptive label to each.
The 28 topics were, in alphabetical order: Addition and subtraction, Analysis, Constructivism, Curriculum (especially reform), Didactical theories, Discussions, reflections, and essays, Dynamic geometry and visualization, Equity, Euclidean geometry, Experimental designs, Formal analyses, Gender, History and obituaries, Mathematics education around the world, Multilingual learners, Novel assessment, Observations of classroom discussion, Problem solving, Proof and argumentation, Quantitative assessment of reasoning, Rational numbers, School algebra, Semiotics and embodied cognition, Sociocultural theory, Spatial reasoning, Statistics and probability, Teachers’ knowledge and beliefs, and Teaching approaches.
Once the topics were identified, the authors calculated “the mean proportion of words from each topic published by each journal in each year” (p. 478) and were then able to chart the extent to which each topic was covered across time.
For a detailed analysis of all the trends, you should see the paper. Here I list items of particular interest to me:
One trend the authors make a particular point about is the “experimental cliff” where studies involving randomized experimental designs, once popular, have fallen almost to nil despite US and UK agencies calling for this type of study and making funding available. Looking into publications in experimental psychology, the authors find this a rich area of research and publication, yet these studies are not being published in maths education journals. The authors point out the rich possibilities of information travelling both ways and encourage exposure to multiple research programmes.
The paper addresses the theoretical diversification apparent in the last 15-20 years and seems to fall on the side of Dreyfus (2006) in cautioning of the dangers of too much diversification. The authors recommend finding connections across theories and unifying them where possible.
Altogether I found this a fascinating picture of what ESM and JRME have been publishing over the last (approximately) 45-50 years. The trends in research are interesting and informative. I would love to see someone use the same methodology on a different set of journals. If journals such as the International Journal of Mathematical Education in Science and Technology (my favourite journal) were included I think we might see some different topics emerge.
Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.
http://www.foster77.co.uk/JRME2018-07-462.pdf
In this remarkable paper, the authors look at almost five decades of publications in Educational Studies in Mathematics and the Journal for Research in Mathematics Education to see whether the field of mathematics education research has changed over this period and, if so, how. They are particularly interested in looking at evidence of the “social turn” in maths education research noticed by Lerman in 2000; is this “social turn” still apparent?
In order to see what has changed, there first needs to be some way of clustering papers or categorizing them and then to see how those clusters have altered in prominence (measured how?) over the years. The authors decide to use Lakatos’s notion of scientific research programmes. Within this methodology, “the base descriptive unit of research” (p. 464) is a research programme. A programme is a connected set of theories sharing
- a hard core (“a collection of key assumptions and beliefs”),
- a protective belt (“a large collection of auxiliary hypotheses that supplement the hard core and can be used to protect it from being falsified”)
- and a heuristic (“the collection of methods and problem-solving techniques [used] to make progress”) (p. 464-5).
To illustrate this model of a research programme, the authors give constructivism as an example where radical constructivism and social constructivism can be seen as part of the protective belt of the hard core of constructivism, whereas sociocultural theory has a different hard core to any type of constructivism (although sharing parts of its heuristic with social constructivism) and therefore is a different research programme entirely. There are progressing programmes and degenerating programmes, based on how these deal with and accommodate anomalies.
The paper’s methodology was to download every article from ESM and JRME from their first publications, to remove words that are topic independent (such as the and a) and then to use the computational method called topic modeling to identify words that co-occur. An optimum number of 35 topics was pre-chosen as the best fit (the paper discusses reducing “perplexity” offset against maintaining interpretability). The results of the analysis finally included 28 usable topics, the others being related to journal administration and to foreign language articles. The authors contemplated each topic’s cluster of co-occurring words as determined by the automated computational process and thereafter assigned a descriptive label to each.
The 28 topics were, in alphabetical order: Addition and subtraction, Analysis, Constructivism, Curriculum (especially reform), Didactical theories, Discussions, reflections, and essays, Dynamic geometry and visualization, Equity, Euclidean geometry, Experimental designs, Formal analyses, Gender, History and obituaries, Mathematics education around the world, Multilingual learners, Novel assessment, Observations of classroom discussion, Problem solving, Proof and argumentation, Quantitative assessment of reasoning, Rational numbers, School algebra, Semiotics and embodied cognition, Sociocultural theory, Spatial reasoning, Statistics and probability, Teachers’ knowledge and beliefs, and Teaching approaches.
Once the topics were identified, the authors calculated “the mean proportion of words from each topic published by each journal in each year” (p. 478) and were then able to chart the extent to which each topic was covered across time.
For a detailed analysis of all the trends, you should see the paper. Here I list items of particular interest to me:
- Proof and argumentation have seen an increase in publications over recent decades; this trend is interesting given my interest in how one teaches proof to engineering students.
- Problem solving has seen a decrease. What drew me into maths education research to begin with was problem solving, particularly Alan Schoenfeld’s work. My PhD was ultimately on problem solving, so I observe the decrease in problem solving interest rather glumly. Also with some confusion – how can problem solving ever not be interesting and complex?
- Curriculum (especially reform) has seen a marked increase. I see the Twente Educational Model somehow fitting in under this topic.
- So has Novel assessment seen an increase. The maths department at the University of Twente is taking digital assessment of linear algebra very seriously and I am peripherally involved with that.
- Multilingual learners has seen a very slight increase, Equity has remained almost steady and Gender has seen a significant decrease. This trend is worrying (to me). These are all issues I would consider of extreme importance.
- Constructivism has seen a sharp decline while sociocultural theory is steeply increasing, supporting the hypothesis that there is a “social turn” in maths education research which is continuing to make itself felt.
One trend the authors make a particular point about is the “experimental cliff” where studies involving randomized experimental designs, once popular, have fallen almost to nil despite US and UK agencies calling for this type of study and making funding available. Looking into publications in experimental psychology, the authors find this a rich area of research and publication, yet these studies are not being published in maths education journals. The authors point out the rich possibilities of information travelling both ways and encourage exposure to multiple research programmes.
The paper addresses the theoretical diversification apparent in the last 15-20 years and seems to fall on the side of Dreyfus (2006) in cautioning of the dangers of too much diversification. The authors recommend finding connections across theories and unifying them where possible.
Altogether I found this a fascinating picture of what ESM and JRME have been publishing over the last (approximately) 45-50 years. The trends in research are interesting and informative. I would love to see someone use the same methodology on a different set of journals. If journals such as the International Journal of Mathematical Education in Science and Technology (my favourite journal) were included I think we might see some different topics emerge.
Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.
