This is a brief one, a coda to my previous post. It’s also an unimportant one, but the thing annoyed me and took up time, and so I want to at least get a post out of it for my troubles.
In chasing down eminent professor David C Geary’s (flimsy) evidence for the prevalence of “maths anxiety”, I was led also to chase down various definitions of “maths anxiety”. Geary provided a semi-definition – “manifested as a fear or apprehension of mathematical activities” – but other researchers employ other definitions, meaning the statistics that Geary might be quoting needn’t readily apply. My search included looking through AMSI’s 2018 Research Report on maths anxiety, written by UWA professor of statistics, Inge Koch. Koch’s report seems much more solid and scholarly than Geary’s. It is still “maths anxiety” and it is still fundamentally silly, but it seems solid. In any case, Koch begins her report with a reasonably clear definition (p 6):
Hembree (1990) defines maths anxiety as ‘an adverse emotional reaction to mathematics or the prospect of doing mathematics’.
Of course this is just “maths anxiety” as Bad Maths Vibes, but at least we know what we’re talking about, and Koch provides the source for her definition. Which I looked up.
Koch notes that Hembree’s 1990 paper is highly cited, and the paper is clearly considered to be one of the important, foundational (meta)studies on “maths anxiety”. I did not read the paper closely, however, since I was simply looking to see how Hembree employed the quoted definition. The definition isn’t there.
This was, to say the least, puzzling. Koch had quoted Hembree. I checked Hembree’s paper many times. I could be going nuts, and the definition might be there, and I know one of these days I’m gonna get one of these things wrong. But it just seems plainly to not be there. Nothing like it seems to be there. It is not clear that Hembree settles on any definition of maths anxiety.
Hembree has a long introduction on the nature of mathematics anxiety (pp 33-34), introduced with a definition of “anxiety” more broadly:
The construct [of anxiety] is broadly defined to be a state of emotion underpinned by qualities of fear and dread (Lewis, 1970).
Of course “fear and dread” is a hell of a lot stronger than “adverse emotional reaction”. Hembree, however, then appears to focus upon specific manifestations of “maths anxiety”, which seems to bring the discussion more back to Bad Maths Vibes. But that was yet another rabbit hole, which I avoided. I simply wanted to understand the origins of Koch’s quoted definition. I hunted.
Along with a few theses that popped up, there were a few research papers framed around an essentially identical definition: here (2014, p 404), here (2014, p 51) and here (2018, p 53). The first of these papers is cited elsewhere by Koch, and may have been her source. All three papers reference Hembree, but without the quotes. In turn,
Math anxiety is an adverse emotional reaction to math or the prospect of doing math [Hembree]
Math anxiety is commonly defined as an adverse emotional reaction to math or the prospect of doing math (Hembree, 1990).
Mathematics anxiety is an adverse emotional reaction to Mathematics or the prospect of doing Mathematics (Hembree, 1990)
It is far from clear to me that this is an accurate paraphrasing of whatever definition, if any, that Hembree employs. But, in any case, it is a paraphrasing of Hembree. It should not have ended up as a quotation in Koch’s report.
In writing this, I’m not trying to pick cherries or nits. Yeah, the definition should not have ended up in quotes but, as I wrote at the beginning, I don’t regard the incorrect quoting as a big deal. The bigger deal, I think, although a deal I have no intention of dealing with, is if the emerged definition of “maths anxiety” is an accurate paraphrasing of what is regarded as a seminal paper. The incorrect quoting exacerbates the issue, but it’s not main issue.
In any case, I am done. The chase annoyed me but I now have my compensatory post. And I can also honestly declare that I am suffering from maths anxiety anxiety. The prospect of writing anything further on this nonsense fills me with fear and dread.