How many dots can you subitize?
I heard the word recently, and, having majored in and taught math, was surprised that I didn't know it. My favorite wordsmith, Anu Garg, writes:
verb tr., intr.: To perceive, without counting, the number of objects in a small group.
From Latin subitus (sudden), from past participle of subire (to appear suddenly), from sub- (under) + ire (to go). Earliest documented use: 1949.
More from Wikipedia:
Subitizing, coined in 1949 by E.L. Kaufman et al. refers to the rapid, accurate, and confident judgments of number performed for small numbers of items. The term is derived from the Latin adjective subitus (meaning "sudden") and captures a feeling of immediately knowing how many items lie within the visual scene, when the number of items present falls within the subitizing range. Number judgments for larger set-sizes were referred to either as counting or estimating, depending on the number of elements present within the display, and the time given to observers in which to respond (i.e., estimation occurs if insufficient time is available for observers to accurately count all the items present).
They also presented me with an amazing new medical term: simultanagnosia.
Clinical evidence supporting the view that subitizing and counting may involve functionally and anatomically distinct brain areas comes from patients with simultanagnosia, one of the key components of Balint's syndrome. Patients with this disorder suffer from an inability to perceive visual scenes properly, being unable to localize objects in space, either by looking at the objects, pointing to them, or by verbally reporting their position. Despite these dramatic symptoms, such patients are able to correctly recognize individual objects. Crucially, people with simultanagnosia are unable to enumerate objects outside the subitizing range, either failing to count certain objects, or alternatively counting the same object several times.
All of which reminded me that I have long been convinced that estimation and guestimation are important skills that we were never taught. Since I always have my phone with me, I probably no longer need to estimate what 17 x 24 is (did I ever?), but I still think that knowing that 10 x 24 is 240 so 20 x 24 is 480 so 17 x 24 is about (3 x 25) 75 less or about 405. It's actually 408. Close enough.
Which leads me back to a discussion I had recently with my friend who is a child development expert—is algebra really an important skill? I know nothing about current math teaching so I do speak only from my past experience. But this topic seems to be front and center with regard to middle and high school curriculum revisions. While I do value abstract thinking and how algebra develops that area, and while it was one of my favorite high school classes and I taught it at a community college, I feel that providing children and teens with actual number experiences—construction and measurement, revising knitting patterns, recipe conversion, calculating miles per gallon, foreign currency conversion, evaluating numbers and statistics in news articles—is possibly more important.
I once taught a class at Duke Continuing Education called Math Anxiety—a course for adults (mostly all women) who had phobiaed out of math. They were completely unable to read a number in a story and make sense of it.
Whoops. This is a language blog. I ramble. Close your eyes and subitize.