How Is Your Math(S)?

[hazelm]

A "must read" - or "must scan, at least".  Expert mathematicians are stumped by simple subtraction.

 

https://neurosciencenews.com/math-simple-subtraction-14451/

 

High-level mathematicians have trouble solving primary school level subtraction problems.  And the fault, of course, is on the shoulders of the educators. 

 

All right.  As an educator, I can only ask:  could not this long-winded story have been written with far fewer words? 

 

 

[GAHD]

I bet it could have been, but they wouldn't have been able to fill up the page or take direct quotes from the article and still justify ad revenue without plagiarism claim.

It doesn't surprise me though. I've had personal experience with MA holders taking 8 hours of mat-lab simulation time to find an answer for a problem I solved in 5 minutes on the back of a coffee receipt. It often comes down to understanding of numbers as objects/values vs concepts IMHO.

[hazelm]

I bet it could have been, but they wouldn't have been able to fill up the page or take direct quotes from the article and still justify ad revenue without plagiarism claim.

 

It doesn't surprise me though. I've had personal experience with MA holders taking 8 hours of mat-lab simulation time to find an answer for a problem I solved in 5 minutes on the back of a coffee receipt. It often comes down to understanding of numbers as objects/values vs concepts IMHO.

It comes down to something else, too.  Publishers - maybe not all but most - pay by the word.  So, the more words .....   My one pet peeve with many instructive books is their plethora of examples.  They will make a simple statement and then recite example after example after .... on and on.  Most of us would get it the first time.  Don't need to hear four or five ongoing stories.

 

Anyway, when I run into that, I think "extra words = extra money + boredom. 

[Dubbelosix]

A "must read" - or "must scan, at least".  Expert mathematicians are stumped by simple subtraction.

 

https://neurosciencenews.com/math-simple-subtraction-14451/

 

High-level mathematicians have trouble solving primary school level subtraction problems.  And the fault, of course, is on the shoulders of the educators. 

 

All right.  As an educator, I can only ask:  could not this long-winded story have been written with far fewer words? 

 

Yes well, I've caught some experts out on simple subtraction terms on physicststack so this does not really surprise me. But it happens. Susskind got his units wrong in one of his lectures and couldn't work out where he went wrong, the difference here is that Susskind doesn't mind such mistakes because his ego isn't over the roof. 

[hazelm]

Yes well, I've caught some experts out on simple subtraction terms on physicststack so this does not really surprise me. But it happens. Susskind got his units wrong in one of his lectures and couldn't work out where he went wrong, the difference here is that Susskind doesn't mind such mistakes because his ego isn't over the roof. 

 

If the story is accurate - and I have trouble believing it - it is a boost to those of us who do not comprehend a lot of the "advanced math".  Let all top-notch mathematicians take notice. 

 

Susskind has company.  I once worked with a woman who was showing a math problem around the departments.  All of the steps in solving the problem were correct (she said) but the final answer was wrong.  Everyone was being very polite and moving on.  I took one look and saw "1 x 0 = 1.  Unfortunately, I said 1 x 0 = 0.  Not at all nice of me.  We all make such mistakes at any level.  Right?

[Jeremiah]

A statistical analysis resulting in an inductive inference following from a flow of deductive steps under a set of assumptions can only be supported by a valid model if random samples are taken. There are no magical mathematical or scientific tricks around this foundation, but scientists often take shortcuts; because doing it the right way is hard, time consuming and costly. However, the tendency to ignore the basic foundations of Statistics has lead science into what some consider a crisis, in which far too many published studies do not meeting the replication criteria of science. Articles are being published for their eye catching titles, rather than their scientific value, because real value is hard to obtain, but slap some “stats” on a news worthy title and you have a quick sell.

 

I would take this study with a giant grain of salt. Their parameters are poorly defined, they failed to clearly detail their "recruitment" methods, there is selection bias and they didn't seem to fully address the limitations of their approach (I am always cautious of a study that does not address its own limitations).

 

I am a graduate student in the field of Statistics, and this study looks like something one of my professors would use an example of what not to do.

 

From the study,

 

https://link.springer.com/article/10.3758%2Fs13423-019-01628-3#aboutcontent

 

 

 

We recruited 85 adults (50 women, mean age = 23.35 years, SD = 7.82) in the Paris region. All had attended university (mean length of university curriculum = 2.85 years, SD = 1.18), but none majored in mathematics. Considering the low complexity of the math problems involved, participants’ curriculum was a clear indicator that they possessed the mathematical expertise required to solve the problems. Sample size was determined using uncertainty and publication bias correction on results from a previous study (Gros et al., 2016), following Anderson, Kelley, and Maxwell’s recommendations (2017).

 

 

 

We recruited 25 experts (two women, mean age = 23.59 years, SD = 2.81) who had successfully passed the entrance exam of the Science section at the École Normale Supérieure (ENS Ulm) in Paris. This exam is considered as the most demanding one in France, with an entrance rate of 2.02% among university-educated participants (“SCEI Statistics”, 2017). The ENS ranked second in Times Higher Education’s World University Rankings 2016–2017 for Best Small University (Bhardwa, 2017). Although the population sample was smaller than in the first study due to the number of graduates from École Normale Supérieure being limited, sample size was deemed sufficient using uncertainty and publication bias correction on results from a previous study (Gros et al., 2016), following Anderson et al.’s recommendations (2017).

Edited July 27, 2019 by Jeremiah