Math: Learning in US is undermined by flawed testing, by Paddington

If I were to single out one thing which holds much of US education back from excellence, it is the structure of tests.

So much of the testing used is multiple-choice, fill in the bubble style, which prevents students from being tested on developments in the Mathematical areas, and from expounding on ideas otherwise.

I think back to the tests that I took in French and German at O-level (age 16), which required translation in both directions, making up a story in the foreign language, reading a passage in the language and answering questions in English, taking dictation, and having a conversation. The English language test was similar, with the translation replaced by having to precis (summarize) a long passage in 150 words or fewer. This latter was a very valuable skill, and one which many people would benefit by learning.

Our Science and Mathematics tests required solving long problems, writing essay descriptions of experiments, and developing theories.

How could multiple-choice tests possibly be that challenging?

To be fair, or possibly reasonable, the tests were set up so that 35% or so was a pass/C and 70% was an A.

And then, when all is said and done, we have students who have had their parents/software/tutors do most of their work throughout high school (and sometimes college as well), yet cannot pass tests. Those students are then claimed to 'not test well', and are given special accommodations. We had cases of assistants provided by of Office of Accessibility simply reading the answers to students, line by line, during tests. When the latter happens, what is the point of testing or grades at all? When those enabled students finally hit a brick wall, the claim is that “tests don't check for learning”, when they most certainly can and do.

FRIDAY MUSIC: Tiny Tim, by JD

Can you remember this very unusual and unique musical talent from the Sixties? The one and only, never to be forgotten, Tiny Tim!

Among his many fans were The Beatles, Bob Dylan with The Band and Jim Morrison of The Doors as can be seen in three of the following videos.

Tiny Tim was born Herbert Buckingham Khaury on April 12, 1932, in New York, New York. His father, Butros Hanna Khaury, was from Lebanon and his mother, Tillie Staff, was a Jewish woman from Poland. Tim was raised in the Washington Heights section of New York City, where he developed a love for American songs and music, mostly from the late 1800s through the early 1900s. An unhappy student, Tim dropped out of high school and learned how to play the guitar and the ukulele.
https://www.biography.com/musician/tiny-tim

"I first saw Tiny Tim very early in his career, in Greenwich Village in the winter of 1962–63. There was a convention of college newspaper editors, and a few of us – I remember Jeff Greenfield coming along – went to the Black Pussycat and found ourselves being entertained by a man the likes of whom we'd not seen before. He was already locally popular."

- film critic Roger Ebert, https://www.rogerebert.com/features/the-last-days-of-tiny-tim

Math: train hard, fight easy, by Paddington

Before implementing solutions to a problem, it is wise to understand what the issues are.

In 1957, our government and business leaders began to recognize that high-level Science and Technology were essential to our economy and national security, requiring a large number of people trained in Mathematics, the language of Science. It also became apparent, and more so over the next 60 years, that the performance of US students in the subject averaged mediocre at best, when compared with other industrialized nations.

The conclusion that the experts came to was that there was too much rote memorization in US education, and not enough understanding. Interestingly, the many groups of Mathematics education reformers rarely include actual mathematicians. When they do, it is most often ones whose work does not require the use of tools such as the Calculus and Trigonometry.

The implemented solution was the 'New Math', and was a disaster, in large part because the teachers didn't understand what they were doing.

Later, when the situation stubbornly refused to improve, the new reformers introduced ideas such as 'lean and lively' Calculus (i.e. teach less) and taught students to use calculators and computer systems to do the rote calculations.

The end result has been that the percentage of students who have learnt the bare required facts and can do the basic computations has shrunk. Of the remainder, many have decayed their skills so far that they cannot correctly input expressions to their computing devices, and cannot understand the resulting outputs. God forbid if you ask them to do anything with fractions or percentages.

The underlying problem was that the 'expert' reformers did not understand that Mathematics is both a language and a mode of thinking. Except for the savants, its learning requires repetition of operations, by hand. After all, we don't expect people to learn instruments by listening to music, do we?

In years past, I had classes prepare a study sheet for first semester Calculus. Most could fit every definition, theorem and rule required on less than one sheet of paper. For how many subjects could one say that?

However, when I awarded 20% of the grade on the final (announced beforehand) to reproduce 3-4 of the definitions and statements of theorems, no more than 1 in 20 of the students could get them correct.

So much for 'rote learning'.

FRIDAY MUSIC: Christmas music (part 2), by JD

Part Two moves eastwards and further away from the 'traditional' carols and closer to the reason for this celebration. 

The fourth video may not be strictly correct (Christmas Eve would normally be compline and not vespers) but the lead singer here has a fabulous voice.

Merry Christmas!

FRIDAY MUSIC: Christmas music (part 1), by JD

"The "Huron Carol" (or "Twas in the Moon of Wintertime") is a Canadian Christmas hymn (Canada's oldest Christmas song), written probably in 1642 by Jean de Brébeuf, a Jesuit missionary at Sainte-Marie among the Hurons in Canada. 

Brébeuf wrote the lyrics in the native language of the Huron/Wendat people; the song's original Huron title is "Jesous Ahatonhia" ("Jesus, he is born")."

https://en.wikipedia.org/wiki/Huron_Carol

This version is by Loreena McKennitt who is a Canadian singer-songwriter, multi-instrumentalist, and composer who writes, records, and performs world music with Celtic and Middle Eastern influences. McKennitt is known for her refined and clear soprano vocals. https://en.wikipedia.org/wiki/Loreena_McKennitt

Marketing is self-serving BS, by Paddington

 For many years, I have wondered about the efficacy of advertising.

Then, I listened to a couple of the 'Freakonomics' podcasts, where they discussed experiments and statistical studies on this very subject. Those studies, and the reaction to them, are very interesting.

If advertising is actually effective, it appears to be only one-tenth as effective as is generally believed by those in the trade. However, the people in marketing in large companies, and those who sell them advertising, just 'know' that it works. They just can't explain how it works, nor provide any unequivocal data to support their conclusion. However, they maintain their cushy jobs on the backs of those beliefs.

One of the knock-on effects of this belief is that Marketing faculty at universities earn 1.5 to 2 times what Mathematicians and Engineers do, because 'everyone knows' how effective they are.

As I have said before, we are the nation of con men and used car salesmen.

FRIDAY MUSIC: Last-minute Christmas Chopin, by JD

A bit of calming music as a blessed relief from the madness of the world. The first video was attributed to Frédéric Chopin but was in fact composed by Paul de Senneville under the name "Mariage d'Amour".

https://www.britannica.com/biography/Frederic-Chopin