Common Core isn’t the first attempt to teach students to understand mathematical concepts, writes Mark Palko, a former math teacher, in the *Washington Post*. If we remember the old new math, perhaps we can learn from its mistakes. But Core reformers suffer from collective amnesia.

# Remembering the old new math

June 17, 2014 by

Math is a subject where it is POINTLESS to re-invent the wheel. 2+2 = 4, no matter what you do with it.

If only.

It’s only pointless if you’re interested in educating kids. But that’s hardly a motivating force in the public education system since it’s largely immaterial whether the kids learn.

The problem for the professionals is how to distinguish themselves, and reap such rewards as are available, when the relevant skill is unvalued by th e institution that employs them. Reinventing the wheel, particularly when you surround it with a thicket of impenetrable jargon is one such way and it’s been a popular route for quite a long time. I understand whole language has been around in various forms and under various guises for about a hundred years.

Base 3?

When I was teaching math, around 1965-70, the first new-math students were coming through — we used to say, “when they were good they were very very good . . . ” but many of them were horrid, and we believed it was often because their teachers in high school didn’t understand what they were supposed to be teaching.

Set theory is of enormous intellectual value.

Yes, set theory is of enormous intellectual value if you are doing mathematics, but not so much for other fields.

I should also add that there were mathematicians doing world class mathematics long before there was set theory. I believe it was invented by George Cantor in 1874.

As someone who taught set theory in the late 60’s and early 70’s, I agree that set theory can be of enormous intellectual value… but not to people that can’t add, subtract, multiple or divide.

When I learned the old new math, the “set theory” was no more than trivial Venn diagram stuff over and over again. This is just a trivial part of the language of mathematicians. REAL set theory is completely different: it is an attempt to formalize the basics of mathematics, and it is only useful and interesting to people who are already mathematicians.

I think that every kid of average or near-average ability should be required to master what used to be known as ES (k-8) arithmetic; math facts, basic operations, fractions, decimals, percentages, time/rate/distance, interest calculation etc – without calculators. Beyond that what kind of math is taken in HS should depend on what program the student is taking; college prep (STEM or otherwise), practical nursing, carpentry, auto mechanics, cosmetology, admin assistant etc. Pretty much everyone should take some kind of math in HS but not everyone can or should take the traditional college-prep sequence, let alone the STEM sequence.

I completely agree. We won’t, however, as long as most educators believe two things:

1. Most every student can learn STEM sequence mathematics.

2. If every student isn’t taught STEM sequence mathematics, they are being denied a chance to make good money in a STEM career–and the country is poorer for wasting some if its brainpower.

The hard truth is that most students can’t learn STEM sequence mathematics. Teaching them math they can do and can use only denies them the chance to be failures.

I think everyone should take some sort of statistics course, as well. We hear statistics thrown at us every day of our lives, and if you don’t have some understanding of them, you can’t interpret them accurately. “Doing XYZ will double your risk for JKL cancer!” only matters if the original risk is significant. Double 1:2,000,000 is only 1:1,000,000 and nothing to fret over. Double 1:100 and it gets scary.

Stats is one of the most important classes we can teach kids, yet it is one of the worst-taught. (And serious career-STEM majors need it too. Many a journal article has fallen apart when the statistical analysis was found wanting.)

A school (university/college) which has CSAB (Comp. Sci Accred. Board) will have the following math subjects as requirements:

Calculus (I/II)

Linear Algebra

Diff Eqns

Applied Statistics

Abstract Algebra

Numerical Analysis

Symbolic Logic (usually in the philosophy dept).

In Science you’ll need at least two semesters of Engineering Physics, plus 9 to 12 hours of upper division science credits, etc.

There is a reason why most persons in STEM majors never make it past the first year, due to the fact they can’t handle the math and science requirements.

momof4,

I’m in agreement here as well, but as long as students are not learning the basics of math (what you’ve outlined), they’ll never have a future in any of the fields you’ve mentioned, in auto mechanics, for example, a student has to pass 8 separate exams to obtain ASE (Automotive Service Excellence) status, and has to have 2 years of work experience to obtain master mechanic status. ASE exams are good for 5 years, btw.

Given that upwards of 80% of all students entering community or junior colleges need 1 or more remedial courses, it’s not looking very good, is it?

Sigh

No, and it won’t get better until the k-5 schools explicitly teach real math and require mastery before advancing. Kids who don’t get a solid foundation in ES rarely make up for it later (also true in reading, writing etc).

There’s an excellent post on Out in Left Field (link at left). Attempts to make math and science more appealing to those who don’t inherently find them so, by making them less mathy/sciency (more artsy, more writing, more “fun”), also make them significantly less appealing to those with a real interest. The former are highly unlikely ever to choose or succeed in a STEM field (lack of interest and/or ability) and the latter aren’t given the real content to prepare them for the STEM fields in which they have significant ability/interest. Sigh, again.

Reminds me of the high school girl here who couldn’t graduate, due to failing three of her four proficiency examinations (she passed the writing exam, failed the math exam by a single point (don’t know if this was before the state board of education lowered the passing score from 300/500 to 244/500), and failed the reading and science exams.

This despite having a 3.4 GPA, enrolled in honors and AP classes, co-captain of the cheerleading squad, etc…

She came home ‘crying’ and is ‘crushed’ because she couldn’t walk the stage at graduation (my state changed the requirements so that students who complete all their coursework, but fail one or more exit exams no longer receive a ‘certificate of attendance’, which isn’t a diploma).

Prior to this, COA holders could walk in graduation ceremonies, but a state legislator (who is running for Lt. Governor on the democratic ticket now) spearheaded the effort to get rid of the COA, stating that students (and their parents) thought they had actually graduated, when in fact, they didn’t.

The “honors” and “AP” courses were as fraudulent as her 3.4 GPA. My kids all attended the same school for 7th-8th grade, when some of the state HS-graduation tests were administered for the first time and literally ALL of the kids in the (real) honors courses had high passes – with no test prep. That was 15-25 years ago and the article I read about last year’s results is similar. The tests are so basic that the MS kids taking real honors courses – those kids in the top schools in the county- still pass easily, while HS seniors from weaker schools fail, despite having taken “upper-level”, “honors” and “AP” courses – which are really none of the above because most of the kids don’t have the ability, preparation &/or motivation to do that level work – and received good grades. Sigh again