## Monday, February 13, 2017

## Monday, February 6, 2017

### Milliken on CUNY Connected and Remediation

As a follow-up to last week's post, CUNY Chancellor James Milliken has this week unveiled out a new strategic plan called "CUNY Connected". Among the promises are increased graduation rates. In the subsection on remediation reform (again), he writes:

These are dictates that were communicated internally at CUNY within the last year. It's interesting that higher passing rates can be dictated in advance by fiat. To be clear: Most CUNY graduates will not need to be algebra proficient, most will not take a course which uses algebra skills, and those who do will not need to succeed on any particular assessment or test to be declared proficient. Another point of clarification: While "college algebra" is mentioned in this section, college algebra is not actually a remedial course (most students

Each fall, approximately 20,000 students—over half of all CUNY freshmen– are assigned to developmental education in at least one subject, usually mathematics. In associate degree programs, 74 percent of freshmen were assigned to developmental education in math in fall 2015, 23 percent in reading, and 33 percent in writing. But CUNY’s one-size-fits-all approach to preparing students has not worked. In fall 2015, just 38% of the 14,215 students in remedial algebra successfully completed it.

Implementing these reforms, the number of students placed in remediation will decline by at least 15 percent. The number of students determined to be proficient after one year of remediation will increase by at least 5 percentage points in year one and will increase as we move to scale.

Under the reforms, 20,000 students per semester will receive tutoring and supplemental instruction and 4,000 will be enrolled in courses with faculty who have been newly trained. Another one thousand students will enroll in immersion programs or new developmental workshops. All students will have access to instructional software.

CUNY will bring to scale two developmental options of proven efficacy: 1) co-requisite courses—credit-bearing courses with additional mandatory supports in the form of workshops or tutoring, and 2)alternatives to math proficiency other than algebra for students pursuing majors or courses of study that do not require algebra. College algebra is necessary for many but not all majors.We will also end the practice of requiring all students to pass common tests in algebra, writing and reading to exit developmental education.Grades, it has been found, are a better predictor of proficiency and success. CUNY will continue the use of standardized common final exams that count for 35 percent of the final course grade.

These are dictates that were communicated internally at CUNY within the last year. It's interesting that higher passing rates can be dictated in advance by fiat. To be clear: Most CUNY graduates will not need to be algebra proficient, most will not take a course which uses algebra skills, and those who do will not need to succeed on any particular assessment or test to be declared proficient. Another point of clarification: While "college algebra" is mentioned in this section, college algebra is not actually a remedial course (most students

*already*have never taken college algebra at CUNY); the remedial/general education expectation which is being removed is at the level of elementary algebra, around 8th-9th grade level skills as identified in the U.S. Common Core and other curricula.## Monday, January 30, 2017

### Milliken on NY1

CUNY Chancellor James Milliken gave an interview Friday night on NY1. Among the things he said:

Consider what institutional mechanisms have radically changed highly politicized statistics like that in the past.Full video here (quote at 3:55):The urban 3-year community college graduation rate in this country is 16%. CUNY 17½. We're committed to doubling that.

# NY1 Online: CUNY's Future

## Monday, January 16, 2017

## Monday, January 9, 2017

### Operations Before Numbers

Most elementary algebra books start on page one with a description of different sets of numbers that will be in use (naturals, integers, rationals, and reals). Then soon after they discuss the different operations to be performed on those numbers, the conventional order-of-operations, etc. This seems satisfying: you get the objects under discussion first, and then modifiers to be performed on those objects (nouns, then prepositions).

But the problem that's irked me for some time is this: the sets of numbers are themselves defined in terms of the operations. Most obvious is the fact that rationals are quotients of integers:

Now, in other mathematical contexts -- where you are only discussing

So if the elementary algebra class wants to cheat in this fashion and present the whole menagerie of number categories in one lecture, I would argue that we need to abstract out the operations

Thoughts? Are you still satisfied with describing numbers before operations?

But the problem that's irked me for some time is this: the sets of numbers are themselves defined in terms of the operations. Most obvious is the fact that rationals are quotients of integers:

*a/b*(*b*nonzero); so this presumes knowledge of division beforehand. Integers, too, are really differences of natural numbers (though usually expressed as something like "signed whole numbers"); they are fundamentally a result of subtraction. So in my courses I resolve this by coming out of the box on day one with a review of the different arithmetic operations, names of results, and their proper ordering; then on day two we can discuss the different sets of numbers thus generated.Now, in other mathematical contexts -- where you are only discussing

*one field at a time*-- it is conventional to discuss the elements of a set first, and then the operations that we might apply on them second. That makes sense. But at the start of an elementary algebra course we tend to be cheating a bit by trying to consolidate a presentation of at least 4 different sets all at once. It would be fairly rigorous to present naturals and their operations (add, subtract, multiply, divide, etc.), and then integers (and their addition, subtraction, multiplication, etc.), then rationals and their operations (etc.), and then finally a separate discussion of real numbers and their operations (etc.). But that would take an inordinate amount of time, and the operations are so very similar that it would seem repetitive and wasteful to most of our students (outside of difference in closures, etc.).So if the elementary algebra class wants to cheat in this fashion and present the whole menagerie of number categories in one lecture, I would argue that we need to abstract out the operations

*first*, and then have those available to describe the differences in our sets of numbers*second*.Thoughts? Are you still satisfied with describing numbers before operations?

## Monday, January 2, 2017

### The Nelson-Tao Case

A case that I read in the past, and have searched fruitlessly for months (or years) to cite-reference -- which I just found via a link on Stack Exchange (hat tip to Noah Snyder). Partly so I have a record for my own purposes, here's an overview:

In 2011 Edward Nelson, a professor at Princeton, was about to publish a book demonstrating a proof that basic arithmetic theory (the Peano Postulates) was essentially inconsistent. This started a discussion on the blog of John Baez, in which the eminent mathematician (and superb mathematical writer) Terry Tao spent some time trying to explain what was wrong with Nelson's proof. After about three cycles of back-and-forth, the end result was this:

This is one of the best examples of what I personally call "the brutal honesty of mathematics". Read the whole exchange here on John Baez' site.

In 2011 Edward Nelson, a professor at Princeton, was about to publish a book demonstrating a proof that basic arithmetic theory (the Peano Postulates) was essentially inconsistent. This started a discussion on the blog of John Baez, in which the eminent mathematician (and superb mathematical writer) Terry Tao spent some time trying to explain what was wrong with Nelson's proof. After about three cycles of back-and-forth, the end result was this:

You are quite right, and my original response was wrong. Thank you for spotting my error.

I withdraw my claim.

Posted by: Edward Nelson on October 1, 2011 1:39 PM

This is one of the best examples of what I personally call "the brutal honesty of mathematics". Read the whole exchange here on John Baez' site.

## Monday, December 26, 2016

### On Famous Things

A quip from Stack Exchange back in 2014 that still fills me with glee on a daily basis:

A poster asks how to convince other people when he's developed an as-yet ignored, revolutionary, world-beating result...

More gifts of wisdom at Stack Exchange.

A poster asks how to convince other people when he's developed an as-yet ignored, revolutionary, world-beating result...

Pete L. Clark writes as part of his response:e.g., you solve the P vs. NP problem or any other well known open problem.

It's like saying "i.e., he found the Holy Grail or some other famous cup".

More gifts of wisdom at Stack Exchange.

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