Math

Our Days Are Numbered: Stats Errors

Our Days Are Numbered is a (new) regular feature with posts about mathematics related topics. Why? Because our students, in general, struggle with math, and if we all know more, perhaps they will learn more.

I’ve been waiting awhile for the paperback of Charles Wheelan’s Naked Statistics. It looked like a great primer on the subject, but it kills me to buy hardcovers and (unfortunately) due to the rise in ebooks, it seems to be taking longer and longer for books to get published in paperback. Anyway, I’m off topic, already.

This adaptation from his book focuses on five ways to make mistakes (intentional or not) using statistics, and gives a nice primer for some related inductive reasoning errors related to causation, but all presented in snappy, easy to read prose with great examples. If you’ve never taken Statistics (or it’s been a long time), you might find it helpful.

Tuesday Teaching Question

Tuesday Teaching Question is a regular feature that attempts to get a conversation going about teaching.  Typically, the questions attempt to be very practical.  TTQ is brought to you by CAST.  If you have a question that you’re dying to have featured in an upcoming TTQ, e-mail me at hwc_cast@ccc.edu.

The mayoral race has been heating up and the primaries are a few weeks away (2 weeks from today to be exact).  I’m attempting to get the preservice teachers in my Math for Elementary teachers classes thinking about the impact that the new mayor would have on their future livelihood by asking them to read the candidates education platforms and discuss them.  (Phew, that was a long sentence!)  Anyway…

Are you incorporating the mayoral race into your classes?  If so, how?

One for the Math People

From review of a new math book for girls by the woman who played “Winnie Cooper” on The Wonder Years:

Mathematics is, in itself, an exercise in the abstract — twiddling funny squiggles on paper, really, which is fairly pointless except to mathematicians. It’s when math is applied to the universe that the mental game becomes something useful. Budgets can be balanced, bridges designed and laws of physics deduced. So good math education is in society’s best interest…

Danica McKellar, better known as Winnie Cooper, Kevin’s love interest on the TV series “The Wonder Years,” retains the rigor yet takes a friendlier approach (she substitutes the word “Happyland” for algebra in the first chapter) in her latest best seller, “Hot X: Algebra Exposed!”

Aimed at teenage girls, “Hot X” is a cross between a math class and a slumber party, and a perky, self-affirming slumber party at that: interspersed among the math are anecdotes about boys and testimonials about struggles and triumphs with math.

Read the rest here.

Chronicle Day–A Math Class I’d Like to Take

This one is what the title describes.

For example:

To demonstrate the concept of infinity to a class of mostly liberal-arts students at Baylor, he sketches a trough that he describes as containing an infinite number of Ping-Pong balls, which are falling into a barrel, 10 at a time, as a hypothetical student reaches in and plucks balls out at shorter and shorter intervals.

“Soon you’ll be working faster than the speed of sound, than the speed of light. You black out, regain consciousness, approach the barrel, look inside. My question to you is, ‘What’s inside? What is in the barrel?'”

The students pair up at their desks and compare guesses. “It has to be infinity,” one says. His partner responds, “He’s trying to trick us. … Maybe the answer’s zero.” Mr. Burger writes these and other guesses, which he draws out of more-hesitant students, on the board. He tells the class to come back on Tuesday for the answer.

And if anyone can explain the answer to me (it is given at the end of the article), I’d be obliged…

Math and Estimation

Apropos of nothing (other than a vague sense that a lot of people are doing a lot of estimating this week–students estimating their grades, teachers estimating student grades, Richardson estimating how long he can put off reading stuff he doesn’t want to grade before getting in trouble with either the students or his family, etc.), I came across this article on (one of) the nation’s foremost expert in estimation.

Talk about a great party trick…

Oh, and just in case you missed it, the New York Times awesome Math Series, which I’ve highlighted before, is still going and they had one on probability theory last week that was pretty phenomenal (and included some information on estimation). You can check it out here. Or thereabouts.

Math Meeting Update #1

Theresa Carlton, our math reporter, was kind enough to share this summary of the Math Faculty’s mandatory meeting last Wednesday:

John Squires, Chair of the Math Department at Chattanooga State Community College, formerly the Chair of the Math Department at Cleveland State Community College (both in Tennessee), gave a full day presentation on the National Center for Academic Transformation (NCAT) redesign guidelines and the Emporium Model redesign that he established for Cleveland State CC.  The faculty were reserved, quiet and respectful during the first hour of his presentation. Then, Mr. Squires opened the floor for questions.  Being the strong, well-informed faculty body that we are at CCC, poor Mr. Squires found himself peppered with questions about his Emporium redesign, before he even had a chance to give his presentation on it.  He addressed the questions with many “we’ll talk about that later” comments.

Michael Maltenfort of Truman College asked the question that we have all been wondering, “Would you recommend moving the developmental courses out of the hands of the full-time faculty [and into pre-credit] with this redesign?”  Mr. Squires responded that the redesign “does not work without the full-time faculty” and he would not recommend handing these courses over entirely to adjunct faculty.  As the day wore on, Mr. Squires became increasingly frustrated as our faculty brought up Union issues and teaching load requirements.  At one point, Angela Henderson, who was with us the entire day, stood up and said that she would be happy to address these questions at the end of Mr. Squires’ presentation.  This of course, never happened, but the thought was there.

After lunch, in some random, haphazard way, we were put into groups and assigned different classrooms to gather and answer a series of questions:  Would we be willing to begin the redesign with a blank slate rather than simply adopting a pre-existing redesign model? What are some of the problems with the developmental math courses? What are some possible solutions?  I think there were more questions, but given that we only had about 10 minutes to address them, we did not get that far.  We reassembled to share our answers, and then the meeting ended.

So, what am I not telling you?  Well, Keith McCoy (current Faculty Council President and Wright College Math faculty) has taken a position working at the district, beginning, I believe, at the end of this semester.  I had a private chat with Keith in which I learned that the district does not want to use the Emporium model for CCC.  This has to do with Union issues as well as lack of space and computers.  So why was Mr. Squires our guest speaker? Your guess is a good as mine.  What was the point of the meeting? To get us thinking about redesigning our developmental math classes.  As of right now, there is no plan in place, no timeline, no rules.  Basically, the district wants us to “do something”, they don’t care what, as long as it is something kind of dramatic, as opposed to just tweaking what we currently do.  Another faculty member, who spoke with Dr. Lopez, was told the exact same thing.

So, now for my opinion:

Getting the Math Faculty together to discuss developmental math, the problems, the curriculum, and possible solutions is a great idea.  However, we did not get any time to actually do this.  The presentation by John Squires, I felt, was pointless.  An Emporium model of developmental math is not something that we want, nor is it something that is feasible for the City Colleges.  There seemed to be a lot of confusion among the faculty, since administration never made clear the purpose, goals and expected outcomes of this meeting.  Are we supposed to try to adopt the Emporium Model? Are we supposed to come up with our own model? Does each college have to do the same thing, or does our autonomy still hold in this circumstance?  Is there a timeline for this? What purpose did the speaker hold?  Angela Henderson did say that she would answer questions, but then never did, even though the speaker ended 30 minutes early.  Administrative feedback was given to individual faculty, but never to the entire group, so many left not knowing what to do next.

In fact, none of us understood why it was necessary to miss a day of classes for a meeting, that, in all honesty, was a waste of time and money.  The administration would have been better off asking each department separately for ideas on how to improve the developmental math courses, and then after compiling the ideas and distributing them to us to review, they could have brought the faculty together to ask questions, debate, share, and perhaps do something productive.

Discuss.

A Little Love for the Maths

I am enjoying the bejeebers out of a series that has been running in the Opinionator section of the New York Times. The conceit is that a college prof, Steven Strogatz, is taking everyone on a ten column journey from the very most basic ideas of mathematics, through its most outlandish, abstract (philosophical) ends (“from basic to baffling”).

It’s phenomenal.

This week’s post, the fifth in the series, is on High School Algebra, which, given the struggles that many of our students have with math, it probably wouldn’t be such a terrible thing to brush up on. The next two (they come out on Sunday nights) are also on High School math topics (geometry and trig).

For the record, though, I strongly recommend checking out the first, second, third, and fourth installments.

Developments in Developmental Math (Part I)

Do you know what’s going on with Developmental Math courses? Lots, apparently.

On February 10th, our math faculty received an email from Dean Metoyer informing them of a mandatory, all day meeting of all district full-time math folks at Malcolm X.

The meeting will feature a presentation and workshop by John Squires whose “Do the Math” project won the 2009 Bellwether Award given by the Community College Futures Assembly. Since this meeting is scheduled during a class date, faculty who teach math will need to schedule alternative educational activities for their classes. If faculty choose to schedule a quiz or test for this date, please consider how the College can assist faculty in finding appropriate proctors.

Needless to say, the math faculty members were not overjoyed. One colleague wrote back, saying, “This term, M/W classes already have TWO holidays not shared by Tu/Th classes. How, in the name of quality education, can you force us to be away a THIRD day? There must be another arrangement that can be had.” He also asked for a little background on the presentation and cc’d Perry Buckley, President of Local 1600.

And so there are clearly two issues here: the scheduling of the meeting and the content. The scheduling is the simpler of the two, so I’ll cover it first, here. Apparently Truman faculty have been aware of the meeting for a few weeks, and raised the same issue (regarding the Wednesday schedule). Once everyone else heard about the meeting, they echoed the sentiment, and Perry describes them as “universally furious.” He said that he spoke with (Interim) Chancellor Lewis about the meeting and that she had not realized that students would miss a third class. She promised to “look into it,” and Perry trusts her to do so.

On the same topic, in an email to local Faculty Councils, Keith McCoy, the President of District Wide Faculty Council, addressed the Board on February 11th and raised the issue with them, proposing the alternative of “obtaining faculty volunteers from each college who would attend, as well as, those who do not have teaching obligations at the time of the meeting.” In an email accompanying his address, he wrote to the Faculty Council representatives that he had spoken with Vice Chancellor Angela Henderson, who told him that it was not the intention of District to mandate the meeting, but that that request had come from the ODs meeting (Officers of the District, i.e., College Presidents). As for why it has to be on Wednesday, March 10th, Perry “was told” (he said the passive voice was purposeful) by someone that it is the only day the speaker is available, a point which he, understandably, doubts.

Perry goes on to say, “As these matters are primarily academic they are more the [purview] of Faculty Council rather than the Union. There is no contract language whereby we can grieve a mandatory class cancellation. I would advise all math faculty to consult with Faculty Council President Keith McCoy (Wright) as he is also a math faculty. He may, combined with the unity of math faculty and the Union’s support, be able to find a better date for this meeting.” Both he and Keith McCoy reminded faculty of the rule that always applies to unsavory administrative directives, “Comply.” Tenure does not protect any of us from punishment for insubordination.

If I were in Vegas and could find someone willing to take my bet, I would lay down a big stack of chips on the meeting taking place on March 10th and being mandatory for all Math faculty, which seems to me like a classic case of administrative short-sightedness, guaranteeing an aggravated, hostile audience for what would, under the best of circumstances, be an extremely controversial and challenging proposal. If I were a conspiracist (Ruggeri!), which I’m not, I might even think that it was intentional to create a negative atmosphere so that they could paint faculty as intractable and obstructionist, thereby dismissing any germane academic objections to the proposal. For the life of me, though, I can’t figure out what they were thinking, except to say that they weren’t.

A Preview of the Proposal (and Responses) in Part II coming up this afternoon.

Developments in Developmental Math (Part II)

At least one thing is pretty much certain: the district is moving ahead with a massive redesign of Developmental Math. The first steps were taken at the Board meeting on February 11th, where there were changes made to the pre-credit math classes. Perry Buckley’s (Union President) description of the changes follows; “[t]hese courses, taught now by AFSCME members, will be called the “Foundations” program. The pay will change and the number of hours their workers can work will be reduced.”

He goes on to say that he’s “been told” that it is the district’s intention to move all developmental math courses into the Foundations program (and so, out of the hands of full time faculty). This is an important point. Via HW Math faculty member, Theresa Carlton (lots more from her to come), “Moving the Math 98 and 99 courses into pre-credit will eliminate 50% of the course offerings available to full-time faculty at HW. This number is higher at some of our sister colleges. Given that we have district-wide seniority, the possibility that we may be bumped from courses at our home campuses and be forced to fulfill our load requirement at other colleges does exist.” Perry suggests that the ultimate goal of the mandatory meeting is to sell the Math faculty on the change.

What are these changes, you might ask, other than a change of faculty? Fair question, but first the pitch…

In an email sent Saturday (2/20) afternoon from President Wright President, Chuck Guengerich to Henry Herzog, Wright Local Faculty Council, and the Wright faculty, President Guengerich writes:

We do know however that the vast majority of our students enter with less than college level skills. This is especially true in math where greater than 90% of Wright students enter at the Foundational Studies (formerly pre-credit) or Math 099 level. The vast majority never successfully reach a general education level math course and then will never complete a degree. Even for those who successfully complete math or Foundational Studies only about 1 in 4 succeeds. What it does tell us that we have to redesign math developmental education ( Please note the statistics are similar across the District.)

There have been some interesting new national models that have evolved over the past several years. The model developed by John Squires in Ohio has achieved over a 70 percent success rate and has been duplicated a four other colleges with similar success stories. The Squires model has won two Bellwether Awards at the Community College Futures assembly.

CCC is bringing Mr. Squires to the District on March 10 and all math full time math faculty are being required to attend. As A District and a college we should have a sense of urgency in looking to research and test new methodologies in developmental education.

Keith McCoy, District wide Faculty Council President and Math faculty member, showed his concurrence, broadly speaking with his College President’s message in his address to the board on February 11th, saying:

The completion and success rates out of CCC developmental math courses, including Foundational Studies (formerly Pre-credit), Math 098 and Math 099, are abysmal. I remember a few years ago the district success rate was a low 40% with no one college receiving over 50%. This is a national issue and not just a local one. Many of us, both faculty and administration, have known this from some time and have endeavored to improve these rates to little avail. Now, we have reached the point where change must occur in the developmental math curriculum. It is because of this very need to change that CCC administration is actively looking to redesign our math curriculum and is looking at good practices and successes that are occurring at other institutions. The importance of this need for redesigning of the developmental math curriculum, while presented very credibly by VC Henderson to district faculty council, has not been communicated well to faculty.

Mr. Squires received the 2009 Bellwether Award for Instructional Programs and Services for spearheading Cleveland State Community College’s course redesign project for developmental and college-level math courses. Cleveland state has had remarkable success with this project that truly warrants its review. While I myself have questions and concerns about the project and this project may not entirely fit the needs of CCC, faculty must be involved and engaged in curricular discussions regarding any CCC redesign efforts. Faculty must also be proactive in participating in driving these efforts. Regardless of whether the meeting mandate holds or is altered (I wish for the latter), going forward, I hope that the college presidents will at least relay a better message emphasizing the importance of this meeting and the involvement of all math instructors in this process so that we can all be on board with any redesign efforts.

That last point is one that he reiterated in his accompanying email, saying, “While I understand the importance of this meeting due to the administration moving forward with redesign efforts of developmental math, I think the message may be lost because of the mandate. I truly hope not. Despite any discontented feelings, it is important that math faculty are very much involved in any redesign effort.”

So what does the proposed redesign look like and who are its sponsors? Back to Perry:

The presentation is from the National Center for Academic Transformation. It is a non-profit think tank dedicated to higher ed. Just google them to get to their web site. Note well that their stated mission is a simple dual pronged statement (and I quote): “improve student learning outcomes and (bold mine) reduce the cost of higher education.” Let me repeat: reduce the cost of higher education. Draw your own conclusions.

I further have been told that part of the presentation will include how to use on-line and/or computer programs whereby students can achieve the “same or better results” with little or no teacher involvement. (If not, that is, part of the NCAT agenda.)

Theresa Carlton, who is the co-chair of HW’s Developmental Education Committee, and so is well versed in the relevant issues and research on this issue, provides a nice summary in another email sent yesterday:

I did some research on this “redesign” that Wright seems to be so obsessed with. An article from the Cleveland Daily Banner dated Dec 28, 2008 describes the redesign as a 1+2 format in which there is a one hour class meeting each week and a 2 hour lab session. Each developmental course consists of 10 modules, and students are required to complete one module per week, and are allowed to work ahead. Students take an online quiz after each module and an online final exam at the end of each course. The results of the redesign are that 37 students completed 2 or more developmental courses in one semester. Of those 37, 33 completed intermediate algebra, and 4 completed basic math and beginning algebra. Nine students completed intermediate algebra and a college level math course.

In the project write up, which can be found on the National Center for Academic Transformation (NCAT) website: it states “Faculty productivity rose by 23%. The average student load per faculty member went from 106 to 130 and the FTE teaching load per faculty member went from 21.2 to 26.0. Going forward, faculty members should expect to teach 10-11 sections, work 8-10 hours in the lab, and handle 150+ students each semester…the increased faculty productivity has enabled the department to eliminate the use of adjunct faculty members at the same time that course offerings are actually increased. Overtime loads have been reduced as a result of the redesign project.”

So there’s your description, essentially, of the pitch and the pitchers. Theresa, goes on to provide some analysis, too:

All this really shows is what we already know. Students at the higher level of developmental math are more successful than those who start out at the basic math or beginning algebra levels. There was only one student who began in elementary algebra and was able to complete a college level math course. This does not prove that the redesign works. It proves that that student was misplaced to begin with.

I am not saying that the redesign idea is completely off base or that it can’t possibly work. It is not something that should be forced upon us. Just because one college claims success does not mean that it will work for CCC. Why does the district think that they can enforce mass changes on us without first testing out the idea and seeing if it actually works? What’s wrong with piloting 2 sections over a few semesters and comparing the results to the courses that are run in the traditional format?

A few points that need to be made about the study:

1. These courses were NOT moved into pre-credit where full-time faculty are not allowed to teach them, and students are not allowed to use financial aid.

2. The redesign did not work for the Basic Math course, as clearly stated in the study write up.

3. All of these courses met in a computer classroom for the one hour session and in a designated computer lab that was staffed with faculty and tutors, and available 54 hours each week.

4. Faculty are REQUIRED to teach these courses.

5. Students must be allowed to register for the next course as soon as they complete the current course. This means that if a student completes beginning algebra during week 4 of the semester, they must then register to take intermediate algebra, and be able to begin that new course immediately.

6. The true measure of success is not how many students completed a developmental course, or even the developmental program, but how many were able to successfully complete a college level math course. The study states that the percent of developmental students who successfully completed a college level math course increased from 71% to 76% due to the redesign. No where does it state that this was actually a statistically significant increase. A 5% increase does not seem good enough, especially when they never tell us exact numbers.

7. The biggest achievement that the study claims is being able to cut costs by eliminating faculty, and increasing faculty “productivity”. I’m sure the Union would have something to say about that, which may be why CCC wants to make these pre-credit courses.

In order for the redesign to be effective in the way that is claimed, CCC needs to be able to offer ALL of the resources that the study offered. Do we have sufficient computer classrooms and a designated computer lab that can accommodate our students? Is our registrar’s office prepared to offer students flexible enrollment throughout the semester? Do we have the money and the personnel to place tutors in the tutor center, the math department and in a computer lab for 54 hours a week? In my experience at CCC, the district likes to enforce a change with no follow-through and no assistance to ensure success.

Discuss.