Friday, April 10, 2009


The Death March

I mentioned a few days ago that Kay McClenney's point about shortening the remediation death march was worth a post in itself. Here goes...

At most cc's that I've seen, students who don't have prior course credit or certain scores on AP or SAT/ACT tests have to take placement tests in reading, writing, and math. Most new students place 'developmental,' meaning that the test shows that they aren't currently performing the particular skill at a level appropriate for college work. (English as a Second Language may or may not be considered remedial, depending on the college. It typically has its own test, the TOEFL.) Depending on the degree to which the student missed the mark for 101-level courses, the student may need anywhere from one to three levels of remediation.

Although intro courses are fairly standard across colleges, developmental courses aren't. Part of that has to do with transfer. Developmental courses don't transfer, since they don't carry graduation credit, so individual campuses usually have considerable autonomy in customizing their own developmental sequences. I've seen some that combine reading and writing into a single course, for example. I've seen others that have three levels of each. In some, the ESL sequence feeds into the lowest level of developmental; in others, ESL is presumed to lead to English 101.

Developmental coursework is usually a tough sell to both the public and the students. The public often isn't wild about it, out of a correct sense that it already paid for that material to be taught by the K-12 system. There's truth in that, but we can either give up on the unsuccessful products of K-12, or not.

The students themselves often resent being placed into developmental classes, especially if they just came out of high school with decent grades. (For reasons that passeth understanding, states that have standardized tests for high school graduation and standardized tests for college placement don't align the two. If I were king of education for a single day...) Developmental courses don't count for graduation, and can be pretty tedious. And according to the national data I've seen, developmental math is often the first and last experience of college for a disturbing number of people.

For a student who shows up expecting a degree in four semesters, to be told that your math or writing skills are so poor that you'll need at least three more semesters before even getting started has to be demoralizing. Many students feel insulted by it, and many more feel ashamed, which doesn't do wonders for their motivation.

In a perfect world, every student would arrive at college literate, numerate, and ready to go. But until that happens, there's a serious challenge to address.

One of the great contributions of data has been to show that no matter the logical or content-based coherence of a sequence, too much remediation is self-defeating. If the march is too long, too many marchers drop out. Some of the expedients various colleges are trying include:

1.Compression of levels. This can be done by combining two courses (reading and writing, or arithmetic and basic algebra) into one course. It can also be done by teaching the courses in shorter formats, so the students can get through quicker. The acceleration approach can work particularly well when the issue isn't so much 'inability' as 'rustiness.'
2.Supplemental Instruction. This involves placing a tutor in the classroom to help students as the class is going on. With peer tutors, it can be cost-effective, though quality can vary. With professional instructors, the quality is high, but the cost is usually prohibitive on a large scale.
3.Cram courses. These are non-course intensive workshops taught in the week or two before a student (re)takes a placement exam. As with the accelerated remediation, they can work pretty well for the adult student for whom rustiness is the real issue, but they're less successful with kids who never got it in the first place.
4.Contextualized remediation. This is the flavor of the month right now. Many grant-funded workforce development programs that target low-income adults use this as a way to get students through certification programs in a relative hurry. The idea is that if you're really there to get a credential in, say, a culinary program, then any developmental courses you have to take should draw on culinary content for their examples. I haven't seen any good data on this one way or the other, although it certainly has an intuitive appeal. The catch is that it really only works in a tight-knit cohort model. If I've got 20 students all enrolling in the same program at the same time, and they all have the same developmental needs, I can do this. But it really can't be generalized to the college as a whole.

Part of my hope in doing this post is that some of my wise and worldly readers will chime in with different models they've seen succeed. My campus, like most others, is trying to improve the success rate of students in developmental courses, but finding it hard to get significant, sustainable results. Any ground-tested hints anyone could share would be greatly appreciated. So, my wise and worldly readers, have you seen anything work on the ground that might be worth a shot elsewhere?

I've seen lots of studies by math departments that say "our placement test predicts achievement in our courses." I believe them.

I haven't seen any studies that say, "the content in our courses reflects the ever-improving technology" or "the content in our courses reflects the many reports issued by the MAA, NSF, CUPM, or MSEB which suggest changing pedagogy and increasing the use of technology."

At my university we proudly outlaw calculators from the Calc sequence even though all the disciplines we "serve" want their students to be proficient with technology including calculators, spreadsheets, and computer-packages.

Maybe, just maybe, the conversation about remediation should also be expanded to include discussion of the credit-bearing courses as well.

I'm trying, but I'm new, young and don't have tenure yet.
Well, the high school standardized tests and the college entrance exams and other tests don't align because the high school tests aren't meant to show readiness for college. There are many, many high schools that intentionally aren't preparing kids for college; they're preparing them for life. One might argue that the two don't have to be misaligned, but it is what it is right now.

I taught developmental English at a 4-year school. One of the things they told us in preparing to teach it was that only about 10% of the class would make it through the first semester. The other 90% would drop out. So, not only were the students demotivated, so were the instructors. Luckily, it wasn't clear which 10% would survive, and I always had the hope that my class would beat the odds. It was a very humbling experience, rewarding and kind of sad all at the same time.
The technology that you need in remedial math is from "Eternal Sunshine of the Spotless Mind." You need to erase every single experience they have ever had with math in the past and then rebuild from scratch.
At my university we proudly outlaw calculators from the Calc sequence even though all the disciplines we "serve" want their students to be proficient with technology including calculators, spreadsheets, and computer-packages.

If you want people to be familiar enough with the concepts of addition and subtraction to be able to continue to algebra and calculus, then they need plenty of practice without calculators. They also need that practice so that they can understand when the output of the calculator makes sense, instead of blindly typing down what the calculator gives them. The disciplines you serve, in which I teach, don't need students who blindly attempt to solve a problem through the plug and chug method on their calculator. We want the students to learn how to do the simple problems from the calculus course by hand so they have the ability to set up the larger problems they'll deal with in our courses along with the ability to check their answers instead of always trusting the machine.
Perhaps the tests need to be re-evaluated. When I started my college journey at a community college, I was tested and judged as needing remediation in English. I argued my way out of it and went on to earn As in the following courses:

Freshman Comp I
Freshman Comp II
British Literature I
British Literature II
American Literature I
American Literature II

What is interesting is that the college originally wanted to place me in Remedial English because the test showed that my writing was not up to par. Yet, at least three of my instructors specifically commented (unprompted) on the sophistication of my writing and commended me for it.

I made it through because I was confident in my ability and unwilling to back down. I wonder how many students drop out through the Remediation Death March because they mistakenly accepted the fact that they needed remediation in the first place.

(I am not in any way arguing that this percentage of students is large. Most of the students placed in remediation probably do need it. Yet, I know that the percentage of students classified as remedial incorrectly is nonzero, and I find this unacceptable.)
(For reasons that passeth understanding, states that have standardized tests for high school graduation and standardized tests for college placement don't align the two. If I were king of education for a single day...)

Look at who sets the tests. And why. I suspect that that will give you the answer.
I don't know if this would work in the CC environment, but there were several interesting programs at my undergrad school to help struggling students without the depressing experience of multiple remedial courses that made me think useful remediation should be possible.

For students who took the regular Composition course and got a D, which was not sufficient proof of competency (or for transfer students who didn't pass the TOEFL or Comp competency exams), there was a tutorial section they could take instead of repeating the class. Instead of writing 30 pages during the semester (the university requirement), they would write 12, with one-hour-weekly sessions with an MA student in the Writing Center.

As an MA student, I taught in this program, and it was incredible. Not only did I get teaching experience (and a small salary), but my students got the individual attention they needed to produce the best work they could. ESL students were forced to practice speaking and writing in an environment in which they couldn't "disappear." They learned, and had motivation to learn. They were "repeating" a class, but in a new environment with different rules.

I could see this working as a sort of model for real remediation. Remedial classes should be shorter, with very small class sizes, and with fewer meetings. They could be taught during the summer (when entering students could get remediation out of the way before starting and continuing students could do the work before the "real" semester starts). With fewer students, the teacher can work faster and more directly for each student's needs. There is more pressure to stay in the class if it's short, personal, and intense.

Imagine a two-week summer class, three hours a day, four days a week, with five people in it. You could run sections all summer. Students who need a lot of remediation could do Algebra, Reading, Writing, and Chemistry in two months--one month if they take two courses at a time--and have just four classmates. It's less depressing because they're getting individual attention and can spend the rest of the summer working or goofing around until the semester starts. None of their friends have to know they took remedial classes.

I know small classes are expensive to offer, which is why making them short would be the tradeoff. But if CCs could develop really effective, non-humiliating college remediation programs like this, CCs could also draw summer students from local 4-year colleges, and make it a specialty rather than an awful thing no one wants to do. Hire adjuncts from local MA programs who want some classroom experience. They're energetic and passionate in situations like this.

That is, I think the model in which remedial classes (some three deep!) are slotted into the regular schedule and just mean a "lost semester" and sitting in a room with 25 other people who are miserable to be there is never going to work. If you're that behind when you hit college, it's because large, impersonal, death-march classes are not getting you where you need the help. Where individual tutoring isn't possible, small, short, intense classes may be.

Another thing they did at my school was a system of student tutoring. If you got an A in a class, you could put your name in to be called for a work-study position as an individual tutor for a student currently taking that class or its prerequisites. It's not remediation, but it helped retain students who would otherwise have dropped out.

I worked as a tutor for advanced Spanish grammar for a few years as an undergrad. Again, I saw all these students who were totally frustrated by the material open up when in an individual tutoring situation. They finally "got" things they couldn't seem to get in the classroom, just because there was someone there to ask them, individually, if they got it. I was cheap for the school, and probably no great teacher, but I was a body sitting there and asking questions. It works.

The student tutoring program also provided casual language-conversation partners for ESL students and students who wanted to learn other languages. This resulted in some kind of cute coincidences, like when one of my tutees in English became a Russian tutor for my roommate. She didn't feel like just some loser who didn't write English well; she was someone who had knowledge to share.
Building on White Bear's thought of changing strategies ... I was working with a remedial math student as a private tutor. She COULD NOT do fractions. At all. We were both getting really frustrated. So finally I took her in the kitchen, gave her a recipe, and had her cut a chocolate chip cookie recipe by some weird fraction (maybe by 3/5 or something). NO PROBLEM AT ALL. Then I had her make another recipe using only the 2/3 cup measure (I happened to know it worked with just the 2/3 cup because I'm spectacularly lazy about dishes so I'm quite clever at figuring out the minimum number of measuring cups for my recipes).

She had almost no problem with this, and the light bulb suddenly went on over her head. For her, a key problem was seeing what fractions DID and why they were important and how they worked. Pie charts didn't do it for her, but measuring cups did. It didn't magically fix the problem, but she a) had a better attitude and b) understood what lay behind the arithmetic operations we were trying to do on the fractions. She also made tasty cookies successfully, which put some confidence back in her.

I've used quilting to help with geometry, musical instruments to help with physics ideas ... there are a lot of students out there who need math and science more concretized before they can grasp the concepts. I'm one of them, and I could usually make the connection on my own, but not always, and that was ALWAYS where I crashed and burned in math and science. One-on-one programs like White Bear mentions could build in some of these kinds of strategies as well.
Eyebrows McGee has an important point on fractions, and it something that's also mentioned prominently in the National Mathematics Advisory Panel final report: facility with fractions is important for success in algebra.

I'm worried if my impression is right that all the talk on remedial courses is Program X vs. Program Y (vs. "let them sink or swim"), and no one talks about WHAT IS BEING TAUGHT. (There's a great quip from Ursula LeGuin's 1986 talk on language where she points out that in Anna Karenina, Tolstoy talks about what all the males are doing around Kitty's labor, including God, but no one talks about what is happening!) The structure is important, but if a student does not know that 2 is a fraction just like 1/2, there's an inherent limit to what the student will be successful at in the quantitative side... and in making decisions as an adult with the right to vote.
Awesome subject.

Comment 1 on "Developmental coursework is usually a tough sell to both the public and the students. The public often isn't wild about it, out of a correct sense that it already paid for that material to be taught by the K-12 system. There's truth in that..."

Only a half truth, in my experience. The half that is true is that the public (and, worse, the students) think they have gotten a K-12 education for their money. The half that can be documented as false is the belief that a HS grad has K-12 skills. I have looked over the "exit" exams used for math in several states and observed that none of them approach a skill level that would place a student into college level math at our CC. If I am interpreting the pass level correctly, and I think I am, a student with a low pass on those exams will place into our 2nd level developmental class *if* ze has not forgotten anything between passing the test in 10th or 11th grade and entering the CC. If they only take seat warming classes on "consumer math" as seniors (something I hear a lot when advising incoming students), they forget a lot. I put most of those exit tests at about K-9 skills, and 9th grade intro to algebra won't get you into college algebra at our CC. Not even close.

Comment 2 on our college compared to yours: We have two levels of each subject (reading, writing, math) and align two levels of ESL with the reading and writing prep classes. We have a third level of math that counts for college credit but is still below college algebra. (Yes, we give college credit for 10th grade math. The answer to your question is "I think this is done to encourage them so they won't be stuck in non-credit classes for more than one year." This also seems to work.) We offer some of these classes in a compressed format and allow retesting to jump over a level if the rust falls off quickly. The choice of what can be compressed is data driven by success rates in the class -vs- success rate in the next class -vs- placement scores coming in. We use peer tutors (good money for advancing students) and are definitely eating the "flavor of the month" (your item 4). Rumor has it that this works, but puts a premium on smaller classes for individualized lessons.

Comment on mthgeek comment: I should blog about this, but I can say what is done in our general vicinity. Our main customer wants their students to be proficient in a *specific* set of software packages, so they integrate that into an "intro" junior course. Scuttlebutt is that they prefer students that can do algebra with symbols (discussion over at Uncertain Principles on this topic is the other reason for my thoughts about blogging this). That is my preference also. A student who has to graph a linear equation to "solve" it will have trouble doing physics and calculus and engineering, but so will a student who can't evaluate a complex expression accurately on a calculator.
on Laura's comment, already partly addressed in my post:

I don't think it is too extreme to say that high schools are lying to their students when they tell them that a diploma means they are ready to go to college. The diploma in our state only means they are eligible to attend college.

The distinction is something I blogged about almost exactly two years ago concerning what I think needs to be said during freshman orientation. See points 1 and 2 in particular.

PS to Eyebrows and Dorn: Some elementary school curricula no longer teach a standard algorithm for doing fractions. They use a "look say" guessing method that is beyond abominable. This may be the cause for what you observe.
I am far from a math genius, but when I was 17, I learned how easy it could be to game the system. That year, my engineer-prof father brought home a problem set for the analytic geometry course from the university bookstore, sat with me for three hours working through the important stuff and the next day? I took an exam to test out of the course (and moved into the honours calculus sequence). If I could learn everything I needed to know in three hours to pass this test, I began to suspect that maybe we could teach some of these subjects more effectively. That goes for first year history as well as first year math or composition.

From my observation, many people who are on the cusp of remediation in subjects have not been taught well how to take tests. That's one skillset that needs to be covered in preparing students for academic streams in HS and college or university. Another issue, as noted here, is the problem with setting these students into a series of semester-long remedial courses that rarely motivate them. Short, intense courses seem better suited for a lot of these endeavours.
A White Bear: "I was cheap for the school, and probably no great teacher, but I was a body sitting there and asking questions. It works."

This is pretty much my memory of tutoring athletes (in both small groups and one-on-one) as an undergrad. The athletes tried, so I don't mean to imply they were slacking, but it was only the Athletic Department that had the money for even this. And as far as I could tell, it did work. I would think expanding this type of program would be relatively cheap, not to mention smart (as in it pays students to focus on their academics even more).

A White Bear: "This resulted in some kind of cute coincidences, like when one of my tutees in English became a Russian tutor for my roommate. She didn't feel like just some loser who didn't write English well; she was someone who had knowledge to share."

Imagine - non-hierarchical skill-sharing. Students teaching their peers. What a novel idea.... and yes, I realize that it's not near as easy to make work as it sounds. But it can have all kinds of benefits, as K-12 educators know, and in addition to the one I noted above.
My CC has had success with the "learning communities" concept. If a student needs two different kinds of remediation, they can take the classes with a cohort. The instructors of the cohort cooperate on assignments etc. There is also more of a classroom community to improve retention.
In general, the "class" concept is wrong for remediation. I'm speaking of math remediation in particular here.

The idea of a "class" is that the student has a set of priors which prepares them to learn some material, they go into the class, they get access to new material and some assistance (lecture, homework, group work, etc.) in mastering it, and then they are tested on that mastery, with the understanding that most folks are going to pretty much get what was being taught, some folks are going to really get it, and some folks are going to really not get it.

This is totally inappropriate for remediation, especially in math. College level math requires a year to teach, perhaps two, for the average adult mind. Kids start having decent minds in 7th grade or so, so if they don't have college math, it's because they didn't master a skill that takes two years over the course of five. This isn't about ignorance, it's about some kind of deficit -- the students' self-worth, the K-12 school's decision to teach poorly (as Anonymous notes above), a learning disability outright, or some other actual incapacity.

This is massively different from the "class" paradigm, which is both highly opt-in and centered around the at least somewhat motivated student.

Remediation is about finding the deficit and fixing it. It can be as simple as making someone bake you a cake. Or it can be as horrifically challenging as uncovering the pattern of emotional abuse that caused the student to shut down their higher reasoning centers to survive. Either way, it's something that needs good faculty given lots of resources, small class sizes to work with, and more freedom to improvise than they are usually given.

It's also vitally important; the skills students acquire from overcoming what was causing the problem are often even more important than the algebra was in the first place (which is hard to do).

In the context of limited CC budgets, I don't know what you can do. The current structure skims off the students with low-level problems and gives them a chance to deal with them, which is much better than nothing. But all of the truly successful remediation I've seen has been based around time-sucking individual instruction and (in many cases) access to therapy.
PunditusMaximus: That makes me wonder how Disability Services offices handle dyscalculate students. Do they? They usually have some kind of structure for handling dyslexia, IME, in that they can get note-takers, tutoring, etc. Are the same services available to students with math-related disabilities?
We want the students to learn how to do the simple problems from the calculus course by hand so they have the ability to set up the larger problems they'll deal with in our courses along with the ability to check their answers instead of always trusting the machine.

Yes, of course, but do you want us to also teach them how to use technology?

And, if all of our examples have nice answers so that the arithmetic is simple what happens when it's not?

And if all of the examples are nicely segregated into sections of text based on the methods that they use what happens when they run into an ill-defined problem?

I'm not arguing that skills-building is unimportant, of course it's important.

But, I am saying that the way that many such courses are constituted only imparts a very small set of skills that students only know how to apply in nicely-formulated problems. I hope you expect more from us, seriously, I do.

This is my 4th higher-ed institution on the faculty side and it's been common to all.

Does a non-random sample of size 4 a study make? No.

But, there's a nice paper located:
Journal of Mathematical Behavior 26 (2007) 348–370

Which found:
The results also show that about 70% of the tasks were solvable by imitative reasoning and that 15 of the exams could be passed using only imitative reasoning.

Which suggests that my experience is not uncommon. Am I saying that I do anything different than my colleagues? No. We coordinate our classes down to choices of examples to demonstrate.
Part of the answer is to go beyond 'placement' tests to tests that actually diagnose which skills are lacking (or atrophied). Then, instead of teaching entire courses, teach a series of modules, each of which address a particular skill. Can't do fractions? Take Module #4. Can't factor polynomials, Take Module #10, etc.

This will work well for those who are rusty, but as other have pointed out, some students never learned the requisite skills in High School. I know our (WA) state high school assessment only tests up to 10th grade math. Good enough to graduate, but not good enough to start taking College-level math.
Al at 12:39 PM (also Punditus at 10:51 AM) mention diagnostic tests -

That is partly the idea of "4.Contextualized remediation." listed by Dean Dad, sometimes by forming learning communities as Philosophy Factory noted, and partly the idea of targeted instruction (a combination of DD's items 2 and 3) within a a "class" based on diagnostic info available to the instructor. Our prep classes have mandatory "lab" time where specific skills can be targeted on an individual basis.

Also, I love your last comment, mthgeek. Our CC does the exact opposite, spending several weeks of "college algebra" teaching kids how to chug away finding roots on their calculator. This might explain their shock and horror at physics or engineering problems that have symbols in them, or their struggles with trig - not to mention trig substitution.
Two related "underlying" issues:

Issue I: Wishful Thinking Fallacy
- Not every north american HS graduate is "Suited" for college level work; even if every single one of them is "Entitled" to get a college degree.
- Social promotion is required therefore to "certify" every students eliibility for their "entitlement" which results in low/no standards (why bother? everybody is going to college anyhow, right?)

Issue II: Regression to the Mean-2 sd's
- Since standards don't matter, and everyone is equal, the "learning objectives" are set abysmally low
- The kids who *could* do well at advanced levels of education (those who may actually "deserve" to go to college) get underserved
- We focus all of our resources on making sure the bottom end of the bell curve get everything they need . . . and take resources away for the other end of hte bell curve to make sure that happens

Issue I + Issue II = unsuccessful remediation


I am not advocating a "European Style" system of education for north america (where we "weed out" people at ages as young as 14 years and tell them "You're going to be a plumber." Centralized rationing of educational opportunity doesn't work for me, thanks.)

But in order for the "you must earn your opportunities" alternative to centralized rationing to work, you must have a merit based system of rationing. Opportunities might be unlimited, but resources aren't.

You have to ration somehow.

"We are all equal in our misery" might be great political theory, but here in the real world all you end up with is equally miserable/underserved people who are being prevented from reaching their potential. We all lose.
CCPhysicist: you might find taking a look at an exit exam from Canada interesting. Alberta has province-wide exams for grade 12 students, which contribute half of their class mark (the other half is teacher-assigned); some prior exams are at (Pure Math is aimed at people who might do university programs in sciences, engineering, etc.; Applied Math is aimed at people who're doing other university or community college programs.)
Resisting the desire to wax frenetically about the problem with educational reform is educational reform per se, I want to say that tutoring in its various forms is the answer, in my humble opinion, to students not being prepared to enter college. I have witnessed a student who is obviously clueless in class nod in delight that he gets it during a one-on-one tutoring session.

I believe "A White Bear" is on to something concerning using the summer to provide short on duration time but long on face-to-face time "classes" for remediation.

I think we spend so much time on why education isn't working we forget that in reality it must be.
Post a Comment

<< Home

This page is powered by Blogger. Isn't yours?