In my last post, I expressed incredulity at Pat Rogan’s statement that by limiting education degrees to no more than 30 hours of pedagogy courses, the state of Indiana would be “put[ting] educators without essential teaching skills into classrooms”. I brought up the example of one-room schoolhouse teachers and homeschooling parents as examples of people who teach successfully without anywhere near that amount of coursework. Another example I realized this morning was my own profession of college teaching. Most college professors have never had a pedagogy course in their lives, and yet many of those are among the best classroom educators our society has to offer. They certainly have “essential teaching skills”.

Of course there are also many professors whose teaching is atrocious. But there are also high school teachers with 30+ hours of pedagogy courses whose teaching is equally atrocious, and it’s highly questionable whether they have “essential teaching skills” despite surviving all that coursework.

What exactly are “essential teaching skills”? How do these differ from one teaching situation to the next — the preschool classroom, elementary schools, public high schools, private high schools, college classrooms, homeschoolers’ living rooms? Is there a single set of “essential teaching skills” that is common to all teachers, regardless of their context? And what role does education coursework play in conveying those skills?

Indiana Superintendent of Public Instruction Tony Bennett is announcing today a plan to overhaul the state’s system for teacher licensure. The announcement is here, and there are three PDF’s linked at the bottom of that page that go into more depth. [Update: There's now a 7-minute video of the press conference at this site as well.] And here’s an Indianapolis Star article (written prior to the announcement, so it’s a bit short on detail) that gives a thumbnail overview and some reactions from local education people. Those reactions seem pretty heated, and when you read the details of the program, you can begin to understand why.

The first point listed in the plan, and the one that seems to have the most impact, is that requirements for content knowledge for pre-service teachers are going to be ratcheted up several notches. Secondary education teachers will now be required to earn a baccalaureate degree in a content area — not in education — and earn a minor in education. Elementary education majors may do this as well, or earn a baccalaureate degree in education with a minor in a content area. Those aspiring to change careers into teaching do not have to get any formal coursework in education at all, but rather be certified by the American Board for Certification of Teacher Excellence, which involves holding a baccalaureate degree (in any subject) and then passing a teaching exam and attending teaching workshops. In addition, the very definition of a “major” or “minor” in education will be changed: A degree in education can have no more than 30 hours in pedagogy, and a minor can have no more than 15. This new system, along with the other changes in the plan I didn’t just mention, would be put into place on July 1, 2010.

In a word: Whoa. These are some  monumental changes to the way things are currently done here in Indiana. And that’s not all. There is more to the proposal than what I mentioned above — in particular, a big change is that the PRAXIS I exam will no longer be required, and there’s an end to a portfolio and mentoring requirement that I know firsthand new teachers hate — but let me give some quick thoughts about the changes I did mention, which affect directly those of us involved with training new teachers.

• The change in degree requirement for secondary education teachers is huge. Consider the Mathematics Teaching major at my college. As it is, students in this program take 24 hours of “professional secondary education” courses (including methods courses, instructional strategies, etc.) along with several semesters of field experiences plus internships in education. Most, if not all, of the courses in the “professional” category would probably be considered “pedagogy” courses under this new system (although there’s no clear definition of that term). Under the new system, all of that would be replaced with an education minor that consists of no more than 15 hours of pedagogy courses. This is effectively cutting the “professional secondary education” courseload for these students by half or more.
• Like I said, this is huge — for both students and faculty. Students wanting to be secondary educators are now going to have much more flexible schedules and greater choice. And if, previously, a secondary education content major was heavy on the education and light on the content area, the whole world will be changing for students in that major. For us, our Math Education degree is just one course away (an independent research project) from a Mathematics degree; students in Math Education usually just double-major, so this change is not going to affect us much. But it could completely change the landscape for other programs where the math (or science or whatever) education major is something like half of the associated content area major plus a bunch of education courses.
• It’s also huge for faculty. Now you can see why some of the teacher education people might be very concerned. Their pedagogy courses are going to be depopulated. And the effect will be far worse at larger schools, where education professors tend to specialize more and you might have some profs whose entire course load, year in and year out, consists of pedagogy courses — courses that are now being taken by only a fraction of the former number of people. If universities were like industry, we’d simply lay off, reassign, or let go the profs whose services are no longer needed. But what if such a prof has tenure? Things get complicated.
• I think the change to allow ABCTE certification is brilliant. I have talked to dozens of students and their parents who are thinking about going into teaching, but they aren’t sure, so they want to major in a content area and then “go back and get a teaching certificate later” if they felt the call. It is painful to have to explain that, in Indiana, you can’t just “go back and get a teaching certificate”. Well, now you can. (Assuming this all passes.) This is an excellent way especially to get more teachers in math and science. I know a lot of scientists and engineers who have wanted to get out of industry and into teaching, but the amount of coursework required was a real hindrance. Now there is an alternate route.
• The speed of the timeline is shocking. If this goes through, this upcoming academic year will be the last one in which the traditional secondary education majors exist. That’s got to be a major jolt to the system for many colleges, especially the education departments. But it becomes less shocking when you read the “Licensing Summary” PDF and see that the Obama administration’s Race to the Top program, and the tons of money contained therein for states with “streamlined” licensing processes, is listed there. They want to get this deal done quickly so they can be better positioned for money from this program.

A telling statement from Pat Rogan, executive associate dean of the education school at IUPUI, was in the Indy Star article: that the proposed limits of 30 credit hours of pedagogy in education courses for education majors and 15 for education minors would “put educators without essential teaching skills into classrooms”. Seriously? It takes more than 30 credit hours — the equivalent of an entire academic year of coursework if the student took nothing but pedagogy courses, 15 hours a week solid for nine months — to convey “essential teaching skills”? Somebody needs to send a memo back to the great one-room schoolhouse teachers from 100 years ago, and all the successful homeschooling parents today, letting them know that they are badly lacking in their preparation and need more pedagogy courses. Perhaps the gist of this entire plan is to say to education schools: Align your conception of what constitutes “essential teaching skills” with reality, and then redesign your programs to match.

This report Frinom the Atlanta Journal-Constitution, citing an article in the June 1 Proceedings of the National Academy of Sciences, says that differences between boys’ and girls’ performance on standardized mathematics tests correlates with the level of gender equity and other socio-cultural factors in the country in which the test was taken.
The study’s co-author says:

“There are countries where the gender disparity in math performance doesn’t exist at either the average or gifted level. These tend to be the same countries that have the greatest gender equality,” article co-author Janet Mertz, an oncology professor at the University of Wisconsin-Madison, said in a university news release.[...]

“If you provide females with more educational opportunities and more job opportunities in fields that require advanced knowledge of math, you’re going to find more women learning and performing very well in mathematics,” Mertz said.

The study goes on to cite the US as a country where there is a relatively high degree of gender equity and hence a relatively equal performance on standardized tests between boys and girls, with more and more girls taking advanced courses in science and math. But, importantly, the study also warns that

“U.S. culture instills in students the belief that math talent is innate; if one is not naturally good at math, there is little one can do to become good at it,” Mertz said. “In some other countries, people more highly value mathematics and view math performance as being largely related to effort.”

This is a point well worth noting. What will it take for the culture in the US to get away from the idea that you’re either born with mathematical ability or born without it — in other words, mathematical predestination?

I’m reading through a number of books and articles related to the scholarship of teaching and learning this summer. One that I read recently was this article (PDF), “Connecting Beliefs with Research on Effective Undergraduate Education” by Ross Miller. There are lots of good points, and teaching tips, in this article. But Miller makes one assertion that doesn’t seem right. He brings up the point, under the general heading of “beliefs”, that “questions arise, both on and off campuses, about whether all students can learn at the college level and whether everyone should attend college” [Miller's emphases]. As to the “should” part of that question, Miller says:

According to Carnevale (2000), from 1998 to 2008, 14.1 million new jobs will require a bachelor’s degree or some form of postsecondary education—more than double those requiring high school level skills or below. Given those data, it makes sense to encourage all students to continue their education past high school. Consistent high expectations for all students to take a challenging high school curriculum and prepare for college (or other postsecondary education) benefit everyone. Our current practices of holding low expectations for many students result in far too many dropouts or graduates unprepared for college, challenging technical careers, and lives as citizens in a diverse democracy.

So, Miller answers, yes — everyone should attend college. But the reasoning seems spurious for a couple of reasons.

• How much of the increasingly common requirement of a bachelor’s degree for new jobs is the result of an existing oversupply of people with bachelor’s degrees? Miller claims that people need to have a postsecondary education because more and more jobs require it. Maybe so. But is that because the jobs themselves inherently use skills developed only through a college education? If so, we have to ask if our higher education system is consistently giving students that kind of education. If not, and if students should get a BA or BS  merely because there are so many people out there with BA’s and BS’s that you have to have one to avoid the appearance of intellectual poverty, then this encourages superficial education at the postsecondary level, and the reasoning here is more mythological than anything and needs to be repudiated.
• As Joanne Jacobs noted back in early 2008 (quoting an article by Paul Barton) it’s not at all settled that the claims about jobs here are even valid. According to that article, only 29% of jobs in 2004 require college credentials, and the percentage is expected to rise only to 31% by 2010 — not exactly a clarion call for all students to matriculate. Also, Barton notes that the wages earned by males with college degrees have slipped, which indicates an oversupply.

College is just not the best choice for every person, and to say that it is merely sets students up for wasting four years of their lives. Some people may have a vocation into a field for which four years of college are a massively inefficient use of time and resources. If you’ve got a vocation to be an electrician, go learn how to be an electrician. If it’s to be a stay-at-home mom, then go do that. Both of these vocations can benefit from a college education if the person is inclined to get one, but neither requires a college education. If you want to go to college and then do those things, fine; but let nobody say that you should go to college, irrespective of your life situation.

We’ve finally made it to final exams week in the second semester of what seemed like the longest academic year ever. I thought I would bump this old post from December 11, 2005 (original with comments here) to give props and encouragement to all the students out there who are getting ready for their exams.

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(Inspired by seeing so many students on AIM tonight studying for finals, which for us start tomorrow.)

Dear Lord:
Let those who are filling the library right now with their bodies and their thoughts
Study hard, but also eventually rest.
Let them realize that success on their exams comes
Not from pulling allnighters
Not from cramming
Not from losing sleep
But as the sweet fruits of a long semester
Of diligence, patience, humility, and sweat
Of losing themselves in the laborious doing
That comes when a long-held dream is finally pursued.
Let them know that their final exams not only measure their knowledge
But also, in the ending of the term, show how faithful You have been to them.
They know more now than they did in August.
They are better students, better stewards, of Your blessing of intellect.
Their thoughts are more like Your thoughts.
And no matter what happens, this cannot be taken away.
In that, let them rest
And tomorrow, Tuesday, and Wednesday, let them learn and be satisfied.
In Your Name: Amen.

The two biggest players in the learning management system world, Blackboard and Angel, will soon be one company, since Blackboard has purchased Angel Learning, Inc. for $95 million.  From a superficial reading of the press release, it appears that Blackboard thinks of itself as having a more technologically innovative product, whereas Angel has a better track record with customers — and Blackboard has the money to pull off the purchase.

I can’t verify any of those claims, but I can say that we switched from Blackboard to Angel at my college a few years ago due to a general dissatisfaction with the quality of the product compared to the price we were paying. I don’t recall Blackboard as being particularly innovative, although admittedly that was 4-5 years ago. Angel has not been much of an improvement, and I’ve blogged before about the maddening UI design decisions that Angel has made. In going from Blackboard to Angel, we basically traded one set of deeply flawed LMS technology for another.

And now we have the situation where the current sub-par LMS technology maker is being bought out by the previous equally-but-differently-subpar LMS technology maker. So who knows what exactly we, the users at my college, are going to end up with. The best-case scenario is that we would get the best of both technologies. There are some things that Angel does  pretty well, well enough at least that I am no longer finding myself forced to roll my own LMS at Wikispaces just to retain my sanity. We shall see.

In the meanwhile, Jon Mott has some excellent thoughts about life post-LMS. I think he’s right that the basic problem isn’t the implementation of the technology (although, as I’ve noted, there are some big problems there with Angel and probably with Blackboard as well) but rather the paradigm on which the technology is based. It makes me wonder if the real LMS that best suits the modern college or university is already out there, in the form of previously-released tools that just need to be cobbled together rather than an expensive proprietary software package that tries to emulate those tools.

On Twitter right now I am soliciting thoughts about calculus courses, the topics we cover in them, and the ways in which we cover them. It’s turning out that 140 characters isn’t enough space to frame my question properly, so I’m making this short post to do just that. Here it is:

Suppose that you teach a calculus course that is designed for a general audience (i.e. not just engineers, not just non-engineers, etc.). Normally the course would be structured as a 4-credit hour course, meaning four 50-minute class meetings per week for 14 weeks. Now, suppose that the decision has been made to cut this to TWO credit hours, or 100 minutes of contact time per week for 14 weeks.

Questions: What topics do you remove from the course? What topics do you keep in the course at all costs? And of those topics you keep, do you teach them the same way or differently? If differently, then how would you do it? Finally, would there be anything NEW you’d introduce in the course that would be pertinent for a 2-hour course that wouldn’t show up in a 4-hour version of that course?

Keep Twittering your comments to me at @RobertTalbert, or comment below. I’ll sum them up later.

UPDATE: I also meant to say, feel free to play with the assumptions I am making here. For example, if it’s impossible to think of a 2-hour calculus course, change that to a 3-credit course and see if you can come up with anything.

From Joanne Jacobs, a handy interactive certification map for prospective teachers.

Chester Finn and Mike Pitrelli say that education needs more efficiency, not more investment. We could at least give it a try.

Killing the buzz over “21st-Century Skills”: ““The error at the heart of P21 is the idea that skills are all-purpose muscles that, once developed, can be applied to new and unforeseen domains of experience.”

Want a job? Don’t major in business. Instead, major in a “classical” liberal arts major and then take 4-6 math courses on the side (i.e. get a math minor).

Using math to make the perfect pancake.

Albrecht Dürer and the heptagon.

Experiments with MATLAB, a high-school (!) level book on MATLAB from Cleve Moler.

Several apps from Omni Group — OmniWeb, OmniDazzle, OmniDiskSweeper, and OmniObjectMeter — are now freeware. These used to be about $25 apiece. I tried OmniWeb once and thought it was really good, and I’ll probably try it out again. If you’ve got a Mac and some disk space, have at ‘em!

Down under, the Australians are going through many of the same arguments about mathematics education that we are here in the US. In this column from The Age, Marty Ross — who holds a PhD in mathematics from Stanford — lambastes the Australian mathematics education community in ways that might seem eerily familiar to those who follow the similar issues in America. Quote:

[H]ere is an exercise from a current Victorian year 9 maths text: a farmer has 2C cows and 3H horses. The exercise is to find the square of the sum of the farmer’s animals.

The Victorian texts are not uniformly that pointless or that bad. But not much is good. Definitions are clumsy, problems are contrived, natural connections and beautiful insights are overlooked. The texts do not reflect a mathematical culture.

It is not just the textbooks. Teachers are poorly trained; the curriculum is moribund, rife with silly, contrived applications; and everywhere there is pointless calculation. And calculators – the cane toads of education.

Is there still proof? Proof is the source of the power of mathematics, the reasoning and the understanding: it’s what holds the discipline together. But it is practically dead. The very little proof that remains is meaningless and ritualised: maths as Latin Mass.

How did it get this bad? Primarily, it results from the failure to involve mathematicians, the people for whom mathematics is their life’s blood. The simple fact is, many of those responsible for mathematics education do not know sufficient mathematics to do the job.

There are lots more “ouch” moments in the article. Ross concludes by saying:

What do I want from a national curriculum? I want a dodecahedron in every classroom, and beautiful diagrams to ponder. I want students to know why there are infinitely many prime numbers, and for them to realise no one knows about twin-primes. I want them to know what the golden mean is, and why it is irrational, and why we care. I want pattern and play and beauty. And I want the times tables.

Is teaching any of the above useful? It is exactly as useful as teaching Harry Potter and Shakespeare.

Mathematicians do mathematics because it is fun and it is beautiful. If the curriculum is not written in that spirit, and if teachers are not trained in that spirit, then we are doomed. We will have yet another generation devoted to gradgrinding students into hating mathematics.

I’ll agree on many of these points — especially why mathematicians are motivated to do mathematics, the criticism about the lack of proof in the math curriculum, and to some extent Ross’ critiques of the mathematical background of mathematics education people. But what do you think — is Ross’ assertion that fun and beauty form the proper basis for a mathematics curriculum really sound? I mean, I’d like all my students to know about the infinitude of primes too, but does that sort of thing make a reasonable organizing principle for an entire curriculum?

The teacher who graded this dismal paper from a physics class is either a lot  braver than I am or cares a lot less about his/her relationships with students; and s/he certainly has better artistic skills and a lot more time on his/her hands than I do:

Read the whole essay and especially the teacher’s marginalia. I think it captures the temptation of every teacher to grade papers by unloading our own cleverness onto  hapless, writing-impaired students.

But the article has a fair question — how does something this bad get a 3/3 grade?