Author: Matthew

Many of you have heard me argue against the term guided pathways in favor of a participle with connotations that I find more compelling: guiding pathways. The present participle suggests to me a more open, engaged, mentoring approach to pathways, which fits better with the liberal arts. As I have often quipped, the Yellow Brick Road was a guided pathway, and look what happened: Witches, Forks, and Flying Monkeys.

In the spirit of guiding pathways, I’d like to start a conversation about serving CoReq students in a more effective, focused way, a way that leverages faculty expertise along three different axes: the developmental ed experts, HUMA1301 Great Questions, and the LA Gateway. CoReq is moving in the direction of an INRW/ENGL1301 pathway, so let’s envision a thoroughly integrated curriculum, to maximize the clarity of the student’s trajectory and simultaneously the effectiveness of support services along the way.

Words have consequences. When we talk about the skills students learn in the liberal arts, what are we saying when we call them “soft”?

First, as I have frequently said, if “soft skills” were all that soft, employers and CEOs wouldn’t be clamoring for them and they wouldn’t be so hard to find. More importantly, “soft” implies that these skills are somehow squishy, touchy-feely things that you just “pick up” by osmosis rather than acquire through application and dedication. You know, like the “hard sciences.”

When you call LA skills “soft,” you’re complicit in a value scheme that has placed these skills lower — but “the market” is telling you otherwise. So obviously, we need a better term.

This Friday, we meet for a wide-ranging discussion of our vision of our future as an AoS, which we want to capture in our Academic Master Plan. I propose this framework as a resource for facilitating and organizing our discussion around four major areas, drawn from the student “life-cycle.” Students engage in education, not in a vacuum, but with areas of strength and needs, with unique contexts and histories, and with aptitudes and interests. The come with ideas about what they want to learn and why, which means there is an inherent intentionality to their pathway, whether or not they can articulate what that trajectory is or what it involves. Each of these areas suggests possibilities for enhancement, ways we can prepare ourselves to serve them on that trajectory — including helping them develop self-reflection on the pathway itself.

This discussion framework identifies three foundational factors in the student experience plus the student’s  aspirations for the future — which is each student’s purpose for coming to ACC in the first place.

• The term liberal arts is inherently aspiration-focused, as these studies were originally conceived as equipping people for lives of autonomy,  community engagement, and self-determination. It’s appropriate, then, to talk about the liberal arts as foundational for thriving in a genuinely pluralistic society.
  
• The tetrahedron represents the pathway from present realities to student aspirations. It’s four vertices represent four main areas for self-reflection and goals for enhancement; in short, these are four major areas for organizing our AMP discussion and visioning. The four areas are:
  • Support: leveraging student assets and addressing needs
  • Study: the “content” of the student’s path toward mastery
  • Situation: the context that forms the student’s support network
  • Aspirations: the ends-in-view of the student’s engagement in education
• Obviously, the division of these four areas is arbitrary, as they are actually inextricably bound together in the student experience. (To give an obvious example, a student’s situation in terms of culture, family, faith, etc., has a direct effect on their formation and understanding of their own aspirations. To serve them, we must respect their autonomy, even as we help them in the transformative process of education.)
• For each of these four, I have taken a stab at some prompts for generating discussion, leading to specific goals, indicated in the slides.

Join the discussion of the future of the liberal arts at ACC! Talk to your colleagues and send your ideas. You are welcome to comment here, email your department chair, or be in touch with me.

Today is 1/27, one of my favorite days of the year. In the number theory game I’ve been playing with dates since my junior high school days, today is the only Mersenne prime day of the year.

First, my game.

• Step 1: Generate a number by writing the digits of the month and day as “mmdd.” Today, for instance, is 0127 or 127.
• Step 2: Investigate the properties of the number you got from step 1 and celebrate. For instance, 127 is a prime number. Sometimes you get other interesting characteristics — as I recently pointed out about my birthday, 108.

Now, what is there to celebrate about 127?

Let’s start with Mersenne’s prime theorem. If a prime number can be represented as a Mersenne number, then the power of 2 that generates that number must be prime. Mersenne numbers have the form

2^p - 1

For instance, 15 is a Mersenne number because it can be expressed as

2^4 - 1 = 15

Obviously, 15 is not prime (among other things, it’s divisible by 3, as my birthday post revealed), but many Mersenne numbers are — like 7:

2^3 - 1 = 7

Now here’s the theorem: if a Mersenne number is prime, then the power to which 2 is raised must be prime. Since we’re looking at 7, notice that the power, 3, is also prime. Very cool.

(And it’s convenient, too, because we can use this theorem to narrow the field of prime candidates. I like looking for primes among large Mersenne numbers, with a little help from Python. In fact, I’m slowly compiling triple-Mersenne primes. These are Mersenne primes whose power is a Mersenne prime whose power is also a Mersenne prime. You can’t get entertainment like that on TV.)

That brings us to 127, which is

2^7 -1 = 127

127 is prime, and 7 is prime. But 127 is the only Mersenne prime that corresponds to a day in the year, according to my game. Why?

The next lower candidate for a Mersenne prime would use the power 5 (Why?), so we have

2^5 - 1 = 31

31 is not a well-formed day-number according to the rules of my game. (I’m fine with dropping leading 0s, but not interspersing 0s willy-nilly to get an arbitrary result—that offends my basic sense of order and fair play). All the smaller Mersenne primes, therefore, won’t qualify for my game.

What about larger Mersenne primes? The next candidate uses 11 (Why?), but let’s see:

2^11 - 1 = 2047

Two problems: 2047 is not prime. (It’s 23 * 89, in fact.) And even so, there’s no 20th month. (By the way, this also shows that not all primes are Mersenne primes — not even close!)

Yes, 127 is the only Mersenne prime day of the year — but there’s more!

127’s power is 7, which is a Mersenne prime, as we say above. But 7’s power is 3, which is also a Mersenne prime!

2^2 - 1 = 3

So, 127 is a triple-Mersenne prime. See if you can parse this lovely relation:

 2^(2^(2^2 - 1) - 1) - 1

The expression in the innermost parentheses generates 3, the expression in the next pair generates 7, and the whole expression makes 127.

There you have it. 127 is not just the only Mersenne prime day of the year, it’s also a triple-Mersenne prime.

That’s cause for prime celebration.

I was moved to post this brief article from TCCTA: