Reflections on online teaching

Imagine a person teaching an online course. Imagine further that the students in this course are tremendously thoughtful and responding with impressive depth and seriousness to the set of tasks in the course.

Imagine further that the instructor in this course had some thoughts to share with the students that included insights he/she has gained from the interactions, and that these insights include both mathematical insights and pedagogical ones (having to do with the pedagogy of the course itself).

What would be the best format for this person to share these insights? Hypothetically speaking?

It occurs to me that in such a situation, some constraints might include wanting to honor and welcome discussion of these insights (including critique), while not wanting to be overbearing. And that they might include wanting to highlight these thoughts without obstructing the narrative flow of the pre-established tasks.

Your thoughts?

Teaching for deeper learning

A good reminder for those of us starting our teaching week. From KQED’s Mind/Shift.

[F]or educators to engage in deeper learning with students, researchers say they must begin with clear goals and let students know what’s expected of them. They must provide multiple and different kinds of ideas and tasks. They must encourage questioning and discussion, challenge them and offer support and guidance. They must use carefully selected curriculum and use formative assessments to measure and support students’ progress.

That bold part is important to me and is so often neglected in mathematics classrooms and curriculum (see also: Khan Academy, ALEKS, Saxon, Explicit Direct Instruction, etc.)

What are student evaluations good for, anyway? RMP, part 2

Ken Bain and his research team have a perspective on student evaluations of college teaching that makes a tremendous amount of sense to me. Bain outlines two points in his excellent book, What the Best College Teachers Do.

point 1: Ask the right question

Bain writes:

If you ask students the right questions, their answers can help you evaluate the quality of teaching…We know, for example, that if you ask students something like, “Rate your learning in this course,” their responses usually have a high positive correlation with independent measures of their learning.

So we shouldn’t ask students whether they like the course, or whether it is easy to take notes from this instructor. We should ask them how much they learned.

Of course, we don’t all agree on what it means to learn in a college course. That’s where Bain encourages us to seek the kernel of truth in student evaluations.

point 2: Skempian analysis

Richard Skemp wrote about the difference between instrumental understanding and relational understanding. This difference comes out (although Skemp is not referenced) in Bain’s writing, referring to a Scottish study,

Students who thought learning meant memorization praised courses that valued recall while those who expected to reason on a higher level reported that they didn’t learn much.

And vice versa. Those who expected to think deeply and explore concepts praised courses in which these things were valued, while these same courses were panned by students who thought of learning as memorizing. This is precisely the conflict Skemp pointed to.

This is where Bain’s research provides some insight. His group’s work identified characteristics and—especially—practices of the best college teachers (identified by a metric Bain spells out nicely). So Bain isn’t worried about what the student evaluations look like for the best college teachers; he is concerned with what the best college teachers do with these evaluations.

One of the teachers in the study exemplifies these practices. Bain quotes him:

I have some students…who come into my class thinking that all they have to do is memorize and regurgitate. The class frustrates them at first because I’m asking them to understand and reason. In the end, if they give me low marks, it’s because I’ve failed to affect their concepts of what it means to learn my discipline

That is, the best college teachers seem to seek the kernel of truth in their student evaluations. It’s not that they take the evaluations at face value; they ask what can be learned from the substance of the evaluations.

I aspire to that.

Kernel of truth, grain of salt: RMP, part 1

The college where I teach made the Top Ten of community colleges on Rate My Professors recently.

Of course this is silly—utterly meaningless but amusing.

But the silliness of the ranking is trumped only by that of the ensuing email discussions in which anecdote replaces evidence. Consider this:

I don’t place much creedance in on-line ratings.  I bought a fish finder once based on on-line ratings–turned out to be a piece of junk. I don’t trust them for anything–not for hotels, professors, beers, colleges, shotguns, or leaf blowers.  I find no satisfaction in my positive ratings nor do I feel bad about my negative ones ’cause I have no faith in any of them.

And this:

Frankly, some of the professors I most strongly disliked as an undergraduate are the very ones I most admire in retrospect.   I was a lousy judge of teacher-quality and I have no reason to suspect today’s students are any different than I was

And this:

At the tender age of 21, I had a graduate professor…  who had a Byronic cloak, a shiny black cane, and a sharp, derisive tongue.  After numerous lashings from her in class, I was ultimately forced to visit her in her third floor palace.  I was rather surprised to find a witty, cordial and forgiving human being.  At the time, we were studying William Blake; and in a comment that later endeared her to me for life, [she] remarked blithely, “Well. . . sometimes the Tygers of Wrath are wiser than the Horses of Instruction. . . “.  If I had gone on ratemyprofessors at the time (had such a website existed), I no doubt would have deplored her pejorative and condescending teaching methods!

And finally, in response to some substantive discussion of the silliness of rankings that have neither meaningful methodology nor representative sampling, there was this:

. . . this is y so many ppl hav lost faith in science–& I thot I was the only 1 who wood ever challenj r feel good mentality

I have no idea what that last one is supposed to mean.

Here is my perspective on Rate My Professors (and on student evaluations more generally)…

Kernel of truth, grain of salt.

Grain of salt

This is the easy part, and it’s the one alluded to in the first quotation above. Students with strong feelings go to Rate My Professors. Students who had run-of-the-mill experiences in a course aren’t going to burn the calories or spend the time to let the world know about it.

So don’t take anything said there too seriously. Similarly, we would be wise to question whether liking a course or a teacher has anything at all to do with whether useful learning has taken place there. This is why I always feel uncomfortable with my professional development work. Feedback forms are different from assessments.

But this doesn’t mean we can totally dismiss everything on those feedback forms…

kernel of truth

Students have no incentive to make stuff up on Rate My Professor. Of course they are going there to vent or to sing the praises of a fabulous experience. But they have no incentive to lie.

So I think we need to read what’s there and ask ourselves what we can learn from what students have written.

For example, I have learned:

1. Too many of my early ratings involved the word fun. I’m OK with students thinking math is fun, but when it appears again and again, I had to ask myself whether the emphasis on hard work and critical thinking needed to be stronger. The change from then to now is noticeable.
2. Students don’t forget when I screw up, but they forgive me too. See the third one down on this page. (And for the record, I remember what the formula was.)
3. That I can manage my online profile. After my first year at the college level, I started showing students my RMP page and asking that they go there with substantive feedback. I don’t tell them to post positive stuff; I tell them to post substantive stuff.
4. That I can’t get a chile pepper to save my life (seriously, what’s up with that?)

More kernels of truth

I have advice for anyone starting a new job in education. On your first day (or as early as possible), ask this question of a few nearby colleagues, What sorts of things could I do wrong that I’ll hear back from the Dean about?

The question comes across as a request for help staying out of trouble. And it is. You’ll get useful information. But you’ll also get insights into your colleagues.

I have strong memories of asking this question twice. And I remember the answers. And I saw evidence of those answers in the corresponding Rate My Professors comments.

Kernel of truth indeed.

More on student evaluations coming soon.

Pushing back on some pushback

New comment in one of my Tabitha posts, from Steve Prosser (who, not coincidentally, has an app he’d like to sell you),

It is important starting around entry to first grade, IMHO, for children to: a) have memorized the patterns of basic arithmetic equations, and to b) understand how more complex problems can break down into simpler step-by-step arithmetic. Doing this in a way that promotes right-minded learning (pattern recognition) is vital. I’ve done my best attempting this for my daughter with my app – mathflashapp – and her performance through the third grade suggest this is the right track.

I have lots to say here and struggled with whether to say it in the comments or on the main part of the blog. So forgive me if this gets too detailed.

The post in question was really about the relationship between research findings and a child’s development. I wasn’t expressing a belief or an opinion in that post, nor a philosophy. I was using the example to make the research come alive.

This points to a more general principle here on the blog. I am interested in examples (whether my own or others’) when they either:

(1) Present a puzzling case that needs explaining, or

(2) Illustrate research findings,

and when they

(3) Are offered with enough detail that others may propose alternate interpretations or hypotheses.

In Boolean algebra, I strive for (puzzling OR illustrative) AND detailed.

Claims of the sort, “It worked for me and I’m OK” or “I did this with my class; they seem to be unharmed” are not particularly helpful to the cause of each of us learning something.

I have no beef with fact memorization, nor with apps that help students to memorize these facts. But we have good research evidence that far more time is spent on low level rule recitation, practice and review in American mathematics classrooms than in other countries with more successful mathematics education programs.

One of the agendas of this blog (there are many) is to explore what other possibilities are within our grasp at a variety of levels. So I’m never going to devote much space to techniques for memorizing arithmetic facts. There’s no new ground for me to cover there. Yes, an app makes it more efficient and gives instantaneous feedback. It’s a marginally better training device than flashcards would be. I have no problem with that.

But I don’t think we learn much from it as a field.

On the other hand, I know for sure that few people outside of the hard-core elementary math education circles know anything substantive about CGI. We have a lot to learn from that project. Examples can help bring the findings to life, and can help people understand the importance of these findings.

Selling a group of math teachers on the proposition that it would be nice if more students knew their addition and multiplication facts? That is not a particularly difficult challenge.

Helping them (and me) to understand the thinking that’s going on in kids’ minds as they learn new stuff? That’s a life’s work.

See also my post on setting norms.