a) I needed to struggle with the problems repeatedly, without help, before I really cemented my learning.

d) I needed to persevere through enmeshment in all the wrong details, and be able to come up for air and entertain ideas about what other people saw, not just the alluring details. And be exposed to people just above my level, and their ideas, not just expert ideas.

I wonder how many of those features my classes and work with teachers have. Are they all necessary? Are they sufficient?

Getting students to realize that they need to struggle with problems repeatedly is one of the most challenging parts of working with discouraged math learners, in my opinion. Discouragement takes hold for many of them when they see their “just a little more advanced” classmates simply “getting” something, then moving on triggers their defense mechanisms like nothing else.

This is one of the reasons why I find it so valuable to get students working individually on some new task or skill before putting them straight into group work. It’s hard to get yourself to wonder about something if your defenses are telling you to hunker down to avoid feeling humiliated.

Anyway, thanks for this food for thought.

- Elizabeth (aka @cheesemonkeysf on Twitter)

I confess I haven’t been able to think about Assignment 3 very much yet. I hope to get cracking on it this weekend!

I really enjoyed reading your reflections on the course and the kind of learning we are doing. I too have found it to be very non-linear… much more like successive approximations than like mastering one skill that leads to another skill that leads to another. I’m glad you’re enjoying it and giving yourself space to not get it right away — I find I struggle with that and get annoyed with myself or the MOOC format when what I need to do is relax and try thinking about the material with others or from a different perspective.

Enjoy!
Max

I like your reflection on learning, and it in turn reflects my own experience so far. I’m really struggling with these sets, perhaps more (or even less), than others, but it is of little consequence, because the journey is what is important, and what we get from it.

Although we are assessed (I was mortified at first when I received 11/21 on the problem sets, and was then penalized for being late for the deadline), I remembered why I joined the MOOC…not to bolster my ego, or receive accolades for academic excellence, but to develop my “mathematical thinking”, which, up until very recently, I thought I was categorically awful at. For me, logical thinking has never been a linear exercise. I now realize that it can be either (linear or non-linear), but that the real thinking happens when you just go through the exercises with an open mind, are willing to stretch, accept and then dispell misconceptions, and then move on.

I am going to try to get up to speed on the vast amount of reading, especially on mathematical notation and symbolism, of which I am woefully lacking fluency. I am a teacher, with a pretty healthy work-load, but I have about a week off coming up (fall break), and I’m looking forward brushing myself off, and moving forward.

How about you? Have you begun Assignment 3? Any advice (mathematically speaking)?

Ronni

I’m a student too of this course, and I’m from Mexico City. It’s been a great experience so far and it’s interesting to work both with people like you and with people like me, who are not mathematicians.

Max

You’re right, I have gotten sloppy about distinguishing among “Problem Sets,” “Course Assignments,” and “In Lecture Quizzes.” Looking back over my notes, I actually used induction and reasoning about elements of sets primarily in the Supplementary Reading on set theory.

Thanks,
Max