Which Comes First, Math Difficulty or Math Anxiety? – Inside School Research – Education Week

A friend sent me this link recently, which pulls together some recent happenings around math anxiety. And as a bonus according to a commenter the whole problem has been solved already. Thank goodness I’m focusing on shame rather than anxiety 🙂

Storify: Which Comes First, Math Difficulty or Math Anxiety? – Inside School Research – Education Week.

Ethics of Care and Mathematics

I was recently introduced to the concept of “Ethics of Care” by Indira Nair, who has written a couple of articles on the subject as applies to STEM fields. When we think about situations in which moral decisions must be made, we can consider how different individuals make those choices. One traditional method is to look at the development of individuals as moving from decisions made from self interest to ones made in terms of justice and universal rights. Feminist philosophers such as Carol Gilligan have developed another frame, which is moving from care of the self, to care of others, to balancing ones own needs with others. This is an ethics based on care, responsibility and relationships.

The most interesting thing about this, from my point of view, is that Nair and her colleagues have applied this to engineering and science. This requires the creativity of expanding what we mean by care. If we see care as the addressing of human needs, then of course engineering, and technology are about care since they grow out of human needs, the needs of people, the tools that people use, the environments in which we live, the things that we need to support our lives and communities. Science often grows out of this kind of care as well.

Nair and Pantazidou have linked four aspects of care: attentiveness, responsibility, competence, and responsiveness to engineering and the design process. Attentivness is about recognizing and identifying the need. Responsibility in terms of engineering design is conceptualizing and determining how to respond to the need. Competence is about actually satisfying the need and producing a product or solution. Responsiveness is about the reception of the product and assessing the solution. Connections can be made with problem solving and with scientific process as well.

I am interested in the application of this idea to mathematics. Mathematics and mathematics education often at least appear to be failing to care in the sense of responding to a need. Often the need is there, but the math doesn’t (or doesn’t appear to) grow out of the need. I think it is often it looks like we are saying, “You definately need this math, but its up to you to figure out why you might need it” or “You need this math in order to get a degree and a good job” (but it has no intrinsic value itself). That of course naturally begs the question of why we need math at all, and I think this is actually an interesting question. We should be asking “Who needs math?” and “What do we need it for?” and “What counts as a need?” For instance, I have a 6-year-old and she “needs” math because she likes making patterns and writing down numbers. I “need” math because I teach it to other people. My spouse “needs” math to model brain rhythms. I have a friend “needs” math to figure out how to bill and pay employees for landscaping work.

I’m going to be thinking more about this, but I’m curious if others have thoughts as well!

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Reference: Pantazidou, M., & Nair, I. (1999). Ethic of care: Guiding principles for engineering teaching and practice. Journal of Engineering Education-Washington, 88, 205–212.

Calculus

My classes started last week. This semester I have only two, which is good because I also have a sabbatical application, a promotion application, and contract renewal this year, along with a large responsibility in committee work. I’m teaching calculus and abstract algebra, both of which are both fun and challenging classes to teach. This semester my calculus class is the largest yet for my institution, which in itself really rocks. But I was unable to find a course assistant, so I’m managing all the work on my own. Thus I’ve tried to organize the heck out of it. I’m having students report on their own work each week and check their own solutions. I’m having them do more work in class that ever, and actually just more work than ever. And I haven’t even given them a textbook. Me and textbooks just don’t get along. I am never satisfied with the textbook for any class, and as a result I generally stop using them by midterms. So I decided to give it up. I’m having the students keep notebooks that are comprehensive and well organized, in part to make up for the lack of textbook. I’m also giving them a weekly handout that describes just what I expect them to know from each week, tied to the course objectives, which I have spelled out in detail, and will expect them to report on their progress toward twice this semester. Too ambitious as always! I’m also having them do weekly “readings” that are sometimes overviews of topics, sometimes “how to” pieces, and sometimes videos of either stripe.

So far the class is great! The energy is really good, and most of the students are talking to each other and participating in discussions. The class energy feels great. For homework I had them work on the “bottle calibration” problem, a favorite of mine since Robin Gottlieb first showed it to me. We had a wonderful discussion and debate in which some people were wrong, but everyone seemed to still feel good about what was happening. That’s one of my favorite kinds of moments to create in class. I’ve been peppering a lot of my class talk and individual conversations with comments about how its great when people disagree, are confused, or don’t know how to do something because that’s the only way we learn. I might give them some reading later in the semester on growth mindsets.

I’m having them ask questions online each week as part of a reading response and class response, and I got a great collection of questions from them and a good sense of their comfort levels — I have a lot feeling comfortable in class but with some nervousness about the material. I think that’s a great place to start and can set us up well for getting that “flow” state. A couple of students have said positive things about the class already. And in my feel-good moment of the week, and probably of the semester, a student of mine from Math, Art, and Design last semester reminded me today that one of the first things she ever said to me was, “You can’t make me like math.” Then she said that it turns out that she does like math now! That feels good, but it also feels even better that I can see her realizing that really does have the power to do math that she thought she was powerless against before. Not everyone can flip themselves around like she has, and it is inspiring to me when it happens. Mind you, I think I have been a good teacher for her, but that shift, it was all her being ferocious and refusing to let go of things she doesn’t understand!