I wish Oliver Steele had been my algebra teacher. He has wonderful illustrations that he calls grounded proofs . For example, multiplication is commutative:

Oliver’s lovely illustrations make these abstract mathematical concepts concrete and simple.

I didn’t really get math until geometry. Word problems were the worst. They never seemed to make pictures for me. They didn’t seem to have anything to do with reality, although in retrospect I imagine that they were trying to accomplish exactly that.

This is the second part of my response to Anna Fels’ thought-provoking, yet unfortunately titled article that was discussed in my last post.

Psychological Foundations of Ambition

Fels introduces a psychological basis for ambition, citing a wide range of research. This provides new insights into how the different treatment of women and girls leads directly to gender imbalance in the workplace. Fels asserts that ambition is fueled by a drive for mastery in the context of recognition:

Approximately half a century after Freud postulated his drive theory of motivation based on sex and aggression, researchers and theoreticians alike realized that a huge portion of behavior simply could not be explained in those terms. Jean Piaget and other developmental psychologists who focused on children’s need to master both intellectual and motor tasks discovered that children would repeat a task over and over until they could predict and determine the outcome. Theorists such as Erik Erikson began to posit that at a certain stage, children develop a “sense of industry,” or the need to do things well, even perfectly. Robert White, one of the seminal investigators of motivation, named this drive toward mastery “effectance.” “It is characteristic of this particular sort of activity,” White noted, “that it is selective, directed, and persistent, and that an instrumental act will be learned for the sole reward of engaging in it.”

Doing a thing well can be a reward in and of itself. The delight provided by the skill repays the effort of learning it. But the pursuit of mastery over an extended period of time requires a specific context: An evaluating, encouraging audience must be present for skills to develop.

Multiple areas of research have demonstrated that recognition is one of the motivational engines that drives the development of almost any type of skill. In the typical learning cycle, recognition fuels the next stage of learning. The early-learning theorist Albert Bandura was clear on this point: “Young children imitate accurately when they have incentives to do so, but their imitations deteriorate rapidly if others do not care how they behave.”

Naturally if someone does not receive positive feedback it is likely to dampen their ambitions. It has been well-documented that in our society girls and women are not encouraged (or actively discouraged) from pursuing many careers and even from many areas of learning.

Luke Hohmann talks about a similar topic in the context of how people become software architects:

“Humans are failure machines. We’re not success machines. We’re failure machines. We fail all the time. And it’s only through processing the feedback of our failure that we learn how to correct for them and do better. That is why it is important to stick with the choices you make and understand how well they worked.” — Becoming an Architect by Bill Venners via HMK’s “stciking with it

One of the wonderful things about software, once you stick to it long enough to get hooked, is that it provides its own feedback. We all need social feedback as well, and it was good to read that Hohmann acknowledges the social aspects of being a software architect.

Call me an optimist. I believe that if we all keep working at treating each other well and fairly, one of these years we’ll have a generation that can pursue their ambitions without regard to attributes of birth such as gender and race — attributes that should have nothing to do with the likelihood of success.

“It is the essence of play that a new relation is created between the field of meaning and the visual field — that is, between situations in thought and real situations.” — Vygotsky Mind in Society

“most of us are so busy trying to solve problems that we fail to notice that in solving problems we sometimes rob ourselves of the opportunity to learn something new.” Michael Hamman offers an interesting equation:

Creativity = competence + a desire to create a problem.

I agree that creativity requires competence, or at least confidence. I have observed in the development of software that I experience two extremes. One is where writing software is work. I relentlessly chase a bug. I perfect a piece of code through sheer persistence and fortitude. It can be satisfying, but it is not fun. The other extreme is where writing software is play. I can’t imagine that someone pays me for such challenging entertainment. Experimentation yields unexpected solutions. The patterns revealed by the trail of a bug lead to insights. Crafting a solution is a tangible, creative experience.

I often wonder what key factors create the experience of play. When I capture that way of working, I am undeniably more productive. I can see no down side to taking that approach all of the time, except that its not a state consciously achieved. One could argue that some things are just no fun. However, I don’t believe that the level of play is inherent to the task.