# Learning vs. Development in Practice as a Math Educator

As a math educator, do you distinguish between the concepts of "learning" and "development?"

If so, what is the distinction for you?

What would you say the consequences of this distinction are to your practice as a math educator?

• I think that the question in its current version is unclear. For example, given two distinct concepts $C_1$ and $C_2$, it's possible for one person to use mapping $\{\text{learning} \to C_1, \text{development} \to C_2\}$ while some other person would use $\{\text{learning} \to C_1, \text{development} \to C_1, \text{some_other_phrase} \to C_2\}$. May 30 '14 at 19:48
• I can see how my question might be misinterpreted; I mean for people to talk about the different ways they distinguish these concepts, not only how they use it to view their students. I will edit. May 30 '14 at 19:53
• Ok, are you asking whether concepts the reader labels "learning" and "development" are the same and if not, what is the distinction? If yes, then for me the primary difference is that learning is based on experience (i.e. you do not learn if the change in your behavior wasn't caused by some experience, perhaps imagined). May 30 '14 at 20:10
• Why is the distinction important to you? I.e., where do you want/need to apply it? The answer to this might lead to much more directly usable comments. May 30 '14 at 20:39
• @vonbrand To answer "where do you want/need to apply it?" would be "I will apply this knowledge when talking and listening to practitioners of mathematics education." This is a question about the ideas and reflections of practitioners. Part of the power of this StackExchange is that it helps give voice to educators of math, which is something we often hear there is not enough of. And not enough attention paid to. So, there is an opportunity to hear instructor views on the (possibly) important concepts of math education (not just of math). May 30 '14 at 23:22

You have asked three questions, and, in mostly answering the second, my response is already quite long. For now, let me not broach the third question about consequences of the distinction in practice.

Yes, I distinguish between the two concepts. As for how I distinguish between them:

Let me note first that a rigorous answer would probably come from within some realm of developmental psychology. The main sources I would start with would be Piaget (who might have said he wasn't working in developmental psychology but rather in "genetic epistemology"; but let us ignore such an objection) and Vygotsky. For the former, one might start by looking at his stages of (cognitive) development, and how learning fits in. As an example introduction, see here. For the latter, one might start by looking at his theory around the zone of proximal development, and, again, how learning fits in. As an example introduction, see here. (This is not directed at the OP, for whom I expect this background information is already known.)

More generally, a rigorous answer might involve asking you first to define what you mean by 'learning' and 'development'; of course, if there were clear-cut definitions, then I expect (1) you would be able to determine if/how they are distinguished without posting here, and (2) probably the main responses would be support for or objections to your definitions.

My sense, then, is that your question effectively boils down to putting forth one's own definitions of these broad terms, whereby the distinguishing features of the two will be elucidated. To this end, I can only answer in a relatively non-rigorous way, for they are very big words indeed.

Let me direct your attention to a different psychologist, Howard Gruber, a contemporary of Piaget's whose work was focused on creativity as inspired by his own lengthy case study on Charles Darwin. (You can find a bit more about Gruber in my earlier MESE response about creativity.)

Roughly speaking, Gruber conceives of the individual as being an evolving system composed of loosely coupled subsystems of knowledge, affect, and purpose; furthermore, he considers how these different subsystems interact with one another over time, and how they relate to the projects in which one is engaged (which Gruber refers to as one's network of enterprises).

So: I will define (hence distinguish between) learning and development as follows. First, I extend the three subsystems (without filling in the newly introduced theoretical lacunae) by allowing each to include some sort of meta- component as well. This means knowledge becomes knowledge and a tower of types of meta-knowledge; speaking messily again, something like cognition and metacognition. (For more on metacognition as broached by Schoenfeld, see my MESE response about time spent on a question.) In the same vein, affect extends from something like feelings to include also feelings about feelings and so forth; and, with more subtleties hence less discussion here, purpose and a tower of types of meta-purpose.

I consider learning to be what happens within a single one of these three subsystems (probably some would limit this to knowledge and its meta- component, which I'll denote knowledge+ as the combined unity; but let us go one step further and allow learning to occur in any one of the three). Heuristically, one can think about them as learning about the world (knowledge+), learning about the self (affect+), and learning about how the self fits into the world (purpose+).

Meanwhile, I consider development to be what happens as these three different subsystems interact with one another over time.

Is there established precedent for conceiving of learning as an intra-system process and development as an inter-system process? I'm not quite sure; but this is my non-rigorous answer.

Lastly, as somewhat of a side-note, let me end by quoting from the final lines of Gruber's Darwin On Man (I highly recommend this final chapter, entitled "Creative Thought: The Work of Purposeful Beings," and ensure you that the excerpt does not ruin anything). Gruber writes:

In his explorations of the world, the individual finds out what needs doing. In his attempts to do some of it, he finds out what he can do and what he cannot. He also comes to see what he need not do. From the intersection of these possibilities there emerges a new imperative, his sense of what he must do. How "It needs" and "I can" give birth to "I must" remains enigmatic (p. 257).

• You have given a fine answer, which I wouldn't have said is non-rigorous. When the question is about the ideas that you find most useful, you're the expert. I'm not familiar with Gruber, but will take a look at his work. Thanks! I am not sure about a precise precedent for the formulation of learning and development you describe, but you might be interested in Bédard and Chi on Expertise. Their view on the structure of knowledge has a similar flavor to your connection between subsystems. Jun 1 '14 at 1:50
• An interesting aspect of their ideas on the connections that structure expert knowledge is that they are based more on meaning rather than surface features. So, not just having connections becomes interesting. Bédard, J., & Chi, M. T. (1992). Expertise. Current Directions in Psychological Science, 1(4), 135–139. Jun 1 '14 at 1:51
• @JPBurke Great; I was just about to ask for a recommendation on what to start with by B & C. As for Gruber's work, it can be a bit tough to track down Darwin on Man. Here is a full copy: dropbox.com/s/869tupknawg7atu/… Jun 1 '14 at 1:52