Every day is a new day. Today, and lately, I’ve been learning about living. Learning about living a fuller more complete life. I find learning about living to be challenging and tiring. Caught in seemingly disparate worlds as tumultuous as a bubbling ocean busying itself during a a storm. I tire my eyes, body, and soul with deep questions that do not have answers. Yet at the same time, catch-y phrases are catching my attention such as “Fight the Impostor Syndrome!” “80 hour a week academic jobs” (are not real–it’s more like 50-60 hours) “Just do it!” “That’s the million dollar question” and hey, what about “Emotional Intelligence?” Is there a pattern in the randomness? What is the Signal in the Noise? My million dollar question right now is what do you want to do? To be? To aspire to?
I realized that my sticking point is no different than a perspective or theory on living–why should there be some pre-determined endpoint that I aspire to achieve? I prefer to think more organically about life, especially in regards to opportunities to learn, live, and grow. Yet at the same time, I know that I aspire to lead, to motivate, and to contribute to the growing and budding field of mathematics education research. One does not reach the stars in a day night or a week, but over a life time of work and dedication.
Some quandaries that stop me in my tracks deal with the contradictions and seeming inconsistencies between learning trajectories and curriculum development. If a learning trajectory, by definition, involves predictions about students’ processes on a task or instructional activity, then a problem or task necessarily exists that can be expressed in written form from which one could identify some gain size of curriculum. Does the reverse hold? If one has some gain size of a curriculum, say a task or activity, and if there is some sequence of tasks or activities that comprise a meaningful ordering of lesser to more sophisticated reasoning of the child, student, or learner, then these tasks can be taken as signposts of a learning trajectory. Now this is not to say that “curriculum” and “learning trajectories” are one in the same. The only case in point made here is the conceptually linked nature of these constructs.