Our Three Approaches to Trajectory Building

August 04, 2016

The overall goal of the LTEC project is relatively simple: to develop and test learning trajectories (LTs) for integrated mathematics and computational thinking in elementary school. Yet the easy statement of our goal belies its difficulty. Many questions come to mind immediately. How many trajectories will we need to create? Can computational thinking (CT) be integrated with all mathematics understandings, skills, and practices? If not, which ones are the best candidates? Conversely, can all aspects of CT be addressed via integration with mathematics? How do we strike a balance between taking advantage of the similarities between CT and mathematical problem-solving and giving them their due as separate skill sets?

In short, there are many things to consider when trying to reach our LTEC goals. The business of building LTs is challenging even when only attending to one subject, through we are fortunate to have the benefit of the work of other researchers before us, such as Clements and Sarama (2004)¹ and Confrey, Malone, and Corley (2014)². Our particular challenge for LTEC is coordinating LT development across three topics. First, we must pay attention to what is known about the development of CT in elementary school. Second, we must pay heed to programming; though our project is focused on CT rather than all of computer science, any treatment of CT will at times involve a computer. And third, we must take care to build on extensive work already completed in LTs for elementary mathematics.

It likely won’t surprise you that, despite the multitude of questions surrounding our project, during the first few months of our work our team was preoccupied with one particular question: Where do we begin? Do we start with CT and build in connections to programming and mathematics? Do we start with programming environments, identify particular CT ideas, and then connect to math? Or do we start with established mathematics sequences and weave in CT and programming?

Through many interesting and productive conversations, we came to the conclusion that any single approach had little hope of achieving balanced integration. Whatever the starting point happens to be – CT, programming, or mathematics – will necessarily be in the driver’s seat. We had two choices: choose a driver and be as mindful of its influence as we could, or let all three topics drive and see what we could do to direct them to the same destination.

Ultimately we chose the second option: We currently have three independent streams of work happening among three overlapping teams.

CT as the driver: One team is hard at work synthesizing information about learning goals from a multitude of CT resources, including scholarly literature, instructional materials, and standards documents.

Programming as the driver: Another team is conducting an analysis of the blocks available in Scratch to consider how programming projects might influence elementary mathematics and CT development.

Mathematics as the driver: A third team is examining the work of a dedicated group of elementary school teachers who have been integrating computer science into their mathematics classes, using Everyday Mathematics as a baseline.

When each of these teams has created trajectories, we plan to study the similarities and differences of their LTs in an effort to create one coherent picture.

In the coming weeks, we’ll say more about what’s going on in each of these streams of work – both successes and challenges. We hope you’ll enjoy following the journey and stick around for our later “big reveal.” Will we discover compatibility or simply produce a jumble of ideas? We’re not sure, but are looking forward to finding out.

References