Possible Research Questions
It's never to early to start thinking about a research question. I can always change my mind and, in fact, it is guaranteed I'll revise my thinking as I learn more about research on this topic. Three possible research questions I'd like to spend the semester learning more about are:
- How do students think about mathematics concepts when engaging with dynamic representations and manipulatives?
- How might real-time feedback on curricular adaptations affect the instructional planning decisions of elementary-school mathematics teachers?
- How does integration of computational thinking concepts into mathematics change the way teachers and students approach mathematics tasks?
The first two research questions stem from issues I faced in my prior work as a curriculum developer of K-12 mathematics curriculum materials. Over the years, my work as a developer changed significantly as digital delivery of mathematics content and tools became more commonplace in schools. The use of digital alternatives to physical tools, for example, raised many questions about students' experiences of the mathematics is affected according to the medium of the tool. Relatedly, the increasing numbers of Open Educational Resources (OERs) on the web made teachers increasingly more likely to adapt and supplement their main curriculum materials, which led to many questions about the intended and unintended consequences of these changes. This made me curious about how communicating the potential consequences of the changes to teachers might affect their planning activity.
The third question stems from the recent push to bring computer science instruction into K-12 schools. Inspired by the CS4All movement, the research and development center for which I worked recently completed an exploratory research project seeking to understand the relationships between computational thinking (CT) -- defined loosely as the thinking processes engaged in by computer scientists, such as abstraction and pattern generalization -- and mathematics. The goal of the project was to build foundational ideas for how CT might be integrated into elementary mathematics instruction. The work led to more questions about the implications of this idea -- one of which I articulate in the third question above.
I am aware that pursuing three seemingly disparate questions may be beyond the scope of this RDP. However, on the advice of my advisor, I plan to dabble a bit each of these three realms of my interest early in the semester, and then follow whatever lines of inquiry interest me the most. One potential advantage of this approach is that exploring all three of them concurrently may reveal places of overlap among the research areas that I would not otherwise discover.
High Quality Sources
Quality research is built on a foundation of other quality research. High quality journals and handbooks are good sources for finding quality research.
Quality journals where I am likely to find good research on my topic are:
- Journal for Research in Mathematics Education. This is one of the first journals that was dedicated specifically to mathematics education as a field of research, and it is published by one of the biggest professional organizations in mathematics education -- the National Council of Teachers of Mathematics (NCTM). I know from personal experience that the editors are quite knowledgeable and provide quality feedback on journal submissions, suggesting that final articles that are published are of high quality.
- Journal of the Learning Sciences. Many of my research interests relate to how to design effective educational tools and environments, and I know (via my completion of a master's degree in learning sciences) that design is considered one of the major aspects of the learning sciences. Review of the tables of contents for this journal additionally revealed many names I recognized from my time in my master's program.
- ACM Transactions on Computing Education. The Association of Computing Machinery (ACM) is affiliated with two major conferences related to computer science education (the ACM Technical Symposium on Computer Science Education, colloquially known as SIGCSE, and the International Computing Education Research (ICER) conference). Because computer science education is an emerging field, publications in these two conference proceedings are currently considered as (or more) prestigious than journal publications. ACM's affiliation with this journal, alongside the conferences, suggests that the journal is high quality.
It is worthy of note that all three of these journals also came at the recommendation of my advisors.
Quality handbooks where I am likely to find good research on my topic are:
- International Handbook of Mathematics Education. This is a series of (at least) three handbooks published between 1996 and 2013, and sections of it have tended to come up in almost any search I conduct related to mathematics education, indicating its importance and quality. The second and third handbooks contain specific sections on technology, and a in brief review of the tables of contents, I recognized many of the researchers' names.
- Mathematics Education and Technology -- Rethinking the Terrain (17th ICMI Study). The International Commission on Mathematical Instruction (ICMI) regularly commissions studies on topics of interest to the field. Each study involves a wide call to researchers for papers on a specific topic, an international conference based on the top submissions, and a published volume representing the work. This particular ICMI study is specifically on the use of technology in mathematics education, and represents the most current thinking on various issues on this topic as of when the study was run in 2010.
- Emerging Research, Practice, and Policy on Computational Thinking. This handbook, published early this year, was specifically compiled to address the burgeoning interest in computational thinking research. As such, it contains much of the most recent research and thinking on the topic, including specific sections on K-12, teacher education, and tools.