Mathematics Research
Students can carry out original, open-ended mathematics investigations
Mathematics is so much more than a set of technical skills. All students should understand that mathematics involves a search for patterns, structures, and connections; that investigations are guided by problem-posing, conjectures, experimentation, and proof; and that there are many important skills and habits of mind that they can practice that will help them in their mathematical journey.
The National Science Foundation supported a project by the Education Development Center (EDC) that developed a curriculum for teaching mathematics research. Originally, it also partnered teachers with mathematicians as online mentors for them and their students as they took on the challenges of open-ended explorations. This project, Making Mathematics, remains an online resource. The original materials have some broken links and out-of-date resources. Making Math has permission to update and republish these materials. That is on our to-do list! Over time, we will present both ways to incorporate pure math investigations into all traditional late elementary through high school classes as well as a freestanding course on teaching math as mathematicians engage in it. Students can be junior mathematicians who pose and solve questions that are original for them (and maybe everyone!). For now, below are some Making Mathematics highlights and some updated resources for our favorite starter investigation, Connect the Dots.
Connect the Dots
This investigation is a research setting -- there is no question to be answered, but, as students experiment, they naturally start making observations that can be reframed as questions. The content is engaging and works wonderfully for grades 4-12.
Here are some fixed and new resources for Connect the Dots (be sure to explore the menu of support materials on the left):
> 16-Dot Handout for opening activity
> Connect-the-Dots application for studying bigger dot number values (but have kids start on paper). Launch ConnectTheDotsOnline (click on "Click to Run Model") or download Netlogo and launch ConnectTheDots5.nlogo.
More Research Projects
The Teacher Handbook describes ways to help students develop their own research questions, but there are many great starting points worth sharing with students. The Making Mathematics site includes structured project settings (no initial question) and Research Projects (there are guiding questions). All projects can be turned into settings -- just don't ask the question!