# Overview and Workplan

OVERVIEW AND WORK PLAN

The present proposal seeks to explore further these approaches for engaging undergraduate students in writing math and/or programming that support thinking about the mathematics in images is further explored. The successful collaborative summer research experiences of the CCLI-funded Math Images I project will be extended to the academic-year curriculum and expanded to include more mathematics for computer science students, and lesson planning for preservice teachers.

- We had to slice this after NSF pointed out the following:
- While outreach to high school teachers is laudable, it is an activity that is not supported by DUE's CCLI (TUES) program. Hence, we cannot provide funds for the activities described in your proposal for high school teachers.

- We replied:
- We continue to feel that the Math Images II project should be valuable for both inservice and pre-service teachers. We considered the preservice and inservice teacher coupling to be essential and generative. Removing these groups from this proposal, allows us to focus resources on scaling for mathematics and developing the work we do with the computer science students. We will submit for other funds for the preservice and inservice teacher work.

In addition, exploration of undergraduate classroom work with page development and programming will be undertaken in college-level mathematics and computer science classes. It is expected that the inquiry-informed experiences of Math Images II could be the kind of extracurricular trigger needed to support undergraduates to make serious connections to mathematics as a discipline, regardless of whether they are undertaken during the summer or during the school year.

During the summer and in courses, students will work collaboratively in groups with their faculty member and interact with other groups of participants by means of videoconferencing and collaborative software. Faculty members, project consultants, Math Forum staff members, and inservice teachers will be involved as resources and support persons. For each of the different disciplinary groups, the process for vetting students’ work with image pages is expected to involve several iterations, including a final review and revision using collaborative software managed by the Math Forum.

Briefly, participating students in math classes or in the summer workshop focused on mathematics writing will be involved in project-based work that includes choosing mathematics-based images, possibly drawn from the extensive collection on the site, and designing a wiki page that in its finished form will contain an image, URL, author name, and descriptive material from the image author’s site. The student will research and work to write explanations of the math behind the image, at a variety of levels. They will be guided in their work by the rubric developed on the basis of evaluation research that examines how people read and work with math that accompanies images. They will work with faculty at their institution and will also be working virtually with Math Forum staff members and inservice teachers who will think with them about the mathematics on which they are working, its use and application.

The students will participate in weekly discussions with the other mathematics students, computer science students, preservice education students, and inservice teachers, as their work proceeds. They will contribute to an agenda for these discussions and will be responsible for helping to address the agendas of each of the other groups as well. Students will research and write image pages, work to revise them, and will receive and make suggestions to others about revisions. As the students and faculty members feel that a given page approaches the specifications of the rubric developed for image page development, it will be so tagged on the wiki, reviewed and mentored. When ready the page will be put on the public Math Images site. As a new page, it will be advertised on the Math Forum site and the original author(s) of the image will be informed that the page has been published. This process leads the undergraduate students to a different level of discussion about the mathematics on which they have been working, further questioning, discussions, and changes to the pages. Because the Math Forum site is heterogeneous, the others with whom they then are engaged following publication can include practicing mathematicians, tradespeople such as plumbers who use mathematics in their work, teachers, other students, math educators, and so forth [36].

The computer science students’ experience will also include writing mathematics and developing image pages, but they will primarily work with the collection of images addressing the mathematics behind computer graphics. The process of their work learning and working to write mathematics for images will be similar to that of the mathematics students. The computer science students will also spend time partnering with math students to address the programming needs of image pages that they have developed. As part of the weekly discussions with other student groups and through information posted on the wiki, they will identify the programming for other students’ pages that they will take on. Typically, programming for other students’ pages will be a collaborative process in which two computer students work together to first understand the math students’ intention for programming, and then think through and research ways to address the programming challenges that this involves. Either one or both of the students will then do the programming. In addition to constructing images, computer science students may develop interactive software. In CCLI I some of these “Math Images Tools” were so successful that they were featured in the Math Forum’s Math Tools catalog.

Preservice teacher participants may also write pages for images and this process will be similar to that of the mathematics students. They will also work with mathematics through thinking about the mathematics of the image pages already constructed and its use in the classroom. The approaches used to explore the images and the mathematics behind them will be developed in the first year of this project using virtual workshops with Math Forum staff members, project faculty members, and preservice teachers. Key considerations will include how to support preservice education students to work with image pages, create lesson plans that include image pages, and communicate about mathematics in collaborative sessions so that they enrich their pedagogical content knowledge, the specific content knowledge that includes understanding of mathematical procedures and representations in order to work effectively with students [42]. This process will be informed by findings from the evaluation work that address how people read image pages and make use of images to understand mathematics.

The plan to build out a preservice experience is modeled on the success of the Math Forum’s Virtual Fieldwork Sequence (NSF #0717732), and the Online Mentoring Project (NSF #0127516) in which preservice students mentored elementary students’ work with mathematics and worked on their own mathematics. Preservice teachers enjoyed work on both of these projects even when they did not begin the project with an interest in mathematics. They like working with pupils and by working with the preservice teachers to work more effectively with their pupils, it is possible to support them to also develop their skills in mathematics.

It is expected that through the wiki tools and the weekly discussions, preservice students will engage the project and other participants in conjunction with their immediate tasks to develop lessons for particular pages. Thus, they might ask questions of the mathematics and computer science students, make suggestions for page development, and contribute suggestions of topics for which images and pages would be useful, as well as for ways in which images might be manipulated (e.g. the possibility of zooming in or rotating) in order to encourage pupils to notice and wonder about them, as supports for working with mathematics.

There is work that needs to be accomplished before the beginning of fall 2010 classes that include refinement of a rubric for writing Math Images pages, identification of collaborative software that will allow management of feedback, and quality control needed before making pages that have been developed available to the general public.

Prior to the beginning of classes in late August of 2010, meetings with the project evaluator are planned to clarify goals of the project and continue the working relationship that allows feedback from the evaluation research to inform project refinement. Faculty members teaching fall courses and project consultants will receive links to image pages for review and summaries of research on this project conducted to date. These data will be used as a basis of a videoconference in which the vision for working with Math Images in participating classes will be discussed, questions answered, and so forth.

Students enrolled in courses of participating faculty members will be project participants. Participants for summer workshops will be recruited in the early spring of 2011 (or 2012), and will be purposefully sampled so that at least half of the participants at each school will be women, and half will be underrepresented minorities insofar as this is possible. In addition, at least half of each of the student groups will have just completed their first year of college, having already taken a STEM course, but not yet having declared a major.