Supporting Collaborative Blended Math Explorations

Concurrent Session 2

Session Materials

Brief Abstract

What happens when an on-campus collaborative math experience goes online? This presentation will focus on what the instructors learned, how it informed their blended
pedagogy, and the questions they now have moving forward as they hone a blended model for graduate math education study.

Sponsored By

Presenters

Laura Zadoff MEd. is the Instructional Designer for Online Learning at Bank Street Graduate School of Education. She supports faculty in the development of online and blended courses. In the past, she worked in online programs as a coach for a teacher education program (Wide World, Harvard Graduate School of Education) and instructional designer for professional online courses (Educational Portal of the Americas, Organization of the American States). She also researched and evaluated uses of digital technologies to enhance college courses (Columbia Center for Teaching and Learning, Columbia University).

Extended Abstract

Supporting Collaborative Blended Math Explorations 

What happens when an on-campus collaborative math experience goes online? This presentation will focus on what the instructors learned, how it informed their blended pedagogy, and the questions they now have moving forward as they hone a blended model for graduate math education study. This presentation will benefit faculty and instructors in higher education who are considering enhancing their instruction with online experiences.  

Context

What happened when an on-campus collaborative math course creates one experience online? This presentation will focus on what the instructors learned, how it informed their blended pedagogy, and the questions they now have moving forward as they hone a blended model for graduate math education study. The context for the research was from a math content course taught in the Leadership in Mathematics Education at Bank Street College of Education. Integrated Mathematics II focuses on the art of equations and the relationship between functions and their graphs. The topic of the blended math exploration was figurate numbers. It is essential to understand that relationships and program norms already existed in this student-centered math class.

Since 1916, Bank Street College has been dedicated to the preparation of educators. Since our inception, we have had a prevailing commitment to creating innovative communities where teachers are inspired to learn about social constructivist theory and apply this knowledge to their craft. Constructivist theory posits that new learning grows out of prior knowledge. As individuals interact with others, they expand their understanding of both the new and the familiar.

Questions  

In a blended format, what was the experience that the instructor wanted to create for students around figurate numbers? What did the instructor learn about feedback and pedagogy? How will doing the math online differ from the experience of doing the math on campus?

Methods

Students started working on figurate numbers in class. Building on beginning work with square, triangular, and oblong numbers, students were assigned more complex figurate numbers to complete online. In class, the instructor described the tools that were available and explained that this one online session would replace one on-campus class. Students worked in pairs online on hexagonal and pentagonal numbers. They were required to record their entire collaboration and then record their reflection after the experience of doing the mathematics. The instructor and the instructional designer watched the videos together inside a tool that allowed them to annotate while viewing the videos. They analyzed their notes while watching the videos and shared these notes with students. The notes included observations about student interactions and feedback on the mathematics.​

Findings

Students relied heavily on the established protocols from the on-campus class to structure their online interaction. Recording the process allowed the instructor and the students to go back and revisit the details of the entire process. The detailed and explicit feedback that the instructor offered during each process had the potential to deepen students’ continued engagement with the mathematics. The online experience gave the instructor the opportunity to be more mindful about what to say, what to ask, and when to say or ask something, which made the feedback more substantive. In addition, the instructor could be part of all of the groups’ process in their entirety and could offer detailed feedback and questions directed at individual students.

Conclusions

The initial research question was to ask which math problems would work well online and which ones would not. The instructor and instructional designer discovered that if a collaborative and reflective process and culture were intact, most problems would work well online. Rich math tasks do not need to occupy the same physical space any more than sharing a good book would. What is needed is shared assumptions and knowledge of a student’s partner’s approach to learning.

Doing math collaboratively online was beneficial for deepening students’ math understanding and contributed to the instructor’s pedagogical growth. In considering other assignments, especially the major assignment for the course, which is currently done in isolation and offline, the instructor and instructional designer are considering a blended final assignment.

In a blended format, creating a collaborative experience for students was made even more explicit. In an on-campus class, even in an environment that has expectations of collaboration, students can choose to work independently. When partners are online, the necessity of working together is more obvious. In addition, checking in with each other with consistency is necessary in order to move the work forward.