My research interests are situated in the following three main directions:
Discussion-Based (Harkness) Mathematics Classroom
From the videotaped classes conducted around a Harkness table, the recordings were transcribed and then, using the Flow Chart tracking tool, discussions were analyzed resulting in a handful of emerging themes. During analysis, I focused on identifying engaged versus unengaged discussions. I asked questions, such as: “What prompted the engagement?”, “When did the engagement occur?”, “What was the student’s body language in the engagement?, and lastly “What is a teacher’s role in discussion and when is it effective to step in and when is it not?” I have created the Flow Chart tool to suit my needs and the classroom environment. The purpose of this tool is to keep a record of the discussion happening in the classroom, the type of utterances and the direction of the replies. I attempt to identify the “climaxes” where the level of engagement is increased and most students are involved in the discourse. The analogy to this as I see it is as follows: if you pretend that each participant is a light bulb, when they are actively engaged (can be seen from their body language as well as direct participation in the discourse), the room lights up with the activity, as the number of utterances and number of people taking part in the discourse drastically increases to a crescendo. Types of information I kept track were: type of utterance (math or non-math related), direction of the utterance (concrete individual or the whole class), direction of gaze, location of tablet (oftentimes the tablet was sent around the room and students used it as main presentation tool and a talking stick when leading a discussion). Below is the legend of the modified Flow Chart tool used.
Assessment in Mathematics Classroom
I have designed and implemented the following assessment method, called the Check-Point System, that was devised for the 2017-2018 school year. The outline of the course was broken down into major topics and subtopics. Each subtopic became a trackable element for each student, which they could view at any point in time as a shared google sheet. So, instead of a regular marks book, now every student had the profile with their continuous progress, as each of the subtopics was repeatedly assessed. Another option given to students was an interview at the end of each term. In this interview students could showcase that they know a certain subtopic better than their overall mark for it. Below is the screen shot of one such spreadsheet:
Contemplative Practices in Mathematics Classroom
The question that came up naturally when looking at contemplative practices in the classrooms was how to organize and track the data to allow for meaningful analysis thereafter. The proposed structure is an extension of Figure 3 (see the Consulting page) where the focus is the Outer Ring of Awareness and the potential formation of MEC. The following spreadsheet is a template for what each student in this research has as a working document of keeping track of data and to be used in the analysis. The top portion of the spreadsheet is used to keep track of contemplative practice reflections, the middle channel is the Outer Ring of Awareness and the bottom section is used to look at the learning reflections data. Finally, the axis on the bottom is time with potential of putting milestones of what was happening in the course as the semester went on, with a possibility of incorporating the instances of time when the Check Points were given and looking at the rate of success on these for each student.