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Instrumental Orchestration in Mathematical Education

Kratky JamesEven at a young age James Kratky had a love of mathematics. As he grew older, so too did that love of mathematics, and when it came time to select an undergraduate major while attending Ferris State University in the central region of Michigan, James followed his strong passion for mathematics and his desire to serve others. He knew that teaching mathematics would be a great career choice.

Upon entering the classroom as a teacher, James quickly realized that what he knew wasn’t nearly enough. He knew that he wasn’t even sure what questions he needed to ask to best improve his teaching practice. People would tell James that he was a good teacher who challenged his students to learn mathematics. However, he believed there had to be more available (both in teaching methods and technology) that could be used together to help students to learn mathematics better. It was because of this that he decided to go to graduate school to expand his understanding of mathematics education.

While obtaining his doctoral degree in Mathematics Education, James conducted a research study surrounding "Instrumental Orchestration"- a construct referring to the teacher’s configuration and exploitation of the classroom and tools while guiding and shaping students’ use of mathematical technologies to enhance their learning.

As the participant in his research study, James selected a college instructor who used both digital statistical tools (e.g. graphing calculators) and specific research-informed teaching practices. The instructor focused on eliciting student thinking to help guide the lesson toward her intended learning goals for the students. Rather than rely on direct lecture, she led her classroom community through group investigations that encouraged conceptual development as the students engaged in each other’s thinking and even challenged the fidelity of the tools they were using! Along the way, she implemented several specific teacher moves to support her pedagogical goals, and James’ research explored and illuminated these characteristics of her instrumental orchestrations.

A goal of James’s research was to see how the teacher was supporting technology in the classroom. He witnessed extensive student exploration. The instructor introduced the mathematical tools to the students and then let them generate whatever statistical representations they thought were appropriate for the given context, while at the same time sharing and building off each other along the way.

James chose to conduct his research and gather his data by placing three video cameras throughout the classroom which captured both classroom interactions and the technology, while at the same time using a wireless mic on the teacher (fed to 1 camera) plus 5 audio recorders for additional audio capture. In a previous study, he had identified tensions between analyzing just transcript data or videos. He sought to alleviate some of that tension by combining data sources. James used transcripts as highly accurate records of what was spoken during class time. However, when the teacher asked questions, she often used wait time (a nonverbal pause lasting for a moment). By allowing for a few seconds of silence, the teacher invited her students to participate and contribute to the statistical conversation. Using a simple transcript would not have highlighted this wait time and other nonverbal subtleties, and therefore James chose to use both transcript data and video data to truly capture a sense of what was taking place in the classroom.

Kratky HR Screen2

James analyzed 18 hours of video and transcript data with Researchware’s qualitative analysis software, HyperRESEARCH. Having previously used HyperRESEARCH, he found it to have a very easy learning curve, and knowing its capabilities, realized that he could manipulate HyperRESEARCH by writing simple scripts on his MAC that enabled him to synchronize both the multiple videos and transcript data together and code the data for the types of teacher moves made during instruction. In addition to ease of use, and the affordable cost to purchase HR, James also found the sorting and annotation features of HyperRESEARCH to be very helpful. Overall HyperRESEARCH proved to be a very effective tool in helping James analyze his data. “To make the most of all that HR has to offer, researchers still have to reflect on what we do and be willing to put in the effort to make the tool work to the best of its ability” says James. “HyperRESEARCH, like any software, won’t do everything for us. We must keep asking questions and make decisions to help us answer those questions in our research. However, James adds, HyperRESEARCH has a lot more to offer if we are prepared to do the work to get there – it’s part of the process of doing worthwhile research.”

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