It is primary Election Day in Maryland which means a day off for teachers and students. I suppose I should be pondering my election choice but I made that determination months ago. So, instead, I've spent the morning catching up on my professional reading and thinking about an upcoming interview.
This morning I sat on my deck having a cup of coffee and reading the Spring 2016 NCSM Journal summarizing research on the technological knowledge of secondary mathematics teachers and its effect on student achievement. When I finished the article, I started to think about things that circle around my brain regularly; how difficult it is to be an effective teacher.
There was a time in the not so distant past that HR people would accept career-changers with strong mathematics content knowledge to receive alternative pathways to teaching. When these retired engineers, veterinarians, and other math-related applicants were hired in August and had resigned by November, no one seemed to understand what had happened. But L.S. Shulman in the late 1980's and then Deborah Ball in the early 2000's started to realize and research the difference between knowing math and knowing math to teach it. Pedagogical Content Knowledge (PCK) is very different than being able to use math in an occupation. Teachers must understand the instructional techniques specific to the subject matter. Only when a teacher has the pedagogical knowledge to accompany the content knowledge will they be on a path to affect student learning. Without PCK, teachers don't have all the tools necessary for establishing an environment conducive to learning. When teachers (and most often career-changers with no real teaching experience) have no or low PCK, they rely on strategies they experienced as learners, utilize teacher-directed as their main instructional strategy, or use repetitive examples during instruction.
Teachers now need to layer the use of technology onto the appropriate instructional strategies they use to develop content. Researchers have now defined a new kind of PCK (Neiss, 2014) that defines the knowledge necessary to teach mathematics with technology. From this perspective, teachers need to understand technological content knowledge, technological pedagogical knowledge, and how to incorporate that knowledge to anticipate the learning needs of students. Teachers must now promote the development of mathematical understanding through the use of technology. For this, the TPACK model was developed to show how decisions about curriculum, assessment, teaching, and learning are related. There are 5 teacher use levels within the themes. A teacher is categorized (these levels can shift depending on the theme or piece of technology) as recognizing, accepting, adapting, exploring, or advancing.
Of course there is a sweet spot where content knowledge, pedagogical knowledge, and technological knowledge overlap on the Venn diagram. Much as Charlotte Danielson describes her 'distinguished' category as a place that teachers visit periodically, I would imagine that teachers would find it hard to live in the TPACK sweet spot for every lesson every day. So, what are the barriers keeping teachers out of the sweet spot and what can resource teachers, coaches, and/or administrators do to help?
Researchers since 1999 including P.A. Ertmer and A. Ottenbreit-Leftwich have identified barriers to teachers' integration of technology in the math classroom. First-order barriers include lack of training opportunities to hardware and software problems, while second-order barriers are about teachers' attitudes, beliefs, and skills. Combining these barriers with low PCK result in low level learning experiences for students.
There is much talk around individualization and customization of student learning, but what is happening with personalization and customization of professional development. Maybe professional development designed by analyzing teachers' needs and developing their PCK will enable them to become more successful in identifying their students' needs, interpreting student error patterns, engaging their students in a true conceptual development of mathematics, thus being open to increasing their instructional capacity. This kind of professional development might also open the door to layering on the use of technology on a higher level of the TPACK model. A teacher with a low pedagogical content knowledge will, most likely, have difficulty progressing beyond the recognizing or accepting level of technology integration. A teacher with a low PCK with its inherent unproductive beliefs will only view technology as an efficient way to confirm computation. With the proper individualized professional development, a teacher could see technology as a way to engage students in high-level thinking activities using technology as the valuable, high-powered learning tool is is meant to be. Without changing teacher beliefs about how they define student learning and increasing their PCK, technology integration will not happen just because a teacher has calculators or computers available in the classroom.
So, as I finish my coffee and head out to vote, I will reflect on the article a bit more and try to develop some specific strategies for raising both PCK and TPACK in the teachers with whom I am lucky to work and have conversations. Please exercise your right to vote!
