PCK and TPACK...Teaching Keeps Evolving

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!

Mathematics is a Story

As I look forward to entering my 40th school year, 26 in the mathematics classroom and the rest as a secondary mathematics resource teacher, I spend most of my waking hours thinking about the art and science of teaching. I have finally hit upon a metaphor that seems to resonate with educators.

I believe that mathematics is a complete and coherent (beautiful) story that begins at birth and ends, I guess, at death. For most, it formally begins in school and continues until a child is out of school. Each of a child's teachers is the sacred keeper of a chapter of this story. It is the teacher's job to make their chapter the most engaging piece of the story possible. Characters, plot, storyline must all develop in a logical sequence. These story aspects must fit coherently into place based on what came before. Connections must be made to previous characters and students need to understand how the characters will fit into the subsequent chapters. The story needs to be exciting, must capture attention, must motivate the students to want to hear and learn more. Think about what has happened to each and every one of us when we started to read a book and it was boring or, for whatever reason, didn't grab our attention. It doesn't matter if someone else tells you what a great book it is, most of us will not pick it back up. Especially when there are so many other options available. Once interest is lost in a story, it's difficult to gain that interest back. Now, think about a story where you were interested but all of a sudden, new characters are introduced or the plot line seems to diverge. Well, now the story loses me for another reason and, most likely, I've lost interest.

I'm thinking about teachers who use slang instead of correct mathematics terminology. As a student, I'm losing the storyline and the characters. Think about the teacher who teaches tricks instead of conceptual understanding. As a student, I can't follow the plot line. Think of the teacher who never lets students engage in a discussion about the story. As a student, I'm tuning out because I have all these thoughts in my head about the story but no one lets me share. Wow! What is the actual probability of any student getting 12+ amazing storytellers in their school life? Unfortunately, the probability must be near zero. This has to change! Every student is entitled to teachers who believe that their chapter of the story is sacred and worth conveying as if it is the beautiful wisdom, the flame of life. This means that teachers need to understand the content and they need to understand the pedagogy that underpins that content.

As I begin this new school year, I am committed to having conversations with math teachers about how their chapter of the mathematics story can be developed and shared with students to keep them clambering for more. I want every math teacher to know the joy when their class period is over and the students say, "WHAT, class is over already?!"

Is It Really New?

Went to a mandatory two-day training last week to be introduced to a digital platform for housing our curriculum. The platform is a component of a system our county has been using for about 8 years. Throughout the training, the facilitators touted the benefits for teachers of having the curriculum available digitally. We were shown how the teachers would be able to take the core documents and develop and change them to fit the needs of their students. They would be able to add resources to make the curriculum fit their needs. WAIT! HOLD UP! Haven't our teachers been doing that forever? Maybe not storing their changes digitally but certainly they have been supplementing the county curriculum however and whenever they chose. Many of them have supplemented and changed programs so much that the core purpose of the course is barely recognizable. As our office has pushed to make courses student-centered; writing instructional guides for the curriculum that suggest interactive activities, connections among content, and ways to improve the pedagogy, many teachers have consistently supplemented or ignored the suggestions giving students worksheets and tricks; offering the same old same old and wondering why their students can't retain information or problem solve. How will a digital platform change instruction?

Regardless of how the curriculum is housed, the teacher is the strongest indicator of whether students will learn the content. Great teachers need nothing more than a good, solid curriculum and their expertise, creativity, and relationship-building skills. It doesn't matter whether the course is built on paper, carried around on a thumb-drive, or accessible online. Showing a video that peels away the layers of a cell is no more effective than when a teacher had a pile of transparencies overlaid in such a way to peel away those same layers. If we think students are more receptive to watching and hearing a stranger on a video present content then we better look inward to find out why they aren't tuned into us as their teachers.

The biggest disappointment at the end of the last day of the training was when the facilitator showed a video of the digital platform being used by a teacher in another state. This commercial for the program did more to turn off the audience in the room than anything that had happened previously. It was the end of the second day and we were starting to brainstorm the capabilities of the program. This video showed the worse case scenario. The teacher in the video had built a 'playlist' of assets that became her 'lesson'. She then turned on the playlist, which played on a Smartboard, and the students sat taking notes. She basically was unnecessary after she hit 'play'. REALLY?! How is this different than death by PowerPoint or death by teacher droning on for 45 minutes? This was new? No, this was kids staring at a screen taking notes while someone spewed information.

Thank goodness our curriculum office personnel were appalled at this scenario. The video gave us a chance to share ideas for using the platform that would make our classrooms look different; a chance to talk about how to use the platform to individualize learning, and a chance to realize that without the principals on our side this will not work. We have been trying to change what happens in the classroom for many years. But, what is evaluated at the schoolhouse level will always trump any pedagogy shifts initiated in the curriculum offices. If our principals interpret what that teacher did as 'using technology', no change will occur.

Nothing is really new. Great teachers will use whatever means necessary to help students achieve. The means may look different but great teachers will never become obsolete because they will continue to grow and reflect. It will be up to the rest of us, principals and curriculum offices, to make sure the other teachers step up and attempt to achieve greatness or at least effectiveness.

Posted with Blogsy