Tracking the facilitation abilities of the four PLC facilitators over two years revealed that the quality of discourse relied heavily on the facilitator's mathematical knowledge, general facilitation moves and ability to listen and understand another member's thinking when interacting with that PLC member. We noticed variation in each of our four facilitators relative to these constructs. However, the facilitators' ability to promote meaningful discourses appeared to rely heavily on her/his ability to listen and understand the meaning that another PLC member was attempting to convey. To facilitate teachers in a professional learning community (PLC) required that the facilitator place himself in the other PLC members' shoes. "Placing oneself in another's shoes" is a classic instance of what Piaget (1955) identified as decentering, or the attempt to adopt a perspective that is not one's own. Steffe and Thompson (2000) extended Piaget's idea of decentering to the case of interactions between teacher and student (or mentor and mentee) by distinguishing between ways in which one person attempts to systematically influence another. In their telling, decentering involves the ways a person adjusts his or her behavior in order to influence another in specific ways. In that process, each person acts as an observer of the other, creating models of the other's ways of thinking. What follows is data that illustrates the various manifestations of decentering that emerged from our data.
Our coding revealed four observable manifestations of decentering.We have characterized these Facilitator Decentering Moves (FDMs) as follows.
FDM1: The facilitator shows no interest in understanding the thinking or perspective of a PLC member with which he/she is interacting.
FDM2: The facilitator takes actions to model a PLC member's thinking, but does not use that model in communication with the PLC member.
FDM3: The facilitator builds a model of a PLC member's thinking and recognizes that it is different from her/his own. The facilitator then acts in ways to move the PLC member to her/his way of thinking, but does so in a manner that does not build on the rationale of the other member.
FDM4: The facilitator builds a model of a PLC member's thinking and acts in ways that respect and build on the rationality of this member's thinking for the purpose of advancing the PLC member's thinking and/or understanding.
The first FDM (FDM1) can be characterized as no attempt to decenter. In this situation, the facilitator may take the action to simply give her/his own explanations without asking for the other member's thinking. FDM1 also encompasses the action in which a facilitator allows members to make explanations, but he/she does not show signs of engagement with the members thinking and is still focused on his/her own thinking. In the second FDM (FDM2), the facilitator takes actions (e.g., general questioning) that appear to show interest in a PLC member's thinking, but the facilitator does not use the resulting expressions of the PLC members in subsequent communication. The third FDM (FDM3) involves a facilitator who, after building a model of another member's thinking, acts in ways that attempt to move the member to her/his thinking without continued consideration of the other member's thinking. The fourth FDM (FDM4) entails the facilitator building a model (second-order observer) of a PLC member's thinking and using this model in order to advance the member's thinking. It is necessary to note that FDM3 can consist of a facilitator taking actions to further a PLC member's thinking, but what separates FDM3 and FDM4 is that in FDM4 the facilitator remains attentive to the understanding the PLC member is constructing. This may be done by the facilitator through continued questioning and probing of the member where the questioning is based on utterances of the member. A common characteristic between FDM3 and FDM4 is that after realizing the difference of understanding, the facilitator doesn't remain attentive to how the other members are interpreting her/him.
Our data also revealed that PLC facilitators appeared to improve most in their decentering abilities when they received specific suggestions from her/his PLC coach. PLC facilitators with stronger content knowledge were more effective in promoting substantive conversations about knowing, learning and teaching mathematics. The nature of the content knowledge that was needed for effective communication about knowing, learning and teaching specific ideas was also revealed during our coding.