In summary, the emergent CME projects evidenced various entry points to the practice of making connections to children's MMKB in instruction.
The following two CME projects represent transitional connections that reflect movement along the trajectory away from superficial connections and toward more meaningful integration of children's MMKB.
In summary, we found that some PSTs entered the practice of making connections to children's MMKB in transitional ways, making notable connections to both CMT and CFoK, albeit with missed opportunities.
Our findings demonstrate that PSTs entered the practice of making connections to children's MMKB in various ways and with varying specificity.
The fact that almost half of our projects reflected connections that went beyond superficial attention to both CMT and CFoK suggests that with scaffolded opportunities to learn about children's MMKB, such as those provided in the CME module, PSTs can make substantive strides in developing an integrated practice that connects to both CMT and CFoK.
Projects in the transitional category also highlight the varied ways that PSTs begin to connect to children's MMKB, further emphasizing the need for learning experiences that support multiple pathways through these practices.
An important implication of this work is to identify specific leverage points that help PSTs develop the practice of connecting to children's MMKB. For example, a prominent pattern that emerged from the meaningful and transitional CME projects was that the lessons emphasized connections to children's and families' experiences and mathematical practices in the community setting (vs.
Alternatively, lessons that attended to CFoK but evidenced limited attention to CMT suggest other strategies for helping PSTs learn to connect to children's MMKB. For example, teacher educators might draw on meaningful projects that reflect connections to CMT to focus PSTs' attention on things such as anticipating children's strategies and possible confusions (e.g., Church Carnival example), and selecting numbers that create multiple entry points and reflect ways to minimize status in the classroom (e.g., Las Socias example).
Our goal is to help mathematics teacher educators and PSTs to explore the practice of making connections to children's MMKB in ways that do not restore the historical separation of CMT and CFoK in the field, but retain the complexity.