Posting a reading reflection I just submitted for my C&I course.
Telling is no longer a seven-letter dirty word in mathematical pedagogy according to Lobato, Clarke and Ellis (2005) in Initiating and Eliciting in Teaching: A Reformulation of Telling. They assert that while constructivists strongly advocate for student discovery in the learning process, it need not be completely absent new information from the teacher. In fact, the proper timing and content of said information could enhance the opportunity for student understanding to occur, especially when students find themselves struggling in their discovery and sense-making processes and not moving forward.
Lobato et. al. go to great lengths to dispel the unfortunate misunderstanding that constructivism and telling are diametrically opposed. Through their own research, case studies, and sound logic, they present a compelling case that telling is critical to the development of students’ conceptual understanding, and is not just a tool for transmitting procedural knowledge.
Instrumental to proper, effective telling is their view that “[telling] attaches priority to the development of the students’ mathematics, rather than to the communication of the teacher’s mathematics.” The challenge, as always with teaching, is how best to ensure students are properly prepared for the specific topic covered in any lesson; do they have the relevant schemas needed to engage in, to pursue, and to persevere with, discovery and sense-making? And if they do not, how do you ensure everyone learns the minimal skills necessary to work productively in the learning process? At the same time, it does seem that if students are at least open to participating in a discovery-based pedagogy, giving it their honest best effort, with a supportive teacher guiding the way, as necessary with appropriate telling, that students have a more likely chance of constructing their own mathematical understanding, one that is more persistent, resilient, and adaptable; something every teacher desires for their students.
Regarding my own experience these past few months in our teacher education program, I find myself struggling with the apparent, but misunderstood, dichotomy between a discovery-based pedagogy and a telling-based pedagogy (aka direct instruction). This article exposes the fallacy in my perception of what we are being taught, while reinforcing the necessity for a new interpretation and implementation of telling. While I still wonder how best to carry out this pedagogical approach, it is with a sigh of relief that I now see how my input in the classroom is still powerful and needed to facilitate student learning, sense-making and ultimately, conceptual understanding. The challenge now is how do I make sure those who have lived off a steady diet of direct instruction in their mathematical evolution are able to transition effectively to the constructivist world order and not simply give up on themselves, or blame the teacher, for any difficulties they may encounter in passing the class.*
* I witnessed firsthand, over a seven-month period, how certain students thrived on direct instruction emphasizing procedural competence and floundered profusely when exposed to constructivist instruction; so much so, that they failed their first semester final, and only passed a re-test, and hence graduated, when tutored by direct instruction focusing on procedural mastery.** Worse, they consistently berated their teacher for her teaching style, a person with a pedagogical style I appreciated and understood why she taught in that manner, but I could not convince those students of its benefits; and while my ego appreciated their praises of my approach, it was clear to me then that they simply wanted to be spoon fed so as to pass the hurdle in front of them so they could graduate – conceptual understanding and sense-making was not at the top of their list. I still wonder what is best for students, show them the way, even if they will minimally recall, but likely pass if they try their hardest, or force them to learn deeply, perhaps requiring much more effort and discomfort on their part, so they carry the knowledge, and a true understanding of its application and transference forward in life.
** There also likely were many other factors in play such as attending class regularly, paying attention, being persistent, doing homework, etc.