Facilitating Learning in Precalculus


Students in Dana DeLoach’s Precalculus class are engaged in the content, serving as creators of their own learning.  A recent visit to Mrs. DeLoach’s classroom revealed a buzz of activity as every student was contributing to the group’s misson of collecting data from a homemade pendulum before using trigonometry to model the behavior.

The image to the left above shows one of the pendulums made of a bob (weight), yarn, washer, and thumbtack. The task the students were to complete included data collection (time, displacement, number of complete swings), attention to precision, and articulation of an equation to model each set of data.

This lesson was designed to provide opportunity for the students to experience the following standards for Precalculus:

(4)  Number and measure. The student uses process standards in mathematics to apply appropriate techniques, tools, and formulas to calculate measures in mathematical and real-world problems. The student is expected to: (G) use the Law of Sines in mathematical and real-world problems; and (H) use the Law of Cosines in mathematical and real-world problems.

To access a full-size version of the student handout, click the image below.

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click for full size image

Rather than provide the students with a contrived set of data, Mrs. DeLoach challenged the teams to create their own data sets and as a result embedded the necessity for them to demonstrate the mathematical process standards of communicating mathematical ideas, reasoning as appropriate, and using precise mathematical language.

While the students were attending to the precision of their experiments, collecting data, communicating with their peers about the task, and making a plan to model the relationship with trigonometry, Mrs. DeLoach was facilitating.  She actively monitored the learning, provided scaffolding to students to make the connection to prior learning, formatively assessed by posing intentional questions, and gave descriptive feedback to the teams on their data collection strategies.  Mrs. DeLoach’s design of the learning experience and her role in the classroom as a facilitator of learning rather than a lecturer or deliverer of knowledge embodies a portion of the Visioning work.

The supporting premises that describe Organizational Transformation in Creating a New Vision for Public Education articulate the necessity for a shift from the traditional teacher role (lecture, direct instruction) to a redefined instructional role as facilitator of learning.

V.b The teacher’s most important role is to be a designer of engaging experiences for students, supporting students in their work by incorporating more traditional roles as planner, presenter, instructor, and performer.

High Level Alignment Indicators for implementation of the premises (as described on the Implementation Rubric) include:

Teachers are engaged in facilitating meaningful learning based on rigorous content. Students are engaged as self-managers of their learning.

In order for a student to be a self-manager of one’s learning, the classroom teacher must set the learning environment in such a way as to provide for access to knowledge, feedback, and safety to take risks, make mistakes, and learn as a result.  True understanding of rigorous content comes as a result of the opportunity to transfer knowledge to new, unique situations.

I had an opportunity to debrief with Mrs. DeLoach following this classroom visit and she shared that her colleagues implemented this Simple Harmonic Motion Pendulum Lab as well.  A sign of a healthy, productive Professional Learning Community is one in which the educators share resources, and then adapt and implement them in each other’s classrooms.

To keep up with the events happening in her classroom, follow Mrs. DeLoach on Twitter: @MrsDDeLoach.

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