Increasing Rigor with Worked Examples
According to Robert J. Marzano in Understanding Rigor in the Classroom, “knowledge that has been proceduralized can be turned into worked examples” (Marzano, Understanding Rigor in the Classroom).
A worked example, as explained by Hattie’s research with Visible Learning, is “a problem statement with step-by-step guidelines for finding the solution. Worked examples enable students to focus on discrete problem-solving tasks, rather than attempting to hold each of the steps in their working memory while solving a complex problem.” (Hattie, Metax). Marzano says, “the cognitive analysis process of comparing can enhance the rigor with which students execute procedural knowledge.” (Marzano, Understanding Rigor in the Classroom).
We created a Desmos activity that models the process of a worked example with the algebra concept of solving quadratics by factoring. Click here to access the lesson and read below for more explanation of the slides.
Desmos Slides:
Slide 1: Students will order the steps for a new problem based on the given worked example.
Slide 2: Students will check their accuracy of ordering on this slide, go back and adjust if needed, and if correct, they can move on to generalize the steps with an explanation.
Slide 3: The teacher will gather student answers from Slide 2 and facilitate a class discussion to make one combined list of steps and “fix any bugs” that might have resulted from student explanation. This enables students to reflect on “how their thinking changed” while providing formative assessment data to the teacher.
Slide 4: Students complete a new example, comparing their process to the worked example and the generalized steps.
Slide 5: Students will reflect on one more formative assessment summary question- “what is one thing you learned about solving a quadratic?”
This Desmos worked example is a snippet of a lesson on solving quadratics by factoring. From here students can engage in an activity independently or collaboratively to complete additional solving quadratic problems and deepen their understanding.