The TfP project members have created an Observation Protocol for Active Learning (OPAL) designed for two purposes: research and professional development. The project members envisions OPAL to serve as a framework for observing the teaching and learning of mathematics, with a focus on active learning in community college settings.

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History

As part of the TfP project, faculty researchers have created the Observation Protocol for Active Learning (OPAL). The goal of this observation protocol is to serve as a framework for observing teaching of mathematics, with a focus on active learning, in community college settings. After much effort to find an observation protocol to meet the needs of the project, TfP personnel decided to create their own, unique tool and named it OPAL. Active learning and the accompanying student learning are complex endeavors. OPAL brings together several frameworks in an attempt to capture and measure this complexity of teaching and learning mathematics in an active, student-centered classroom. OPAL is designed to measure a particular worldview when it comes to the teaching and learning of mathematics. In short, this worldview holds that students should be actively engaged in making sense of mathematics ideas as they develop strong problem-solving strategies, both of which can be transferred to further academics, career, and life. This worldview stands in contrast to the traditional worldview where students are mostly asked to mimic computational procedures that could have been completed by a machine. As Jordan Ellenberg explains in his book How Not to Be Wrong: The Power of Mathematical Thinking, a math teacher has to be a guide to good reasoning, and “a math course that fails to do so is essentially teaching the student to be a very slow, buggy version of Microsoft Excel. And, let’s be frank, that really is what many of our math courses are doing.”

Purpose

The purpose of OPAL is to serve as a tool to better understand and capture the desired elements of teaching and learning mathematics at the community college level when the learning occurs through an active and engaging process. The OPAL tool includes 12 traits clustered into 4 themes to capture research-based features of effective active learning. The order of the themes, summarized below, is intentional. First, it is important to think about the important mathematical ideas (Theme 1) in order to design powerful lessons (Theme 2) that include discourse (Theme 3) and support high quality instruction for all students (Theme 4). 

Theme 1: Making Sense of Mathematical Ideas

The first focus is on mathematics and students’ deep thinking about the mathematics and is paramount above all other traits. Developing mathematical habits of mind (Trait 0), fostering conceptual understanding (Trait 1), and making connections (Trait 2) is the focus of this theme.

Theme 2: Lesson Design and Implementation

The second focus is on lesson design/intentions and being purposeful about the learning trajectory. Starting with learning goals (Trait 3), targeting tasks to meet those goals (Trait 4), implementing the lesson with questioning in mind (Trait 5), and using mathematical tools (Trait 6) is the focus of this theme.

Theme 3: Active Learning and Classroom Discourse

The third focus is on fostering active learning through discourse. Facilitating meaningful mathematical discourse (Trait 7) through precise communication (Trait 8) and justifying and critiquing thinking (Trait 9) is the focus of this theme. 

Theme 4: Mathematical Mindsets and Equity

The fourth focus is on cultivating student mindsets that are productive for learning. Developing student perseverance and mathematical prowess (Trait 10) is key to cultivating such productive mindsets. Maintaining equitable and high expectations for all students (Trait 11), regardless of their mathematical journey, is the focus of this theme.