2.2 Lesson Importance

2.2 Lesson Importance: The structure of the lesson allowed students to engage with and/or explore important concepts in mathematics or science (instead of focusing on techniques that may only be useful on exams).

This indicator measures the degree to which the lesson was structured to allow students to grapple with relevant mathematics or science concepts and become engaged in learning. This engagement may happen through discovery, exploration or laboratory activities, but this is not a necessary condition of the indicator. For example, a well-structured lecture can enhance students’ abilities to engage with the content if it’s communicated clearly, timely, connected to students’ prior knowledge, experiences, and interests, and allows students to actively participate during the lesson. This type of lesson is contrasted with a structure that focuses only on techniques for exam preparation. A lesson rated highly on this indicator is structured to allow students to understand and engage with both underlying concepts and problem-solving procedures/processes rather than simply perform the procedures without exploring what concepts these procedures are built upon. In a lesson rated highly on this indicator, the lesson will be structured such that students will build meaning and have ownership of important mathematical or scientific ideas.

General Rubric

1. This item should be rated a 1 if the structure of the lesson did not allow students to either engage with or explore concepts in mathematics or science.
   
    
2. This item should be rated a 2 if the structure of the lesson occasionally or sporadically (only 20–30% of the time) allowed for student engagement in mathematics or science concepts.
   
    
3. This item should be rated a 3 if the structure of the lesson allowed students to engage with and/or explore the mathematics or science content, but these opportunities were only in place during the lesson approximately 50% of the time.
   
    
4. This item should be rated a 4 if the structure of the lesson allowed students to engage with and/or explore mathematics or science concepts for most of the class period (80–90% of the time). There may have been a minor missed opportunity or small portion of the lesson that was not designed to be as engaging.
   
    
5. This item should be rated a 5 if during most (greater than 90%) of the class period, the structure of the lesson allowed students to engage with and explore important mathematics or science concepts. This was a continuous and explicit focus of the teacher’s plan, and the structure and sequence were clearly designed to ensure that students remained engaged throughout the entire class period.

Specific Examples of Supporting Evidence

1. During the class period, the teacher’s plan was to introduce the students to a simple mathematical procedure while they silently and independently took notes at their desks. The teacher modeled a number of instances of this procedure on the overhead projector while the students copied them down in their notes. The structure of the lesson did not provide for any mechanism for students to engage with or explore the content—the problems being worked were closed-ended, and the teacher’s plan was to explicitly model every step. The only type of questions the teacher had prepared to ask the students was for the number that the teacher would write in the next step of the problem she solved for them on the overhead.
   
    
2. During the warm up portion of the lesson, the teacher’s introductory lesson structure did not elicit elements of student engagement or exploration. During the group work portion of the lesson, the students were assigned a relatively engaging investigation, but the math concepts were secondary to the main objectives for the lesson; the focus and the majority of time spent was on procedures, “cookbook” lab processes, and collecting data. The lesson structure did not provide opportunities for students to become engaged with or even made aware of the mathematical ideas central to this lesson or the scientific concepts underpinning the phenomena they were to observe and explore.
   
    
3. The movie clips the teacher showed and the sound files the teacher played were clearly chosen and sequenced appropriately to allow students to engage with central concepts of the lesson. The design of the worksheet also allowed students to engage with and further explore the content using interesting, real-world pictures, scenarios, and phenomena they could recognize or had prior experience with. However, the lesson segments that reverted to student note-taking followed by teacher-centered demonstrations of procedures or manipulatives were a missed opportunity for students to engage with or explore the concepts on their own—they were non-interactive for approximately half of the class time.
   
    
4. The lesson design incorporated instructional strategies that included giving challenging problem-solving tasks to the students and having students solve them either as a whole class using multiple strategies or in small groups as the teacher circulated and provided feedback. At the end of the class, the students were able to further explore and explain their understanding of the content by creating their own problems for other students to solve. The sequence of the lesson used a real-world application launch activity that enhanced students’ ability to engage in the content, although this was not brought up again in the lesson segments that followed throughout the lesson.
   
    
5. The instructional strategies included group and then whole-class discussions over a story/scenario about a student that was trying to solve a dilemma using mathematics—the small amount and poor quality of recreational space that schools in poor neighborhoods have compared to schools in rich neighborhoods. Students were engaged in the story and discussed how it related to their lives and experiences. The teacher’s plan was to use these discussions to introduce a unit that would result in a group project—to develop a plan for a space-efficient and high-quality playground for a school in their community. The project was clearly designed to create opportunity for students to explore multiple approaches by conducting research using books and computers and engaging in discussion with their peers and the teacher. Following this introductory segment, and in completing the project, students would be challenged to apply mathematics and science concepts in a manner that gave them a lot of freedom to explore their ideas and be creative.