1.1 Classroom Engagement

1.1 Classroom Engagement: The classroom environment facilitated by the teacher encouraged students to generate ideas, questions, conjectures, and/or propositions that reflected engagement or exploration with important mathematics and science concepts.

This indicator captures how well the classroom environment established by the teacher supports students in exploration of mathematical or scientific ideas and deep engagement in mathematical or scientific thinking. Such a classroom can be described as one in which students feel free to ask questions, engage in critical discussion, make predictions, suggest approaches to exploration or problem solving, and challenge statements of the teacher and other students in order to propose alternate methods or deepen understanding of fundamental concepts. It is also one in which the teacher devotes a sufficient amount of time to addressing students’ questions, comments, misconceptions, and nascent ideas related to the subject matter.

In other words, there is a culture of learning. A classroom rated highly on this indicator creates multiple opportunities and provides rich evidence for student–student discussion and argumentation, with students encouraged to reflect on their own learning.

To rate this indicator, make note of instances during the lesson where you observe students generating ideas, questions, conjectures, or propositions. Keep in mind that giving a simple response to a direct teacher question is not really “generating an idea,” and that asking a simple clarification question does not reflect deep student engagement with the mathematics and/or scientific content and concepts.

General Rubric

1. This item should be rated a 1 if there were no examples of students attempting to or being encouraged by the teacher to generate their own ideas, questions, conjectures, or propositions, and no significant intellectual engagement was observed.
   
    
2. This item should be rated a 2 if there were only occasional examples of students generating nascent ideas and questions, these contributions were of low quality, and the teacher did not respond in a manner to draw out the students’ thinking.
   
    
3. This item should be rated a 3 if there were several examples of students generating nascent ideas, conjectures, and questions of medium quality during the lesson, and the teacher was making moves to encourage these contributions. However, the teacher missed several opportunities to elicit and elaborate on students’ thinking in an open discussion.
   
    
4. This item should be rated a 4 if students generated ideas and questions of medium to high quality during the lesson and the teacher regularly made attempts to elicit further student thinking and encouraged other students to contribute. The students also offered some of their own conjectures or propositions, and these offerings demonstrated clear engagement with the content. Perhaps there was a missed opportunity by the teacher that could have facilitated deeper student learning.
   
    
5. This item should be rated a 5 if students were highly engaged in the content and consistently offered high-quality ideas, questions, propositions, and conjectures. The teacher facilitated these contributions throughout the majority of the class period, allowing for deep and meaningful student learning opportunities.

Specific Examples of Supporting Evidence

1. There were no ideas, conjectures, or propositions generated by students during this class. Only one student asked a question. The teacher worked at the board, moving from one step of the problem she posed to the next, only stopping to get the student input as necessary to ensure that the students were awake. The teacher showed students how to do each step of each problem or talked them through each part of the lab activity from beginning to end, not asking for students to predict what might happen before doing the activity or propose their own approach to solving the problems. The teacher did not elicit students’ thoughts or strategies.
   
    
2. There was some evidence of students generating ideas, questions, or conjectures during the whole-class portions of the lesson. The students did seem to be talking about their assignment during the group work portion of the lesson, but the ideas generated were related to collecting data or the procedures for manipulating the variables in the equations or which step in the lab procedure was next, since the mathematics content and/or science activity was straightforward. Occasionally groups would call on the teacher when they had a question about whether they were “doing this right,” and the teacher would respond with a simple “yes” or “no.”
   
    
3. The students in this class seemed to be comfortable proposing and sharing their strategies and ideas for solving problems and were not afraid to make mistakes in front of the teacher or their classmates. There were some instances of students generating interesting questions and proposing original ideas about their work, and, although the teacher seemed to welcome these comments, she did not probe their ideas to encourage higher-level reasoning or get them to elaborate on their propositions/conjectures. One student discovered an important mathematical pattern, but he generated this conjecture on his own and was not prompted to share his idea with the whole class.
   
    
4. There was frequent evidence of the students explaining their reasoning to each other or the whole class and the teacher asking for multiple approaches and strategies. The teacher also asked for conjectures relating to how the mathematics and/or science content related to the world and human activity. At one point in the class, students questioned the teacher and challenged the strategies she was using to solve problems because they held some misconceptions about the underlying mathematics and science content. The teacher chose not to open this misconception for student discussion but instead carefully showed the students where they had “gone wrong” in their solution strategy. Overall, there was a congenial atmosphere for conjectures, questions, and ideas on how to solve mathematics problems or conduct scientific experiments, and many students were engaged.
   
    
5. The students in this classroom were constantly generating high-quality ideas, conjectures, and propositions. They frequently and persistently asked each other questions about solutions strategies and provided thoughtful comments to each other’s propositions. They also backed up their own propositions using evidence and analysis of data, presenting graphs and charts or citing and sharing valid resources found on the Internet. Because the conversation was so free and rich, the teacher noted a recurring misunderstanding revealed in the student talk and, at that point, she stopped the class and used probing questions to facilitate an open discussion that unpacked the underlying misconception for the whole class or the small group.