4.2 Content Fluency: Content communicated through direct and non-direct instruction by the teacher is consistent with deep knowledge and fluency with the mathematics or science concepts of the lesson (e.g., fluent use of examples, discussions, and explanation).
This indicator assesses the degree to which the teacher demonstrates deep knowledge and fluidity with the content, as evidenced by the teacher giving detailed and clear explanations, using the big ideas of the content area as a unifying theme, calling attention to applications of the concepts being taught, and fluidly using examples and connections within the subject area. The teacher’s depth of subject matter knowledge can also be assessed by observing how his or her understanding of student mistakes, common misconceptions, or alternative ways of thinking about and solving problems is used to help build student knowledge. The teacher’s fluency with the discipline can also be evidenced by skillful facilitation of group discussions using probing questions to guide students’ thinking, as well as the ability to give clear and, if needed, multiple examples and to use different methods for the explanation of concepts.
General Rubric
- This item should be rated a 1 if there was a significant issue with the teacher’s understanding and/or communication of the content that negatively impacted student learning during the class period.
- This item should be rated a 2 if there were several smaller issues with the teacher’s understanding and/or communication of the content that sometimes had a negative impact on student learning.
- This item should be rated a 3 if there were no issues with the teacher’s understanding of the content and its accuracy, but the teacher was not always fluid or did not try to present the content in multiple ways. When students appeared confused, the teacher was unable to reteach the content in a completely clear, understandable, and/or transparent way such that most students understood.
- This item should be rated a 4 if the teacher clearly understood the content and how to successfully communicate the content to most students in the class. The teacher used multiple examples and strategies to engage students with the content. The teacher’s depth of content knowledge enhanced student learning.
- This item should be rated a 5 if the teacher clearly understood the content and how to successfully communicate the content to all students in the class. The teacher was able to present interesting and relevant examples, explain concepts in multiple ways, facilitate discussions, connect the content to the big ideas of the discipline, use advanced questioning strategies to guide student learning, and identify and use common misconceptions or alternative ideas as learning tools. The teacher’s depth of content knowledge greatly enhanced student learning.
Specific Examples of Supporting Evidence
Science
- The teacher’s lecture on using balanced chemical equations to solve stoichiometry problems was very confusing; he kept changing what he was saying and correcting himself and was constantly referring to the example from the teacher’s guide, which he had presented on the overhead projector. The teacher did not check if the students understood, and, even though some of the students called out questions or made suggestions about how to solve the problem, the teacher did not appear to listen or respond to them.
- The teacher was able to go through and discuss each step of the example stoichiometry problem on the overhead projector—using a pre-printed overhead master from the teacher’s guide materials provided by the publisher. However, when the students asked the teacher to explain a homework problem on the board, the teacher confused himself and the students because he forgot to balance the chemical equation before setting up the stoichiometric ratios of reactants to products.
- The teacher illustrated how to solve stoichiometry problems step-by-step at the board, starting with balancing chemical equations, predicting the appropriate products given certain reactants, and then applying correct stoichiometric ratios to calculate masses of products that could be formed. The teacher was able to answer students’ questions by using another problem, starting from the beginning each time and carrying out each step in sequence. Some students seemed unable to predict appropriate products when given reactants, and the teacher did not address this by connecting to their previous work on identifying types of chemical reactions; he simply repeated, with emphasis, each step that he had written on the board.
- Before beginning to illustrate how to solve stoichiometry problems step-by-step on the board with the whole class, the teacher had each group of students complete a warm up activity that connected to their prior work with predicting products of reactions and refreshed their ability to characterize types of chemical reactions from the reactants given. Once most of the students successfully demonstrated this skill, the teacher had each group write a balanced chemical equation for a different set of reactants, then go to the board to solve for the mass of products that could be produced, step-by-step. The teacher monitored each group’s work, facilitated with questions to those working at the board and those watching in class, and then used the student examples to explain and correct any mistakes.
- The teacher began this lesson on solving stoichiometry problems with a warm up activity that connected to and assessed the students’ ability to predict products of a reaction by recognizing and characterizing the type of chemical reactions possible given specific products and conditions. Once most of the students successfully demonstrated this skill, the teacher introduced the concept of stoichiometric ratios as recipes for chemical reactions by describing how she modified a recipe for chocolate chip cookies when she only had one-half the amount of chocolate chips to use. The teacher had each group write a balanced chemical equation for a different set of reactants and go to the board to solve for the mass of products that could be produced, step-by-step. The teacher monitored each group’s work, facilitated with questions to those working at the board and those watching in class, and then used the student examples to explain and correct any mistakes.
Mathematics
- This teacher’s lecture was very confusing. The teacher kept changing what he was saying and correcting himself and was constantly referring to his notes. The teacher did not check whether the students understood, and his explanations were disorganized and unclear.
- The teacher was able to clearly communicate the procedures for operations on matrices but had a lot of trouble addressing students’ questions about the process responding when students said they didn’t understand.
- The teacher’s board work was clear. The teacher showed all of the steps and began each problem by writing down the equation that was going to be used to solve the problem. The teacher gave the students an algorithm/list of steps for solving linear inequalities. The teacher’s examples were sometimes difficult to connect to the lesson. For example, the teacher gave a real-life example of a concept that didn’t make sense.
- The teacher seemed competent to deliver the content, give real-world examples, and field occasional question from the students, even if the question was not something directly related to the day’s prepared content. The teacher seemed to have a lot of knowledge about the applications of what being taught and integrated this discussion throughout the lesson.
- The teacher was consistently able to explain the concepts of the lesson in more than one way and often did this even without being prompted to by students. He regularly used real-world applications to make the content more understandable, fluidly moving between examples and strategies, and was able to clear up student misconceptions and incomplete understandings without any issues or hesitance.