In 2010, there were seven teachers in the Las Montanas High School math department (see post of August 7, 2010). During my study of the school, I had collected 18 observations of lessons in their classes. Administrators gave me copies of what they called “Walk Throughs” (12) or when the principal or assistant principal spent 10-15 minutes watching a lesson and jotting down notes on a form. My observations (6)–which no administrator saw–were of the entire lesson (56 minutes) from the beginning of class when the tardy buzzer sounded to when the chimes ended class.
These experienced teachers (most had 10-plus years in classrooms) used computers daily at home and school, according to their questionnaires. A few years ago, interactive white boards (IWB)–see post of March 17, 2010–were installed in each math classroom. Teachers received training from the vendor. For the most part, these seven teachers used their IWBs daily; only a few combined the IWB with student laptops in class.
Like other academic departments at Las Montanas, math teachers were very aware of the California Standards Test (CST) and the consequences of low math scores. In 2004, when the school was on academic probation, the math department decided to use district-developed benchmark tests to prepare for the annual CST. In 2009, I observed a Geometry lesson taught by a veteran teacher.*
Twenty-five 10th grade students (mostly Latino with a scattering of whites and African Americans) sat at desks arranged in rows facing the IWB and teacher’s desk. On the walls were lists of what the teacher expected in student behavior, posters about the importance of math in daily life, examples of student work, and assignments for the three different math classes that she taught. On the IWB was an agenda for the day’s lesson.
After the tardy bell rang, the teacher said: “You need to bring your laptops tomorrow to prepare for next benchmark test.” She then directed class to do the “warm-up” listed on the IWB. These daily “warm-ups,” a staple of high school math lessons, can range from riddles to unusual tasks to specific math problems related to day’s material. This warm-up dealt with the surface area of a prism.
All students worked on the warm-up. After five minutes, the teacher asked a student to go to the IWB and give his answer as well as how he had worked it out. Taking the stylus, an electronic pen, the student swiftly laid out the answer and how he did it. The teacher checked out his answer on a calculator that appeared on the IWB after a tap from her pen. She asked how many students had the answer to the warm up; most raised their hands. She then segued to the textbook homework for today’s lesson on “scale factor.”
Teacher penned the question on the IWB: What is Scale Factor? Some students called out answers and others raised their arms. After listening to answers, she gave further examples that were in textbook. She tapped the IWB to use figures that she had entered from her laptop that morning on “Similar Solids.” Laid out on IWB were words “Shape, Scale, Surface Area, and Volume.” She walked around the room and up-and-down rows as she explained each concept and gave examples. She took questions from three students who had their laptops out. They were looking up math URLs that the teacher had given the class earlier in the semester. I noted that nearly all of the students were attentive or whispering questions to nearby classmates about the words on the IWB.
Teacher returned to IWB to give an example of a cube with a 1:1 ratio on scale, surface area, and volume going to a cube with a 1:3 ratio on each. She explained the example and then asked: Can you see pattern?” A few students nodded their heads. She asked one of the nodders, “what pattern do you see?” Student responded and she then asked a non-nodder. Student said she was stuck. Teacher then used example of a Baskin-Robbins ice cream cone doubling and tripling volume and surface area with additional scoops. What would the scale be?, she asked class. A few students gave correct answer. Then she returned to cube that is at a 1:3 ratio and asked what happens if it goes to 1:5?
Teacher then directed class to work in pairs for the rest of the period to answer that question. She walked around, answering student questions and talking with individual students. Five minutes before the end of the period, she gave the assignment for the next day. Students worked until the chimes rang ending the class.
Is this description of her lesson on “scale factor” an instance of “good” teaching?
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*I take notes every few minutes for the entire lesson of what the teacher is doing interspersed with notes of what different students are doing.
Larry Cuban on School Reform and Classroom Practice 
Good question at the end.
I always wonder this: Does teaching have to be scalable? What is important about being able to scale a method to masses of teachers?
If the answers to those questions are for cookie-cutter curriculum to be developed, then we are missing the issue. Scaling a method of presenting material, if done for the sake of publisher-profit should not be the purpose of developing presentation methods.
If the students in this teacher’s class learned what they needed to learn, then this was an example of good teaching. Good learning is the result of good teaching. If this teacher uses this method, and it works for the students in that classroom, then the teacher should be given the professional courtesy of continuing to use the method.
If that same method does not work in Nebraska, or Florida, or anywhere else, then should it be scaled and forced upon the teachers and students in those locations? Does it make the method in California less valuable? I say, “No,” in answer to both questions.
Teaching is being treated too much as a science, without regard for the fact that students may not share common characteristics throughout the country. Teaching is just as much an art as a science, and if a teacher is able to get the students to learn what is to be learned, then the objective is achieved…regardless of scalability.
I found this post very thought provoking, like your other posts. My knowledge of teaching is zip, so I don’t have any idea if this is a “good teaching” or not, but you certainly have me interested!
I don’t know that “good teaching” can be fully assessed from a description of one class. Your description certainly sounds promising (students sound engaged, are actively working together on the task at hand)… but much also depends on what happened the class before, the class after, and on whatever assessment this is heading towards. My definition of “good teaching” is hugely dependent on curriculum/syllabus too, and includes:
– engaging students effectively (how to do this varies tremendously from one class to another)
– helping students grasp the key concept(s) (too many texts emphasize procedures over concepts)
– helping students master the key skills/procedures (sometimes they are not obvious, despite having a good grasp of the concept)
– helping student connect both of the above to related concepts/skills/procedures (the more something is connected to both existing and future knowledge, the more likely it is to be remembered well)
– emphasizing and assessing understanding, not reproduction or memorization of procedures
A “good teacher” who is following a poor curriculum/syllabus without adapting it to the class’ needs can have weak results. I think it takes a combination of a good teacher and a good curricular approach to produce “great” results, but the definition of what is “good” will vary by class, school, and culture.
So, it helps to agree on desired overall outcomes, but we need to allow for a some variation in how they are measured and achieved.