I observed an Algebra 2 class at Hacienda (pseudonym), a Northern California high school, on September 9, 2016. The high school has over 1900 students, mostly minority (Asian and Latino). About 20 percent of the students are eligible for free and reduced lunch–a measure of poverty used in U.S. public schools. Over 98 percent graduate and a very high percentage of those graduates enter college. About one-third of students take Advanced Placement exams with well over 80 percent qualifying for college credit. Less than 10 percent of students are English Language Learners and just over that percentage have been identified with disabilities. This is a high school that prides itself on academic and sports achievements and is recognized in the region, state, and nation as first-rate.
Beverly Young (pseudonym) is a veteran teacher of 22 years at Hacienda. A slim woman of average height, wearing black slacks, white blouse with a beige sweater, she has been department head and very involved in coordinating the math curriculum at the school. Since 2008, she has embraced different technologies for the efficiency they brought to her in making out quizzes and tests and their help in connecting to students. She has been using an iPad with educational apps particularly Doceri for her math lessons since the tablet appeared.
The 50-minute lesson on Friday morning went swiftly by as the fast-paced, organized teacher taught about factoring quadratic equations. Announcements about upcoming quiz are posted on bulletin board next to whiteboard: “9/14—9/15, Quiz 4.1 to 4.2” –and upcoming test—“9/21—9/22, Test on 4.1 to 4.4.” The numbers refer to textbook sections.
There are 26 students in the room sitting at five rows of three desks next to one another, all facing the whiteboard. Young, carrying her iPad with her as she walks around, uses a remote to post slides and videos on the whiteboard during the lesson.
For the first five minutes, Young shows a video about the Rio Paralympics. As students watch the brief video, Young, holding her iPad, walks around recording who is present and then stamping homework that students had laid out on their desks. I look around the class; they were watching intently athletes with disabilities who perform extraordinary feats.
Two minutes later, school announcements appear as a video on the whiteboard. Hacienda students prepare the daily announcements. A student anchors the announcements showing clips prepared by other students for different daily and weekly school activities (e.g., upcoming mini-bike racing event in Quad). In most schools where I observe classes, announcements are on the public address system and generally students ignore them as they drone on. I looked around and saw that all but a few of the students watched each announcement.
After announcements end, Young turns to the lesson for the day. The slide on the whiteboard is the objective for the day: “Factoring and Solving x²+bx+c=0.” She asks if there are any questions on the homework. No hands go up. Young then passes out handout for the day and directs students to go to Google Classroom on their devices (I see those students sitting near me have a mix of different laptops and tablets). She then asks students to go to Socrative, a software program, and gives instructions how they should login. She walks up and down aisles to see what is on students’ screens. After all students have logged in, she clicks on a short video that explains factoring quadratic equations by using an example of jellyfish.
Young explains what the key terms are, the different variables described in video and then applies it to factoring. She gives examples of binominals and asks questions as she goes along. She encourages students to talk to one another if they are stuck. She walks up and down aisles with iPad in hand as students answer. She then reviews binominals and moves to trinominals. “Now, look at polynominals.“ One student asks for clarification of terms. Young clarifies and asks: “You guys understand?” A few heads nod.
(For readers who wish to delve into the details of this lesson’s content, the teacher has made a five minute YouTube video for students that explains the content of this lesson.)
Young moves to next set of slides about “x intercepts” and examples of “distribution.” She then asks: Why do we do factoring? A few students answer. Young explains what the key points are and the differences between factoring and solving an equation. She asks students more questions, encouraging them to talk to one another to figure out answers.
The teacher segues back to a Socrative slide and to a question that she wants student to answer.
Young encourages students to help one another—as she circulates in the room. “If you don’t remember, write it down. It’s OK.” She checks her tablet to see what each student is doing and says aloud—“I see two guys who got it right—I am waiting for 15 of you guys to finish—talk to one another.” A few minutes later, looking at her tablet, she says—“most of you got it. I will give you another minute—I am waiting on eight more here.”
She talks to individual students answering questions and complimenting students as she traverses the aisles.
“Looks like most of you have the idea,” she says.
I scan the class and all students have eyes on screen, and are clicking away or whispering to a neighbor what appears to be an answer to the teacher’s question.
“Now you guys work on the second question.” She chats easily with students—“do you have answer here?” she asks all the while checking the iPad she carries around.
She then directs class to go to next question. “Do it and give me an answer for this—it’s a little tricky. You are more than welcome to ask one another.”
One student asked a question and then the teacher used the student question to correct misconception about solving a quadratic equation. Young answers the student and refers back to jellyfish video.
In scanning the class, all students look engaged. “If you guys have an answer like this—pointing to what she wrote on the whiteboard, then you got it wrong. Here’s a little hint—[could not catch what teacher says]. I’ll give you another 50 seconds—I just want to see what you guys remember”
Again, checking her iPad she can see each student’s work and can help student in real time as she cruises through the classroom.
“Now let’s go to fun stuff.” After she posts slide from her iPad on the whiteboard on how to factor trinominals, Young explains each problem.
Young sees that some students are confused so she starts over. She continues to work on the numbered problems appearing on the slide, explaining what she is doing at each step. Then, she asks students to factor particular parts of equations. She checks her iPad and says: “I hear guys having an answer already—that’s great!”
“When is a 9 equal to zero or a plus nine equal to zero—now can you answer no. 8?” Students talk to one another, as I scan the room. Young circulates and listens to different students to further explain if they are stuck.
She asks: “Are we ready?” Teacher walks students through how she solves problem on whiteboard using the iPad. She then asks whether students know the difference between factoring and solving. One student says yes. She then asks students to jot down their answers to central question of the lesson —she walks around and talks with students as they click away.
The teacher ends class a few minutes before bell rings and then talks to different students, answering their questions. Other students begin packing up their things to await the end of the class. Bell rings.
Larry Cuban on School Reform and Classroom Practice 
Thanks for a description of a lesson that was math based and not a unit intro lesson. This was a lesson on a topic that is typical in an algebra class so it is very interesting.
A few things I see
1) tight organization and focus, although I don’t see the para Olympic connection. Maybe a school focus?
2) carefully chosen examples for students to try
3) traditional” I show and now you do” format ( traditional does not mean bad or ineffective)
4) compliant students
5) tech allowed teacher to,perhaps, be out among students, although I am not sure if it is radically more than with any other presentation device of the past 20 years or more.
What I didn’t see:
1) students being asked for their reasoning or explanations verbally or written. I maybe wrong but it appeared that the teacher only received their final answers. There are lots of ways to get right answers doing wrong math. Where did they do their mathematical work? Paper & pencill? Stylus & screen?
2) examples of what the students talked about. I’m going to call out the line about ” whispering to each other about the teachers question”. Do we know that ? This phrase seems to need your usual qualifier of “appears to” as when you write of engagement
These last two missing parts worry me because I have seen my students working together unproductively with one student mostly giving answers to another. They are talking but not necessarily learning. In math and math based science classes, we want to see the work of our students. The barriers to this via a math editors on screens has been a topic of conversations at my school.
Yes, Alice, in 1 and 2 under “What I didn’t see” did not occur during the 50 minutes. And, yes, I will add “appears to.” Thank you for your comments.
Penultimate paragraph –
One student says yes.
Thanks for comment, Howard.
#Alice in Pa raises a number of good points and concerns. The description of this lesson makes me feel like you saw the sort of class that would readily pass muster with a lot of people both in education and out. If the class appeared to be well-behaved and on-task (“appeared” being the operative term), the teacher would get high marks. Whether much learning was going on and how many students were, in fact, far more confused than is evident is another matter entirely.
The technology here is useful and allows the teacher to get some idea of what students might be able to do, though we can’t be certain that answers on computation questions always reflect understanding (particularly individual understanding if it’s quite possible for kids to just copy from other students). But it’s hard not to like the idea of quick input. The nature of that input and how the teacher interprets and uses it are open for interrogation.
Somewhere, however, there has to be some chance for students to explain and question, and for teachers to probe more deeply. The “efficiency” here seems to override depth. It’s only one lesson, of course, but if most in this class run this way, I’d be surprised if students are doing much thinking past “how do I get the right answer to this computation?”
Thanks for the comment, Mike. Impossible for me to generalize beyond the one lesson.
My post on using the “rectangle” to multiply binomials and beyond is one of the most heavily viewed on the site. https://educationrealist.wordpress.com/2012/09/14/binomial-multiplication-and-factoring-trinomials-with-the-rectangle/
She’s only teaching a 50 minute class, but it appears that she’s teaching it in a pretty traditional way. The bigger issue, I think, is whether the kids can take that understanding to a higher level, and whether the lower level kids are given enough time to absorb and practice. I take much longer on this, myself.
Thanks for providing the link to your lesson on multiplying binomials and beyond. And whether students, much less “lower level kids,” are given sufficient time to absorb and practice, I cannot say for the time I observed. But I did not observe subsequent lessons. Thanks for taking the time to comment.