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.