**Kristina Rizga is a journalist who spent four years observing and interviewing teachers and students at Mission High School in San Francisco. Her book called Mission High (New York: Nation Books, 2015) contains descriptions of both students and teachers inside and outside classrooms.* Mission High School has 950 students with the vast majority coming from Latino, African American, and Asian American families. Seventy-five percent are poor and 38 percent are English Language Learners. **

**What distinguishes Rizga’s book from so many journalist and researcher accounts about high schools with largely minority and poor students are two facts: First, she spent four years–a life time to researchers–at the school. Few researchers or journalists ever spend more than a year in a high school. The second fact is that Rizga addresses a long-time paradox buried at the core of U.S. schooling in an age of reform when federal and state mandates (No Child Left Behind) label many schools as failing. The paradox is straightforward. Mission High School had been tagged as a failing school–“low performing” is the jargon of the day–and had been a step away from being shut down through No Child Left Behind rules. Yet 84 percent of its graduates were accepted to college, attendance rates have risen above the district high school average and suspensions have fallen between 2008 and 2014 nearly 90 percent. As one student put it: “How can my school be flunking when I am succeeding?” Indeed, the contradiction of a school labeled by authorities as failing, succeeding with students beyond what other district high schools achieve is the puzzle that Rizga unravels in this book. **

**With Rizga’s permission, I offer here descriptions of lessons in math, social studies, and English. The first is a math lesson taught by Taica Hsu, a seven year veteran teacher.**

Taica [Hsu] came to Mission High right after graduating from Stanford in 2007 and has been teaching math for seven years he says, sitting in front of a large bookshelf that contains a small microwave, a sewing machine, and rows of books on algebra, CI math, statistics, and precalculus. He taught math more “procedurally” in the first two years at Mission and then more “conceptually” in the last five. Taica is convinced that the approach he learned at Stanford — which also informed the new Common Core Standards — is a better way to learn math and help more students like the subject.

“Approaching math conceptually is not just about doing calculations quickly or memorization,” Hsu explains. “You are still learning procedural fluency, but you are also seeing connections, patterns, choosing your own strategy in solving something and justifying it. You are seeing how it interprets and explains the world around you. It allows students to develop a more intuitive understanding and a deeper connection with math.”

It is nearly ten in the morning at Mission High, and a stream of eighteen freshmen has just entered the classroom for their Algebra I class. Rasheed, a tall young man with a head full of long, black braids, drops his backpack on the table. The desks are organized in rectangles, and students sit in groups of four. Rasheed sits down near Jenny, who noticed her friend as soon as he walked through the door.

Jenny is wearing thick sweatpants over her light blue jeans on this cool, grey February morning in 2011. She has been out sick for a week and has asked Brandon to help her finish her homework. “I believe you multiply first before you add here,” Brandon is explaining patiently while writing out every step of the solution on a separate piece of paper. “Jenny, you are really smart,” he adds. “You can do it. You just need to take your time.” Joaquin, a young man with a pink, boyish face partially covered by an oversized “Golden State Warriors” hat, walks in and stretches out on the two chairs at his desk. He puts his hat over his face and closes his eyes. Joaquin is about two heads shorter than Rasheed, who is a about a foot taller than the rest of his ninth-grade classmates.

Warm and charming, Rasheed is a formidable social force in the classroom. He can pull his friends away from work in an instant, but when class is in session, he uses that power to engage them with math. For now, before the bell rings, Rasheed puts his large headphones on Jenny’s ears and plays some songs for her. Shipra is trying her earrings on Jenny’s ears. Brandon throws a little paper ball at Shipra’s head and turns away sharply to hide his prank. Unlike their peers in the twelfth grade across the hall, these freshmen are buzzing with electricity as they are settling in their seats—shouting, joking, flirting, and fidgeting.

“And that was our bell,” twenty-seven-year-old Hsu says as he starts the class. He is dressed in a grey T-shirt, dark blue jeans, and turquoise Puma sneakers. “Happy Friday, everyone,” he greets the class as the noise drops. “I want to thank many of you who came to see me after school if you had any questions. I really appreciated that.”

“Please sit at the same table as on Wednesday,” he continues. “Start with the ‘Do Now’ and then continue to work on the ‘group challenge’ from last week. Remember, everyone needs to participate in the challenge. What are some ways in which we participate?”

“Asking questions,” students take turns answering. “Justifying steps. Answering questions of others. Asking for help. Plugging in numbers. Using resources from previous classes. Listening to someone else’s ideas.”

“Smart, smart, smart! Let’s get to work,” Hsu responds and starts walking around the classroom, gliding between the desks. Hsu’s colleague, special education teacher Blair Groefsema, checks in with the other tables that need attention. This class has seven students with special needs, including one student in a wheelchair who communicates through a voice-activated electronic device.

Within a few minutes, Hsu notices a common error as students work through the ‘Do Now’ exercise, in which they are reviewing skills and knowledge from their previous lessons. Several students have mixed up distribution steps today and solved 3(x+2) incorrectly, as 3x + 2**. **Hsu sits on the edge of his desk and reviews the correct sequence of the steps with his students. Joaquin gets up to view what Mr. Hsu is demonstrating more closely.

As the students get back to work, Hsu continues to move around the classroom quickly, with a calming presence—asking questions, naming different skills students are exercising, praising effort. “I see Jenny and Brandon are drawing boxes,” Hsu comments. “That’s a really good technique. I really like how Irene is referencing her homework to help her solve this problem.”

“Check your answers with everyone in the group before you finish,” he reminds them.

“Mr. Hsu, are these ‘like’ terms?” Jenny asks with her hand raised.

“Yes, they are. Can you combine them?”

“Yes.”

“What do you think you should do here, Joaquin?” Hsu walks over to the next table. “How did you get that answer?”

After the exercise, Hsu moves on to the group challenge, a multistep, “open-ended” math problem that students are asked to solve in a workshop-style group of four. Such exercises may or may not lead to a single answer, but they always allow for different paths to various solutions. Hsu says that open-ended problems illustrate the real depth of math for students and show them that math—like most things in the real world—requires multiple skills and approaches. “If you are only solving for ‘x,” Hsu explains to me after the class, “the problem has only one path and one solution. Students who get stuck on one, small step throw their hands up and say that they are not good at math. In open-ended group problems, students are more likely to keep trying. They realize that there are many ways to approach problems, and if you are not good at one part of math, it doesn’t mean that you are not good at all of it.”

Today’s group challenge is asking students to analyze and graph different types of lines—parallel, perpendicular, and intersecting—and solve for points of intersection. Students are asked to interact with each line as multiple representations—as a graph, equation, and a table—as well as to make a connection between solutions and visually represented points on the graph. The same lesson in a traditional classroom would be taught in narrower way, Hsu notes. Students might be asked to memorize the equations of the lines and a few conclusions without visualizing them as multiple representations. When students are only asked to solve the equation, they may not completely understand all of the connections. When students don’t make such connections, Hsu says, they are not learning deeply, but simply memorizing equations that are mysteries to them. Such knowledge is more likely to fade quickly.…

Following the group challenge, students do individual exercises in which they are asked to practice their skills and knowledge. As students do the work, Hsu walks around and provides personalized coaching. Individual practice time in Hsu’s classes is typically followed by a low-stakes “mini-quiz” without any help from the teacher. He reviews these quizzes at the end of each day to make notes on which students need extra help and adjust his lesson plans for the next day.

Traditional classrooms typically don’t follow this format. In most American classrooms, students watch their teachers lecture and model exercises at the front of the room. After a lecture or demonstration on the blackboard that many don’t fully absorb, students are then asked to practice tasks individually, some in class but most at home… Students who can get help with homework at home usually progress smoothly. Students whose parents work long hours or who can’t afford expensive tutors typically fall behind.

Such teaching allows for an efficient delivery of the standardized content. The problem is that this standardized approach doesn’t work, because no one is “standard,” Hsu argues. That’s why Hsu—along with his co-chair of the math department, Mary Maher, and other math teachers—has spent the last several years working to update the traditional script. Hsu’s classrooms function more like group-style workshops than like lecture halls. Students spend most of the time producing work, alone and in groups, talking about math to their teacher and peers, while Hsu provides individualized coaching.

“Who would like to present their findings?” Hsu asks.

The students in Rasheed’s group raise their hands.

“First of all,” Rasheed begins, pointing to equations on the projection, “how did we know that these lines are perpendicular? We saw that the line is crossing. Second thing we noticed is that slopes are switched around.”

“What’s the only solution?” Hsu asks.

“Four and minus one,” Jenny answers.

“Why?” Hsu probes.

“It’s the only place where the lines cross,” she adds.

“How did you know to go down three, and over two?” Joaquin asks.

“This part of the formula,” Rasheed points at the board.

“Does this make sense? Are we convinced?” Hsu turns to the class.

“Yes,” several students respond.

“Does anyone disagree?” he asks.

No hands go up.

“Time for a quick, individual check-in, everyone,” says Hsu, who calls tests and quizzes “check-ins” to help ease the testing tension.

“I’m not prepared for this test,” Shipra admits, clearly upset.

“I’ve seen you do these problems many times, Shipra,” Ms. Groefsema reassures her.

The students get to work. A young man trained in working with students who use electronic devices for communication, is helping a student in the wheelchair.

A few minutes later Jenny exclaims that she is done. So does Rasheed. Hsu walks over to them. Joaquin gets stuck and asks for help. He has forgotten how to pick numbers for the table to draw a parabola. Ms. Groefsema reminds him with a series of questions. He gets back to work. Hsu looks over Shipra’s quiz. She has mixed up the steps: added first, rather than multiplied, he tells me quietly. She was asking for help more than anyone today. She will need extra one-on-one work with Hsu and a lot more individual practice to help her develop self-reliance and more confidence.

The bell rings, and Hsu finishes collecting the rest of the quizzes.

“I am so smart, I can teach this class,” Rasheed says with a slight smirk on his face, as he looks back at Jenny.

_______________________

*Full disclosure: for this book, Rizga and I had several conversations about the history of school reform past and present. I also visited Mission High School for one day, saw three lessons, and interviewed the principal.

You note that Hsu’s approach, learned at Stanford, also informed the Common Core math standards (specifically the Standards for Mathematical Practice). Credit for making conceptual understanding de rigueur in math instruction is owed to the National Council of Teachers of Mathematics (NCTM) whose transformative mathematics standards were first published in 1989, long before Common Core and written by experts in both mathematics education and content.

Thanks for the comment. Kristina Rizga wrote about Hsu in her new book on Mission High School, not I. She will respond to your point although as I read the piece, Rizga did not imply that conceptual understanding of math either began or ended at Stanford.

Thank you for reading and adding this fact. In this chapter, as with all of my chapters on teachers in the book, I primarily focused on the intellectual history and evolution of these educators. I didn’t intend to imply that it’s where it started, but I think sometimes it may seem that way in a shorter excerpt.

Having worked briefly with Taica this summer, I can attest to his passion for, and dedication to, teaching mathematics via complex instruction (CI) infused with the National Council of Teachers of Mathematics’ (NCTM) mathematical process standards and National Research Council’s (NRC) strands of mathematical proficiency, from which the Common Core’s mathematical practices were drawn.

Thanks, Dave, for taking the time to comment. I wish you well in the new school year.

Thanks, Larry. It is going to be a GREAT year!

Thank you, Larry for excerpting sections of Mission High, and most importantly, for all of your guidance in the research process. Your book “How Teachers Taught: Constancy and Change in American Classrooms 1890-1990” was an indispensable resource as I was trying to make sense of all of the polarizing debates. There are thousands of books out there on education policy and politics and so few on the actual craft of teaching and its history.

Thanks for the generous words, Kristina. You had a fine piece in the LA Times today.