Superintendent Richard Carranza's Remarks on the Secondary Math Sequence

Superintendent Thoughts for the Evening – March 10, 2015, Richard Carranza 

1. What people are considering algebra is no longer algebra.

The pre-CCSS Algebra 1 course no longer exists. CCSS Math 8 and CCSS Algebra courses are much more rigorous than the Algebra 1 course of the past. The previous Algebra 1 course expected students to learn the procedural skills almost exclusively. In today’s CCSS Grade 8 and CCSS Algebra, students must learn those skills AND are also expected to explain their thinking and understand the thinking of others, which require conceptual understanding, as well as application of their knowledge to contexts that are novel to them.

Additionally, today’s more rigorous courses include content that was not previously part of the old Algebra 1 course, such as data analysis and mathematical modeling (which is using abstract math equations to explain and forecast real world problems). These are critical content pieces required for higher level math courses.

2. What did the old algebra consist of and what does the new 8th grade math consist of?

The content that defined an Algebra 1 course under the old California standards is now evenly divided between our new CCSS Math 8 course and the CCSS Algebra course.

  • CCSS Grade 8 Math now contains all of the content from the first semester of the previous Algebra 1 course (proportional relationships, linear functions, systems of equations, …) and is combined with concepts from geometry and statistics courses.
  • The new CCSS Algebra course includes the second semester of the old Algebra 1 course (quadratic equations, polynomials, …) as well as content not previously taught in high school math, such as mathematical modeling and categorical data analysis.
  • In the SFUSD, unlike other school districts across the state, we included over 300 math teachers who were involved in the writing, piloting, and revision of core curriculum in mathematics, based on the CCSS. Our approach has truly empowered our internal experts—our teachers—and has been validated by experts in the field of mathematics and mathematics instruction.

The inclusion of these new topics is vital to students being able to apply the mathematics in the 21st century. We live in a world in which the ability to evaluate and analyze data is paramount. Students in these two courses are learning to apply algebraic concepts and skills to real world contexts and situations, as is called for in our Vision 2025.

3. Regarding University admissions: What are you finding in terms of admissions? Could our sequence harm kids?

There is no one in the classroom, leadership, or on the Board of Education that wants to harm kids. It’s not what we do. SFUSD’s new course sequence allows all students who wish to take AP Math the opportunity to progress and take AP courses. By taking the more rigorous CCSS Algebra in 9th grade, Geometry in 10th grade, and Algebra 2/Precalculus in 11th grade, students can take AP Calculus (AB or BC) in their senior year.

If a student wishes to progress faster and take AP Calculus in 11th grade, they may “double-up” by taking Geometry simultaneously with an Algebra course during their 9th or 10th grade years. This practice has been allowed in the past at SFUSD high schools, this policy does not alter that practice.

As a case in point, consider this:

At one of our most high performing high school:

  • In 2012/13, 281 students took AP Calculus (either AB or BC) and only 2 were juniors. The other 279 were seniors.
  • In 2013/14, 369 students took AP Calculus. 9 were juniors and 360 were seniors. The 11 students who took Calculus before their senior year would easily be accommodated within the current policy.

Additionally: our goal is to ensure ALL students prepared for and enrolled in courses that will lead to college acceptance and success. Our Board of Education has been visionary in this regard with their adoption of the A–G requirements as the default requirements for an SFUSD diploma.

Yet, it’s ironic that 50 years post the March on Selma—where American citizens marched for the most basic of democratic ideals, the right to vote—and over 60 years post the US Supreme Court case of Brown v. the Board of Education, where the supreme court of the land reaffirmed that separate education is NOT equal, we are being accused of “only caring about black and brown kids.”

Then consider this:

At the same high performing high school previously mentioned, an analysis and breakdown of the students in AP math over the last two years found that:

  • In the 2012/13 school year, 453 students took AP math exams (either AP Calculus or Statistics), and in the 2013/14 school year, 475 students took either AP Calculus or Statistics.
  • We all should rightfully be proud of this statistic—and we are. However, upon closer inspection, there is a glaring and alarming trend.
  • Of the 928 students who took those AP Math courses at this high school over the past two years, only 7 were African American, and only 21 were Latino: NOT 7 and 21 percent, but 7 and 21 actual students. (At this school approximately 10% Latino student population, and 3% African American student population.) Our students are certainly not being served in separate facilities, but they are most definitely NOT being served equally. That will stop!

4. What is the appropriate age to make decisions regarding students’ ability to accelerate mathematically?

If we compress at middle school, we will be making these decisions when students are 11 or 12 years old. Students’ academic and social identities are far too nascent to make well-informed decisions. This stage of adolescent development is not optimal for such critical decision making and not supported by the research.

Why compress later?: (Quoted directly from the research of Dr. Alan Schoenfeld)

Depends on how you conceptualize what mathematics is and what it means to understand mathematics.

  • At one end of the spectrum, mathematical knowledge is seen as a body of facts and procedures dealing with quantities, magnitudes, and forms, and the relationships among them. Knowing mathematics is seen as having mastered these facts and procedures. That’s what has been the former math curriculum.
  • At the other end of the spectrum, mathematics is conceptualized as the “science of patterns,” an almost empirical discipline closely akin to the sciences in its emphasis on pattern-­seeking on the basis of empirical evidence. This is the promise of the common core math curriculum and the basis of our approach.
  • Why is this important? In my view (and the view of most mathematics experts), conceptualizing mathematics only as a “body of facts and procedures to master,” trivializes mathematics and severely impoverishes it—in much the same way that an English curriculum would be considered impoverished if it focused largely, if not exclusively, on issues of grammar.

Mathematics as a science of patterns, and as articulated by the new common core mathematics curriculum, renders mathematics as empowering to ALL students. Mathematically powerful students are quantitatively literate. They are capable of interpreting the vast amounts of quantitative data they encounter on a daily basis and of making balanced judgments on the basis of those interpretations. They can use mathematics in practical ways, from simple applications such as using proportional reasoning for recipes or scale models, to complex budget projections, statistical analyses, and computer modeling. They are flexible thinkers with a broad repertoire of techniques and perspectives for dealing with novel problems and situations. They are analytical, both in thinking through issues themselves and in examining the arguments put forth by others.

They are the definition of what we aspire to produce in our Vision 2025 graduate profile.

5. Why is this important?

  • Poor American showings on international comparisons of student competence in math. We’re getting our lunch handed to us.
  • We live in San Francisco: Technology, Biotech, Bio-industry
  • Our students need to compete not only with other students in California, but from across the world in order to land the very jobs that will allow them to live, work, and raise their families in San Francisco.
  • We are the Mesopotamia of innovation and technology, we are the premier center of technological innovation in the world—so our mathematics curriculum must be able to produce the world-class graduates able to compete for these jobs. Our previous curriculum didn’t meet the mark; the CCSS math sequence promises to do just that.

6. Why is no one else compressing like us?

  • We’re ahead of the game.
  • Our approach of teacher driven implementation is unique in California
  • Others considered going our way, but found it too hard
  • San Francisco always goes first, the rest eventually catch up:
  • Restorative Practices
  • District level waiver and balanced approach to student achievement
  • Ethnic Studies
  • Universal health care in the City
  • Gay marriage

7. What are we doing for high achieving students?

  • Currently invest close to $6 million dollars to support AP curriculum and assessments
  • Offer dual enrollment with City College for students (currently over 500 students from 11 high schools). Working with CCSF to expand to offer high level math dual enrollment options for students
  • Exploring class size adjustments for 8th grade math during phase in period for CCSS math
  • Open to discussing other ideas from staff, parents, and students.

- Superintendent Richard Carranza

Quotes from Dr. Alan Schoenfeld, Professor, University of California Berkeley

“The notion of acceleration was built on the assumption that what counts is procedural mastery rather than deep understanding—the idea being to move students through the content as long as they could do the symbolic manipulations, never mind if they really understood. This seemed unproblematic as long as the tests were skills-oriented, because if all you measured was skills (which is what the CST measured), then it looked like kids could make rapid progress. But in fact, the supposed understanding was illusory. Many years ago, the Mathematical Association of America released a document saying, in essence, “Please don’t rush students through the curriculum so that they can take calculus in their senior year.

So many of them have to re-take it in college because their understandings are superficial that it’s a waste of their time and ours. You should only move students into calculus if you're prepared to give them a full-­fledged college-level course (and they’re ready for it).” What we’ve learned is that it’s much better for everyone to proceed at a more measured pace, going deeper rather than faster. In the end, they learn more, and do better. (There’s also evidence that the kids who could accelerate actually learn as much or more in heterogeneous classes, when the classes are structured so that they do deeper thinking and explaining.)

The arguments I’ve seen for early acceleration are based on the wrong stuff—procedural mastery. That looks good at the beginning, and it bites you in the end. If you want deep understanding, students can go deeper at grade level, and ultimately (after 10th grade) you can start accelerating, or doubling up.

(FYI, I never accelerated as a studentI took precalculus in high school, and calculus as a college freshman. I don’t think I was harmed by this—my mathematics Ph.D. from Stanford isn’t too shabby.)”

This page was last updated on October 21, 2022