In moving to the Common Core State Standards this year, California school districts had to choose between serving up high school math as one big stew or as the curricular equivalent of separate courses. That option has created strong, sometimes passionate disagreements among parents and teachers who argue that a blended or “integrated” approach offers a clearer method of instruction and those who prefer sticking with a familiar sequence of courses. The latter group includes high-achieving districts in Silicon Valley.

In the “traditional” sequence, Algebra I will be taught in 9^{th} grade, followed by Geometry, then Algebra II in the junior year, leading to pre-calculus, Advanced Placement statistics, or, if students are more advanced, Calculus in their senior year. In “integrated” math, as the name implies, the same standards for algebra, geometry, trigonometry and statistics are reassembled and woven together to show their interrelationships in three yearly courses of increasing difficulty. Proponents are also calling this Mathematics I, II, and III or International I, II and III, because, they point out, math is taught this way in most high performing nations.

California was one of 46 states, along with Washington, D.C., that adopted the nationwide Common Core standards in math and English language arts four years ago, although three states – Indiana, South Carolina and Oklahoma – have recently rescinded them, and two more states may also do so. The academicians who wrote the Common Core math standards on behalf of the nation’s chief state school officers and a bipartisan group of governors were agnostic about the two pathways for high school math. Either, if taught effectively, they said, would prepare students well for work and college in the 21^{st} century.

Some states, including New York, have chosen the traditional sequence, while others, including Utah and West Virginia, have chosen the integrated approach. In adopting the Common Core and subsequently approving a set of frameworks or guidelines for implementing them, the California State Board of Education decided that school districts should decide which pathway works best for them.

There is no current count of which approach districts are choosing. A questionnaire by the California County Superintendents Educational Services Association in fall 2013 found slightly more districts choosing integrated (34 percent) than traditional (26 percent) but 40 percent hadn’t yet decided. Among California’s largest districts, Los Angeles Unified, Long Beach Unified and – for at least next year – Fresno Unified are going with the traditional sequence while San Diego Unified, San Francisco Unified, Sacramento City Unified and Santa Ana are going with integrated math.

Among the proponents of integrated math is David Foster, the executive director of the Silicon Valley Math Initiative, which trains teachers and provides testing resources to districts, charter organizations and private schools. Common Core’s K-8 curriculum is already integrated, he said, introducing concepts of algebraic thinking (problems involving division and multiplication), fractions and geometry (areas of rectangles) in early grades, and then gradually adding complexity in middle school. Only in American high schools, he said, are Algebra and Geometry segregated, with a gap of a year separating beginning and advanced algebra and trigonometry.

“It makes a lot more sense for students to learn some Algebra this year and some next year, than to say, ‘Stop, do Geometry and then go back to Algebra,’” he said.

#### Less frustration, higher completion?

Barbara Schallau, the subject area coordinator for math in East Side Union High School District in San Jose, agreed. The district is transitioning to integrated math starting this fall. “All students would be better off going through an integrated pathway because it allows the development of concepts over time,” she said. “There is continuity and, more importantly, students revisit topics at a higher level, when they are more mathematically mature.”

Schallau is confident that the new Common Core 8^{ th} grade math, which will include some of what had been covered before under Algebra I, will give students a solid grounding for high school math. Before, she said, students who initially struggled with Algebra I in 8^{th} grade would become frustrated and hate math after repeating it once, sometimes twice in high school. Because high school students will view three years of integrated math as a package, not discrete courses, more will graduate qualified to attend the University of California or the California State University, she predicts. And more, she hopes, will go on to take pre-calculus or AP statistics.

There’s also agreement that Common Core will be a heavy lift for teachers, who will be asked to do more coaching and less lecturing from the front of the class.

Although some East Side Union math teachers are as optimistic, some are skeptical. Catherine Duhring, a fifth-year Algebra and Geometry teacher at Mount Pleasant High who is leading the school’s transition to Integrated I, said she is excited about Common Core’s potential to engage students in real-world problems and challenge their passive approach to learning math. “Some kids just want to memorize the tricks to solving problems. I want them to make sense of math, to persevere to find answers on their own so they can say with confidence, ‘I can handle this.’”

But her colleague at Mount Pleasant, 20-year veteran Sudhir Karandikar, says it is unrealistic to expect students in a standard class period to learn skills and procedures in multiple math domains and do project-based learning. “There will be far more engagement in theory but there also could be more frustration,” he said.

#### Safer option for a challenging transition

Duhring and Karandikar do agree that implementing Integrated I in the coming year will be difficult. They expect incoming 9^{th}-graders who have not benefited from Common Core math in 8^{th} grade will have big gaps in knowledge. And they will be teaching on the fly, developing lesson plans for an open-source curriculum, the Mathematics Vision Project, developed in Utah. “It’s very overwhelming,” Duhring said. “Every time I think about it my brain shakes.”

James Lianides, superintendent of the Sequoia Union High School District, whose students come from high- and low-income communities in San Mateo County, said that, in theory, integrated math “wins on points.”

“In an ideal sense, I agree integrated is a stronger approach to math,” Lianides said. But there’s no data to show that integrated will get better results, he said, especially in the transition, when all districts are struggling to train teachers in the new standards and find adequate textbooks and materials. Asked for their views, about 60 percent of teachers responding in Sequoia favored the integrated approach. Lianides recommended traditional and the five-member schools board backed that choice, 3-2.

For Lianides and Barry Groves, superintendent of the Mountain View-Los Altos High School District, where 20 percent of students come from low-income families and 70 percent of graduates go on to four-year colleges, the decision to stick with the traditional sequence was pragmatic.

“We’ve had a lot of success with the current math program in getting kids ready for college,” Groves said. Making accommodations within an existing curriculum instead of starting from scratch to build a new one removes a layer of complexity and creates one less worry for teachers who already are feeling pressure, he said.

But districts that choose traditional could be missing an opportunity,said Gina Dalma, senior education program officer for the Silicon Valley Community Foundation. The foundation has underwritten discussions between K-8 feeder districts and high school districts throughout Silicon Valley about Common Core math options. Dalma worries “there will be no impetus to change instruction,” which is necessary to effectively implement Common Core, with its dramatically different mix of content and skills.

“Integrated math is more of a refresh – an opportunity to rethink how kids are placed and start with a clean slate,” she said. She is concerned that without that clean break, the traditional sequence will perpetuate the status quo, including the tracking of students, a practice based on the assumption, starting in early grades, that minority kids and English learners can’t handle advanced math courses.

East Palo Alto Academy, a charter high affiliated with the Stanford School of Education, will be the one school within Sequoia Union High School District that will teach integrated math this fall. With 40 percent English learners and nearly all low-income students, East Palo Alto Academy already has begun introducing Common Core math, says Morgan Marchbanks, a former assistant Sequoia superintendent who is now principal of East Palo Alto Academy and chief academic officer of Stanford New Schools.

Like Schallau, a firm believer in the value of integrated math, Marchbanks predicts that districts will consider switching to the integrated pathway “once we demonstrate that kids will do well and college acceptances won’t be hurt.”

#### UC, CSU are agnostic on pathways

When it comes to the math debate, there is common ground.

Supporters of both pathways say that each approach, by stressing problem solving over memorization and mastery of procedures – a common criticism of California’s math standards – will be very demanding. In a presentation before the State Board of Education, Chris Dell, director of K-12 Mathematics and Technology for the Shasta County Office of Education, characterized Common Core’s focus on a deeper understanding as a shift from “how to why.” There’s also agreement that Common Core will be a heavy lift for teachers, who will be asked to do more coaching and less lecturing from the front of the class.

“I had not one request from a parent to go integrated,” said Barry Groves, superintendent of the Mountain View-Los Altos High School District. “I got many questions from parents worried we might go integrated.”

Compared with the old Algebra I, both Integrated I and Common Core Algebra I will assume that students know more at the start of the year and will take students further by the end of year. That’s because Common Core’s 8^{th}-grade math will cover topics previously offered in California’s version of Algebra I.

But that didn’t mollify many parents in the wealthier districts of Silicon Valley, where students compete to get into the top University of California campuses and private colleges. For those parents, the traditional path was the safer option. “I had not one request from a parent to go integrated,” said Groves. “I got many questions from parents worried we might go integrated.” None of the private schools in the region are choosing integrated, Groves said, another factor behind their decision.

Foster characterized the parents’ perceptions as, “We are winning, so don’t change the rules. We already can get kids to go to Stanford and MIT.” Parents who know how to help their students with Geometry didn’t understand the rationale behind Integrated II and why it might be better for their kids, he said.

But Foster also acknowledged that in the end, what will matter most will be implementation in the classroom, not the choice of pathway.

“Nobody has ever said standards change education or teaching,” he said. “Class size does not matter, what curriculum you use does not matter. All that ever matters is teaching. And so will this help teachers be better at teaching? I hope so.”

## Comments (36)

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Don4 years ago4 years agoConsider San Francisco Unified's decision to stop teaching Algebra 1 in 8th grade. Superintendent Carranza who promoted the policy change admits that it will drive out some families from SFUSD. Exacerbating the picture, some private schools families that traditionally entered SFUSD via Lowell HS are opting not to do so as we now see a significant drop in such enrollment next year. The SFUSD Board of Education has decided that this public school district … Read More

Consider San Francisco Unified’s decision to stop teaching Algebra 1 in 8th grade. Superintendent Carranza who promoted the policy change admits that it will drive out some families from SFUSD. Exacerbating the picture, some private schools families that traditionally entered SFUSD via Lowell HS are opting not to do so as we now see a significant drop in such enrollment next year.

The SFUSD Board of Education has decided that this public school district cannot meet the needs of both the higher and the average to lower achievers. What does this portend for SFUSD enrollment? Carranza’s warning aside, the Board claims differentiated learning will suffice to meet the needs of both ends of the academic spectrum in classes of 35 plus. This is wishful thinking at best as few teaching actually believe it to be true.

Private schools are already ramping up seats to meet demand created by public education policy gone mad. The remaining white upper middle class public school participants will be the first to go and the process has already begun. Then the Chinese will start to exit SF when they realize the prospects for college readiness will be damaged by the current policy. Though their community roots are deep, economic pressure and a strong education culture combined with reduced public school opportunity will encourage further flight to the suburbs while SF’s real estate bubble expands.

There does exist the remote possibility of a political backlash should the higher performing community decide to challenge the political status quo and change the Board of Education for one more mainstream in its agenda. San Francisco’s schism as a city split between the younger, highly educated and wealthy tech earners who are buying up real estate will soon start families and that of public housing dwellers doesn’t bode well for public education. There no reason to expect the former group to engage the system for change, but rather to choose to private as they begin to enter the age of settling down and family life. There’s possibility of a Chitech political union, though I don’t think the techies have the political will for a prolonged education battle.

SFUSD is now to face the prospect of

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Don4 years ago4 years agoContinued…. SFUSD is now to face the prospect of another policy-induced flight to the suburbs and private schools reminiscent of the busing era and also the result of policy decisions. San Francisco public schools are now officially entering the era of compensatory-only education.

FloydThursby19414 years ago4 years agoI agree, this is a horrible decision by SFUSD. Carranza is off target. SFUSD should be fighting to get more kids into public schools as we have one of the worst ratios in the country.

Subbalakshmi Kumar4 years ago4 years agoBeing a parent is not a walk in the park, especially if you are a parent of a growing child who has just started learning Math. Making the child understand the importance of Mathematics in the early age is very important as they not only use the concepts in textbooks but also implement them in real life. It certainly matters in future career choices and selecting professional careers. Learning mathematics can open a wide array … Read More

Being a parent is not a walk in the park, especially if you are a parent of a growing child who has just started learning Math. Making the child understand the importance of Mathematics in the early age is very important as they not only use the concepts in textbooks but also implement them in real life. It certainly matters in future career choices and selecting professional careers. Learning mathematics can open a wide array of career choices. Parents play a very important role in nurturing children in various aspects of development. Parents have to instill the love for literature and mathematics in children, as it is indeed necessary. There are many activities that can be implemented to increase the child’s ability to learn and grasp maths with a very positive attitude.

Larry Hawkins4 years ago4 years agoIn February 2014 the Board of Education of the San Francisco Unified School District adopted a resolution (Resolution 142-11Sp2) approving the traditional curriculum recommended by the superintendent, but Mr. Fensterwald says that “San Francisco Unified (is) going with integrated math.” What is the source your assertion, Mr. Fensterwald?

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John Fensterwald4 years ago4 years agoLarry: The information I was given was obviously wrong. Thanks for the correction; wish you had written sooner.

Don4 years ago4 years agoJohn, SFUSD adopted the the integrative model as you correctly claimed and moved Alegbra 1 from the 8th to 9 grade with an option, as of late, to test out of 9th grade Alegbra in 9th for 2015-16, though only some students, primarily from private school, are likely to find that a useful option since public school students will only have the integrated CCSS-M 8th grade course under their belt. Middle schools no … Read More

John, SFUSD adopted the the integrative model as you correctly claimed and moved Alegbra 1 from the 8th to 9 grade with an option, as of late, to test out of 9th grade Alegbra in 9th for 2015-16, though only some students, primarily from private school, are likely to find that a useful option since public school students will only have the integrated CCSS-M 8th grade course under their belt. Middle schools no longer offer more advanced students the opportunity to move ahead and this has riled their parents and put academic magnet high school, Lowell, between a rock and a hard place since it caters to those higher performing students. It only gets students to basic Calculus by compressing pre-calculus and Alegbra II into one year – a model that the teachers at Lowell have claimed to be unworkable given the amount of content in each.

Dropping honors math in SFUSD middle schools is not a researched-based data-driven decision. We have nothing to demonstrate that CCSS-M is effective. This was an ideological decision. The success or failure of a CCSS-M integrative approach hinges on the ability of the teacher to differentiate learning unless we have decided to impose a doctrine that says all students have the same needs.

navigio4 years ago4 years agoBased on the appendix John linked to, at a very general level, the primary difference between the two tracks seems to be a spreading out or delaying of some algebra concepts while moving some of the initial geometry concepts up to the first year (not surprisingly). Here is a high-level breakdown for interested parties.. Numbers and Quantities: Real Numbers: moved back a year, from first year to second year. Quantities: still first year … Read More

Based on the appendix John linked to, at a very general level, the primary difference between the two tracks seems to be a spreading out or delaying of some algebra concepts while moving some of the initial geometry concepts up to the first year (not surprisingly). Here is a high-level breakdown for interested parties..

Numbers and Quantities:

Real Numbers: moved back a year, from first year to second year.

Quantities: still first year

Complex Numbers: moved up a year, from third year to second year (partially optional)

Vector Quantities: remained same (all optional 4th year)

Algebra:

Seeing structure in Expressions: partly moved back a year, partly same (mostly 2nd and 3rd year now)

Arith with Polynomials and Rat. Expr: mostly same (3rd year)

Creating Equations: Mostly spread from year 1 & 3 to all 3 years

Reasoning with Equations and Ineqalities: mostly remained 1st year, a couple items moved back to 2nd year

Functions:

Interpreting functions: Mostly spread from year 1 & 3 to all 3 years

Building functions: Mostly spread from year 1 & 3 to all 3 years

Linear, Quadratic and Exponential Models: mostly same (1st or 3rd)

Trig Functions: mostly same (3rd year or optional 4th)

Geometry:

Congruence: mostly moved up from 2nd to 1st year

Similarity, right triangles and Trig: mostly same (2nd year) but a couple items made optional

Circles: remained 2nd year

Expressing geometric properties with equations: half still 2nd year, half moved up to 1st year

Geometric measure and dimension: mostly same, but one moved back to 3rd year

Modeling with geometry: same (2nd year)

Stats and Prob (all same):

Interpreting Categorical and Quantitative data: same (mostly 1st year)

Inferences and Conclusions: same (3rd year)

Conditional Prob: same (2nd year)

Using prob to make decisions: same (all optional mostly 4th year, some 2nd and 3rd)

navigio4 years ago4 years agoWhere is the integrated sequence defined? CDE? Private curriculum companies?

How will SBAC handle the difference in testing required, including multiple tracks for ‘adaptive’ testing?

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John Fensterwald4 years ago4 years agoYou can find integrated math discussed in Appendix A of the Common Core standards. There is also a chapter devoted to it in California's math frameworks, guidelines for teaching the standards that were created by a committee made up primarily of math teachers, navigio. There will only be one Smarter Balanced math test for 11th grade. It will be adaptive. I've heard it argued that students taking Integrated math may do better, because the material … Read More

You can find integrated math discussed in Appendix A of the Common Core standards. There is also a chapter devoted to it in California’s math frameworks, guidelines for teaching the standards that were created by a committee made up primarily of math teachers, navigio.

There will only be one Smarter Balanced math test for 11th grade. It will be adaptive. I’ve heard it argued that students taking Integrated math may do better, because the material in the various strands – algebra, geometry – will be fresher to them. Beyond that, I invite math teachers to weigh in with their experiences and what will be covered in the test.

navigio4 years ago4 years agoBeautiful John, thank you.

I seem to remember someone (?) indicating that SBAC would provide instructional assessment material for either approach, though as you point out, summative assessments should not need to differ if students are on track the ‘summation point’ is the end of 11th grade. Obviously formative materials would need to be different.

Don4 years ago4 years agoCCSS claims to apply equally well across the four pathways - traditional, compacted trad., integrated and compacted integrated. SBAC, OTOH, is designed to advantage the integrated approach as it doesn't test each distinct discipline in 11th grade. Would it be fair to say that districts would be well advised to adopt an integrated approach if they want to maximize test scores? Both traditional and integrated have their pros and cons. I would wager … Read More

CCSS claims to apply equally well across the four pathways – traditional, compacted trad., integrated and compacted integrated. SBAC, OTOH, is designed to advantage the integrated approach as it doesn’t test each distinct discipline in 11th grade. Would it be fair to say that districts would be well advised to adopt an integrated approach if they want to maximize test scores?

Both traditional and integrated have their pros and cons. I would wager an opinion as to which is better as it isn’t my discipline, but advocates of integrated claim it will reduce the math drop-out rate. Fair enough in its own right, but which disciple is likely to result in greater achievement in higher performing students?

The fact that district have to choose one pathway or another is troubling because it may be that some students do much better with integrated and others with traditional.

navigio4 years ago4 years agoAll good points. The desire to reduce testing at the high school level dovetails well with the integrated model for the reason you mention. Whether one is actually driving the other is up for debate. Though the idea of an integrated sequence has existed for a while and I believe predates CC. It definitely is noteworthy that many districts chose against the change. I would love to hear why, though I expect higher achieving districts … Read More

All good points.

The desire to reduce testing at the high school level dovetails well with the integrated model for the reason you mention. Whether one is actually driving the other is up for debate. Though the idea of an integrated sequence has existed for a while and I believe predates CC.

It definitely is noteworthy that many districts chose against the change. I would love to hear why, though I expect higher achieving districts to see less reason to make such a change for the simple reason what they have now has been working and is a known quantity.

I would not expect either track to be of more benefit to higher achievers due to the fact that math can already be ‘integrated’ under the traditional approach in the sense that those students are more likely to already be using that math for other reasons (eg electives, sciences, etc), ie the ‘continuity benefit’ may already exist.

It’s worth noting the transition would take at least three years to complete anyway, and during that time districts will have to support both tracks.

There may be different ways to achieve continuity, but this is probably a good approach.

Karen4 years ago4 years agoMy friend's child attends a private school in the Bay Area where through a 21st Century Learning program, a CC related curriculum, he has not been taught any math since 5th grade. She has had to go outside the school with non CC programs and tutors to make sure he is actually learning real math, not waisting time and being hopelessly confused. It seems to be an attempt to slow down capable learners. She … Read More

My friend’s child attends a private school in the Bay Area where through a 21st Century Learning program, a CC related curriculum, he has not been taught any math since 5th grade. She has had to go outside the school with non CC programs and tutors to make sure he is actually learning real math, not waisting time and being hopelessly confused. It seems to be an attempt to slow down capable learners. She mentioned recently the dismay of parents who have depended upon this CC based system to teach their children math and the dismal scores they are getting on the SSAT, which is used for high school placement, after being “non taught” math. Additionally, she mentioned that the recent graduates of this program are, for the first time ever, having extreme difficulty with the private high school curriculum, which is not scheduled to make the switch over until 2015. A parent’s worst nightmare.

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Gary Ravani4 years ago4 years agoAs any number of law enforcement personnel can attest “eyewitness accounts” are often the most unreliable. Talk to some teachers who have actually been trained in CCSS math. What you, and your friend, think of as “real math” may just be the math you are used to.

el4 years ago4 years agoI find it hard to understand why parents would keep their child in a private school whose education they find so inadequate.

Steve Waterman4 years ago4 years agoThe high school districts that have not made the leap to integrated math seem to be reacting to the pressure of advantaged parents - parents who appreciate the way the current system keeps their children on track to calculus. However, because tracking in math often results in tracking in science and other core subjects, the current system often has kept less advantaged students in a deadened program. Thus, the best hope for the … Read More

The high school districts that have not made the leap to integrated math seem to be reacting to the pressure of advantaged parents – parents who appreciate the way the current system keeps their children on track to calculus. However, because tracking in math often results in tracking in science and other core subjects, the current system often has kept less advantaged students in a deadened program. Thus, the best hope for the rest of the students is the integrated approach.

Sadly, once again, the state had developed an insightful, thoughtful set of standards that if taught would result in our being able to satisfy the US needs for engineers, but the state had not provided the resources needed to help teachers change their belief systems and transform their instruction to meet the standards. The Silicon Valley Community foundation has tried to fill the funding gap, but I am afraid that the training, excellent as it will be, will not be sufficient. Google and Apple could step in, and instead of using their resources to lobby for more Green Cards, they could develop farm teams of students in Santa Clara and San Mateo Counties with relatively modest investments for them – freeing up teachers for a year of training of sufficient intensity to allow the teachers the time they need to transform their instruction and create a Valley where neither gender nor poverty stand in the way of success.

Don4 years ago4 years agoElizabeth Cohen, the author of the research upon which SFUSD's math philosophy is based, is described in Stanford's memorial tribute as a " liberal activist." It doesn't surprise me to know that SFUSD uses liberal activist "researchers" to support its political agenda to "educate" the students of San Francisco public schools in social justice. The only problem is that there's nothing socially just about providing developmentally inappropriate content to students. Read More

Elizabeth Cohen, the author of the research upon which SFUSD’s math philosophy is based, is described in Stanford’s memorial tribute as a ” liberal activist.” It doesn’t surprise me to know that SFUSD uses liberal activist “researchers” to support its political agenda to “educate” the students of San Francisco public schools in social justice. The only problem is that there’s nothing socially just about providing developmentally inappropriate content to students.

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Ze'ev Wurman4 years ago4 years agoRemember Lysenko.

Science never stands a chance in face of Utopian ideology.

http://en.wikipedia.org/wiki/Trofim_Lysenko

Gary Ravani4 years ago4 years ago"Science unleavened by the human heart and human spirit is sterile, cold, and self absorbed." Gregory Petsko, Brandeis University biochemist. See Brad Huff's comment above. Brad, I believe is a university instructor himself. He notes that we (in the teaching profession) teach students, not content. Ze 'ev does have a point, as does Brad, that the key is having teachers appropriately prepared and resourced to do the job of implementing CCSS in math (and in ELA and … Read More

“Science unleavened by the human heart and human spirit is sterile, cold, and self absorbed.”

Gregory Petsko, Brandeis University biochemist.

See Brad Huff’s comment above. Brad, I believe is a university instructor himself. He notes that we (in the teaching profession) teach students, not content.

Ze ‘ev does have a point, as does Brad, that the key is having teachers appropriately prepared and resourced to do the job of implementing CCSS in math (and in ELA and NGSS). That, of course, in CA is a stretch. When NY flubbed its implementation of CCSS, as far as I know, they have chosen to take a five year hiatus on any kind of formal assessment. That would likely make sense here too, but making sense in the face of the political “sky-is-falling” antics that would come from the usual suspects in the public school criticism industry makes doing something that makes sense incredibly difficult.

This not a new situation. The implementation of the last set of standards followed pretty much the same course. There was limited quality professional development around. There were no new curricular materials widely available. Teachers, on their own, and in the face of “pacing guides” formulated by highly paid consultants and non-classroom personnel, had to do a triage of the standards to try and see what might actually work in real classrooms with real kids with huge class sizes and limited supports (librarians, counselors, nurses, etc.) Deja vu all over again, except for the new added expense of all the technology that is “needed” because, well it’s just needed and technology is everywhere and it’s needed and that’s it. No further questions will be entertained.

Don4 years ago4 years agoWhy do you support CCSS as you do if you believe that the necessary professional development and other various structural impediments will not be sufficiently addressed to ensure a successful implementation ?

Ze'ev Wurman4 years ago4 years agoGary, This not a new situation. The implementation of the last set of standards followed pretty much the same course. There was limited quality professional development around. There were no new curricular materials widely available. Teachers, on their own, and in the face of “pacing guides” formulated by highly paid consultants and non-classroom personnel, had to do a triage of the standards to try and see what might actually work in real classrooms with real kids … Read More

Gary,

This not a new situation. The implementation of the last set of standards followed pretty much the same course. There was limited quality professional development around. There were no new curricular materials widely available. Teachers, on their own, and in the face of “pacing guides” formulated by highly paid consultants and non-classroom personnel, had to do a triage of the standards to try and see what might actually work in real classrooms with real kids with huge class sizes and limited supports (librarians, counselors, nurses, etc.) Deja vu all over again, except for the new added expense of all the technology that is “needed” because, well it’s just needed and technology is everywhere and it’s needed and that’s it. No further questions will be entertained.

Except for the last point about technology with which I agree, I somehow sense we lived in a different state. I remember the 1999 Schiff-Bustamante bill allocating an extra $1 billion (in 1999 money, $1.43 B today!) for accelerated purchase of instructional materials aligned to the new standards. I remember AB2519 accelerated instructional material adoption process in 1998. I remember AB466 that added another 120 hours of professional development on top of what we had before. And there were more bills that even I forgot since then.

So I guess we must have lived in two different Californias.

Gary Ravani4 years ago4 years agoHow true, Ze’ev. I live in the part of CA that actually inhabits classrooms and works in real schools and not conferences in upscale hotels put on by Silicon Valley savants.

Don4 years ago4 years agoCI Program Objectives Through the Complex Instruction Professional Development Program: 1. Teachers will learn to engage all students in rigorous mathematics learning. a. Teachers will question and rethink their beliefs about what it means to do and learn mathematics, who can be successful learning mathematics, and how all students are mathematically smart. b. Teachers will develop and use practical tools to create authentic and rigorous mathematical learning opportunities for every student by recognizing and mitigating hierarchical … Read More

CI Program Objectives

Through the Complex Instruction Professional Development Program:

1. Teachers will learn to engage all students in rigorous mathematics learning.

a. Teachers will question and rethink their beliefs about what it means to do and learn mathematics, who can be successful learning mathematics, and how all students are mathematically smart.

b. Teachers will develop and use practical tools to create authentic and rigorous mathematical learning opportunities for every student by recognizing and mitigating hierarchical status roles in the classroom.

c. Teachers will enact the CCSS Mathematical Practices in classroom communities and integrate them as powerful ways of doing math and being mathematically smart.

2. Equity-centered professional learning communities will support teachers to engage every student in rigorous mathematics learning.

a. Self-sustaining mathematics departments will support teachers on a daily basis.

b.Cross-site collaboration between sites will provide teachers with additional resources and perspectives.

c. Leadership capacity to support sustained equity-oriented mathematics teaching will grow.

3. Students from traditionally marginalized groups (AA, Latino, ELs, and Spec. Ed) will learn and achieve more in mathematics

End

In 1.a above, I can only add that I certainly hope SFUSD teacher do question their beliefs.

This crap could come straight out of a Soviet five year plan.

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FloydThursby19414 years ago4 years ago5 year plans and new deals, wrapped in golden chains, and I wonder, how I wonder, who'll stop the rain.... Not all children are equal in math. Even if every parent were great, some have more of a propensity for it than others. If my son and my daughter were the same age and in the same class, she'd hold him back. She is smarter in some other ways, writing, etc. He … Read More

5 year plans and new deals, wrapped in golden chains, and I wonder, how I wonder, who’ll stop the rain….

Not all children are equal in math. Even if every parent were great, some have more of a propensity for it than others. If my son and my daughter were the same age and in the same class, she’d hold him back. She is smarter in some other ways, writing, etc. He just has more aptitude for math.

There is no way to do both. This is why most engineers come from other nations where kids are allowed to excel without being held back by other kids and accused of racism and unfairness to the underachievers.

It’s good for black and Latino kids to have middle class and better off whites and high performing Asians in their schools, the diversity helps them, which is why I wish more people were aware of the book showing private schools have no academic advantage (The Public School Advantage) and this would lead to more integration. However, I can only think this may cause more parents to go private or white flight it to a suburb, both of which actions will reduce the parents who donate and volunteer and do irreparable damage to the poor black and Latino kids left behind.

The PTA donations and relationships and interaction all help poor kids. But there is a point where you need tracking to keep kids in a school who have options. The far left 5-year plan type people always forget that every time a well off family throws up their hands and moves or goes private, it hurts lower income and black and Latino kids. This is a huge mistake and will cause this. They imagine the same kids in the school no matter what they do, but some actions cause certain families who improve a school to flee.

Don’t stop … thinkin’ about tomorrow..on a midnight train….

Don4 years ago4 years agoHere's the rhetoric out of SFUSD's math department: What is Complex Instruction? The complex instruction model aims to “disrupt typical hierarchies of who is ‘smart’ and who is not” by promoting equal status interactions amongst students so that they engage with tasks that have high cognitive demand within a cooperative learning environment. Find out about CI Program Components here: CI Program Components CI is a coherent program of pedagogical strategies grounded in the sociological research of Elizabeth Cohen … Read More

Here’s the rhetoric out of SFUSD’s math department:

What is Complex Instruction?

The complex instruction model aims to “disrupt typical hierarchies of who is ‘smart’ and who is not” by promoting equal status interactions amongst students so that they engage with tasks that have high cognitive demand within a cooperative learning environment.

Find out about CI Program Components here:

CI Program Components

CI is a coherent program of pedagogical strategies grounded in the sociological research of Elizabeth Cohen and her colleagues (Cohen & Lotan, 1997; Cohen, 1994). CI targets equity and, in particular, three ideas: first, that all students are smart; second, that issues of status—who is perceived as smart and who is not—interfere with students’ participation and learning; and third, that it is teachers’ responsibility to provide all students with opportunities to reveal how they are smart and develop/recognize new ways of being smart. The complex instruction model aims to “disrupt typical hierarchies of who is ‘smart’ and who is not” (Sapon-Shevin, 2004) by promoting equal status interactions amongst students so that they engage with tasks that have high cognitive demand within a cooperative learning environment.

Three principles of CI, when simultaneously enacted, support equitable participation and increased student learning (Cohen & Lotan, 1997):

1.Multiple Ability Curriculum – provide curricular tasks that are open-ended, rich in multiple mathematical abilities, and support learning of important mathematical concepts and skills central to a big idea.

2.Instructional Strategies – develop autonomy of and interdependence within each group through the use of norms, roles, and teacher interventions.

3.Status and Accountability – raise intellectual expectations for all students, hold individuals and small groups accountable for learning, and intervene in status issues.

CI Program Objectives

End

As you can see the philosophy behind the integrated math approach starts with the idea that “all kids are smart”.

Apparently this is intended to substitute for regard to placement. Everyone is on an equal footing. Unfortunately, this is clearly fantasyland.

More of SFUSD’s approach in next comment

SD Parent4 years ago4 years agoSan Diego Unified has been challenged in the process. It decided to adopt the integrated math pathway with zero stakeholder input (merely an executive committee comprised of a few high school math teachers). Rather than grandfather students already in the "traditional" Alg-Geom-Alg II pathway, the district then produced new integrated pathways for students who were not already in Geometry. These transition protocols literally changed several middle school math course materials at the … Read More

San Diego Unified has been challenged in the process. It decided to adopt the integrated math pathway with zero stakeholder input (merely an executive committee comprised of a few high school math teachers). Rather than grandfather students already in the “traditional” Alg-Geom-Alg II pathway, the district then produced new integrated pathways for students who were not already in Geometry. These transition protocols literally changed several middle school math course materials at the semester break, with a month’s notice, and these protocols placed students based on their grade, not what math concepts they had already learned. For example, teachers of Algebra I courses were supposed to stop introducing the algebra concepts and instead teach Math 8 concepts or Integrated Math I concepts (depending not on placement criteria but just the student’s current grade level, which created issues for many classes where the student populations were different grade levels mixed together). And talk about difficulty for transferring students–students in these courses would not have completed either Algebra I or Math 8/Integrated Math I! Teachers and parents were dismayed, particularly at schools with historically high-achieving students for which the existing system worked well.

It is only because of parent and teacher intervention that the semester change was averted (less than two weeks before it was to be implemented) and that better placement criteria for middle school students was made, but parents are still leery of just how students who were already on the “traditional” Alg-Geom-Alg II track will fare while teachers grapple with filling in the gaps of Common Core math standards that should have been covered in Math 6,7, and 8 and adjusting curriculum in the integrated math courses so that they don’t repeat concepts they have already learned, all while learning to teaching using Common Core teaching techniques. Considering that as of the last day of school, the district did not have pacing guides and had only some of the new texts for this coming school year, it’s hard to believe that even the best teachers will have the guidance and preparation they need to provide the best instruction for these students caught in the middle of the transition.

Meanwhile, I am unaware of any private school in the area that has adopted the integrated math pathways. In fact, their recruitment flyers proudly state that they have not adopted these pathways, a draw for those who can afford to transfer out of the public schools.

I bring SDUSD’s process to light for those districts that have not yet decided (which, frankly, concerns me, as this is not a simple flick of a switch). The moral is that you must engage all stakeholders in the process and do some critical thinking (isn’t that a motto for Common Core instruction?) in deciding which direction to proceed and how to transition students to the integrated math pathway, if that is the path chosen.

Paul Muench4 years ago4 years agoHow will this impact students that need to change districts?

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Paul Muench4 years ago4 years agoThis is a really important question as spelled out here: http://neatoday.org/2013/05/10/six-ways-the-common-core-is-good-for-students/ One of the strengths of Common Core was supposed to be the commonality. This was supposed to help our most mobile students, who often are our poorest students. In practice, is integrated math going to be poor student math? I suppose if that's the case then they will have the commonality they need. If not, then we need some answer of how … Read More

This is a really important question as spelled out here:

http://neatoday.org/2013/05/10/six-ways-the-common-core-is-good-for-students/

One of the strengths of Common Core was supposed to be the commonality. This was supposed to help our most mobile students, who often are our poorest students.

In practice, is integrated math going to be poor student math? I suppose if that’s the case then they will have the commonality they need. If not, then we need some answer of how children will transition between the two systems.

And if in practice affluent districts use the traditional pathway we’re going to create a whole bunch of questions about equity. Both in terms of the quality of instruction and in terms of mobility between communities. Will families now have to pass through the math gate to move from poorer communities to wealthier communities?

Brad Huff4 years ago4 years agoWhich is more important, the curriculum or the instruction? Good and great teachers teach students, not content.

I support our teachers and expect those unfamiliar with the integrated approach will figure out how to teach an integrated curriculum so as to ensure their students know what they need to know.

Integrated math only becomes a “mish-mash” when taught by instructors who don’t really understand the scope and sequence of mathematics. I hope there are only a few of these.

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Ze'ev Wurman4 years ago4 years agoI also “hope” there are only few of them. But I also realize that hope is not reality.

Integrated math has been pushed in California since 1985, and particularly since the 1992 Calif. Framework. That how it achieved 25% share by 1999. So teachers had a chance to learn it an apply it. Yet districts abandoned it like a plague once comparable results were available. Draw your own conclusions. Or don’t.

Gary Ravani4 years ago4 years agoExcept for high wealth students I don't know of any empirical evidence to suggest math scores on either the NAEP or TIMMS improved by using the traditional organization of math. Granted "scores" per se may not be the best way to evaluate this question, but the test scores are "the coin of the realm" currently. To assert that any of the tests are "objective" seem more than a stretch. Tests do not "emerge whole and perfect … Read More

Except for high wealth students I don’t know of any empirical evidence to suggest math scores on either the NAEP or TIMMS improved by using the traditional organization of math. Granted “scores” per se may not be the best way to evaluate this question, but the test scores are “the coin of the realm” currently.

To assert that any of the tests are “objective” seem more than a stretch. Tests do not “emerge whole and perfect from the mouth of Brahma.” Tests are the product of middle-class test makers who create the questions, decide the best answers, and then create cut scores for many of the tests. It is all quite subjective, One of the more destructive myths of the test-based accountability system now in place for over a decade that resulted in flatlining NAEP scores was the fantasy that this process was “objective,”

Experts in both math and science are asserting that integrated curriculums work best to help students learn those subjects. (We do live in an “integrated world.”) The fact that parents are confused by it and some teachers are appalled at how management is bungling the implementation is no reason to condemn the curriculums themselves. If the focus is to be learning, which has not been the case since the rollout of NCLB, then every effort needs to go into educating parents and providing teachers with the time, materials, and professional development needed to do them right. The same thing has to be said for CCSS.

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Don4 years ago4 years agoThe mid term and final tests you gave your students were subjective as well. Did you ignore those test results? SBAC and STAR may be subjective in the sense you outlined above, but so are college admissions, who gets a job, what it means to succeed and how to get there. We could apply uncertainty theory and just give up on standards. What do you suggest the test makers do or is … Read More

The mid term and final tests you gave your students were subjective as well. Did you ignore those test results? SBAC and STAR may be subjective in the sense you outlined above, but so are college admissions, who gets a job, what it means to succeed and how to get there. We could apply uncertainty theory and just give up on standards. What do you suggest the test makers do or is this your way of saying that we should abandon testing? That is your goal hidden in your comment, isn’t it?

Michael G4 years ago4 years agoI am seeing first hand how this integrated approach is playing out and it is not working well. There is a placement test at the end of 5th grade and kids are *tracked* into either a 3-year Alg.-Geo mish-mash or into a *track* that at best (another placement test in 6th grade) go into a 8th grade Algebra *track*. Your kid misses the 5th grade cutoff score by a point or two and … Read More

I am seeing first hand how this integrated approach is playing out and it is not working well. There is a placement test at the end of 5th grade and kids are *tracked* into either a 3-year Alg.-Geo mish-mash or into a *track* that at best (another placement test in 6th grade) go into a 8th grade Algebra *track*. Your kid misses the 5th grade cutoff score by a point or two and she will never get into that Alg-Geo track. I have no idea what will happen to kids who transfer from a “traditional” middle school with a 7th grade Alg. 1 course (like my kids went through) to this “integrated” approach or vice versa. Is the thought that no one transfers schools? This was not well thought out (if at all). For much of CA this may not be an issue since getting into 8th grade Alg. 1 is a step forward, but for the high performing schools it is *huge*. Parents I talk to are frantic if their kids miss the cutoff.

In the traditional approach, your kid might go into pre-algebra or not in 6th grade but with a little work and help it was possible to get into Alg. 1 in 7th grade. Closing that option is a tragedy.

I agree that doing a year of Geometry between Alg. 1 and Alg 2 is a problem, but there are other solutions. You could have kids take Alg 2 simultaneousy with Geometry since they have no logical sequencing order. The CA common core document actually reccommends that as a possibility.

One item people fail to mention is that countries to which we compare ourselves usually have a single nationwide curriculum to which everyone adheres, often to the very day in which a lesson is taught. That is unimaginable in this country, for better or worse.

I predict a huge boom in private schools’ Summer programs as frustrated middle-class parents try to work around this mess by having their kids take traditional Alg. 1 and Geometry in 6 week sessions because their kid missed the cutoff. Too bad for poor parents that can’t afford private school but educators apparently are so happy to get tracking back they don’t care.

This will doom Common Core. I was for Common Core because I rather like the idea of a single unified curriculum. In practice it seems to be reintroducing the worst of all old math ideas.

BTW, Ze’ev is right. Be guided by him and all will be well.

Ze'ev Wurman4 years ago4 years agoThere seem to be three separate problematic issues with this piece. First has to do with general effectiveness of integrated versus course-based. Actually, there exists strong empirical California data that shows course-based programs seem to work much better. Specifically, the STAR test offered both an integrated and a course-based test to support both paths in mathematics since 1999. When STAR started in 1999, about 25% of California students took Integrated, but once objective assessment of … Read More

There seem to be three separate problematic issues with this piece.

First has to do with general effectiveness of integrated versus course-based. Actually, there

existsstrong empirical California data that shows course-based programs seem to work much better. Specifically, the STAR test offered both an integrated and a course-based test to support both paths in mathematics since 1999. When STAR started in 1999, about 25% of California students took Integrated, but once objective assessment of the results became widely available under STAR, districts abandoned integrated in droves. By 2002 only 7.5% of California students were enrolled in integrated courses, and by 2013 that fraction dropped to less than 1.5%. In other words, districts voted with their feet — overwhelmingly — when they actually observed student achievement results.Second, there is a common argument that internationally, high achievers do “integrated math.” This is a broadly held misconception. What high achieving countries do is to spend dedicated time on *units* of, say, Algebra and Geometry, over a single year. So one may spend two trimesters studying algebra, and one trimester studying geometry — sometime even by different teachers. In any case, each discipline respects its disciplinary conventions, traditions, and integrity. In contrast, what goes for “integrated” in America is a mishmash of half-baked ideas centered around “big problems” that have aspects from multiple areas, such as geometrical and algebraic aspects. Much of the mathematics is taught ad-hoc as needed for that particular problem, abandoning any semblance of coherent development of the discipline. The results is — at best — kids that know disjoint bits and pieces of math as happened to be needed for the handful of “big projects” they were exposed to, and — more typically — kids that just know very little of anything and have no understanding of the logical and cohesive body of knowledge represented by mathematics.

Finally, here is the issue of people arguing baseless rubbish like this one:

“Integrated math is more of a refresh – an opportunity to rethink how kids are placed and start with a clean slate,” she said. She is concerned that without that clean break, the traditional sequence will perpetuate the status quo, including the tracking of students, a practice based on the assumption, starting in early grades, that minority kids and English learners can’t handle advanced math courses.

What this basically seems to say is that if we kick out what worked very well for so many, even if not for all, we have a chance to “start fresh.” In other words, let’s screw up the high achieving kids and make sure nobody achieves too high, so the low achievers won’t stand out as much. For these people, it seems, it’s all about social justice and not about teaching kids math.

How unsurprising.

Mike McMahon4 years ago4 years agoIt will be interesting to see how college admission offices evaluate the transcripts of those graduates with an integrated math curriculum.