‘Integrated’ math is hodge-podge math

To force math teachers to change their teaching to fit the Common Core, Darren’s school district is switching to “integrated math,” he writes on Right on the Left Coast.

The new books mix algebra and geometry, but don’t integrate the concepts, he complains. It’s just a “hodge-podge.”

Instead of Algebra, Geometry and Advanced Algebra, his high school will offer Integrated Math 1, Integrated 2 and Integrated 3, then the option of Pre-calculus, Stats and Calculus.

While Common Core opposes acceleration in middle school, his district will allow the best students to take Integrated 1 in eighth grade.

So if we want kids to be able to take AP Calculus AB and/or BC in high school, we need to accelerate them in high school.  . . . so in addition to Integrated 2 and 3 we’ll now have Integrated 2+ and Integrated 3+.  And if a student isn’t quite ready for Integrated 3 we’ll offer Transition to Integrated 3.  Of course that means we’ll also have to offer Transition to Integrated 1 (which would in effect be an 8th grade math course, or the pre-algebra course we haven’t been allowed to have in years) and a Transition to Integrated 2 course.

Integrated math has been around for a long time. I remember when San Jose Unified tried it. And then abandoned it. Common Core standards don’t require integrated math, but some think it’s a better fit than the traditional math sequence.

Core meltdown

In Core Meltdown Coming, Education Realist looks at how the Common Core will change math instruction.

Right now middle school math, which should ideally focus almost entirely on proportions, is burdened with introductions to exponents, a little geometry, some simple single variable equations. Algebra I has a whole second semester in which students who can’t tell a positive from negative slope are expected to master quadratics in all their glory and all sorts of word problems.

But Common Core standards add exponential functions to the algebra one course load and compensate by moving systems of equations and exponent laws to eighth grade while much of isolating variables is booted all the way down to sixth grade. Seventh grade alone bears the weight of proportions and ratios, and it’s one of several curricular objectives. So in the three years when, ideally, our teachers should be doing their level best to beat proportional thinking into students’ heads, Common Core expects our students to learn half of what used to be called algebra I, with a slight nod to proportional thinking . . .

“Half” of geometry is being pushed down to middle school too, writes Ed Realist.

In theory, students will arrive in high school ready to learn “complex, real-world mathematical tasks.” But only if they’re able to learn in middle school what many students are not able to learn in high school.

Under Common Core, college and career readiness requires passing Algebra II. Education Secretary Arne Duncan says Common Core will stop us “lying to kids about whether they are ready. Finally, we are telling them the truth, telling their parents the truth, and telling their future employers the truth. Finally, we are holding ourselves accountable to giving our children a true college and career-ready education.”

Honesty doesn’t require new standards and tests, writes Ed Realist.

 We could just say to any kid who can’t score 500 on the SAT math section or 23 on the ACT: Hey, sorry. You aren’t ready for college. Probably won’t ever be. Time to go get a job.

If we don’t have the gumption to do that now, what about Common Core will give us the necessary stones? Can I remind everyone again that these kids will be disproportionately black and Hispanic?

Common Core math was designed to get schools to teach “integrated math” rather than the traditional algebra, geometry and advanced algebra sequence, writes Ed Realist. North Carolina, Utah and West Virginia have made the switch. Integrated math is a great way to hide the fact that many students aren’t prepared for college math, writes Ed Realist.

Two paths to algebra in California

California will not block eighth-graders from taking algebra if the governor signs SB 1200, writes Deputy Superintendent Lupita Cortez Alcalá in a letter to Bill Lucia of EdVoice. School districts will not be forced “into a misguided one-size-fits-all approach to math education,” she writes.

What it does do is provide for clear and viable pathways: one for students who are ready for higher mathematics (algebra 1 in a traditional sequence and course 1 in an integrated sequence) and another for students who would progress through the grade level standards as called for in the Common Core standards.

Placement of students in mathematics courses, based on their readiness, remains a local decision – as it should be.

. . . adoption of the Common Core State Standards with California’s additions presented some unique challenges. California adopted two sets of eighth grade mathematics standards: the Common Core set and a set that combined elements of the Common Core eighth-grade and high school mathematics standards with California’s own algebra standards. Unfortunately, the “Algebra 1 at Grade 8” standards have created confusion in our school districts as it is a unique amalgamation, different from Algebra I, and not supported by instructional materials or curricula.

In focus groups, teachers and curriculum said “they want high expectations and high standards for their students – but also flexibility to decide when a student is ready for higher mathematics, based upon each student’s classroom performance – not impersonal directives from the Capitol,” concludes Alcalá.

I think this means algebra-ready students will take Algebra I without any Common Core additions. I think . . . (A reform of years gone by, integrated math teaches bits of algebra, geometry, trig and stats each year till students have mastered the concepts. It’s lost popularity.)

New standards, tests may kill teacher ratings

New common standards, which will require new tests, may put the kibosh on value-added ratings of teachers, speculates WashPost columnist Jay Mathews.

California will switch to Common Core Standards in 2014, get new tests in 2015, but no new textbooks aligned with the new standards and tests until 2017, teacher Jerry Heverly learned at a conference organized by his union. The state can’t afford new books.

(Heverly) has no strong feelings about the current tests, but the big change in 2015 is akin to watching a rising tide approach sand castles carefully constructed on the beach.

Integrated Math I, II and III will replace the traditional algebra, geometry, advanced algebra sequence, Heverly was told.  (This is a blast from the past: California adopted integrated math — algebra, geometry and statistics are taught at each level — in 1992. After protests, districts won the right to choose a traditional or integrated approach. New math standards were adopted  five years later, which required a new exam. Integrated math went out of fashion.)

The new standards will require changes in other subjects, as well. And developers say the new tests will be quite different, stressing students’ ability to explain their thinking, not just right answers.  Mathews writes:

These new tests in nearly every state will delay, if not stop altogether, the national move toward rating teachers by student score improvements. School districts can’t do that when the tests change so radically. They might have to wait years to work out the kinks in the tests before using them to assess teachers.

Once the new tests are accepted as valid, it will take years of data on students’ progress to create valid value-added measures of teacher effectiveness.