Monday, May 11, 2015

How deeply do UCARE: “Going deep” in 21st Century, Common Core-inspired math

Four feet deep, to be precise.

In the 21st century, a deep understanding of mathematics, and the ability to apply that understanding, is more important than it has ever been. In Montgomery County Public Schools (MCPS), and across the country, mathematics instruction is changing to make sure we provide our students with the skills and knowledge they need for success in college and the workplace. From the MCPS’s math website.
Sound familiar? Yes, it’s all about our friends the CCCSS and the PARCC, along with the collaborative, 21st century workplace all our kids are going to end up in:
The improvements to the math curriculum are in response to several factors and will results in MCPS students having a stronger, more comprehensive understanding of mathematical concepts.  
Reasons include:
• The adoption of the internationally-driven Common Core State Standards (CCSS) and new, more difficult assessments being developed by the Partnership for Assessment of Readiness for College and Careers (PARCC), of which Maryland is a member… 
• The changing demands of the work force, including 21st century skills, such as, collaboration, persistence, critical thinking, and creative thinking…
The CCSS, the website notes, “demand a higher level of thinking in math for all students”:
Computation and procedures were sufficient to reach success in previous curriculum [sic] and assessments. The CCSS requires students to show greater depth by demonstrating their Understanding, Computing, Applying, Reasoning and Engagement (UCARE) in mathematics. As a result, the math content at each grade level is more difficult than previous curriculum [sic; boldface, here and elsewhere, mine].
So difficult that much more is required in order to advance through it:
Following the CCSS, the elementary program is designed to go deeper in the topics of number (counting, addition, subtraction, multiplication, division, fractions, and decimals) to ensure that students have a strong foundation before moving on to more advanced content.  
…Students at all levels are expected to express a deep understanding of the math content they are studying before moving to more advanced content. This means students will need to demonstrate their understanding in multiple ways, beyond just memorizing a formula or single procedure for solving a problem.  
Despite these hurdles, and despite all the ways in which the new curriculum is “more difficult” for all students, gifted students will get even more challenge:
C2.0 [Curriculum 2.0--the new curriculum] includes enrichment and acceleration options added by MCPS to ensure that students who demonstrate understanding of a topic will be able to deepen and extend their learning.
Indeed, MCPS’s C2.0’s enrichment opportunities “exceed the requirements” of the CCSS. In particular, students who “demonstrate readiness” in grade 3 will have the option to enroll in the 4/5 Compacted Math class. However:
due to the increase in the rigor of the grade level curriculum, far fewer students than in previous years will need to skip a grade level in elementary mathematics to be challenged.
Readers who’ve read this far must be burning with curiosity about just how deep a deep new, CCSS-exceeding curriculum goes for those select few who’ve already demonstrated exceptionally deep understanding. So here’s an example from the compacted 4/5 curriculum—a problem so deep that the class spent two weeks on it:
What is the opposite of 4 feet ABOVE sea level? What is the opposite of the opposite of 4 feet ABOVE sea level?"
The parent who shared this problem (on a listserv for MCPS parents) adds that:
Kids who learned negative numbers years before do not get any acceleration through this, and group work is a huge part of every math concept. If your kid learned long division years ago and understands the concept completely, they will still have to memorize all the different, laborious "strategies" and spit them out verbatim…
She concludes:
MCPS is not a place for rapid learners anymore… Our daughter has been bored to tears in math and science, as she has been every year. Most of the kids at the top 1% or so come home from school and then do a private math program in order to keep them engaged in math…
For more examples of what the MCPS website calls “Changing Expectation in Curriculum 2.0 Mathematics,” see this past week's Problems of the week.

According to a 2014 article in the Boston Globe:
many, or even most [gifted kids]... aren’t identified early, and they don’t necessarily get special attention from their schools. [Researchers at Vanderbilt] have .. found that those who weren’t challenged in school were less likely to live up to the potential indicated by their test scores. Other research has shown that under-stimulated gifted students quickly become bored and frustrated—especially if they come from low-income families that are not equipped to provide them with enrichment outside of school.
One of the researchers, Vanderbilt psychologist David Lubinski, worries about the broader impact of shortchanging our most academically capable students.
“We are in a talent war, and we’re living in a global economy now,” Lubinski says. “These are the people who are going to figure out all the riddles. Schizophrenia, cancer—they’re going to fight terrorism, they’re going to create patents and the scientific innovations that drive our economy. But they are not given a lot of opportunities in schools that are designed for typically developing kids.”


Hainish said...

I agree with everything you've written here, BUT I think it's a bit unfair to pin the problems on CCSS, which is being used as a Trojan horse to get to do the kid of teaching these people wanted all along. If anything, having common standards solves a massive coordination problem -- they can be fixed for many states at once, instead of piecemeal.

Anonymous said...

Are we to understand that this BS is the result of collaboration, persistence, critical thinking, and creative thinking?

Barry Garelick said...

While CCSS is being used to advance the constructivist and other faddish trends, they are not entirely without blame. They lend themselves to such interpretations, particularly through the Standards of Mathematical Practice which are the old and recast NCTM Process Standards.

Hainish said...

Barry, I found the Practice Standards here:

(With the exception of 3, they don't seem unreasonable to me.)

I thought I would see "Students should be able to solve problems in more than one way," but I didn't find that particular phrase on the page I linked to. Do you know where it comes from?

Barry Garelick said...

They are not unreasonable if implemented sensibly. But requiring lower grade students to critique and analyze the reasoning of others is nonsense, but that's what some are doing. I wrote a series of articles on how the SMP can be implemented sensibly, compared to how they are be implemented in the real world.

There's nothing wrong with having students persevere in solving problems, but this has been interpreted as "struggle is good", and giving students problems without much help or guidance and having them "struggle" so that they can learn. There are ways to do this productively, of course. But the "struggle is good" philosophy is one that's been around for a while, and the SMP's are gasoline on the fire of bad math practices that have been around for 20+_years.

SteveH said...

Is it possible for CCSS to be anything but what lies in the hearts and minds of ed school pedagogues? No. Testing companies, like PARCC, define what CCSS is or is not. It doesn't matter what the SMP says. PARCC says that the highest level of achievement ("distinguished") only means that one is likely to pass a course in college algebra. This highest level of expectations starts in the earliest grades, so CCSS is a non-STEM curriculum by definition no matter what the SMPs say.

However, MCPS defines accelerated tracks on their web site. Acceleration opportunities start in grade 4, and in one option, this leads to algebra I in grade 7. Considering that CCSS, at most, expects only pseudo-algebra II content, it's not clear how they prepare these kids for algebra in 7th grade. (They don't.)Whatever they do has to be something not based on anything to do with CCSS. They can use their fuzzy UCARE words, but something else has to happen.

They start compacting the material in fourth grade, but the acceleration is based on the same fuzzy content and ideas of K-6 curricula. The only real change is when they get to a real algebra textbook that is far above what CCSS expects. Instead of a proper pre-algebra course, they force kids to suffer through "Investigations in Math." In other words, the only kids who will be on a STEM track are those who get math help at home or with tutors.

K-6 math ignorance has not been fixed by CCSS. It is just hidden by acronyms like UCARE. MCPS can make a connection to Calc AP as a junior in high school, but the onus is completely on the students and parents to make the nonlinear transition from K-6 fluff math to the real math textbook high school sequence.

CCSS is a one-size-fits-all (algebra II) expectation and anything above that is left up to the students and parents. MCPS can define the paths and students can make it onto those paths, but educators don't (want to) know how kids get on those paths.

I went through this exact process with my son. I worked with him on the (stupid) 6th grade Everyday Math material in the summer before 6th grade so that he could take pre-algebra in 6th grade. I know exactly what that nonlinear transition is all about. CCSS fails in that it does not address the transition from the fluff ideas of K-6 to the real world STEM options of the calculus track in high school. When I was in school, I got to calculus with absolutely no help from my parents. This is impossible to do now.