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.”