In 2014, Pennsylvania adopted new K-12 mathematics standards after deciding to "un-adopt" the National Common Core Standards. In deciding to chart its own course, the commonwealth was well within its rights. But it still has a responsibility to make sure its math standards are rigorous and clear. And on that count, it fell short.

Academic standards are the foundation on which much of public education rests. They dictate the knowledge and skills that students are expected to master, grade by grade, and communicate those expectations to educators, parents, curriculum writers, and other stakeholders. That's why we at the Thomas B. Fordham Institute have been reviewing state standards for more than 20 years.

In our most recent review, which we published last month, our team of subject-matter experts rated Pennsylvania's standards for English Language Arts & Literacy as "good" overall, meaning they would benefit from "targeted revisions" but are generally sensible. In contrast, our reviewers rated Pennsylvania's math standards "inadequate," meaning they need a complete overhaul, the sooner the better.

On the language arts/literacy side, reviewers' biggest complaint was that Pennsylvania doesn't identify the specific literary and information texts to which students should be exposed. (For example, that everyone should read the Declaration of Independence.) However, things are much worse in math, where Pennsylvania's standards are simply too brief and vague to convey a detailed sense of the knowledge and skills required for college and career readiness.

For example, right now Pennsylvania doesn't expect students to know basic addition and multiplication facts from memory (e.g., 2+2=4). Nor does it expect them to learn the standard algorithms for addition, subtraction, multiplication, and division. (Yep. You read that right.) Similarly, the word "proof" doesn't appear in the high school geometry standards. Nor is there any mention of perpendicular lines or pi. And there is no attempt to organize the high school math standards into actual courses.

Fortunately, all these shortcomings are fixable with a bit of effort. So instead of kicking the can down the road, Pennsylvania should act: Draft a new set of math standards that are worthy of the next generation. Clearly specify the skills and content they must master to be college and career ready, starting with the fundamentals of arithmetic and geometry. Give teachers a clear road map to follow so they understand how the concepts in one grade connect to those in the next. And for heaven's sake, don't let politics get in the way. If the state doesn't want to adopt the Common Core, fine—Texas went its own way and developed exemplary math standards. Perhaps Pennsylvania could start with those.

"We have to stop being so schizophrenic about what we do with our kids," state board of education member Mollie O'Connell Phillips said when the current standards were adopted.

Precisely. Which is why things like the standard approach to multiplication should never have been removed from the standards in the first place.

Amber M. Northern and Michael J. Petrilli are senior vice president for research and president, respectively, at the Thomas B. Fordham Institute.