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patchwork collection of online courses that's difficult for students to navigate.

they can improve their online-education efforts to help students find streamlined, affordable pathways to a degree.

Changes in voice, appearance, marking key points in color, variation in font size, hats, movement, lessons outdoors, music, curious photos, unexpected objects (a radish on each desk when students enter the classroom) get the RAS attentive to admit the accompanying sensory input of lessons that relates to the curious sensory input!

the assumption that there is a single established body of mathematical skills that everyone needs to know to be prepared for 21st-century careers. This assumption is wrong. The truth is that different sets of math skills are useful for different careers, and our math education should be changed to reflect this fact.

Today, American high schools offer a sequence of algebra, geometry, more algebra, pre-calculus and calculus (or a “reform” version in which these topics are interwoven). This has been codified by the Common Core State Standards, recently adopted by more than 40 states. This highly abstract curriculum is simply not the best way to prepare a vast majority of high school students for life.

A math curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. But there is a world of difference between teaching “pure” math, with no context, and teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations.

Her presentation contained a slide that said academic dishonesty included plagiarizing yourself—i.e., taking a paper you had written for one course and turning it in for credit in another course. That, she explained, constituted a dishonest representation of your work for a course. "Unless," one of my colleagues chimed in at that point, "you're an academic, and you're presenting the same idea at a bunch of different conferences. Then it's clearly not dishonest."

"Are we allowed to use ideas from our writing exercise to help us write this paper?" she asked. "Of course," I said. "That was the whole point of the writing exercise—to get you a head start in thinking about how you want to approach your paper." "OK," she said. And then after a brief pause: "Because at orientation they told us we weren't allowed to use our own work twice." "Ah," I said. "That doesn't really apply in this case. And anyway, I don't really mind, in this course, if you take a paper that you've written for another course and revise it for an assignment in here. You just have to make sure that what you turn in fulfills my specific assignment. Other professors might feel differently, though. So I would always ask before you tried to do that."

So does the injunction against plagiarizing from yourself fall into the category of one of those hypocritical rules that we like to impose on our children: Drinking soda every day would be bad for your health, honey, but it's fine for me? If a categorical difference exists here between what we do and what we forbid our students to do, I confess, I have a hard time seeing it.

A broad focus on testing and new standards can lead schools to neglect the individualized needs of students,

unless U.S. schools can better align learning strategies and objectives with fundamental aspects of human nature, they will always struggle to help students achieve their full potential

Researchers classified 31 percent of teachers as “engaged” at work under that index, compared with 30 percent of respondents overall. But, among all occupations tracked in the survey, teachers were the least likely to say that their opinions counted at work.

We should be very careful in thinking about whether we’re working on the right problems. If we don’t, that ties into the problem that we don’t have experimental evidence that could move us forward. We're trying to develop theories that we use to find out which are good experiments to make, and these are the experiments that we build. &nbsp; We build particle detectors and try to find dark matter; we build larger colliders in the hope of producing new particles; we shoot satellites into orbit and try to look back into the early universe, and we do that because we hope there’s something new to find there. We think there is because we have some idea from the theories that we’ve been working on that this would be something good to probe. If we are working with the wrong theories, we are making the wrong extrapolations, we have the wrong expectations, we make the wrong experiments, and then we don’t get any new data. We have no guidance to develop these theories. So, it’s a chicken and egg problem. We have to break the cycle. I don’t have a miracle cure to these problems. These are hard problems. It’s not clear what a good theory is to develop. I’m not any wiser than all the other 20,000 people in the field.

I’m still asking myself the same question that I asked myself ten years ago: "What is going on in my community?" I work in the foundations of physics, and I see a lot of strange things happening there. When I look at the papers that are being published, many of them seem to be produced simply because papers have to be produced. They don’t move us forward in any significant way. I get the impression that people are working on them not so much because it’s what they’re interested in but because they have to produce outcomes in a short amount of time. They sit on short-term positions and have short-term contracts, and papers must be produced.

The field that I mostly work in is the foundations of physics, which is, roughly speaking, composed of cosmology, the foundations of quantum mechanics, high-energy particle physics, and quantum gravity. It’s a peculiar field because there hasn’t been new data for almost four decades, since we established the Standard Model of particle physics. There has been, of course, the Higgs particle that was discovered at the LHC in 2012, and there have been some additions to the Standard Model, but there has not been a great new paradigm change, as Kuhn would have put it. We’re still using the same techniques, and we’re still working with the same theories as we did in the 1970s.