Group items tagged

Characters in alphabets began as pictures with meaning (West, 1997).

As history repeats itself, we may find that a great deal of information is better presented visually rather than verbally.

culture's

Mathematics, as defined by the CCSS, isn't just a series of discrete content standards. It contains practice standards, too: modeling, critiquing arguments, using tools strategically, reasoning abstractly, and others.

Students’ confidence will build further with their recognition of the strategies they used that brought them success.

much of the effort put into teaching and studying is wasted because students do not adequately process their experiences, nor are they given time to reflect upon them.

The degree to which one understands rests on the connections or relationships and the richness of these relationships.

Our four corners and a diamond graphic organizer has five areas: What do you need to find? What do you already know? Brainstorm possible ways to solve this problem. Try your ways here. What things do you need to include in your response? What mathematics did you learn by working this problem?

teachers reported dramatic improvements in students' mathematics scores on open-response items after implementing the four corners and a diamond graphic organizer.

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.   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.