Seeing how a secant line 'becomes' a tangent line, using a limit

Desmos has a very nice Applet that allows us to play with a curve and its secant and tangent lines. We can play with it to see what needs to be done, using the notion of a limit, to get a secant line to become a tangent line. Tangent lines define the slope of a curve at a specific point on that curve, and is the heart and soul of derivatives (differential calculus)!

If you are not familiar with it, Desmos is one of the good math sites for graphing and manipulating just about any function or dataset you will ever see.

What does good "Critical Thinking" look like?

Any survey of employers, such as CEOs of Fortune 500 companies and others, of characteristics they are looking for from today's students, in the top 3 will be 'critical thinking.' In general, this is being able to take a complex problem or situation and think it through logically and with an open mind, finding and using evidence to support whatever answer or conclusion you come up with for that problem. It is also being able to research the problem using credible, reliable sources of information to do so.

Here is a pretty good guide or rubric to determine whether you are doing a good job with critical thinking, on a 4-point scale:

1. does not contribute to the solution, using opinion instead of independent evidence;
2. answers question but without justification, agree/disagree but without saying why, incomplete sentences/thoughts and punctuation;
3. justify your position, opinion or answer to the problem, say why you agree or disagree, using complete sentences and thoughts;
4. justify your position, opinion or answer using text evidence (from credible, reliable sources) and real-world examples, ask questions of others, use complete sentences and thoughts with correct punctuation and grammar

Having Cellphones and Laptops out during class leads to less learning, lower scores

What is more or less common sense, a new study shows significant drops in learning when students are allowed to have cellphones and laptops out during class. And this happens not only to those students using personal devices, it also affects students who do not have their devices out.

This matches numerous personal anecdotes, and seems to match common sense. Many teens and college students believe they are able to multi-task, and state that personal devices do not affect how effective they are as they split attention, but this study shows pretty conclusively this belief is incorrect.

Now in my classes, I want cellphones and Chromebooks away most of the time. There IS a time and place for devices, depending on the nature of the activity we are doing. Also, do not forget there are studies that show significant decreases in scores and learning comprehension for those students who take notes on a laptop compared to those who write out notes by hand.

Tech is wonderful in so many ways, but we are finding out 'old school' methods should NOT all be thrown out quite yet!

Battle between Calculus and Physics - A ChemPhys Classic

Going back a few years, Noah Korman's "In Newton We Trust" is still asked about. Check it out!


In Newton We Trust from Noah Korman on Vimeo.