Hi Ash,
I teach at the 2-year college level, and so I can't comment with any expertise on primary and secondary-school education, but I do encounter many students recently graduated from high school who are woefully unprepared in basic areas such as mathematics and reading comprehension.
One strategy I've found extremely helpful, especially for these students, is to divide the concepts taught in each of my courses into two categories: "have to know" and "good to know". The "good to know" concepts get tested on a percentage scale, with a certain minimum score for passing. Those concepts which are "have to know" (i.e. critically important) get tested at a mastery level -- students cannot pass the course unless and until they demonstrate mastery (100% competence) of those concepts on both written tests and performance evaluations. At first this might seem unnecessarily strict and/or disheartening to students who fail to demonstrate mastery. The key to its success is that students are given multiple opportunities to demonstrate mastery, with each re-try triggering a one-on-one conference with me to identify where they're experiencing trouble and what to do to prepare for their next try. This process focuses both student and instructor attention directly on what they need the most. In fact, mastery assessment has proven most beneficial to those students who arrive most unprepared from high school.
One huge problem I see with the structure of most courses is that it's based on a percentage scale, allowing a fairly large amount of concent to go unlearned. If a student knows that their grade is based on a 500-point scale, and all they need is 370 points to pass, the course is likely to be treated by the student as a kind of game: a cynical act of collecting points to win. With mastery-based assessment, however, it's no longer a game one can cut corners on.

# Tony Kuphaldt

Instructor - college

Bellingham, WA, United States

## About Tony

### Languages

### Areas of Expertise

Instrumentation & Control Engineering, Electronic Circuits, curriculum developer, Technical Writing

### An idea worth spreading

That the ultimate purpose of public education should be to teach people how to learn independently, because this is the key to unlocking the doors of personal understanding and opportunity.

### I'm passionate about

Education, energy, sustainability, mathematics, computer programming, Socratic inquiry, open-source development, writing, reading

### People don't know I'm good at

Spinning pillows on my fingertips, like some people can spin basketballs.

## Comments & conversations

Hi Reza,
My criticism is directed toward's Taylors remarks, not his actual accomplishments (which are quite impressive) and especially not his future potential. His presentations are misleading because they are easily misinterpreted by non-specialists: when Taylor speaks of molten salt reactors, Brayton gas cycles, small-scale reactors with decades of fuel capacity, and other technical details foreign to a general audience, claiming that it's his own "radical plan", people will come away with the impression no one else has thought of or tried this before, when even a cursory Google search reveals this is not the case.
The major challenges of MSRs won't be addressed by any aspect of Taylor's plan as presented. In fact, one element of his plan (to have the reactor be a sealed system) actually exacerbates one of the main problems with MSRs, and that is the removal of fission products which will wreak all kinds of havoc with the system components as they accumulate. His post to this thread claiming his reactors to be "some of the best" is in fact what pushed me from observer to participant in this discussion. Bold assertions demand commensurate evidence, especially in the sciences. This is my point of contention with Taylor, nothing more and nothing less.
What's at stake here is Taylor's reputation as a young researcher, which is going to become critically important as he seeks funding to pursue his dreams. By providing Taylor a high-profile platform to make these claims unvetted, TED may have unwittingly done damage to this bright young man's professional future.

No, I certainly wouldn't expect Taylor to reveal patentable solutions to these problems in a public talk, but I would expect him to mention that as being his innovation if it were the case. As the talk stands now it is conspicuously devoid of original ideas, or acknowledgement of the work that's been done in this direction by others so far.
Please understand that I did not mean the words "non-technical" or "ignorant" to be pejorative. All I'm trying to say is that this is a subject of specialists, and it's easy for someone unfamiliar with details of nuclear reactors to be overly impressed. Even Lawrence Lessig -- brilliant and innovative man that he is -- cited Taylor's first talk as an example of innovation in nuclear fusion, when in fact it was just a really cool lab project based on a 50-year-old design.
For the record, I think Taylor is an incredibly bright and motivated young man, and I sincerely hope he is able to realize his aspirations. It takes serious technical chops to do half the stuff he's done. However, after reading many of the replies from TEDsters, it's apparent many people here think these ideas are much more than they actually are.
My advice to Taylor is to always keep in mind who his audience is, and to make sure he's not giving false impressions that could damage his credibility, or the credibility of TED talks for that matter.

If Elon Musk were to present an "innovative" new rocket engine design to a general audience, claiming it was innovative precisely because it used "liquid fuel" instead of solid powder, he would be criticized just the same. It's the context of the audience that matters here. To a non-technical audience ignorant of reactor design, your presentation sounds like a collection of original design ideas ("my radical plan . . .") publicly unveiled for the first time ("a big announcement"). To the technically savvy, it seems like all you've proposed is building small versions of the GIF reactor and burying them underground, without addressing any of the known challenges.
Unless you have invented real solutions to real problems in this reactor design (e.g. material corrosion in high-temperature salt loops over decades of time), you can hardly claim to have "designed some of the best darn Small Modular Molten Salt Reactors out there."

How to think critically and solve technical problems is probably the most important skill set I've acquired on my own, and this was primarily enabled by my having a personal computer when I was in elementary school (late 1970's) with which I could write programs in the BASIC language. Self-learning requires a feedback loop where the learner can evaulate the effectiveness of what they've learned and make corrections based on the results, and computer programming offers this in spades (e.g. if there's a mistake anywhere, the program won't run the way you intend).
There are more profound lessons in life I've learned by way of personal experiences, but I cannot truly say I learned them "on my own" because in most cases the lessons were offered to me by others and it just took me a long time to recognize the wisdom of what they were trying to teach me.

Ideas to help kids see the power of math is blending their mathematical learning with practical tools. I heard once of a geometry teacher who taught the use of computer-drafting software (I think it was Rhino) simultaneously with teaching geometrical axioms. Not only did the students immediately see the truth of those axioms and thereby grasp the concepts easier, but they also learned to use real-life software useful in certain careers.
Microsoft Excel (or any spreadsheet for that matter) is another way to integrate real-world tools with mathematical education. Applying algebra to get a spreadsheet to do the calculations you want it to, or using a spreadsheet to visually represent data, is a powerful thing. I have my (2-year technical) college students use Excel regularly as a mathematical modeling tool.
One of the most memorable examples of math education for kids I've seen is my fifth-grade teacher, who had us building model rockets and using trigonometry to estimate how high they flew. First, we would stand 100 feet away from the launchpad, sight the apogee of the rocket using a special protractor, then look up the value of the tangent of that angle (this was in 1980 -- we used trig tables rather than hand calculators) and multiply by 100 to find the rocket's height. Very cool stuff, and it took all the fear away from trigonometry when I encountered it much later in school.

Simpler forms of math are used by technicians in a variety of fields to perform diagnosis on complex systems. Understanding the mathematical relationships between variables allows one to determine potential causes by careful analysis of the effects.
One example that comes to mind is a diagnosis I once made on a leaking compressed air system at a commercial facility. Compressed air was leaking out of the pipes somewhere in this expansive system, but we did not know where. We connected a pressure sensor to the main pipe and used a computer to graph pressure versus time. This revealed an inverse-exponential curve, which is precisely what you would expect if the air pressure at the leak were falling with time -- an air leak occurring at some location where the leak pressure was constant would produce a linear drop of main supply pressure over time (based on differentiating the Ideal Gas Law: dP/dt = dn/dt R T / V). We knew this system had pressure-regulated as well as unregulated segments to it, and from this analysis of the pressure drop we could tell the leak must have been in one of the unregulated segments of piping. This knowledge allowed us to eliminate large portions of the piping and focus our search on a smaller part of the system, to find the leak faster than if we searched the entire piping system.
A subset of mathematics education is estimation. A person who can rapidly estimate quantities is able to apply basic arithmetic to a wide variety of problems in life (time to arrive at a destination, costs versus returns of financial decisions). An understanding of probability is crucial to making intelligent decisions involving risk and reward. As I like to tell my students, lotteries are a form of taxation on the math-illiterate.
Simply put, math is a powerful tool for understanding the physical world around us. Who wouldn't want to have a powerful tool at their disposal to help them make good decisions in life?

Here are some examples:
* Fourier analysis of waves: Jean Baptiste Fourier discovered that any repeating waveform is mathematically equivalent to a series of sinusoids (sine and cosine waves) added together at different amplitudes, phase shifts, and harmonic (integer-multiple) frequencies. When you look at a graphical equailizer on a stereo system and see the individual bargraphs showing how much of each frequency comprises the sound, you are seeing the results of a Fourier transform function applied to that wave. Fourier transforms work for *all* waves, not just pressure waves (sound). In machine vibration analysis, for example, technicians and engineers use Fourier tranforms to decompose a vibration waveform into its different harmonic frequencies, those decomposed signals holding clues about the health of the machine.
* Charles Proteus Steinmetz applied the notation of imaginary (vs. real) numbers to the solution of alternating-current electric circuits near the turn of the last century. His mathematical contribution to the then most empirical subject of electrical engineering revolutionized the field. As it turns out, complex numbers work wonderfully well to represent electrical signals (there are those waves again!) changing in time. Technicians and engineers in the electrical industries use Steinmetz's principles continually to calculate voltage and current quantities in power systems.
* The calculus principles of integration and differentiation are widely used in automatic control systems. Differentiation is used to calculate the rapidity of some variable's change, for the purpose of damping rapid changes. Integral is used to calculate how much control action is necessary to bring a variable back to its "setpoint" (target value), by integrating the error (variable-setpoint) over time. Technicians and engineers "tune" control systems by adjusting the coefficient multipliers of the differentiation and integration functions to achieve stable control.

Great topic, Edward! At the risk of being too general, here are my three nominations:
(1) Infallibility
(2) Utopianism
(3) Entitlement

Hi Peter,
"Is your contention then that a being capable of creating the universe is incapable of directing men to write a book? Presumably you also doubt his ability to communicate directly with we mere mortals?"
Clearly no. By the same token I also don't doubt Barack Obama's ability to call you on the telephone tonight and brief you on top-secret matters of foreign policy concerning the present situation with Iran. However, if you told me tomorrow that the President of the United States did exactly that, I could not believe you unless and until you could prove to me that you were in such a position as to be privy to this kind of information. Even then, I would need some reasonable evidence demonstrating that such a thing did happen, after having established the fact that it could.
"Folks have absolutely nothing to lose, but most refuse what is the option of eternal life. Why? Beats me; pride I guess."
Please consider that a position of non-belief could spring from humility rather than pride. I, and others like me, consciensciously refuse to place faith in matters like heaven and hell when the spectrum of alternative possibilities is so broad. Speaking on behalf of all those people who do not have a direct line of communication with God, we simply have no rational basis for certitude in these areas. To ask someone in this position to make a positive leap of faith in certain doctrines is tantamount to requesting they lie: asking them to claim to know something they do not in fact know. What this person stands to lose by making the leap of faith is their integrity.
The promise of eternal life in heaven for making this leap only makes the proposal sound all the more suspicious.