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Critically, pushing around symbols on paper is just a symbolic representation of the real math taking place within one’s head. When one does a calculation, whether it is by hand or by machine, an important feature of whether or not one can be said to be doing the calculation is whether or not one can predict the potential output from the algorithm, or if one understands the process they are using.

We also require, as a system, much more flexibility in the mathematics taught at the K-to-12 level. I’d like to see a system where many different types of mathematics are taught besides just the standard hierarchy leading to calculus.

His mathematical models are tailored to identify word patterns and thematic elements in written text. The number and strength of links among novels determine influence, much the way Google ranks Web sites.

Data-centric specialties are growing fast, giving rise to a new vocabulary. In political science, this quantitative analysis is called political methodology. In history, there is cliometrics, which applies econometrics to history. In literature, stylometry is the study of an author’s writing style, and these days it leans heavily on computing and statistical analysis. Culturomics is the umbrella term used to describe rigorous quantitative inquiries in the social sciences and humanities.

“What is critical and distinctive to human evolution is ideas, and how they evolve,” says Jean-Baptiste Michel, a postdoctoral fellow at Harvard.

Students at Manor New Tech typically complete nearly 200 projects over the course of their high school experience, with each project lasting about two to four weeks.

"How can we use mathematics to design and use a Dobsonian telescope?"

he rubric often includes time lines and information on essential elements of successful final products (for example, if a report may be produced as a podcast rather than a paper, the rubric specifies minimum length for the podcast).

First, there are fewer of them, with 156 standards for grades 9-12. In addition, 38 of those standards are identified as "advanced" standards, which leaves us with 118 standards for all students spread out over four years of high school, or just under 30 per year.

(My not-so-modest proposal is that no state legislature is allowed to require standards that they couldn't demonstrate proficiency on themselves. Since they are clearly successful adults and they are saying that these standards are necessary for all students to be successful, surely they'd be able to demonstrate proficiency by taking the same tests our students do. But I digress.

I'm still not sure whether teaching algebra as a separate course is the best way to accomplish it -- even for that small subset of our student population that is passionate about math and science.