During most of the twentieth century, the United States dominated the math field with its output of important mathematicians and its great strides in engineering, science, and finance. But the depth of the country's decline is apparent in some frightening statistics: Less than one-third of eighth-grade students and fewer than one out of four seniors now test as proficient or better for math, according to recent National Assessment of Education Progress reports.

One technology that jump-starts algebraic thinking for middle school students is SimCalc, a program that uses computer-based graphs, animation, symbols, and tables to make difficult concepts, such as mathematical rates of change and accumulation, easier for students to learn.

Cindi Rigsbee, for example, makes sure her students know when text language is appropriate and, more important, when it's not. She talks frequently in class about types of writing, the intended reader, and the evolution of language. At the beginning of each school year, she introduces a discussion about the way English has transformed over time. "We look at Old English, Middle English, and what was contemporary English in the time of Jane Eyre. Then I show them a MySpace page."

Most IQ tests attempt to measure two types of intelligence--crystallized and fluid intelligence. Crystallized intelligence draws on existing skills, knowledge and experiences to solve problems by accessing information from long-term memory. Fluid intelligence, on the other hand, draws on the ability to understand relationships between various concepts, independent of any previous knowledge or skills, to solve new problems. The research shows that this part of intelligence can be improved through memory training.

So the shift to public display, a shift to expected social interaction, changed the way the students learned and the effort they put into their education. If that’s not an incentive to experiment with and use social software I don’t know what is. Social software isn’t just a new way to work, it changes the effort we put into that work. Now there is a sound byte for social media consultants.

I put the Illinois Learning Standards and the Synapse side-by-side to suggest that we require students to learn subjects inside of little boxes, while students think about them in highly connected networks. The boxes in the Standards are separated from each other in all sorts of ways: living things are in different boxes than processes of the Earth. Different things about the same subject are spread out over five different grade levels. There seems little chance of having a thought that relates an early box in “A” to a late box in “E.”

A little brain boost is something we could all use now and then. A new option may be on the horizon. Researchers at the National Institute for Neurological Disorders and Stroke, in Bethesda, MD, are studying how applying gentle electrical current to the scalp can improve learning.

The creativity at the faire wasn't limited to hardware and electronics, either. There were tables of people silk-screening their own designs and creating new things with old cloth and thread. The overall lesson of the day: Ingenuity and creativity is something we all possess, and, as with any other skill, your inner DIYer can be cultivated.

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Resilience is the ability to successfully manage life and adapt to stressful events. Resilience is developed in childhood, when there are loving people available to help during difficult times, but if a child feels alone, resilience is not developed just because challenging things are happening.

Due to recent brain research on neuroplasticity, we know that brains are growing and creating neural pathways during childhood and through adolescence. What's new in this book is the focus on a repetitive practice that strengthens these neural pathways and teaches young people concrete skills to calm themselves and focus their attention.

The interesting part of the connection between stress and learning is that the prefrontal cortex of the brain is the area for paying attention, calming, and focusing as well as the area for short- and long-term memory.

Finnie's students designed an emergency plan for the home, and an emergency kit. They also created a newspaper, complete with illustrations, that "tells someone who doesn't know anything about earth science all about earthquakes, volcanoes, and plate tectonics how they're all related, and why we have earthquakes." In addition, the students videotaped a five-minute earthquake-safety commercial in the form of a rap song, and victory was theirs.