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For instance, how often do most adults encounter a situation in which they need to solve a quadratic equation? Do they need to know what constitutes a “group of transformations” or a “complex number”? Of course professional mathematicians, physicists and engineers need to know all this, but most citizens would be better served by studying how mortgages are priced, how computers are programmed and how the statistical results of a medical trial are to be understood.

Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering.

Traditionalists will object that the standard curriculum teaches valuable abstract reasoning, even if the specific skills acquired are not immediately useful in later life. A generation ago, traditionalists were also arguing that studying Latin, though it had no practical application, helped students develop unique linguistic skills. We believe that studying applied math, like learning living languages, provides both useable knowledge and abstract skills.

In math, what we need is “quantitative literacy,” the ability to make quantitative connections whenever life requires (as when we are confronted with conflicting medical test results but need to decide whether to undergo a further procedure) and “mathematical modeling,” the ability to move practically between everyday problems and mathematical formulations (as when we decide whether it is better to buy or lease a new car).

I always knew there was more I wanted to convey to them about their writing, about how they had or had not created meaning for the reader.

It took me about 10 minutes per paper, times 68 papers, so the last week and a half have been intense. If you’re doing the math, that’s over 11 hours of paper grading. If I am going to put in that kind of time for grading, I must see my students growing as writers. Period.

 I liked knowing that my essay got individual attention, individual feedback, and I feel like you cared about what I wrote.

A small number of students (actually, fewer than 5) said that they didn’t feel that the verbal comments were all that helpful.

hurtful to hear me say out loud what was wrong with their papers

Writing is personal, and feedback can feel like an attack.

tried out a new way of assessing student work — screencasting

always evolving

We have to keep developing our capabilities and avoid falling behind.

no matter how well prepared people are in their formative years, few can achieve and maintain their best performance on their own.

outside ears, and eyes, are important

For decades, research has confirmed that the big factor in determining how much students learn is not class size or the extent of standardized testing but the quality of their teachers.

California researchers in the early nineteen-eighties conducted a five-year study of teacher-skill development in eighty schools, and noticed something interesting. Workshops led teachers to use new skills in the classroom only ten per cent of the time. Even when a practice session with demonstrations and personal feedback was added, fewer than twenty per cent made the change. But when coaching was introduced—when a colleague watched them try the new skills in their own classroom and provided suggestions—adoption rates passed ninety per cent. A spate of small randomized trials confirmed the effect. Coached teachers were more effective, and their students did better on tests.

they did not necessarily have any special expertise in a content area, like math or science.

The coaches let the teachers choose the direction for coaching. They usually know better than anyone what their difficulties are.

teaches coaches to observe a few specifics: whether the teacher has an effective plan for instruction; how many students are engaged in the material; whether they interact respectfully; whether they engage in high-level conversations; whether they understand how they are progressing, or failing to progress.

must engage in “deliberate practice”—sustained, mindful efforts to develop the full range of abilities that success requires. You have to work at what you’re not good at.

most people do not know where to start or how to proceed. Expertise, as the formula goes, requires going from unconscious incompetence to conscious incompetence to conscious competence and finally to unconscious competence.

The coach provides the outside eyes and ears, and makes you aware of where you’re falling short.

So coaches use a variety of approaches—showing what other, respected colleagues do, for instance, or reviewing videos of the subject’s performance. The most common, however, is just conversation.

“What worked?”

“How could you help her?”

“What else did you notice?”

something to try.

three colleagues on a lunch break

Good coaches, he said, speak with credibility, make a personal connection, and focus little on themselves.

“listened more than they talked,” Knight said. “They were one hundred per cent present in the conversation.”

coaching has definitely changed how satisfying teaching is

trying to get residents to think—to think like surgeons—and his questions exposed how much we had to learn.

a whole list of observations like this.

one twenty-minute discussion gave me more to consider and work on than I’d had in the past five years.

watch other colleagues operate in order to gather ideas about what I could do.

routine, high-quality video recordings of operations could enable us to figure out why some patients fare better than others.

I know that I’m learning again.

It’s teaching with a trendier name. Coaching aimed at improving the performance of people who are already professionals is less usual.

modern society increasingly depends on ordinary people taking responsibility for doing extraordinary things

coaching may prove essential to the success of modern society.

We care about results in sports, and if we care half as much about results in schools and in hospitals we may reach the same conclusion.

district was innovating

there is no good way to quantify those achievements — putting them in a tough spot with voters deciding whether to bankroll this approach again

“We’ve jumped on bandwagons for different eras without knowing fully what we’re doing. This might just be the new bandwagon,” he said. “I hope not.”

$46.3 million for laptops, classroom projectors, networking gear and other technology for teachers and administrators.

If we know something works

it is hard to separate the effect of the laptops from the effect of the teacher training

The high-level analyses that sum up these various studies, not surprisingly, give researchers pause about whether big investments in technology make sense.

Good teachers, he said, can make good use of computers, while bad teachers won’t, and they and their students could wind up becoming distracted by the technology.

“It’s not the stuff that counts — it’s what you do with it that matters.”

“Test scores are the same, but look at all the other things students are doing: learning to use the Internet to research, learning to organize their work, learning to use professional writing tools, learning to collaborate with others.”

that computers can distract and not instruct.

“They’re inundated with 24/7 media, so they expect it,”

The 30 students in the classroom held wireless clickers into which they punched their answers. Seconds later, a pie chart appeared on the screen: 23 percent answered “True,” 70 percent “False,” and 6 percent didn’t know.

rofessor Cuban at Stanford argues that keeping children engaged requires an environment of constant novelty, which cannot be sustained.

engagement is a “fluffy

term” that can slide past critical analysis.

creating an impetus to rethink education entirely

guide on the side.

Professor Cuban at Stanford

But she loves the fact that her two children, a fourth-grader and first-grader, are learning technology, including PowerPoint

“There is a connection between the physical hand on the paper and the words on the page,” she said. “It’s intimate.”

Mr. Share bases his buying decisions on two main factors: what his teachers tell him they need, and his experience. For instance, he said he resisted getting the interactive whiteboards sold as Smart Boards until, one day in 2008, he saw a teacher trying to mimic the product with a jury-rigged projector setup. “It was an ‘Aha!’ moment,” he said, leading him to buy Smart Boards, made by a company called Smart Technologies.

This is big business.

“Do we really need technology to learn?” she said. “It’s a very valid time to ask the question, right before this goes on the ballot.”

Continuously upgrade educators' classroom technology skills as a pre-requisite of "highly effective" teaching

Home Advocacy Top Ten in '10: ISTE's Education Technology Priorities for 2010 Through a common focus on boosting student achievement and closing the achievement gap, policymakers and educators alike are now reiterating their commitment to the sorts of programs and instructional efforts that can have maximum effect on instruction and student outcomes. This commitment requires a keen understanding of both past accomplishment and strategies for future success. Regardless of the specific improvement paths a state or school district may chart, the use of technology in teaching and learning is non-negotiable if we are to make real and lasting change.  With growing anticipation for Race to the Top (RttT) and Investing in Innovation (i3) awards in 2010, states and school districts are seeing increased attention on educational improvement, backed by financial support through these grants. As we think about plans for the future, the International Society for Technology in Education (ISTE) has identified 10 priorities essential for making good on this commitment in 2010: 1. Establish technology in education as the backbone of school improvement . To truly improve our schools for the long term and ensure that all students are equipped with the knowledge and skills necessary to achieve in the 21st century, education technology must permeate every corner of the learning process. From years of research, we know that technology can serve as a primary driver for systemic school improvement, including school leadership, an improved learning culture and excellence in professional practice. We must ensure that technology is at the foundation of current education reform efforts, and is explicit and clear in its role, mission, and expected impact. 2. Leverage education technology as a gateway for college and career readiness . Last year, President Obama established a national goal of producing the highest percentage of college graduates in the world by the year 2020. To achieve this goal in the next 10 years, we must embrace new instructional approaches that both increase the college-going rates and the high school graduation rates. By effectively engaging learning through technology, teachers can demonstrate the relevance of 21st century education, keeping more children in the pipeline as they pursue a rigorous, interesting and pertinent PK-12 public education. 3. Ensure technology expertise is infused throughout our schools and classrooms.  In addition to providing all teachers with digital tools and content we must ensure technology experts are integrated throughout all schools, particularly as we increase focus and priority on STEM (science-technology-engineering-mathematics) instruction and expand distance and online learning opportunities for students. Just as we prioritize reading and math experts, so too must we place a premium on technology experts who can help the entire school maximize its resources and opportunities. To support these experts, as well as all educators who integrate technology into the overall curriculum, we must substantially increase our support for the federal Enhancing Education Through Technology (EETT) program.  EETT provides critical support for on-going professional development, implementation of data-driven decision-making, personalized learning opportunities, and increased parental involvement. EETT should be increased to $500 million in FY2011. 4. Continuously upgrade educators' classroom technology skills as a pre-requisite of "highly effective" teaching . As part of our nation's continued push to ensure every classroom is led by a qualified, highly effective teacher, we must commit that all P-12 educators have the skills to use modern information tools and digital content to support student learning in content areas and for student assessment. Effective teachers in the 21st Century should be, by definition, technologically savvy teachers. 5. Invest in pre-service education technology