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How many? The U.S. Bureau of Labor Statistics says, “Employment of mathematicians is expected to increase by 16 percent from 2010 to 2020…. There will be competition for jobs because of the small number of openings in this occupation.”

1) Humankind’s hope for the future lies, as it always has, in the richness of human variability. We differ in experience, situation, aspirations, attitudes, abilities, interests, motivations, emotions, life chances, prospects, potential, and luck. To survive and prosper, these differences need to be exploited to the maximum. The core curriculum minimizes them. (2) Knowledge is exploding at an ever-accelerating rate. Whole new fields of study unimagined even a few years ago are emerging. The explosion isn’t just going to continue, it’s going to accelerate. Thinking we know enough to lock ANY curriculum in place — much less one that’s more than a hundred years old — is either naïve or malicious. (3) The future is unknowable. Period. Even if it were possible to standardize and program kids, we don’t know — NOBODY knows — what they’ll need to know next week, much less for the rest of their lives. They may need technical skills no one now has, or the ability to survive on edible weeds and a quart of water a day. Neither the Common Core nor the tests that manufacturers are able to write can take adequate account of an unknown future.

Discussions are led by the students where outside content is brought in and expanded.  These discussions typically reach higher orders of critical thinking.Collaborative work is fluid with students shifting between various simultaneous discussions depending on their needs and interests.Content is given context as it relates to real-world scenarios.Students challenge one another during class on content.Student-led tutoring and collaborative learning forms spontaneously.  Students take ownership of the material and use their knowledge to lead one another without prompting from the teacher.Students ask exploratory questions and have the freedom to delve beyond core curriculum.Students are actively engaged in problem solving and critical thinking that reaches beyond the traditional scope of the course.Students are transforming from passive listeners to active learners.

Modeling -- involves an expert's carrying out a task so that student can observe and build a conceptual model of the processes that are required to accomplish the task. For example, a teacher might model the reading process by reading aloud in one voice, while verbalizing her thought processes (summarize what she just read, what she thinks might happen next) in another voice. Coaching - consists of observing students while they carry out a task and offering hints, feedback, modeling, reminders, etc. Articulation - includes any method of getting students to articulate their knowledge, reasoning, or problem-solving processes. Reflection - enables students to compare their own problem-solving processes with those of an expert or another student. Exploration - involves pushing students into a mode of problem solving on their own. Forcing them to do exploration is critical, if they are to learn how to frame questions or problems that are interesting and that they can solve (Collins, Brown, Newman, 1989, 481-482).