Process Model for SecondSchool ™

1. Process Model for SecondSchool ™ Massive On-Line Tutoring System (MOTS) * * Presentation by Paul Stephen Prueitt, PhD January 11, 2013

2. The Tale of Two Systems • K-12 education uses pedagogy and curriculum that rarely prepares an individual in the way typical university mathematics facility would like to see • College or university expectations is that the great majority of students will be unable to learn

3. Summary of Challenges • Mathematics Learning Support programs are not working for almost all under prepared students • New online delivery systems do not take into account the unique nature of communication about higher mathematics • Rote memorization is used in high school but this pedagogy fails to open the doors to higher mathematics • Mathematics faculty have a difficult time changing pedagogy from rote memorization to deep learning • The learning challenges of today’s students are all too often misrepresented • The majority of the learning task is not in learning mathematics, but in understanding why learning mathematics is so difficult

4. Solutions • MOOC (massive open online course) techniques for managing tens of thousands of participants • Right size, just in time, competency based presentations of topics using a repository of short videos • Adaptive assessment of skill using ALEKS software • Deep learning methods, including narrative presentations by students using a four step method and individualized grading by domain expert • 7-24 availability of a repository of topic videos • Peer-2-Peer interaction via social networks • Rolling four-week placement into learning communities • Develop separate Massive Online Tutoring Systems (MOTS) for each of the fifty states

5. Process • Due to grant from McGraw-Hill, free ALEKS course support is available for spring 2013 • Adaptive instruction based on four week re-assessment strategy designed to take each student as far as possible in one semester • Online lectures and tutoring support to parallel class instruction • Handwritten exchanges that communicate knowledge of higher mathematics • Combination of Q&A tests, self study, guided interaction, peer-to-peer social media, and measurement of synthesis using narrative tests (the Blank Paper Test) • Possible radical change in success in STEM enrollments • High school to college transition techniques might be seen nationally as a Best Practice, to be duplicated

6. Visual Representation of the Communication Problem “The Topics Foundational to the Study of Higher Mathematics 1) Communicating about the topics in mathematics MUST use the notation that mathematicians use to describe sets, functions, and the various abstractions in the foundations of higher mathematics sets fractions functions fractions addition Real Numbers abstraction graphs Replacement set Realizing Dreams History and Civilization Communicating things Private Feeling about Capacity of Self Democracy and Citizenship Future oriented learning Social Responsibility Internet Individual capacity Using Smart Systems Jobs and Security Use of Knowledge Technologies Application to Real World 2) Self-imposed limitations caused by priori experience in math class MUST be recognized Buzzing Confusion about what Higher Mathematics is 3) Applications to real world problem solving, including non-technology applications, MUST be absorbed along with the pure elements of higher mathematics

7. Use of Knowledge Technology “The Topics Foundational to the Study of Higher Mathematics 1) The near future requires a different type of education than was required in the agricultural age Realizing Dreams Communicating things Private Feeling about Capacity of Self Future oriented learning Internet Application to Real World 2) Individual realization of dreams MUST be more universally expressed and to connected philosophically and financially to foundational concepts in STEM literatures Individual capacity Using Smart Systems Use of Knowledge Technologies 3) Just in time, right size learning systems MUST soon be everywhere adopted and must not have financial barriers

8. Foundations of Higher Mathematics “The Topics Foundational to the Study of Higher Mathematics sets fractions 1) Higher mathematics cannot be seen as the property of an elite few functions fractions addition Real Numbers abstraction graphs Replacement set Realizing Dreams History and Civilization Communicating things Private Feeling about Capacity of Self 2) The connection of scholarship and history must be made so that the role mathematics plays in our everyday world is revealed, clearly Application to Real World Use of Knowledge Technologies 3) Advanced foundational topics MUST be part of K-12 instruction, these should include topological notions of nearness, and the abstract properties of arithmetic in the set of real numbers

9. Applications to Real World 1) “K-12 type word problems” do not represent the primary value that an understanding of higher mathematics brings “The Topics Foundational to the Study of Higher Mathematics History and Civilization Private Feeling about Capacity of Self Democracy and Citizenship Social Responsibility Use of Knowledge Technologies 2) This primary value in is honing critical and analytic reasons skills Using Smart Systems Jobs and Security Application to Real World 3) Future and current jobs depend on integrating a whole curriculum in colleges, not something watered down because students are not properly prepared and professors are busy with other things

10. Next Steps • Proto-type the Second School ™ Massive On-line Tutoring System during the spring semester 2013 • Develop publishable data on deep learning methods • Develop political support for a National Education Bridge