Futures in the Math Class
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We should teach as much about the future as we do about the past! This presentation makes that case and provides some mathematical concepts that help students forecast future values.

We should teach as much about the future as we do about the past! This presentation makes that case and provides some mathematical concepts that help students forecast future values.

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  • Course objective: Student will be able to describe changes that are going in the environment and initiate change to create a preferred future for themselves and for TRADOC. Audience : TRADOC Interns Length: Four hours
  • Goals To highlight some of the attributes assigned to the Millennial generation To look at how the world has changed in the past three generations- so that we might understand the interaction between generations that we find in schools/work. To look at why this might be important to education Generations are characterized by groups of people born within the same time period– and have a strikingly similar values and view of the world based on shared early life experiences. It is about passing through life stages together… The theory is that b/c of our shared experiences- we might share beliefs towards science, technology, government, ‘progress’, national pride, gender, celebrity… Story isn’t that young people have changed- or parents have changed– but that some things in our world have changed– and others have stayed the same… We are all just responding and adapting as best we can…. It’s not about finding the best approach. Just recognizing how we might look at the world differently b/c we were born at a certain time– and passed thru the world changing at a different stage in life…
  • Goals To highlight some of the attributes assigned to the Millennial generation To look at how the world has changed in the past three generations- so that we might understand the interaction between generations that we find in schools/work. To look at why this might be important to education Generations are characterized by groups of people born within the same time period– and have a strikingly similar values and view of the world based on shared early life experiences. It is about passing through life stages together… The theory is that b/c of our shared experiences- we might share beliefs towards science, technology, government, ‘progress’, national pride, gender, celebrity… Story isn’t that young people have changed- or parents have changed– but that some things in our world have changed– and others have stayed the same… We are all just responding and adapting as best we can…. It’s not about finding the best approach. Just recognizing how we might look at the world differently b/c we were born at a certain time– and passed thru the world changing at a different stage in life…
  • The two major divisions of futures studies and four important roles. (Marine images again!)
  • A summary of futures techniques in six steps. These are the steps we use to build the survey of futures techniques.
  • Goals To highlight some of the attributes assigned to the Millennial generation To look at how the world has changed in the past three generations- so that we might understand the interaction between generations that we find in schools/work. To look at why this might be important to education Generations are characterized by groups of people born within the same time period– and have a strikingly similar values and view of the world based on shared early life experiences. It is about passing through life stages together… The theory is that b/c of our shared experiences- we might share beliefs towards science, technology, government, ‘progress’, national pride, gender, celebrity… Story isn’t that young people have changed- or parents have changed– but that some things in our world have changed– and others have stayed the same… We are all just responding and adapting as best we can…. It’s not about finding the best approach. Just recognizing how we might look at the world differently b/c we were born at a certain time– and passed thru the world changing at a different stage in life…
  • A wider set of factors to consider when describing change. These are the famous STEEP categories (Social, Technological, Economic, Environmental and Political) with Social divided into Demographic and Cultural. We just found out that we think that the categories came from STEP, created by Arnold Brown of Weiner, Edrich and Brown when he was publishing the Trend Analysis Reports for the Life Insurance Council of America in the late 1960s. According to Joe Coates, someone added Environmental in the 1970s after the flowering of the environmental movement. Other common categorizations are PEST and EPISTLE (by adding Information and Legal).
  • Goals To highlight some of the attributes assigned to the Millennial generation To look at how the world has changed in the past three generations- so that we might understand the interaction between generations that we find in schools/work. To look at why this might be important to education Generations are characterized by groups of people born within the same time period– and have a strikingly similar values and view of the world based on shared early life experiences. It is about passing through life stages together… The theory is that b/c of our shared experiences- we might share beliefs towards science, technology, government, ‘progress’, national pride, gender, celebrity… Story isn’t that young people have changed- or parents have changed– but that some things in our world have changed– and others have stayed the same… We are all just responding and adapting as best we can…. It’s not about finding the best approach. Just recognizing how we might look at the world differently b/c we were born at a certain time– and passed thru the world changing at a different stage in life…
  • These are common shapes of continuous change used to trend forecasters to predict what value a variable will have in the future.
  • Goals To highlight some of the attributes assigned to the Millennial generation To look at how the world has changed in the past three generations- so that we might understand the interaction between generations that we find in schools/work. To look at why this might be important to education Generations are characterized by groups of people born within the same time period– and have a strikingly similar values and view of the world based on shared early life experiences. It is about passing through life stages together… The theory is that b/c of our shared experiences- we might share beliefs towards science, technology, government, ‘progress’, national pride, gender, celebrity… Story isn’t that young people have changed- or parents have changed– but that some things in our world have changed– and others have stayed the same… We are all just responding and adapting as best we can…. It’s not about finding the best approach. Just recognizing how we might look at the world differently b/c we were born at a certain time– and passed thru the world changing at a different stage in life…
  • Org chart and Network picture

Futures in the Math Class Presentation Transcript

  • 1. Futures in the Math Class Dr. Peter Bishop Futures Studies University of Houston
  • 2. The Study of the Future
  • 3. Questions
    • What is the purpose of education?
    • How many of us were specifically prepared for a different (or changed) future?
    • How many of us were specifically prepared to influence (or change) the future?
    • Should we specifically prepare (teach) students to anticipate and/or influence the future?
    • If so, are we doing it?
    • If not, why not?
    ? ? ? ? ?
  • 4. Thinking about the Future
    • Foresight is a natural human ability -- the human ability to create (or re-create) sensations and images that are not immediately present
      • Some of those lie in the past – memory
      • Some lie in the present -- imagination
      • Some lie in the future – foresight
      • Some are fanciful – fiction
    • In lieu of formal training in foresight, we learn to think about the future in three different ways from three different sources, but not where you would expect to.
  • 5. Sociology and Social Change
    • Tables of contents from the 10 highest ranked sociology textbooks on Amazon.com
      • Average of 15 sections in each book (15 weeks in a semester)
      • Three did not have a chapter on social change
      • Seven did…
        • 7% of the chapters
        • 3% of the pages
    • No social change textbook in print for a years
  • 6. The Scientific Future
    • Predictability, according to natural law, was one of the most powerful cornerstones of the scientific revolution -- Newton, Leibniz, Enlightenment
    • So much so that it became the default assumption about the future for physical science,
      • social science, and the professions
    • Based on the belief of order,
    • causality, connectedness, and flow
    • The future as a river, following
    • one path and leading to a specific point
  • 7. The Contingent Future
    • We learn history as a series of events and actions usually with clear causal connections.
    • But, in last century, the contingencies and uncertainties inherent even in natural phenomena have become apparent
      • Stochastic processes -- Galton
      • Quantum mechanics -- Bohr, Heisenberg
      • Biological evolution -- Gould
      • Chaos theory -- Lorenz
      • Complexity science -- von Neuman, Wolfram, Kauffman
    • Based on the dominance of chance and uncertainty over determinism and predictability
    • The future as a dice game
  • 8. The Chosen Future
    • The religious, economic and political traditions of Western society place primary responsibility for the future on individuals—on their intentions and their actions.
    • Examples –
      • Religion claims that we will be rewarded and punished according to our actions; the law also holds individuals responsible for their actions.
      • Individuals in a market economy must provide for themselves and their families.
      • When something goes wrong, we look for someone to blame; when something goes well, we hand out awards.
    • Based on the dominance of human agency and free will over the forces of determinism and chance
    • The future as a blueprint
  • 9. The Actual Future
    • Which one is correct? If we teach about the future, which one should we use?
    • Why not use all three as the best way to think about the future?
      • The Expected Future
        • Where we are headed
        • The future if everything continues as it has
        • The result of conditions and trends (momentum)
      • The Alternative Futures
        • What might happen instead
        • The set of plausible futures if something less likely or unexpected happens
        • The result of events and issues (contingencies)
      • The Preferred Future(s)
        • What we want to happen
        • Either the expected or any of the alternative futures that is preferable
        • The result of our vision, goals, plans and actions (agency)
  • 10. Foresight in the Classroom
    • Three simple questions
    • What is going to happen? – Expected future
    • What might happen instead? – Alternative futures
    • What do you want to happen? – Preferred future(s)
    Present Vision Limit of Plausibility Alternative Futures Limit of Plausibility Past Expected
  • 11. Strategic Foresight
  • 12. Strategic Foresight
    • Forecasting
    • Describing the future
    • With maps, vistas, landscapes
    • Planning
    • Influencing the future
    • With compasses, headings, navigation
    Captain Leader First Mate Manager Navigator Planner Lookout Scanner
  • 13. Foresight Techniques
    • Framing Purpose, scope
    • Research Information, Scanning Intelligence
    • Forecasting Baseline, Scenarios
    • Visioning Vision, Goals
    • Planning Mission, Strategy
    • Acting Initiatives, Results
    Thinking about the Future: Guidelines for Strategic Foresight, Andy Hines & Peter Bishop, 2007
  • 14. Futures Methods
  • 15. Quantitative Futures Methods
  • 16. Current Conditions How big?
  • 17. How Big is What? People Number, place, sex, age, ethnic use technology Farming, energy, construction, manufacturing, transportation, information, military, biology to transform resources Water, food, materials, energy into economic goods Global, national, industrial, occupational, organizational (and waste products) Air, water, solid, hazardous under government International, financial, regulation social, infrastructure in a cultural context Traditions, beliefs, values Language Beliefs Values Norms People Nature Technology Government Economy
  • 18. Top 15 Most Important Quantities for U.S. and World
    • Population – number
    • Environment – amount of food produced, energy produced/imported, carbon released, temperature increased
    • Technology – number of autos, phones, computers, Internet nodes
    • Economy – size of workforce, GDP
    • Government – size of budget, proportion by major category
    • Culture – number of books, movies produced
  • 19. But they are all big (or small) numbers
    • Orders of magnitude, powers of ten, zeros (thousand, million, billion, etc.), prefixes (micro, nano, pico, etc.)
    • Cosmic Voyage, positive only, Morgan Freeman (4:51) – Copy 1 , Copy 2
    • Power of 10 , French translated to English, both positive and negative (10:17)
    • Population clocks
  • 20. #1a – Cutting numbers down to size -- Best between .01 and 100
    • Ratios – similar units
      • Proportions, percents of same quantities
      • Compare one time with another
      • Compare one location with another or a part to whole – city, county, Michigan, US, North America, Western Hemisphere, World
    • Examples
      • Population – age, ethnic distribution
      • Energy – source, use
      • Economy – industry, occupation, income (median, mean, percentiles)
      • Government – govt budget compared to GDP, employment compared to total
      • Maps – World Mapper
  • 21. U.S. Energy Flow, 2009 http://www.eia.gov/emeu/aer/pdf/pages/sec1_3.pdf
  • 22. #1b – Cutting numbers down to size -- Best between .01 and 100
    • Rates – different units
      • Same quantities but per something else
      • Rate of change (per unit of time) covered in the next section
    • Examples
      • Population – per capita, per household
      • Environment – parts per million, per billion
      • Technology – processor speed, number of devices per capita
      • Economy – , per worker, per $ GDP
      • Government – per Congressional district, per candidate
  • 23. Benefits
    • Individual numbers are meaningless!
      • European population = 831 million
      • CO2 emitted per year = 29.3 billion tons
      • # transistors on a chip = 2 billion
      • Size of Michigan economy = $382 billion
      • # Federal employees = 2.1 million
    • Knowledge comes from comparisons
      • U.S. population = 331 million
      • China emissions = 6.5 billion tons
      • # neurons in human brain = 100 billion
      • Size of Taiwan economy = $379 billion
      • # transportation employees = 4.2 million
    So what do you know now? What can you conclude? What can say that’s interesting?
  • 24. Trends How fast? World Population in 2:45 min
  • 25. Data Sources
    • The Statistical Abstract of the U.S.
    • The Statistical Abstract of the U.S.: Historical Statistics
    • U.S. Energy Information Agency
    • International Energy Agency
    • The Economic Report of the President
    What’s your favorite?
  • 26. U.S. Energy Overview http://www.eia.gov/emeu/aer/pdf/pages/sec1.pdf
  • 27. A picture is a worth a thousand numbers! What do you see?
  • 28. Impressions make a big difference
  • 29. Rates of Change
    • Continuous change
      • gradual improvement over long periods
      • usually preserves the framework/context
    • Discontinuous change
      • sudden change to new levels
      • usually destroys the framework/context
      • always involves short-term loss
  • 30. The Shapes of Incremental Change Linear Cyclic Asymptotic Exponential
  • 31. The Real Shape of Change Logistic Gompertz Pearl Fisher-Pry S-Curve 1 No problem. 2 What is going on here? 3 Whew!
  • 32. Eras in Information Technology
  • 33. Other disruptions Source:http://www.bsos.umd.edu/socy/vanneman/socy441/trends/divorce.jpg
  • 34. Transportation Eras Speed Riding Motoring Flying Law of diminishing returns Running Inherent capacity for performance
  • 35. Measurements of Change Absolute = X 2 – X 1 Percent change (x 2 - x 1 ) / x 1 * 100 Index numbers x 2 / x 1 * 100 Base of 100 Proportional change (x 2 - x 1 ) / x 1 Ratio change x 2 / x 1 Base of x 1 Numerator of difference Numerator of x 2
  • 36. U.S. Energy Production, 1949-2009 Absolute = 41.2 Quads Percent change 130% Index numbers 230 Base of 100 Proportional change 1.30 Ratio change 2.30 Base of x 1 Numerator of difference Numerator of x 2
  • 37. U.S. Energy Production, 1949-1970 Absolute = 31.8 Quads Percent change 111% Index numbers Base of 100 Proportional change Ratio change Base of x 1 Numerator of difference Numerator of x 2
  • 38. U.S. Energy Production, 1949-1970 Absolute = 31.8 Quads Percent change 111% Index numbers 211 Base of 100 Proportional change 1.11 Ratio change 2.11 Base of x 1 Numerator of difference Numerator of x 2
  • 39. Measures per Unit of Time 3.6% 5.3% 1.5 Q 1949 -1970 0.7% 1.4% (x 2 / x 1 ) ^ (1 / # yrs) – 1 [ Solving x 2 = x 1 * ( 1 + r ) ^ # yrs for r ] Compound average growth rate (CAGR) 0.8% 2.2% (x 2 - x 1 ) / x 1 * 100) / # yrs percent change / # yrs Annual average growth rate (AAGR) 0.2 Q 68.7 Q (x 2 - x 1 ) / # yrs absolute change / # yrs Average change per unit (year) 1970 -2009 1949 - 2009
  • 40. Forecasts How far?
  • 41. Assumptions in Trend Extrapolation
  • 42. Forecast to 2040 90.8 Q 110.7 Q X 3 = x 2 * ( 1 + CAGR) ^ 30 Compound average growth rate (CAGR) 91.5 Q 120.4 Q X 3 = x 2 * ( 1 + AAGR * 30 ) Annual average growth rate (AAGR) 80.3 Q 93.6 Q X 3 = X 2 + AAC * 30 Annual absolute change (AAC) 1970 -2009 1949 - 2009
  • 43. Three Different Measures
  • 44. Forecasting from 1970
  • 45. Still a Choice from 2009
  • 46. The Cone of Plausibility The Future is many, not one. Source: Charles Taylor, Army War College Present Limit of Plausibility Alternative Futures Limit of Plausibility Past Implications Baseline
  • 47. Take Aways
    • Things vary in size more than they appear to. It’s easy to underestimate orders of magnitude.
    • Graphs are better than tables for seeing patterns over time. And longer series show more patterns.
    • Impressions matter as much as actual numbers do, perhaps even more; different formulations give different impressions
    • Teach estimations on the fly. Close can be better than exact under the right circumstances.
    • Always compare ! Single numbers are meaningless.
    • Compare across similar objects (one country vs another), with larger or smaller sets (proportion of the whole), or across time (difference or time series)
    • Make inferences based on the comparisons. What do you know that you didn’t know before? What is interesting, troubling, unbelievable?
    • All extrapolations are based on models, and all models have assumptions . Different assumptions give different result.
  • 48. So What?
  • 49. Foresight by Discipline
    • Mathematics – time series, extrapolation, probability, preference ranking, criteria weighting
    • History – flow, change over time, time series, patterns, uncertainties, contingencies, alternative histories, historical images of the future, historical analogy
    • Literature, language –future tense, subjunctive mood, science fiction, three questions for fictional conditions and characters
    • Physical science – time series, extrapolation, technological applications, social consequences, public issues
    • Social science – social change, time series, cultural concepts of time, national and global awareness
  • 50. Benefits – the bottom line
    • The expected future
      • Causal reasoning
      • Mathematical extrapolation
      • Critical thinking, identifying assumptions
      • Implications analysis
      • Evaluation
    • The alternative futures
      • Challenging assumptions
      • Creativity, imagination
      • Causal reasoning from different premises
      • Estimation of plausibility
      • Implication analysis, evaluation
    • The preferred future
      • Values clarification
      • Preference ranking, criteria weighting
      • Communication, persuasion
      • Planning, organizing
  • 51. The Language of Plausibility
    • Indicative
    • Will
    • Must
    • Should
    Subjunctive May Might Could Past Present Future
  • 52. Rules for Talking about the Future
    • 1. The future is uncertain Admit uncertainty
    • 2. The future is plural Talk possibilities
    • 3. Different assumptions create Uncover and discuss different futures assumptions
    • 4. The future is being created--
    • -- outside in the environment Tell stories
    • --- inside people’s aspirations Encourage visions
  • 53. The Futures Education Project
    • Mission: help teachers include (more) material about the future in their existing courses and to offer (more) stand-alone courses in secondary schools, colleges and professional programs around the world
    • Target populations
      • Experienced futures educators – support and enhance their teaching
      • Aspiring futures educators – get them started on teaching about the future
    • Sponsored (at least initially) by the Futures Studies program at the University of Houston in collaboration with:
      • Learning Section, World Futures Society
      • Online Centre for Pedagogical Resarch, World Futures Studies Federation
      • Institute for the Future, Ann Arundel Community College
      • Futures Education and Research Network
      • Texas Future Problem Solving Program
      • Proteus, U.S Army War College
      • And the many universities and educators who already teach about the future
    We teach as much about the future as we teach about the past!
  • 54. For Additional Information
    • Phone 281-433-4160
    • E-mail [email_address]
    • Web futureseducation.wetpaint.org
    Dr. Peter C. Bishop Educator, Facilitator, Futurist
  • 55. Appendix 90.8 211.4 110.7 CAGR 91.5 188.2 120.4 AAGR 80.3 118.4 93.6 AAC Forecast to 2040 0.7% 3.6% 1.4% CAGR 0.8% 5.3% 2.2% AAGR 0.2 1.5 0.69 AAC 39 21 60 Years 1.33 2.11 2.30 Ratio change 33% 111% 130% Percent change 9.5 31.8 41.2 Absolute change 1970-2009 1949-1970 1949-2009