Sense from Non-Sense:
Making Meaning with Statistics

Introduction

Today's infotectives welcome the arrival of user-friendly statistical packages which simplify number crunching and picture making. After all, we know that "a picture is worth a thousand words." A graph is often the best way to communicate the meaning lying hidden in a scattering of thousands of data points.

What is an infotective? . . . a student thinker capable of asking great questions about data (with analysis) in order to convert the data into information (data organized so as to reveal patterns and relationships) and eventually into insight (information which may suggest action or strategy of some kind. An infotective solves information puzzles and riddles using all kinds of clues and new technologies. The problem-solving requires synthesis (invention) and evaluation (careful choices from lists of options).

Infotective is a new term designed for education in an Age of Information. In the smokestack school, teachers imparted meanings for students to digest, memorize and regurgitate. In Information Age schools, students make the meaning. They puzzle their way through piles of fragments - sorting, sifting, weighing and arranging them until a picture emerges.

New technologies enable even young students to test the power of relationships between variables in order to explore cause-and-effect and to attempt fore-casting. These new technologies support hypothesis-testing, theory testing and model building by intermediate and middle school students as well as the older ones. They allow systems thinking to creep down into elementary classrooms.

For decades, school math has been flawed by its lack of explanatory power and its divorce from real world applications. The NCTM standards call for a dramatic shift to remedy this flaw. Statistical packages can support this kind of change, empowering students to use math to increase their understanding of the world by converting the data they have collected into insight.

A turbulent, rapidly changing world offers us with a great deal of non-sense, a swirling ocean of data bombarding the average citizen at a remarkable pace with an unrelenting intensity. Some of this data has been organized and manipulated in order to twist and control our thinking, as with political advertising, sound-bites and infomercials. Toffler calls this manipulation infotactics . We need to raise a generation of infotectives who are capable of navigating through the oceans of data, even when the surface is heavy with fog, making sense out of non-sense in order to build a healthier and stronger world community.

I. The Infotective at Work: Exploring Essential Questions and Key Variables

Back in the early 1980s when databases first made an appearance, many pioneering teachers were content with student data-gathering to fill these great computer file-cabinets, but data-collection without purpose was soon revealed to be a waste of time. If the data is collected without first determining a driving research question, what Sizer's folk might call an "essential question," several problems often develop:

* The data collected is returned in a mixture of formats making retrieval and analysis difficult.

* The design of the database fields and data entry codes makes retrieval and analysis difficult.

* Without identifying all key factors and variables which influence a system, data collection is likely to be incomplete and the explanatory potential of the study is limited.

Students in one class collected all kinds of data about presidents, for example, only to find that they could do little with the data once entered. They were left with the frustrating question, "So what?"

"So what?" belongs at the beginning of the research. It is a fundamental insight question. "Why are we gathering all this data? What do we hope to prove? What mystery are we solving? What theory are we testing? What strategies are we evaluating?"

For most of these research questions, we are hoping to find out how something works in order to make wise decisions and solve various problems. The more we know about a system and how its key variables interact, so the theory goes, the more likely we are to act in ways which are fruitful. (For an excellent introduction to systems thinking and how it relates to organizations like schools, take a look at Peter Senge's Fifth Discipline.)

The student collects data about African countries, for example, in order to understand which factors are most closely associated with high or low rates of infant mortality. Which health delivery systems are most likely to reduce infant mortality? Which factors outside the health delivery systems might also be key factors? What is the inter-play of these factors?

Why do we bother with such research? We expect that infotectives will thereby develop insights that will guide their voting, their career selection and their eventual contribution to the society. Rather than being befuddled by infomercials and propaganda, they can muddle and puzzle their way through, learning to see both the trees and the forest. Shown a series of graphs, they will ask what models lie behind the pictures. What assumptions are hidden below the surface pictures?

II. An Example: PEMD Discovery Software

PEMD is a HyperCard based system which empowers students to collect and analyze data in powerful ways, providing graphing tools and supporting predictive thinking.

The thinking behind the software emphasizes the visual "understanding" of data:

Ultimately, we want to "understand" data to the point where we can use it to accomplish some worth-while end. The end in business and government may be the development of a strategic plan of action; in science, it may be the generation of novel theoretical and experimental directions; and in education, it may be a student's insights and find- ings, even if already achieved by others.

We understand data to the extent we have insight into the system or systems that the data describe. Data can be most appropriately used when these systems are viewed as wholes of highly interconnected parts. Getting to this level requires an innovative analysis which allows for the detection and recognition of patterns, trends and inter-- relationshps.

Innovation with data originates with questions, questions for which answers are intensely sought. Innovation originates in an active, energetic and free interaction with the data. It requires not only the ability to raise pivotal questions, but also to look at the answers in such a way that we recognize the next set of critical questions to further deal with the data.

A software system for understanding numerical data is therefore not a system for computer-generated answers. It is rather a system in which the user can explore, adjust, re-arrange and investigate his data so that he may find answers and further questions for himself.

Discovery Software is a data analysis tool to aid in gaining insight into the behavior of systems which are described by numerical data. It is perhaps best viewed as a laboratory. You bring data of interest and Discovery provides apparatus by which to investigate it. It has been designed to allow a particularly user-oriented access to and interroga- tion of data. Its ease of graphical representation drives the innovative process of creating additional questions out of the answers one obtains. These questions will lead you further with Discovery itself, but they will also lead you outside of the program to people and more data and other tools. The purpose is understanding, which is inherently compre- hensive in its methods.

PEMD Discovery Users Manual, page 9

PEMD supports data collection and analysis, but it also provides data from around the world related to many topics of interest to students. Schools may purchase such data for use with CD-ROM and other storage devices.

AIDS Learning Module

Ozone Depletion Learning Module

Global Warming Learning Module

CO2 Emissions Learning Module

Petroleum Outlook Learning Module

If you would like to try out PEMD, go to the 3rd Party folder on the AppleLink desktop and find the PEMD folder. You can down-link a demonstration program. You can also AppleLink them at PEMD2.

III. An Example: DataDesk

DataDesk is a statistical package from Odesta (800-334-6041) with a visual emphasis. While it is capable of performing all of the statistical calculations you might wish to perform with a database, it goes much further by providing many different forms of visual display, many of which can be adjusted and manipulated to explore relationships visually.

Calculations

* Correlations (Pearson Product Moment, Kendall's tau, Spearman Rank Correlation, Covariance)

* Regression

* ANOVA

* Cluster Analysis

* Frequency Breakdowns

* Contingency Tables

Displays

* Histograms

* Bar Charts

* Pie Charts

* Scatterplots

* Rotation Plot

* Dotplots

* Boxplots

* Lineplots

You can obtain a free demo disk from Odesta which shows you quite dramatically what can be done with data.

The demo disk comes with a sample database about 79 U.S. corporations which allows you to explore relationships between variables such as sales, profits, assets, number of employees, market value, etc. Open the "sector" field, pull down a menu, select "pie chart" and you see the results in a few seconds. Pull down another menu, select "use colors" and the black-and-white patterns of the pie chart are converted to brilliant colors. Want to know how many companies fall into each sector? Pull down a menu, select "frequencies of sector" and a table appears with numbers of companies and percentages.

Interested in whether there is a stronger relationship between sales, assets or cash flow, on the one hand, with profits, on the other hand? Click on the "sales" field while holding down the option key to designate that as the "Y" axis and then on "profits" while holding down the shift key to designate that as the "X" axis. Pull down the "Plots" menu and select "scatterplot." A graph appears with colored dots showing the data points. Pull down the menu and ask your computer to calculate the correlation (.814). Ask for the regression line. Now repeat the process for assets (corr= .602) and cash flow (corr=.989). You can see three graphs all at the same time and compare the slant of the lines. The comparative strength of the correlation is visually evident.

Want to compare sectors? High tech vs retail? Back on the pie chart showing sectors, click on the pie segment for "high tech" and all the dots from that sector change color before your eyes on all three scatterplots. Repeat the same for "retail." Want to see which companies are anomalies (outliers)? Select a questioning tool, click on the dot and the name of the company appears.

Because of its emphasis upon visual displays and the many tools provided to adjust those visual displays, DataDesk supports student exploration of mathematical relationships without requiring understanding of graduate school level statistical formulas and concepts.

Correlations, for example, make sense to elementary students without them understanding the mathematical procedures required to calculate them. In the case of the 79 companies mentioned above, it is easy to see that cash flow (corr=.989) is more strongly correlated with profits than sales (corr=.814) or assets (corr= .602). Once they learn how to square a decimal, they can ask what percentage of the variance between the two variables is explained by their relationship to each other (cash flow=97.8%, sales=66.3%, assets=36.2%).

IV. Moving Past Description to Explanation

The kinds of programs described above support student exploration of causative relationships in order to permit prediction and guide decision-making. New technologies provide students with tools which enable them to do kinds of thinking and research hitherto considered "unthinkable."

The implications for a democratic society in an Age of Information are dramatic. Given the potentially damaging impact of infoglut and infotactics, education which creates infotectives becomes essential. What if a leader like Ross Perot actually does introduce "electronic town halls" which ask citizens to express preferences on complicated policy issues? How well prepared is the public for this kind of responsibility? If we are accustomed to teachers and other powerful figures always making meaning for us, how independently will we develop our own thinking about policy issues?

Smokestack education sees student research as "go find out about." Such research is predominantly descriptive. Students gather up what other people have thought and written and then rearrange their findings in a report. Information Age schools will place a premium on students doing their own thinking, drawing their own inferences, crunching their own numbers and testing their own hypotheses and theories.

V. A Note of Caution

Even though statistical inference can be illuminating, there are many questions which resist the tools of mathematics. This is especially true when it comes to human behavior. We must acquaint students with the limitations of mathematical models when trying to understand people or predict their behavior.

If life were so easily reduced to models, we might not have need for artists and poets, those wonderful people who help us understand those life meanings which seem to drop through the mathematical cracks. The positivists keep trying to uncover the scientific structures underlying and governing all behavior and experience, offering us artificial intelligence and scientific management, for example, but the mysterious side of life keeps confounding their efforts. Some of us think of this mystery as reassuring at a time when technologies provide would-be puppeteers with remarkably powerful electronic strings with which to try to control our thinking and our behavior.

We must acquaint students with the limitations of scientific and mathematical thinking even as we sharpen their skills in that domain. For readers interested in delving further into this issue, Lewis Thomas' Biography of a Cell and Elliott Eisner's work on the arts in education are inspirational.

In illustration, at last year's National Staff Development national convention, Elliot Eisner shared the following thoughts:

"Schooling is the process by which we acquire tools to build beautiful edifices."

The task of schools is to ". . . convert brains into minds." We work to increase powers of understanding, the construction of meaning, the making of sense.

Our task is " . . . the cultivation of productive idiosyncrasies We need multiple forms of literacy, such as poetry. We have poetry to exceed the limitations of language."

Conclusion

As new technologies appear at the school house door, we must keep asking how we might best use them to empower student thinking and development. In asking such questions, we must try to lay aside smokestack mind-sets and paradigms in order to see the full potential of the new tools. Some of these tools have the potential to shift the curriculum in dramatic ways, introducing statistical inference, for example, to elementary students exploring plant growth or community streams.

Education for citizenship in an Age of Information must move past the development of basic skills to include the nurturing of good judgement - decision-making based upon careful analysis and data. We are in the business of raising a generation of what Catford and Ray (The Path of the Everyday Hero) call "everyday heroes," young people who are committed to lifting the quality of life for their community and their world. Readers of the April, 1992 issue of From Now On may recall the four main tools of the hero:

* Faith in one's creativity

* Open-mindedness

* Questioning

* Careful observation

This article has sought to demonstrate the insight which can emerge when applying these heroic tools if we equip students with software which crunches numbers and helps them to make sense out of non-sense. Imagine the consequences of sending forth a wave of infotectives prepared to accept the torch of leadership when the baby-boomers reach retirement!

Creating Effective District Technology Plans

Introduction

Recognizing that an Age of Information, a global economy and a rapidly approaching new century will all require technological literacy at a high level from graduates of their schools, the Board of Education and its Superintendent of Schools are determined to create a technology plan. This plan will guide decision-making into that new century while delivering an educational program which will equip students with a knowledge/skill base guaranteeing them a competitive edge in the highly technological workplace of their future.

While aspiring to achievement of such goals within a reasonable period of time, the Board and Superintendent recognize that the project cannot be rushed or hastily implemented. Success will depend upon the creation of a district vision jointly fashioned by all key constituencies and the laying of appropriate foundations to support the newly envisioned programs. In order to provide adequate training and support for staff to sustain a successful program while pacing acquisition of equipment to match available financial resources, it is reasonable for the technology plan to define an eight year journey extending from 1982 to 2000.

I. Goals of a Technology Plan

A technology plan, if properly constructed, becomes a living document, one which serves as a continually evolving guide to help steer the district through the shifting sands of rapidly emerging new technologies. The board must recognize the likelihood that external conditions and opportunities may either slow or speed the district's implementation and the exact form of the program might shift in order to benefit from new technologies and developments not available to the planning committee in 1992-93.

At the same time, a good plan will provide a clarity of purpose and sound structure which should survive and endure regardless. As with the construction of a cathedral, a sound foundation will support a vast assortment of stained glass windows and gargoyles which the original architects may not have envisioned. So it can be with a carefully planned technology program.

An effective technology plan should accomplish the following goals:

Establish a clear vision of learning outcomes (skills, knowledge and attitudes) associated with successful citizenship and employment in the 21st Century.

Identify ways that new technologies can best support achievement of such learning outcomes.

Involve all key constituencies in the development or consideration of this vision so that all groups will pull together during implementation of the plan in order to make it a success.

Provide an eight year action plan outlining all key strategies, activities and investments required such as staff development, program development and hardware acquisition.

Offer an evaluation model to guide implementation and assess return on investment.

II. Outline of Technology Plan Project (1992-93)

Network 609 proposes a planning project commencing in November or December of 1992 in order to conclude in May of 1993 with Board adoption of a plan for the district. The outline offered below is a sketch meant for discussion purposes.

November, 1992 * Board approves planning project

December, 1992 * Board 2 day retreat

to consider 21st Century goals

* Board appointment of planning committee

* Board approves charge to committee

January, 1993 * Joint Board and Technology Planning Committee - 2 day retreat to consider 21st

Century goals, develop scenarios and develop planning skills

February, 1993 * Technology Planning Committee - 2 days exploring research on exemplary technology programs

March, 1993 * Technology Planning Committee - 2 days

visiting exemplary programs

April, 1993 * Technology Planning Committee - 2 days

developing local plan

* Technology Planning Committee - 1 day

reviewing, critiquing and revising draft of plan

May, 1993 * Technology Planning Committee - evening meeting to hear reactions to draft from key constituencies

* Technology Planning Committee - revisions to plan and presentation to Board

* Board reviews, debates and approves version of technology plan

III. 21st Century Goals

The district will create forward-looking technology programs which emphasize the development of student reasoning and problem-solving skills.

The planning committee will explore leading edge thinking regarding the potential of new technologies to support highly effective school programs with impressive student outcomes. It will review an exciting menu of high tech learning experiences available to engage students in higher level thinking, independent problem-solving, meaningful research and invention. It will examine the connection between such learning and the workplace skills students will need as citizens of the next century, identifying technologies which will open new worlds and expand the power of student thought.

Possible outcomes to emerge from the planning process:

District media centers will become information hubs, electronically linked to all other learning centers and classrooms, supporting "real time research" which engages students in the construction of meaning from timely raw data.

The district "electronic highway" will support investigation and research from within all subject areas so that technology is fully integrated into the learning of all disciplines.

The district will establish exemplary programs in areas such as the sciences - employing simulations, modeling, imaging, systems theory and statistical analysis, among other elements, to engage students in the kinds of scientific thinking which will place students at the top of industrialized nations. The technology plan will provide the learning infrastructure to support inventive implementation of many of the pioneering concepts contained in Project 2061, a dynamic proposal for restructuring science education to meet the needs of the next century. Learning strategies will include attempts to improve significantly the attitudes toward scientific careers of traditionally non-participating groups such as young women and minorities.

The district will dovetail innovative programs with corporate partnerships and will identify external funding sources to reduce the impact of technology acquisition upon the local tax payers.

Staff members will feel pride in their high level of information and technology literacy as a result of a comprehensive staff development program.

Student access to higher education and high tech jobs will be enhanced.

Key values such as "high touch" will be protected.