Experimental Evidence for Mixed Reality States

1
A web-based course in
2
scientific reasoning and
Alfred Hubler, a-hubler_at_illinois.edu Center of
Complex Systems Research, Physics, UIUC
http//server10.how-why.com/blog
3
its acceptance in Islamic
4
countries
5
Summary Quantitative reasoning skills are a
fundamental tool in many part of Society, ranging
from Mathematics and Science to Engineering and
from Law and Business to Rhetoric. In Middle
School and High School quantitative reasoning is
almost never taught , except in the context of
other disciplines, such as Mathematics or
Physics. Recently a Middle School course in
reasoning was developed and field tested 1. The
course introduces basic elements of reasoning,
such as the definition of a concept and the
definition of a strategy. The course concepts are
applied to algebraic proofing. We find that a
diverse population of female middle school
students readily accepts this approach and
achieves proofing skills on a level which is
comparable to university freshmen1. We have
established collaborations with educators in
Jordan, Saudi Arabia, Egypt, and Palestine and
find that approach is readily accepted
there. 1 A. Hübler, A. Vlasic, E. Stiegler, L.
Bievenue, D. Raineri, Interactive Middle School
Courseware on Abstract Reasoning Skills, in C.
Crawford et al. (Eds.), Proceedings of Society
for Information Technology and Teacher Education
International Conference 2006 (AACE Chesapeake,
VA, 2006) pp 389-394 http//server10.how-why.com/
publications/2006/Site.pdf This work was funded
in part by National Science Foundation Grant No.
NSF DMS 03-25939 ITR, and NSF DGE 03-38215.
6

• High quality course ware
• Why is Wikipedia so popular among researchers and
  students?
• -Its free.
• Deeper reason
• Many concepts are explained well, in contrast
  to standard textbooks. Standard textbooks give
  little intuition They do not explain the range
  of applicability of Newtons law, EM, band
  structure, .
• Example Light bulb

7
High quality course ware
8
High quality course ware
Name of the concept

9
High quality course ware
Icon for the concept

10
High quality course ware

Context of the concept
11
High quality course ware

Definition of the concept
12
High quality course ware
Discussion of the concept

More abstract versions of the concept
13
High quality course ware Discussion of the joke

Range of applicability, and examples
14
High quality course ware Discussion of the joke.

Relations to other concepts
15
High quality course ware
Definition of a Concept 1. A descriptive name,
such as Light bulb joke 2. An identification
number, such as Law 7 and a logo 3. A
description of the context in which the concept
is typically used, such The punch line of the
joke is generally derogatory to a group. 4. A
definition of the concept in terms of
sub-concepts, prerequisite concepts, and common
knowledge. 5. Discussion -A range of
applicability identifies when the concept is true
and useful. Further synonyms and opposites are
introduced. Examples The weight force is Wmg
for an object on the surface of the earth. , or
For any real number x - Several single
concept examples use the concept all by itself,
such as What is the weight force on a 2kg
object? - Several multiple concept examples and
exercises use the concept plus one or several
substitutions. They can also include translations
to other fields and common knowledge examples
(50 of content).
16
High quality course ware
The Definition of the concept Prime Factoring
in the Mathematics handbook Math on Call
(Kaplan 1998). Prime Factoring is the name.
061 is the identification number and the graph
of the factor tree serves as a logo. The first
sentence describes the use context. The One
Way symbol indicates the definition of the
concept in terms of sub-concepts. Further a
single concept example is given. There are no
multiple concept examples. The authors omitted
multiple concept examples since this book is
considered a companion to a regular text book.
Still, multiple concept examples would improve
the definition of the concept Prime Factoring.
17
High quality course ware facts about reasoning

• Conceptualization of Strategies Reasoning
• Some facts about reasoning
• Fact 1 Most reasoning is chaotic, -i.e. small
  uncertainties in the assumptions lead to larger
  and larger differences in the conclusions, in a
  long chains of arguments . There are almost
  always small uncertainties in the assumptions.
• gt inverse problem only short chains of
  arguments can be inferred from knowing the
  assumptions and conclusions.
• - Fact 2 A large fraction of reasoning is in
  English, and not in terms of symbols. Only basic
  concepts are in symbols , -, , , in
  contrast to sin(), is smooth, Solve for the
  unknown,

18
High quality course ware facts about reasoning
abstract concepts are worded in English
Most of the reasoning is in English, only basic
concepts are phrased in symbols. Example
Edwards and Penney, Calculus with Analytical
Geometry, Fourth Edition (Prentice Hall,
Englewood Cliffs, New Jersey, 1994), p399
19
High quality course ware facts about reasoning
Fact 3 We have to learn to reason and to
communicate reasoningits a language and the
main reason why we learn it is We do not want to
disappoint our teacher, -i.e. a one-on-one
relation with the teacher Fact 4 Teachers in
public schools are often overworked
(150students/day) and underpaid, -i.e. are not
the primary bread winner of a family gt teachers
are seen as distant and cold Conclusion Quality
education for a large fraction of the population
is only achievable with virtual tutors, that can
reason and show emotions, humor, and have high
expectations.
Edwards and Penney, Calculus with Analytical
Geometry, Fourth Edition (Prentice Hall,
Englewood Cliffs, New Jersey, 1994), p399
20
High quality course ware virtual tutor
evaluating expressions
The language of reasoning
21
High quality course ware virtual tutor
evaluating expressions
22
High quality course ware virtual tutor
evaluating expressions
23
High quality course ware virtual tutor
evaluating expressions
24
High quality course ware virtual tutor
25
High quality course ware virtual tutor
26
High quality course ware virtual tutor
27
High quality course ware virtual tutor
28
High quality course ware virtual tutor
evaluating expressions
29
High quality course ware virtual tutor
evaluating expressions
30
High quality course ware virtual tutor
evaluating expressions
31
High quality course ware virtual tutor
evaluating expressions
32
High quality course ware virtual tutor
evaluating expressions
33
High quality course ware virtual tutor proofing
Computer assisted proofing A typical set of
given concepts for a Middle School level proof
34
High quality course ware virtual tutor proofing
35
High quality course ware virtual tutor proofing

Tutor shows emotions.
36
(No Transcript)
37
High quality course ware virtual tutor proofing
Geometry, Conditionals, Physical Quantities
38
High quality course ware virtual tutor proofing

Before e-learning

After e-learning
Students use reasononing skills even in hand
written homework
39
High quality course ware virtual tutor results
Computer assisted reasoning, a 3-year test at
Campus Middle School Results
Students complete 15-20 homework problems/day

40
High quality course ware virtual tutor proofing
A cumbersome evaluation .

41
High quality course ware virtual tutor proofing
takes less than one minute

42

• Summary
• Why is Wikipedia so popular among students and
  scientist?
• - Its well conceptualized. A concept contains a
  name, icon, definition discussion. Strategies
  are recipies, algorithms. Methods are short
  strategies.
• Why do students do their homework?
• - Because they do not want to disappoint the
  teacher.
• Why do students have to show their work?
• - Most reasoning is chaotic, -i.e. small
  uncertainties in the assumptions lead to
• larger and larger differences in the conclusions,
  in a long chains of arguments
• gt inverse problem only short chains of
  arguments can be inferred from knowing the
  assumptions and conclusions.
• Most multiple choice homework problems require
  very little reasoning, test methods, but dont
  test strategies.
• The students learn to communicate their
  reasoning.
• The virtual teacher can learn new strategies from
  the students.
• Why does the virtual teacher have to speak and
  understand English (Arabic)?
• Abstract concepts are phrased in English
  (Arabic).
• -Everybody who knows something about the subject
  area, can teach the virtual teacher, no computer
  programming knowledge is required. Students,
  teachers, researchers, everybody who speaks
  English (Arabic) can teach the virtual teacher.
• - The virtual teacher can rephrase an abstract
  concept in terms of everyday concepts, and group
  a set of everyday concepts into an abstract
  concepts and name it.

43
From Dr. Zain Yamani ltzhyamani_at_kfupm.edu.sagt Date
Fri, Nov 28, 2008 at 1041 PM Subject RE
draft report of the nano energy and electronic
group To Alfred Hubler lthubler.alfred_at_gmail.comgt
Cc Zain Yamani ltzhyamani_at_kfupm.edu.sagt Dear
Professor Hubler, This issue of teaching high
school teachers is also one of my favorites.
Since we do not expect many of them to be used to
mathematical rigor, and even if they did the
actual high schools students are not
interested..hence.. it is a challenge for us (me
and you..) to get the gut-feelings of physics
into their souls. Regarding your kind offer that
we might develop something together re- HTW.. I'd
LOVE that!! However, I face "one" problem, my
current Administrative responsibility as Center
Director which has kept me away from my lab AND
undergraduate students. We have holidays coming
up next week. May it be a time for me to have
some peace of mind, and to reflect on how can
(better) balance my different wishes and
responsibilities. So, I promise to get back to
you after the holidays. Thank you for taking
initiative. I really appreciate that. Take
care, Zain
44
On Fri, Jan 16, 2009 at 1248 AM,
ltShawabka_at_birzeit.edugt wrote Dear Professor
Hubler, Thank you very much for your email. I am
willing to collaborate on creating an online
interactive course on nanotechnology. In fact
just last week we suggested to the vice president
for academic affairs to create such a modular
course for senior students of science,
engineering, and IT students. Your collaboration
in such an effort will be highly appreciated. I
am currently working on an online course in
introductory mechanics physics course for science
and engineering students. This course will be
offered and evaluated next semester. For the
high and middle school material in science and
math, I have been involved in such activity for
a long time, and will be willing to collaborate
in writing a proposal to enhance science and math
education in Palestine. Thanks again, and
looking forward to hearing from you. Aziz
45
ConclusionAlfred Hubler, a-hubler_at_illinois.edu
Center of Complex Systems Research, Physics,
UIUC http//server10.how-why.com/blog

• The greatest natural resource in the Middle
  East is the thoughtfulness and ingenuity of the
  students.
• Quantitative reasoning skills are a fundamental
  tool in many fields, ranging from Mathematics to
  Engineering and from Business to Rhetoric.
• Quantitative reasoning is almost never taught
  as a course, but in the context of other
  disciplines, such as Mathematics or Physics.
• We introduce basic elements of reasoning, such
  as the definition of a concept, a method, and a
  strategy and study the impact on the students.

46

• We also conceptualize strategies .
• We teach understanding teach translating
  real world problems to Algebra, Physics, and
  back, - abstract concepts to practical concepts
  und vice versa Biology problems to Algebra and
  back.
• We find that a diverse population of female
  middle school students readily accepts this
  approach and outperforms their peers, and we
  noticed a low drop out rate in Physics
  Chemistry UG introductory courses.
• We are open for collaborations.
• Thank you.
• - D. Raineri, A. Hübler, B. Mertens, CyberprofTM
  An Intelligent Human-Computer Interface for
  Interactive Instruction on the World Wide Web,
  JALN 1, 20 (1997)
• - A. Hübler, A. Vlasic, E. Stiegler, L. Bievenue,
  D. Raineri, Interactive Middle School Courseware
  on Abstract Reasoning Skills, in C. Crawford et
  al. (Eds.), (AACE Chesapeake, VA, 2006) pp
  389-394.