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Physics with
Calculus
by
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David V. Anderson & Peter Tarsi
assisted by students
Carolyn McCrosson & Andrew Trott
Lecturette 1: Preliminaries
Welcome to Asora’s Stellar Schools course Physics with Calculus. This
is the first of several hundred short lectures that cover the course. We
call these short presentations “lecturettes.” My name is David
Anderson and I am one of two instructors for this course. Peter Tarsi,
here on my right, is the other. Mr. Tarsi will now give you a little
background information about this course specifically and about the
Stellar Schools instructional format in general.
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Not Following
Hillsdale This Time
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Thank you Mr. Anderson. Before we dive into the physics course
material, I want to tell you about our methods of instruction- especially
for newcomers to Stellar Schools who may not have been in a course
structured like this before. As you’re probably aware, most Stellar
Schools courses are patterned on the curriculum used by the Hillsdale Academy of Hillsdale, Michigan.
This course is an exception to that rule because it uses calculus while the Hillsdale course does not.
The Physics Curriculum
Our curriculum for Physics with Calculus is taken mainly from the textbooks by Giancoli:
Physics for Scientists & Engineers, Volume I, Third Edition
Physics for Scientists & Engineers, Volume II, Third Edition
By Douglas C. Giancoli
Prentice Hall
A few additional curriculum items were taken from Kaplan Publishing’s AP Physics B & C review book to
insure that our course meets the AP curricular requirements as well.
Now since Mr. Anderson developed the instructional formats for the Physics course, we’ll ask him what
this is all about.
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Curriculum is
the Universe
of Examination
Questions
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In this course and others provided by Stellar
Schools, we want to have a clear presentation
of what is in the curriculum and what is not. We define it operationally and with a great
deal of specificity. Accordingly, our definition of the curriculum for this course (as with all
Stellar Schools courses) is simply the “universe” of all possible examination questions and
answers that pertain to it.
Ideally, students would be questioned on the thousands of facts and concepts that
typically define a course’s curriculum. Practical considerations limit any given exam to well
less than 100 questions and thus any given test will only measure a student’s mastery of a
random subset of the course’s knowledge base.
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Mastery is a
95% Score
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Yes, as Mr. Anderson alludes, there is a
tradeoff between measuring a student’s
comprehensive knowledge, which favors more test questions to the time and expense
required to administer each examination, which favors fewer test questions. Since Stellar
Schools expects students to demonstrate their mastery by getting examination scores of
95% and above we wanted to choose the number of questions in a consistent fashion in
such a way that exactly 95% is one of the scores. As your mathematical knowledge or
intuition will suggest, this means the number of questions needs to be an integer multiple of
20. We currently use tests of 60 questions. If you get 3 or fewer wrong, your score will be
95% or higher allowing you to be certified as having mastered the course. Let’s now ask Dr.
Anderson to tell you about Learning Concept Statements (LCS) and Learning Concept
Numbers (LCN).
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Learning Concept
Statements
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I earlier mentioned that the curriculum is the examination
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building a related database of knowledge items. Each such
knowledge item is called a “learning concept statement” or
LCS. To keep track of each LCS we assign a Learning
Concept Number or LCN to facilitate organizing
the course’s full set of LCS’s into a database. Additionally,
we combine related Learning Concept Statements into a
Learning Concept Group or LCG, which would roughly
correspond to a section within a textbook chapter. Related to concept of the LCG, is the Lecturette,
which is a short lecture format presentation of the content associated with that Learning Concept
Group’s set of Learning Concept Statements (LCS). So for example, this lecturette you’re watching
here corresponds to LCG = 1. Given that LCG 1 is focused on housekeeping issues you’ll not be
surprised to learn that there are only two physics related LCS presented.in this first lecturette.
Examinations you will take to demonstrate your mastery of this course will be based only on the
collection of LCS presented in this course and on those from prerequisite mathematics and science
courses. The LCS for each course are maintained in a spreadsheet.
Physics Course Learning Environments
As with other Stellar Schools courses, in this physics course we provide several overlapping ondemand learning environments to help students master the content. There are twelve such
components. Mr. Tarsi, would you elaborate on them?
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Twelve Instructional
Components
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Yes, as presently conceived the twelve instructional components are:
1.
Lecturettes: For each Learning Concept Group students may, on
demand, view/hear short video lectures presented by the instructional
team, which in the case of physics has two teachers and two student
questioners. By “short” we mean that these lecture segments rarely run longer than 10 minutes.
2.
Supplemental Lecturettes: For a subset of Learning Concept Groups, which students often find more
difficult than others, we present additional short lectures to help students “around” common mistakes
and misconceptions.
3.
Lecturette Notes Online: Expanded “scripts” of the Lecturettes are presented online in textbook format
and is the primary textbook for the course as it contains all of the Learning Concept Statements and
explanatory material that the student is expected to master. Material from the Supplemental Lecturettes
is included in its appendices.
4.
Lecturette Notes Hardcopy: A physical paper bound version of the Lecturette Notes is also provided
to each student.
5.
Secondary Text Hardcopy: A physical “trade” textbook. In fact, this course uses the aforementioned
calculus based textbooks by Giancoli.
6.
Secondary Text Online: When available, an e-book version of the secondary textbooks will be
provided as well. Giancoli’s book is not available in this format.
Twelve Instructional
Components Cont.
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7.
Confidence Based Assessment System: We use the assessment
system of KnowledgeFactor, which we describe in more detail in a
following section. By knowing the confidence with which a student may
hold a misconception, it enables the instructional systems to better
remediate the misunderstanding. Practice tests and official tests are
drawn, in each instance, from a random sampling of the examination
data base- the only difference being that official tests are proctored.
8.
CyberTutor: After each test administration, the CyberTutor compiles a remediation document that
includes textual and video presentations of the issues and concepts surrounding each question
answered incorrectly. This means that you’ll encounter your video instructors again in this mode.
9.
CyberGames: Various computer games will be organized around the concepts of this course. Each will
be designed such that students who have mastered the physics course will tend to win more often.
10.
Schoolroom Teacher: Within each Stellar Schools schoolroom there will be at least one teacheroperating in tutoring mode- who can help you learn the material.
11.
Student Tutors: Many schoolrooms will also use advanced students as student tutors. To be accorded
the status of student tutor, the student must have mastered the relevant courses at a higher level.
12.
Hub Help Desk: Finally, at the Stellar Schools Central Service Center or Hub- from which we operate
the Stellar Schools network- additional teachers will be available to answer questions when the
resources at the schoolroom level prove inadequate.
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Bob Asks If
This Long List
is Superflous?
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Thanks, Mr. Tarsi. I see we have a hand
raised. Yes, Bob, go ahead.
Bob asks, “Gee, I’m a little confused about all these different methods of
learning the course materials. Are all of these twelve things really
necessary? Won’t it take a lot of time to study if we have so many
different ways to study the course?”
Mr. Anderson responds: That’s a good question, Bob. It leads into the next comment I was
going to make anyway.
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Many Options
Provide Flexibility
While this list of services may seem overwhelming, we don’t
require students to use any of them except # 7- the assessment
service. It’s for the student and his or her tutors to decide how
best to use these services in their efforts to master the course
content. Rather than being ominous, the wide variety of services
give you choices from which you can choose what approaches
are most comfortable or suitable for your learning styles. And if
you enjoy games, you’ll learn that way too.
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As to the time you’ll devote to studying the concepts in this course, we find
that certain difficult concepts, which can differ from student to student, are
what often “stump” a pupil. That often leads to much time being spent in an effort to resolve the confusion.
With the many different approaches used in this course, we think students will be able to use more than one of
them or even several to finally understand a concept that had previously bedeviled them. That can actually be
a time saver when confusion is more quickly overcome. And I should add, we provide convenient crossindexing so you can quickly find the pertinent areas within each component.
So I’d say that I think this variety provides you with a rich learning environment in which to pursue this
fascinating body of knowledge.
About The Physics Curriculum Database
As we have said, all of the Learning Concept Statements (LCS) are maintained in a database, which serves to
operationally define the course curriculum. An associated database containing the actual universe of
examination questions more precisely defines the course curriculum.
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Learning Concept
Statement Example
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For an example of how this database is organized, we show the
LCS corresponding to the course’s Learning Concept Number
(LCN) 579 in the figure shown below.
The graphic shown here displays one of the Learning Concept Statements (LCS), that for Learning
Concept Number (LCN) 579 as it appears in the spreadsheet that is used to define the course
curriculum. The lecture notes also display these same graphic representations for all of the course’s
LCS’s. It also provides the relevant textbook chapter number together with the LCN. They enable you to
find relevant information in the various course materials- both hardcopy and online. The remaining four
columns show the concept name, its description, an idealized question, and the answer to that question.
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How Examinations
Derive From
Learning Concept
Statements
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In the preceding display a possible question and
its correct answer were shown in the last two
columns. In practice there will be many different “sub-species” questions and answers
pertaining to each LCS (Learning Concept Statement). The course is designed so you will
be able to answer any of these questions if you understand the LCS (and all previous LCS
because in most cases a concept builds on items learned earlier). Thus the banks of
examination questions will contain far more questions than the number of LCS on which
they are based because as we have just indicated there will often be several questions for
each LCS.
It is for convenience in record keeping- both the school’s and the student’s- that each
learning concept (knowledge item) has been assigned a Learning Concept Number (LCN).
I see Ann has her hand up. Go ahead Ann.
Can a Question
Cover More
Than One LCS?
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Ann asks, “Does this mean that there
would be questions that test more than
one Learning Concept Statement?”
Yes, that’s right. In fact, many questions
will be of that form because it will allow a
60 question test to cover many more than 60 LCS (Learning Concept Statements).
“Should I then get a question wrong, how will I find the various portions of text and
other materials relevant to the LCS’s that were tested?”
Well, each question will be tagged with a primary LCN number and possibly one or
more secondary LCN numbers. That will allow you to rapidly find the content areas
tested by the question. An example of this linking will be shown shortly.
Nothing Else is
Tested Except
the Learning
Concept
Statements
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What this all means is that examinations you
will take to demonstrate your mastery of this course will be based only on the collection of
“learning concept statements” (LCS) presented in this course and on those from prerequisite
mathematics and science courses.
There are well over two thousand LCS in Physics with Calculus but any examination, for
practical reasons discussed earlier, will only employ a small subset of questions addressing
the subject matter. That subset will be determined by applying a random number generator to
each subtopic in this course. Thus, if and when you retake the course’s examination, the
questions will almost always be different than those encountered before- though they will be
covering similar or related “ground.”
Example of
LCN 579’s Two
Questions
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Corresponding to LCN 579, just shown, a
number of different examination questions
could be posed. Two such possible questions, as they would appear in the examination
instructions, are shown in the next section.
Our examinations apply the most advanced assessment methodologies of which we are
aware. We have been working with KnowledgeFactor, Inc to develop a confidence based
examination system in which students are assessed according to the two parameters of
competence and confidence. We want to know how students arrive at wrong answers. Do
they simply guess? Or do they “confidently” know something that “just ain’t so”- quoting here
from Mark Twain who had some thoughts in this area. As you will see from the choices
presented to the students, the examinations will gauge both of these important parameters.
In turn, subsequent remedial efforts will be more effective if we have a better understanding
about a student’s confident knowledge.
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Example Question #1
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Some examples will help. Let me show you
two of the examination questions that pertain
to LCN 579. As the nearby display shows, a
nominal four-prong multiple choice question
opens up to provide the student many other
choices (14 in all) to demonstrate partial
mastery of the concept.
As is evident the top four choices are simply
those of a standard multiple-choice format.
The remaining choices allow you to indicate
various “states” of lower confidence.
Another question pertaining to LCN 579 is
shown next.
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Example Question #2
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This example question depends on two
LCN: 579 and 576. If each question, say,
depended on two LCS’s then a 60
question examination, could, in principle,
test on 120 concepts.
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On Partial
Knowledge
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When students do not confidently know
one of the first four answers, they should
choose one of the other combination answers.
Accordingly, students who choose items with “dual uncertainty” (e. through j.) are in what
might be called a “sort of know” status.
Others who choose among the “triplet” items (k. through m.) have what we’ll call a “whiff” of
knowledge because they can identify only one alternative as being false.
Finally, those with no knowledge of the answer would choose item n.
Perspective on
the Confidence
Based
Assessment
System
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One way to look at the confidence based assessment system is that it gives the teaching
staff and the student a better indication of where they are ignorant, where they have
misconceptions, and where they are truly knowledgeable.
With this better information, these parties can then better apply remedial measures. In the
case of ignorance, the solution is, if you will, education. But in the case of misconceptions,
a more intensive process of re-education is advised.
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What is
Physics?
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Before concluding Lecturette 1, we
wanted to provide as extremely brief
introduction to the subject of physics.
What is it?
It is simply (or complicatedly if you like) the study of the four fundamental forces found in
nature. Sometimes physicists talk about the four fundamental interactions instead of forces,
but their names remain the same: gravity, electromagnetism, strong nuclear, and weak
nuclear. Our first Learning Concept Statement (LCS) for LCN = 1 recites this list.
Giancoli
Chapter
1
Learning
Concept
Number
1
Concept Name
What is Physics
Description
Physics is the study of the
fundamental forces: Gravity,
electromagnetism, strong nuclear,
and weak nuclear.
Question
What are the four fundamental forces
studied in physics?
Correct Answer
Gravity, electromagnetism, strong
nuclear, weak nuclear
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Physics
Relationship
to other
Sciences
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These four interactions or forces underlie the
mechanisms of all other sciences. Chemistry,
for example, is built on a foundation of physics.
The two of them together, in turn, form the basis of several other sciences including, biology,
geology, astronomy, and a host of other disciplines dependent on combinations of these.
Sometimes it is said that mathematics is even more basic than physics and as a subject that is true.
However, mathematics is not a science in the sense that science studies phenomena of the real
world and universe. Rather, mathematics is a logical structure and quantitative language upon
which physics and other sciences are described and evaluated. Given this relationship of physics to
the other sciences, brings us to LCN 2 which states that physics is the most basic science.
Lecturette Summary:
Physics With
Calculus Course
Preliminaries
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As in other courses in the Stellar Schools
core curricula, Physics with Calculus is
taught through a variety of approaches,
with twelve different modes of learning
applied. The curriculum is essentially defined by the examination database and its
many Learning Concept Statements (LCS). You are expected to achieve a
mastery level of competence in the examinations by attaining scores of 95% or
higher. Our assessment system measures both the content mastery of each
student and his or her confidence level in that mastery. It is unlikely that you will
master the course in your first attempt at taking the examination, but after further
review you will find your scores increasing until you surpass the 95% level at
which point you’ll receive certification that you mastered Physics with Calculus.
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Preview of Lecturette 2:
The Scientific
Method & the
Nature of Science
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Science is more than a field of study. It is also a method of study. Physics is both a field of
study and it depends on a method of study, which we call the “Scientific Method.” Thus
physics is a science.
The conjectures, ideas, and theories of physics are explanations of physical phenomena.
Only those that can be proven through repeated observation and experiment become the
accepted scientific theories of physics.
The description of physical phenomena is often quantified by means of mathematics. The
mathematical discipline of calculus was originally developed for physics applications.
Physics with Calculus: Credits
•
•
•
•
David Anderson
Peter Tarsi
Carolyn McCrossen
Andrew Trott
Instructor
Instructor
Student
Student