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The Student-Centered Class
A
great lecture is one where central information is concise and clearly
explained, and when appropriate, with demonstrations. The students value such a
lecture because clear explanations are what they are there for. A not-so-great
class is one where the instructor covers peripheral information, not central,
and not clearly explained. Poorly executed demonstrations do little to make the
fix. Either way, in traditional classes where lectures are the main
focus, the students remain seated with pen and paper taking notes to be studied
in more detail later.
The
traditional class format can be effective, at least if we are looking at
short-term goals. Educational research suggests, however, that better results
are obtained when the instructor makes the students active participants.
Check-Your-Neighbor type questions are a good starting point for active
participation. This is where you as the instructor ask a question of the class
and students discuss possible answers amongst themselves.
You can
take this interactive approach a step further by allowing students to use class
time to collaborate on projects, worksheets, or hands-on activities.
Collaborative, student-centered learning can be achieved through various
teaching strategies. For example, students can be asked to do the science
demonstrations themselves and asked to explain the underlying concepts. Any
lecture presentation you provide can be short and sweet, and provided “on the
fly” in response to students’ specific needs as revealed by the demonstrations.
In such a scenario, students are in the spotlight. They find that class is akin
to a grand study session where the instructor is their study leader, who
migrates from team to team providing expert assistance on demand. This is the
essence of the “student-centered” class. Lectures are minimized for the sake of
increased class participation.
Students Must Come
Prepared
The prerequisite to an effective student-centered class is
that the student arrives to class prepared. Assignments need to have been read beforehand and exercises attempted beforehand such that a hazy
understanding has already begun to take form. But as any instructor knows,
student resistance to coming to class prepared can be intense. How then do we
motivate students to come to class prepared? There are numerous tools. First of
all, it is vital that the textbook be as user-friendly as possible—students
should enjoy reading it! This, of course, has been one of the main goals in
developing the Conceptual Integrated Science
textbook. The student should be able to learn about science concepts on his
or her own with minimal assistance from the instructor—and it should make good
reading! This, in turn, supports the instructor who is wishing to move toward a
student-centered class.
Another important tool for
encouraging students to study is a short quiz given at the beginning of class,
or even before class with the quiz
posted on the course website. This quiz should assess students for their
familiarity, not their expertise, of the material about to be covered.
Following the quiz and a brief introduction, students work on various
activities within teams. If a student comes ill-prepared, he or she then faces
the motivating factor of peer pressure.
Of course, not everyone can always come prepared. Students know this and
are generally forgiving and welcoming of all input either weak or strong. So
peer pressure needn’t be unkind.
If you are ready to make your
classes more student-centered, you need to let your students know at the
beginning of the semester how this approach will help their learning, provide
for an enjoyable experience, and, ultimately, improve their test scores.
Notably, the interpersonal skills gained through collaborative learning is an
added plus. Also, students are much more willing to participate if the in-class
activities are unequivocally related to the quizzes and exams they take.
Lastly, a student-centered
approach consumes a large portion of class and so the instructor has less
opportunity to deliver content, though a greater opportunity to facilitate the
learning of content. Consequently, in order to keep pace with a traditional
syllabus, the instructor needs to decide whether there will be material on
exams not covered directly in class. If so, the instructor should be mindful to
reserve class time for the more challenging concepts.
Students Are the
Players and You Are Their Coach
There
is great pedagogical potential in transforming a class from passive learning to
active, student-centered learning. To achieve the potential, what is needed is
a willingness to get creative and to push the responsibilities of learning more
squarely on the student. The role of the instructor is to provide students with
good questions rather than good answers. We can think of students as team
players out on the field doing all the hard work, which means finding answers
for themselves. We are their coaches here to direct their learning efforts.
Sometimes the best way to do this is by knowing when to cheer and when to
remain silent.
Getting Started
So, is it better to retool one’s teaching methods in a
single semester or to explore new activities one at a time over many years?
Revolution or evolution? If you’re like most of us, the thought of revamping
everything within a single semester is most undesirable. Indeed, implementation
of any student-centered activity requires a fair amount of trial and error.
Imagine implementing many new activities all within a few weeks only to have
them fail miserably. This would be a disservice to your students and to
yourself. The best practice is to introduce only the activities you think will
work in a time frame that allows for successful development.
The
techniques presented here are a select few that we authors know work well. Some
work for large classes while others are better suited for smaller classes.
Chances are that you have already implemented techniques of your own or that
new ideas will soon be coming to you as you forge ahead. Also, you need look no
further than journals, such as those of the National Science Teachers
Association or through the web to find a constant flow of student-centered
learning innovations. Some references are included at the end of this essay.
The point to be made is that student-centered learning can be implemented
profitably even by teachers who have had great success with lecturing.
Student-Centered Assessment Techniques
(What students can do to articulate what
they think they’ve learned)
We give homework,
quizzes and exams so that we can provide students with a grade. But there is
another important reason for these assessment tools, which is to provide
students with feedback on their learning. Interestingly, assessment and grading
need not be paired. So if you’re looking for a stress-free, non-penalizing way
to support your students as they struggle to learn, consider providing
“suggested homework”, “practice quizzes”, “practice exams”, and even “practice
worksheets”. To show you appreciate the great value of practice (as would any
coach, including an academic coach), let your students do these practice
activities right during class where you’ll be personally available to offer
assistance to individuals and to teams. Students appreciate the opportunity to
practice, which is why we say: assess often, grade only when needed.
The Concepts Inventory
The Concepts Inventory is a
short test taken by students at the beginning of the semester and definitely
not graded. In fact, you might consider having the students take the test
anonymously. At the end of the semester, the Concept Inventory with the very
same questions is given again to provide a semi-objective measure of overall
student learning. This is an assessment not only of the students but of the course
as well. Inventory questions should reflect concepts that you hope the students
will learn by taking the course. A good inventory will also include questions
that address common misconceptions.
Rather than giving the inventory again at the end of the semester, you
might consider sneaking the questions (some or all) into the final exam.
EOC Exams
At the end of each chapter (EOC)
of Conceptual Integrated Science are
numerous questions. These are provided so that students can practice applying
the concepts they think they have learned. But of course, many students tend
not to work on these questions unless they are assigned by the instructor for
homework, usually just a selected few. As an alternative, students can be given
a longer list of each of the instructor’s favorite EOC questions that are
applicable to the course syllabus. The students are then told that a certain
number of these questions will definitely be posted on an upcoming exam. Keep
in mind that only the answers to the odd-numbered EOC questions appear at the
back of the textbook. Also, many of these EOC questions can be found in
multiple-choice format within the Conceptual
Integrated Science test bank.
The Minute Quiz
As said, a quickie quiz given at the beginning of class it is
a valuable component of your course. Their purpose, as said, is to motivate
reading material for the day before class. Call them “minute quizzes” because
the students have only one minute to answer a question that calls for a word or
very short sentence. They can pass their quizzes to the front of the room, or
put into boxes passed around the class. If you have the time and motivation to
grade and record responses, good for you. But as said, even if you tell the
class that you’ll not look at every day’s quizzes, and you won’t record scores,
the process still works! Students don’t like handing in blank papers!
The Two Minute Quiz
The minute quiz described above can be extended in to two
phases. For the first phase, students get about a minute to answer the
question, which may be printed on a narrow strip of paper. They can put their answers
into a box that gets passed around the class. A right answer is worth, say, 25
points while a wrong answer is worth 10 points. A student, however, may opt not
to put his or her quiz into this box and may instead hold onto the quiz until
the second phase, which begins when students are told they can now open their
notes, their textbooks, and talk with their neighbors about the possible
answer. After another one minute period they place the quiz into a second box,
which means they get, say, 20 points for a right answer and 15 points for a
wrong answer. Students soon to catch onto the best strategy, which is to wait
for the second round if they’re not sure of the answer.
The Importance of Fairness in Exams
There should be no big
surprises on an exam. Students should know what to expect, which is coverage of
course topics, with question difficulty that finds your top students getting
perfect or near-perfect scores. Your fairness as an instructor is judged by the
fairness of your exams. Exams that cover what students expect are fair. Exams
wherein top students excel also display your sense of fairness. How
discouraging for students when class averages are so low that your not being on
target moves you to play God at semester’s end and grade on the curve. Please
read Paul Hewitt’s history of teaching and how he handled exams to lure more
than a thousand students to his non-required conceptual physics course at City
College of San Francisco in the October 2011 issue of The Physics Teacher.
Collaborative Exams
For a significant learning
experience, an exam may be offered in three phases: individual, team, and
class. In the first phase each student takes the exam individually while also
filling out a duplicate exam (or Scantron) that contains their answers but not
their name. Assessment for this individual effort should be weighted the
greatest. For example, each question may be worth 5 points, while for the
second phase each question is worth 3 points, and for the third phase just 1
point.
A ten-minute warning is given to assure that all
students finish with the first phase at about the same time. Exams are turned
in while the duplicate student answers are spread out onto a broad table.
Students then congregate into their teams to take the exam again, but this time
working together and with resources, such as the textbook. They are also
permitted to send a scout to inspect the duplicates to see how the rest of the
class answered specific questions. Each member of the team should have a copy
of the exam, but only one exam is to be turned in for assessment. Meanwhile,
the instructor and/or TA is quickly grading the individual exams. (Use a
Scantron if available.) The goal is to post the class average before the teams
finish their team exams. This feedback allows teams to gauge the value of the
displayed duplicates. A quick alternative to grading all the exams is to post
the average score of five random individual exams.
After teams turn in their team exams they are ready for the
third phase in which they take the exam yet again together as a class. The
instructor records their answers on a single master copy of the exam. Teams
vote for an answer by holding up color-coded flash cards. Teams are allowed to
argue their answers, but majority wins. If there is a tie among teams, then
there is a recount after some healthy debate. After each class answer is
recorded students are then told the correct answer, which is often followed by
cheers or groans.
The length of the
exam is determined by the duration of the class. For a 75-minute class, the
exam can contain up to 25 questions. For 50-minute class, the exam should be
narrowed down to about 15 questions. Timing is an important factor. In particular,
students should finish the first phase all at about the same time. Slower
students can be encouraged to come to class early for a head start. It is also
helpful to have a second room where slower students can go in the event they
need another 5 or 10 minutes to finish the first phase while their team move
ahead. For the second phase, which is the team phase, it helps to include a
“toughie” bonus short-essay question at the end of the exam. This is useful for
teams who finish early—it keeps them busy while other teams are still working
on the regular questions. There is not always sufficient time to have the third
phase, which is when the class takes the exam together as a whole. To expedite
the third phase, the instructor lays out the team answers so he or she can see
all the team answers at a glance. Instant credit is given to questions that are
unanimously correct. This allows the instructor to move on to some of the more
difficult questions, which tend to have different answers from different teams.
By the time the class period is over, students have taken the
exam three times and know their final score. Individual effort is
preferentially rewarded, yet students still get the valuable experience of
working together as a team. Furthermore, with such a format, the instructor can
include challenging questions that may foil many individuals but not many
teams. The individual phase of the exam may average 65 percent or less. This is
balanced, however, by the team and class phases, which may run 80 percent and
95 percent, respectively, so that the overall average is within the mid-70’s.
One drawback to this format is that it consumes a lot of paper. If each student
has access to a computer, however, the paper can be replaced by online
delivery, which would also assist with the instant grading that makes this
activity so effective.
Appeals
With end-of-semester course
evaluations, a number one concern shown by most students is whether or not the
course was fair. Toward satisfying this need, students may be permitted to
appeal any question for which they believe they deserve credit. The instructor
sets up the conditions of the appeal. For example, the student’s explanation
for why they think they deserve credit must be hand-written and submitted
within a certain time frame. Also, only those who were actively involved in the
appeal, as indicated by their signature, have the possibility of gaining
points. Appeals are reviewed by the instructor in the safety of his or her home
or office where he/she may assign full, partial or no credit. Aside from
providing students a sense of fairness on your part, the appeals provide the
feedback you need to modify questions that might not be worded optimally. We
should underscore that students really appreciate the opportunity to appeal, as
will become evident on your course evaluations.
Student-Centered Learning Activities
(What students can do when the instructor is
not lecturing)
Team Formations
Collaborative learning tends to
work best when students are grouped together in teams consisting of either 3 or
4 students. For a team of 5 students, invariably, the fifth student takes a
back seat and is less involved. For a team of 2 students, there is not a
sufficient diversity of ideas. Who goes on what team is the difficult
responsibility of the instructor who knows that each team needs to be
well-balanced in terms of academic abilities and gender. At the start of the
semester, the instructor can eye-ball who goes where. Putting friends initially
together is a good thing. Alternatively, the instructor can await the results
of a Concepts Inventory and use student scores as the basis for team
formations.
The
instructor should consider new team formations after each exam. Students thus
work together in the same team on up to the next exam, which is collaborative
as described earlier. Exam scores are then used as the basis for new team
formations.
The
first assignment of any team is to agree upon a team name. The periodic table
provides a wealth of possibilities. Team Titanium, Team Gold, and Team
Einsteinium are some of the more popular choices.
Hands-On Science
Within each chapter of Conceptual Integrated Science are
home-project type activities. These brief activities are most conducive to team
learning in the classroom. As you can imagine, students appreciate the hands-on
exploratory nature of these activities—they really help to liven up a class.
The drawback is the time it takes to make sure that each team is set up with
the proper materials, and to make sure that students clean up after themselves.
We need not restrict all lab activities to the lab when there are so many
small, safe, easy-to-set- up activities that can also be done effectively in
class.
An important
ancillary is Suzanne Lyons book, “Minds On Hands On,” loaded with intriguing
activities and more. This ancillary is especially important to the instructor
new to teaching the wide swath of Conceptual
Integrated Science.
Practice Pages
An important supplement to Conceptual Integrated Science are the
Practice Pages, which are a set of minds-on concept review worksheets. The
Practice Pages are designed as a study aid that students can work on outside of
class. They are far more effective, however, when students work on them
together as a team under the expert supervision of the course instructor, who
travels from team to team to assist students as necessary. It is common that a
Practice Page will prompt a question from a student that, in turn, prompts the
instructor to give a short lecture presentation to the team. In such instances,
neighboring teams can be encouraged to eavesdrop. This is known as “targeted
teaching” and it arises as the instructor roams about the room checking on team
progress. Occasionally, it prompts the instructor to switch gears and give his
or her mini-presentation to the whole class. Targeted teaching is impromptu and
in response to immediate student need.
Think-Pair-Share
This technique was made popular by Eric Mazur of Harvard
University in his book Peer Instruction:
A User’s Manual. A multiple-choice question is presented to the class.
Students contemplate the question on their own and then commit to an answer
preferably in writing or via flash cards so that the instructor can quickly
gauge student performance. Students then discuss their reasoning with
neighboring students. After student–student discussions, a second survey of
answers is taken. If the responses prove satisfactory, the instructor can move
on to the next concept. If students are struggling, then the instructor may
decide to spend more time clearing up misconceptions.
Readiness Assurance Test
(RAT)
Hands down, this is the student’s favorite activity—not for
the joy of it but because it is most related to helping him or her perform well
on exams. The RAT is simply a trial exam given before the actual exam. It helps
students assess how ready they may or may not be for the exam. Everything about
the RAT should be identical to the exam except that the points don’t count and
the questions are different!
You will find that
there are short RATs already given at the end of each chapter. You might
consider building your RAT using these questions. Alternatively, if you
formulate your own RAT questions, you might consider using some of the
textbook’s RAT questions for your exam to reward students who have been working
with the questions at the back of each chapter.
But in
implementing a RAT you will come across a deep question, which is “Should you
offer a RAT during a class before an exam when this means losing a day of
instruction?” If you use the “collaborative exams” technique described earlier,
then you will quickly come to find that you are by no means “losing a day of
instruction” when you implement a RAT.
Rather, you are helping your students to solidify their understanding of
science, which may be an important aspect of your job description.
Does implementing a RAT mean you will need
to cut back on topics normally covered in your syllabus? Not necessarily. Some
students actually learn well by reading the textbook. Others prefer watching
the textbook authors deliver their “talking textbook” video lessons at
ConceptualAcademy.com (Please check us out!). All students will appreciate
solidifying their understanding of these topics (such as rainbows, nuclear
physics, natural selection, the rock cycle or the solar system) in class under
your expert guidance. The RAT is a good vehicle for this purpose.
Class Presentations with Activity Intervals
Select questions are assigned to teams of students who then
have a short period of time (10 minutes) to prepare and practice articulating
an answer. Students as individuals or as a team then get up in front of the
class to articulate their answers in a short two-minute presentation. They then
ask the class if there are any questions. The instructor, meanwhile, has
planted some well-thought-out questions among the audience who then ask these
questions, which probe deeper into the concepts. The presenting student or
students can either respond or choose to serve as moderators of a class
discussion.
Certain questions lend themselves to short but effective
hands-on activities. After a student presentation on surface tension, for
example, the class can be challenged to float a paperclip on water. Or after a
presentation on condensation, the instructor can invert a steam-filled soda can
in water. Students are then prompted to explain why the can imploded. Of
course, if they can’t figure it out, it is the responsibility of the instructor
to keep quiet or provide only hints.
Questions that work well for this
technique include the Think and Explain questions from the textbook. These
questions also lend themselves well to study group sessions either outside of
class or during class. A student should be reminded that if he or she
understands the answer to one of these questions—if he or she really does—then
he or she should be able to articulate the answer (verbally!) to someone else, such
as a fellow student. Note: Isn’t this remindful of when we learned most about a
subject: when we articulated it to others?
Focused Listing
On a blank sheet of paper,
students write down a list of 4 or 5 terms or phrases that summarize the
content of a textbook section or reading assignment. This activity quickly
assesses what key concepts were difficult for the student to understand. A
related activity described by Angelo and Cross is called “The Muddiest Point”
whereby students write down concepts from a chapter that were most unclear. The
instructor then uses this information to launch a class presentation
(mini-lecture or demonstration) or a class discussion à la the Socratic method
whereby everything the instructor says is phrased as a question.
Reward Race
A set of not-so-easy multiple choice questions are posted
around the room. Students work in teams to answer these questions. The first
team to get all answers correct wins the prize, preferably something made of
chocolate. Strategies are important. Some teams will decide to split up. Others
will stay huddled as they migrate from one question to the next. Also, if a
team submits answers but gets at least one wrong, they are not allowed to
submit answers again until either all the other teams have had a chance or
after a specified amount of time. Furthermore, the instructor does not tell
teams which questions they got wrong, only the number of them they got wrong.
This is certainly one of the more fun activities.
Office Visits
While the class is occupied with some learning activity
(pensive activities, such as the Practice Sheets are best), the instructor
pulls individual students away for a required brief office visit. The
instructor inquires about how things are going and whether the student has any
general or specific questions or concerns. This is also a good time to show the
student his or her present course grade and provide advice on how to do well in
the course. Furthermore, this activity serves as an important ice-breaker that
makes students more inclined to visit you outside of class.
Field Trip
Class-size permitting, take students on a tour of any science
research laboratories near you. Ask your colleagues and University researchers
whether they would be willing to talk to your students about why they like
science and why they chose it as a profession.
The Conceptual Café
Bring in a stack of recent science journals, both popular and
technical, and set the classroom up as though it were a coffee house—quiet
background music, tea, donuts, etc. Students merely spend the class time
reading through these journals and discussing science-related topics with their
peers as well as the instructor. Few, if any, students will likely have looked
through a rigorous technical journal, such as the Journal of the American Chemical Society. These journals can be
intimidating for their detail, especially the experimental sections. But
students should have some first hand experience at the utterly vast amount of
information that has been generated and is being generated by scientists around
the world. After looking at the technical journals, students will find the
popular science magazines to be a breath of fresh air. It’s likely that most of
your students have never read through a popular science magazine. Perhaps, down
the road this activity will help them to think twice about throwing away one of
those pervasive science magazine subscription offers.
Instructor-Centered Learning Activities
(What the instructor can do outside of
class)
Class Journal
Student-centered
learning is such fertile ground for educational innovation. As soon as possible
after class, we encourage you to open up your Class Journal and start recording
what went well and what went wrong. We can almost guarantee that through this
process ideas for improvements will arise. The process of writing in your
journal, especially soon after class, is a great way to allow these ideas to
come to the surface where you can consider them in fuller detail.
Think-Pair-Share
Try Think-Pair-Share with your colleagues. First, think about your curriculum using your
class journal. Discuss your experiences and ideas with your colleagues. Then
share your ideas with others through departmental seminars or regional or
national meetings. The key word here is synergy.
We instructors don’t work in a vacuum. In working together we can fast-forward
to better ways of reaching our non-science oriented students.
Explore
References
Here are a few references about student-centered learning techniques.
Thomas A. Angelo, K.
Patricia Cross, Classroom Assessment
Techniques, A Handbook for College Teachers, 2nd ed., Jossey-Bass, 1993.
Eric Mazur, Peer Instruction: A User’s Manual,
Prentice-Hall, 1997.
Jeffrey P. Adams,
Timothy F. Slater, Strategies for Astro
101, Prentice-Hall, 2003.
Chemical Concepts
Inventory
http://jchemed.chem.wisc.edu/JCEDLib/QBank/collection/CQandChP/CQs/ConceptsInventory/CCIIntro.html
or just type: “Chemical
Concepts Inventory” into Google.
Collaborative learning activities
www.wcer.wisc.edu/nise/cl1/cl/
Field-Tested Assessment
Guide (CATs)
www.flaguide.org
Just in Time Teaching
www.JiTT.org
Process Oriented Guided
Inquiry Learning (POGIL)
www.POGIL.com
“The Missing Essential
— A Conceptual Understanding of Physics” Paul Hewitt’s Millikan Award talk,
American Journal of Physics, January 1983.
Some Teaching Tips
•
Attitude toward students and attitude about science in general is of utmost
importance: Consider yourself not the master in your classroom, but the main
resource person, the pacesetter, and the guide. Consider yourself a bridge
between your student’s ignorance and some of the information you’ve acquired in
your study. Guide their study—steer them away from the dead ends you
encountered, and keep them on essentials and away from time-draining
peripherals. You are there to help them. If they see you so, they’ll appreciate
your efforts. This is a matter of self-interest. An appreciated teacher has an
altogether richer teaching experience than an under-appreciated teacher.
•
Don’t be a “know-it-all.“ When you don’t know your material, don’t pretend you
do. You’ll lose more respect faking knowledge, than not having it. If you’re
new to teaching, students will understand you’re still pulling it together, and
will respect you nonetheless. But if you fake it, and they CAN tell, whatever
respect you’ve earned plummets.
•
Be firm, and expect good work of your students. But be fair and get papers
graded and returned quickly. Be sure the bell curve of grades reflects a
reasonable average. If you have excellent students, some should score 100% or
near 100% on exams. This way you avoid the practice of fudging grades at the
end of the term to compensate for off-the-mark low exam scores. The least
respected professor in my memory was one who made exams so difficult that the
class average was near the noise level, where the highest marks were some 50%.
•
Be sure that what knowledge you want from your students is reflected by your
test items. The student question, “Will that be on the test?“ is a good
question. What is important—by definition—is what’s on the test. If you
consider a topic important, allow your students credit for their feedback on
that topic. An excellent student should be able to predict what will be on your
test. Remember your own frustration in your student days of preparing for a
topic only to find it not part of the test? Don’t let your students experience
the same. Many short questions that fairly span course content is the way to
go.
•
Consider having students repeat work that you judge to be poor—before it gets a
final grade. A note on a paper saying you’d rather not grade it until they’ve
given it another try is the mark of a concerned and caring teacher.
•
Do less professing and more questioning. Information that is of value ought to
be the answer to a question. Having frequent “check-your-neighbor“ intervals
should be an important feature of your class. Their feedback to you can be
immediate with the use of student whiteboards, or their electronic
counterparts. Beware of the pitfall of too quickly answering your own
questions. Use “wait-time,“ where you allow ample time before giving the next
hint.
•
Show respect for your students. Although all your students are more ignorant of
physics than you are, some are likely more intelligent than you are.
Underestimating their intelligence is likely overestimating your own. Respect
is a two-way street.
1 About
Science
1.1 A
Brief History of Advances in Science
1.2 Mathematics
and Conceptual Integrated Science
Math Connection: Equations as Guides
to Thinking
1.3 The
Scientific Method—A Classic Tool
1.4 The
Scientific Hypothesis
1.5 The
Scientific Experiment
1.6 Facts,
Theories, and Laws
Science and Society: Pseudoscience
1.7 Science
Has Limitations
1.8 Science,
Art, and Religion
1.9 Technology—The Practical Use of Science
1.10 The
Natural Sciences: Physics, Chemistry, Biology, Earth Science, and Astronomy
1.11 Integrated
Science
Integrated Science—Chemistry and
Biology: An Investigation of Sea Butterflies
A
common practice is spending the first week of a science class on the tools of
science—unit conversions, significant figures, making measurements, and using
scientific notation. This is anything but exciting to most students. The
authors of this book believe that this is pedagogical folly. How much better it
is if the first week acts as a hook to promote class interest, with tools
introduced if and when they are needed later in the course. So, this book
begins by introducing the nature of science, the value of integrated science,
the scientific method, the role of science in society, and other topical issues
such as pseuodoscience, the relationship between science and religion, and the
similarities and differences among science and art.
Screen
casts on the web, “Hewitt drew it”:
Although
there’s no cast particularly for this chapter, Hewitt’s passion for physics is
nicely treated in the first Screencast #1; The Equilibrium Rule.
In
Next-Time Questions:
• Hypotheses
In
the Lab Manual:
• Tuning the Senses (enhancing perception)
• Making Cents (introduces the mass balance
and the making of a simple graph)
Suggested
Presentation
A
Brief History of Advances in Science
Science
is organized knowledge. Its roots are found in every culture. The Chinese
discovered printing, the compass, and rockets; Islamic cultures developed
algebra and lenses; mathematicians in India developed the concept of zero and
infinity. This text, nevertheless, emphasizes Western science. Science did
advance faster in Western than in Eastern cultures, largely because of the
different social and political climates.
While
early Greeks, in an era of experimental democracy and free thinking, were
questioning their speculations about the world, their counterparts in the more
authoritarian eastern parts of the world were largely occupied in absorbing the
knowledge of their forebears. In regions like China, absorbing this knowledge
was the key to personal success. So scientific progress in Eastern cultures was
without the early period of questioning that accelerated the scientific
advances of Europe and Eurasia. In any event, it is important to emphasize
throughout your course that all science
is a human endeavor. In addition to being a legacy of what humans have
learned about nature, it’s also a human activity that answers questions of
human interest. It is done by and for humans.
You
may consider elaborating the idea that the test of correctness in science is
experiment. As Einstein once said, “many experiments may show that I’m right,
but it takes only one experiment (that can be repeated) to show that I’m
wrong.” Ideas must be verifiable by other scientists. In this way science tends
to be self-correcting.
Mathematics
and Conceptual Integrated Science
The
mathematical structure of science is evident in this book by the many
equations. These are shorthand notations of the connections and relationships
of nature. They are seen primarily as guides to thinking, and only secondarily
as recipes for solving problems. Many instructors bemoan students who reach for
a formula when asked a scientific question. We authors take a more positive
view of this, for formulas are shorthand statements about the connections of
concepts. For example, if asked if speed affects the force of gravity on earth
satellites, a look at the equation for gravitation tells us no—only mass and distance affect force. Now
if speed changes the distance, then in that case, yes. When equations are seen
as guides to thinking, then conceptual thinking is present. Hooray!
You
can provide a specific example of “equations as guides to thinking” by going
over the Math Connection box. This feature is meant to clarify the role of math
in Conceptual Integrated Science
rather than to challenge students. The notions of direct and inverse
proportions are intuitively easy to grasp—showing that science often has a
mathematical structure, but this structure need not be difficult to grasp.
The
Scientific Method—A Classic Tool
The
scientific method is given in a six-step form. We say that science is
structured common sense. The scientific method is an example. The scientific
method is to be seen as a sensible way to go about investigating nature.
Although the six steps are useful, they don’t merit your students memorizing
them. And most often, they are not the specific steps used in scientific
discoveries. The scientific attitude,
more than a particular method, underlies scientific discovery.
A Scientific Attitude
Underlies Good Science Expand
on the idea that honesty in science is not only a matter of public interest but
is also a matter of self-interest. Any scientist who misrepresents or fudges
data, or is caught lying about scientific information, is ostracized by the
scientific community. There are no second chances. The high standards for
acceptable performance in science, unfortunately, do not extend to other fields
that are as important to the human condition. For example, consider the
standards of performance required of politicians.
Scientific
Hypotheses
Distinguish
between hypothesis, theory, fact, and concept. Point out that theory and
hypothesis are not the same. A theory
applies to a synthesis of a large body of information. The criterion of a
theory is not whether it is true or untrue, but rather whether it is useful or
not. It is useful even though the ultimate causes of the phenomena it
encompasses are unknown. For example, we accept the theory of gravitation as a
useful synthesis of available knowledge that relates to the mutual attraction
of bodies. The theory can be refined, or with new information, it can take on a
new direction. It is important to acknowledge the common misunderstanding of
what a scientific theory is, as revealed by those who say, “But it is not a
fact; it is only a theory.” Many
people have the mistaken notion that a theory is tentative or speculative,
while a fact is absolute.
Impress
upon your class that a fact is not
immutable and absolute, but it is generally a close agreement by competent
observers of a series of observations of the same phenomena. The observations
must be verifiable. Because the activity of science is the determination of the
most probable, there are no absolutes. Facts that were held to be absolute in
the past are seen altogether differently in the light of present-day knowledge
and observational equipment.
By concept, we mean an
intellectual framework that is part of a theory. We speak of the concept of
time, the concept of energy, or the concept of a force field. Time is related
to motion in space and is the substance of the Theory of Special Relativity. We
find that energy exists in tiny grains, or quanta, which is a central concept
in the Quantum Theory. An important concept in Newton’s Theory of Universal
Gravitation is the idea of a force field that surrounds a material body. A
concept is an idea with various applications. Thus, when we think
“conceptually,” we use a generalized way of looking at things.
Prediction in science is different from
prediction in other areas. In the everyday sense, one speaks of predicting what
has not yet occurred, like whether or not it will rain next weekend. In
science, however, prediction is not so much about what will happen, but about what is
happening and is not yet noticed, like what the properties of a hypothetical
particle are or are not. A scientist predicts what can and cannot happen,
rather than what will or will not happen.
Science
Has Limitations
Just
as a great strength of a democracy is its openness to criticism, likewise with
science. This is in sharp contrast to dogma, which is seen as absolute. The
limitations of science, like those of democracy, are open for improvement. The
world has suffered enormously from those who have felt their views were beyond
question. Author K. C. Cole says it well when she asserts that belief in only
one truth and being the possessor of it is the deepest root of all the evil
that is in the world.
Pseudoscience
The
material on pseudoscience should be excellent for student discussions. A
stimulating exercise is to ask students to formulate a series of questions that
help determine whether a given claim is a case of pseudoscience. Such a list
might include the following questions, and more:
• Does the claim use technical-sounding
jargon that is not precisely defined?
• Does the claim use scientific words
imprecisely and in a nonscientific context (e.g., “energy,” “frequency,”
“vibration”)?
• Do proponents complain of being overly
criticized?
• Is one reason given for the supposed
validity of the claim that it has been around a long time (so it must be true)?
• Do proponents of the claim use the logical
fallacy of the ad hominum to respond to critics? (An ad hominem argument is a
challenge directed at he who expresses an idea rather than at the idea itself.)
Pseudoscience
is very big business, and examples of it abound. Help students understand the
difference between nonscience, science, pseudoscience, and protoscience (a new science trying to establish legitimacy).
The
Search for Order—Science, Art, and
Religion
Einstein
said, “Science without religion is deaf; religion without science is blind.”
The topic of religion in a science text is rare. We treat it briefly only to
address what is foremost on many students’ minds. Do religion and science
contradict each other? Must one choose between them? We hope our very brief
treatment presents a satisfactory answer to these questions. Our take is that
religion and science are compatible when they address different realms. When
the certainty often associated with particular religions spills over into
science, then there is an unfortunate incompatibility between religion and
science.
Technology—Practical Use of the Findings of Science
In
discussions of science and technology and their side effects, a useful
statement is: You can never do just one
thing. Doing this affects that. Or, You can never change only one thing. Every time you
show an equation, it’s evident that changing a variable on one side of the
equation changes one or more on the other side. This idea is nicely extended
with “there is never just one force” in discussions of Newton’s third law.
The
Natural Sciences: Physics, Chemistry, Biology, Earth Science, and Astronomy
With
regard to science courses and liberal arts courses, there is a central factor
that makes it difficult for liberal arts students to delve into science courses
the way that science students can delve into liberal arts courses—and that’s the vertical nature of science courses. They build upon each other, as
noted by their prerequisites. A science student can take an intermediate course
in literature, poetry, or history at any time. But in no way can a humanities
student take an intermediate physics or chemistry course without first having a
foundation in elementary physics and mathematics. Hence the importance of this
conceptual course.
Integrated
Science
Coming
into this course, students may be hazy about what integrated science is. Yet, once
you explain it to them, they will readily grasp the value of it. When asked
“Why study integrated science?” one student simply stated “Because life is
integrated.” We fully agree. Point out to students that they will see over and
over in this text—and in their
everyday lives—that the branches of
science are interconnected. How can one understand the host of interesting and
important scientific phenomena—from
global warming to the origin of the solar system to forensic medicine—without integrating concepts from
different branches of science?
An
Investigation of Sea Butterflies This case study examines the scientific method as
actually applied as well as provides a specific example of integrated science.
Another important point discussed is the idea of a scientific control—a
basic feature of a valid scientific experiment. This idea can be rather subtle,
so you may want to emphasize it in your lecture. Consider using the concept
check questions for this feature as check-your-neighbor questions—they get at the main ideas of this
section.
2 Describing Motion
2.1 Aristotle
on Motion
2.2 Galileo’s
Concept of Inertia
History of Science: Aristotle
History of Science: Galileo
2.3 Mass—A Measure of Inertia
2.4 Net
Force
2.5 The
Equilibrium Rule
Science and Society: Paul Hewitt and
the Origin of Conceptual Integrated Science
2.6 The
Support Force
Math Connection: Applying the
Equilibrium Rule
2.7 Equilibrium
of Moving Things
2.8 The
Force of Friction
Integrated Science—Biology, Astronomy, Chemistry, and Earth
Science: Friction Is
Universal
2.9 Speed
and Velocity
2.10 Acceleration
Integrated Science—Biology: Hang Time
Demonstration
Equipment
Coat
hanger and clay blobs
Wooden
block stapled to a piece of cloth (to simulate tablecloth pull)
Tablecloth
(without a hem) and a few dishes (for the tablecloth pull)
Piece
of rope for a classroom tug-of-war
Wooden
cube that will fit on a pan balance (another material such as cardboard will
do)
Pan
balance
This
chapter introduces students to kinematics
and dynamics. Kinematics is the study of motion without regard to the forces
that produce it. When forces are considered, the study is then of dynamics. The
authors believe that one of the great follies of physics instruction is
overtime on kinematics. Whereas many physics books begin with a chapter on
kinematics, this is downplayed in this book. We treat only the amount of
kinematics needed, mainly distinguishing between velocity and acceleration as a
launching to Newton’s laws that follow. Please do not focus undue attention on
the kinematics concepts of speed and the “puzzels” that better belong in a math
class. And please spare your students graphical analysis of these topics, which
is better left to a math class or a follow-up physics course. Mastering motion
graphs is more of an uphill task than getting a grip on the concepts themselves
(but try telling that to a teacher who has a passion for graphical analysis!)
Too-early emphasis on kinematics can bog a course down at the outset. So,
lightly treat the sections on speed, velocity, and acceleration. Develop the
concept of net force, then move as smoothly as you can to where the meat is—the next chapter on Newton’s laws of
motion.
Of
particular interest to me (Hewitt) is the Personal Essay in the chapter, which
relates to events that inspired me to pursue a life in physics—my meeting with Burl Grey on the
sign-painting stages of Miami, Florida. Relative tensions in supporting cables
is what first caught my interest in physics, and I hope to instill the same
interest in your students with this chapter. My first screencast (look under
“Hewit drew it” on the web) tells the story of my meeting Burl, and how I was
inspired to study physics.
So
force, rather than kinematics, is the emphasis of this chapter. And force
vectors, only parallel ones at this point, are the easiest to understand. They
underlie the equilibrium rule: SF = 0 for systems in equilibrium.
These are further developed in the Practice
Book. (Not using the Practice Book
is like teaching swimming away from water. This is an important book—the authors’ most imaginative and pedagogically
useful tool for student learning!)
Note
that in introducing force, we first use pounds—most
familiar to your students. A quick transition, without fanfare, introduces the
newton. We don’t make units a big deal and don’t get into the laborious task of
unit conversions, which is more appropriate for physics majors.
A
brief treatment of units and systems of measurement is provided in Appendix A.
If
you get deeply into motion, you can consider the Sonic Ranger lab, which uses a sonar ranging device to plot in real
time the motion of students, rolling balls, or whatever. This lab can be
intriguing, so be careful that it doesn’t swallow too much time. Again,
overtime on kinematics is the black hole of physics teaching!
Screen
casts on the web, “Hewitt drew it”:
• 1. The Equilibrium Rule
• 2. Equilibrium Problems
• 3. Net Force and Vectors
• 4. Nellie’s Rope Tensions
• 5. Nellie’s Ropes
• 7. Force Vectors on an Incline
• 8. Linear Motion Definitions
• 9. Bikes and Bee Problem
• 10. Unit Conversion
• 11. Velocity Vectors
• 12. Free Fall
• 18. Acceleration Units
In
the Practice Book:
• Vectors and Equilibrium
• Free Fall Speed
• Acceleration of Free Fall
In
Next-Time Questions:
• The Scaffold in Equilibrium
• The Bee and the Bicycle
In
the Lab Manual:
• Go Go Go! (experiment on graphing motion)
• Sonic Ranger (activity on graphing motion)
• Walking the Plank (activity)
Suggested
Presentation
Begin
by holding up the textbook and remarking on its vast amount of information. A
look at the table of contents shows there is much to cover. Whereas some
material will be covered in depth, some will not. State that they will come to
feel quite comfortable with an understanding of much of the content, but not
all. There isn’t time for a thorough treatment of all material. So rather than
bogging down at the beginning of your course and ending up racing over material
at the term’s end, you’re going to do it the other way around, and race through
this beginning chapter. Rather than tilling this soil with a deep plow setting,
you’re going to skim it and dig in later. (This will help you avoid overtime on
kinematics!)
Your
first question: What means of motion has done more to change the way cities are
built than any other? [Answer: The elevator!]
Explain
the importance of simplifying. Explain that motion, for example, is best
understood by first neglecting the effects of air resistance, buoyancy, spin,
and the shape of the moving object. Beneath these factors are simple
relationships that may otherwise be masked. So you’ll concentrate on simple
cases and avoid complexities. State that you’re not trying to challenge them,
but to teach them some of the physical science that you yourself have learned.
Better they understand a simple case than be miffed by a complicated one that less
clearly focuses on the main concept being treated.
Aristotle’s
Classification of Motion
Briefly
discuss Aristotle’s views on motion. His views were a good beginning for his
time. They were flawed from the point of view of what we know today, but his efforts
to classify all things, motion being one of them, was a boost in human
thinking. Perhaps we remember him too much for his errors, when in total, he
did much to shape good thinking in his time.
Galileo’s
Concept of Inertia
Acknowledge
the chief difference between Aristotle’s approach and that of Galileo. The big
difference between these two giant intellects was the role of experiment—emphasized by Galileo. The legendary
experiment at the Leaning Tower of Pisa is a good example. Interestingly,
legend has it that many people who saw the falling objects fall together
continued to teach otherwise. Seeing is not always believing. Ideas that are
firmly established in one’s thinking are difficult to change. People in science
must be prepared to have their thinking challenged often.
Point
to an object in the room and state that if it started moving, one would
reasonably look for a cause for its motion. We would say that a force of some
kind was responsible, and that would seem reasonable. By force, you mean quite
simply, a push or a pull. Tie this idea to the notion of force maintaining
motion as Aristotle saw it. State that a cannonball remains at rest in the
cannon until a force is applied, and that the force of expanding gases drives
the ball out of the barrel when it is fired. But what keeps the cannonball
moving when the gases no longer act on it? Galileo wondered about the same
question when a ball gained speed in rolling down an incline but moved at
constant speed on a level surface. This leads you into a discussion of inertia.
In the everyday sense, inertia refers to a habit or a rut. In physics, it’s
another word for laziness, or the resistance to change as far as the state of
motion of an object is concerned. Inertia was first introduced not by Newton, but
by Galileo as a result of his inclined-plane experiments. You’ll return to this
concept when Newton’s first law is treated in the following chapter.
How
much inertia an object has is related to the amount of mass the object has.
Mass is a measure of the amount of material in an object. Weight is the
gravitational attraction of the earth for this amount of material. Whereas mass
is basic, weight depends on location. You’d weigh a lot more on Jupiter than on
Earth, and a lot less on the surface of the moon. Mass and weight are
proportional; hence, they are often confused.
Mass
is sometimes confused with volume. Comparing an overstuffed fluffy pillow to a
small automobile battery should convince anyone that mass and volume are
different. The unit of mass is the kilogram, and the unit of volume is cubic
meters or liters.
Density
is a concept of fundamental importance and is often confused with both mass and
volume. Try the following demo to make the concept of density clear. Measure
the dimensions of a large wooden cube in centimeters, and find its mass with a
pan balance. Define density = mass/volume. (Use the same cube when you discuss
flotation later.) Some of your students will unfortunately conceptualize
density as massiveness or bulkiness rather than massiveness per bulkiness, even
when they give a verbal definition properly. This can be helped with the
following:
CHECK
YOUR NEIGHBOR: Which has the greater density, a cupful of water or a lake-full
of water? A kilogram of lead or a kilogram of feathers? A single uranium atom
or the world?
I
jokingly relate breaking a candy bar in two and giving the smaller piece to my
friend who looks disturbed. “I gave you the same density of candy bar as I
have.”
Contrast
the density of matter and the density of atomic nuclei that comprise so tiny a
fraction of space within matter. From about 2 g/cm3 to 2 ¥ 1014 g/cm3. And in a further crushed
state, the interior of neutron stars, about 1016 gm/cm3.
Mass
Versus Weight
To
distinguish between mass and weight, compare the efforts of pushing
horizontally on a block of slippery ice on a frozen pond versus lifting it. Or
consider the weightlessness of a massive anvil in outer space and how it would
be difficult to shake. And if it were moving toward you, it would be harmful to
be in its way because of its great tendency to remain in motion. The following
demo (often used to illustrate impulse and momentum) makes the distinction
nicely:
DEMONSTRATION:
Hang a massive ball by a string and show that the top string breaks when the
bottom is pulled with gradually more force, but the bottom string breaks when
the string is jerked. Ask which of these cases illustrates weight.
(Interestingly enough, it’s the weight of the ball that makes for the greater
tension in the top string.) Then ask which of these cases illustrates inertia.
(When jerked, the tendency of the ball to resist the sudden downward
acceleration, its inertia, is responsible for the lower string breaking.) This
is the best demo we know of for showing the different effects of weight and
mass.
One
Kilogram Weighs 10 Newtons
Suspend
a 1-kg mass from a spring scale and show that it weighs 9.8 N. We round this
off to 10 N, for precision is not needed at this stage of learning.
Units
of Force—Newtons
I
suggest not making a big deal about the unfamiliar unit of force—the newton. I simply state that it is
the unit of force used by physicists, and if students find themselves
uncomfortable with it, simply think of “pounds” in its place. Relative
magnitudes, rather than actual magnitudes, are the emphasis of conceptual
integrated science anyway. Do as my inspirational friend Burl Grey does in
Figure 2.10 and suspend a familiar mass from a spring scale. If the mass is a
kilogram and the scale is calibrated in newtons, it will read 9.8 N. If the
scale is calibrated in pounds, it will read 2.2 pounds. State that you’re not
going to waste valued time in unit conversions. (Students can do enough of that
in one of those dull physics courses they’ve heard about.) [I do a short lesson
on Unit Conversion in Screencast #10 that will save you classtime.]
CHECK
YOUR NEIGHBOR: Which has more mass, a 1-kg stone or a 1-lb stone? [A 1-kg stone
has more mass, for it weighs 2.2 lb. But we’re not going to make a fuss about
such conversions. If the unit newton bugs you, think of it as a unit of force
or weight in a foreign language for now!]
Net
Force
Discuss
the idea of more than one force acting on something, and the resulting net
force. Figure 2.9 captures the essence. Here’s where you can introduce vectors.
Note that the forces in the figure are represented by arrows. Drawn to scale,
these are vectors. Briefly distinguish between vector quantities (like force,
velocity, and, as we shall see, acceleration) and scalar quantities (time,
mass, volume).[Screencast #3 on Net Force is also a time saver.]
Equilibrium
for Objects at Rest
Cite
other static examples, where the net
force is zero as evidenced by no changes in motion. Hold the 1-kg mass at rest
in your hand and ask how much net force acts on it. Be sure they distinguish
between the 9.8 N gravitational force on the object and the zero net force on it—as evidenced by its state of rest. (The
concept of acceleration is introduced shortly.) When suspended by the spring
scale, point out that the scale is pulling up on the object, with just as much
force as the earth pulls down on it. Pretend to step on a bathroom scale. Ask
how much gravity is pulling on you. This is evident by the scale reading. Then
ask what the net force is that acts on you. This is evident by your absence of
any motion change. Consider two scales, one foot on each, and ask how each
scale would read. Then ask how the scales would read if you shifted your weight
more on one scale than the other. Ask if there is a rule to guide the answers
to these questions. There is: SF = 0 For any object in equilibrium, the net force
on it must be zero. Before answering, consider the skit outlined below.
Sign Painter
Skit Draw
on the board the sketch below, which shows two painters on a painting rig
suspended by two ropes. [Again, Screencast #1 covers this.]
Step 1: If both painters have the same
weight and each stands next to a rope, the supporting force in the ropes will
be equal. If spring scales were used, one on each rope, the forces in the ropes
would be evident. Ask what the scale readings in each rope would be in this
case. [The answer is that each rope will support the weight of one man + half
the weight of the rig—both scales will show equal readings.]
Step 2: Suppose one painter walks toward
the other as shown in the sketch, which you draw on the chalkboard (or show via
overhead projector). Will the reading in the left rope increase? Will the
reading in the right rope decrease? Grand question: Will the reading in the
left rope increase exactly as much as the decrease in tension in the right
rope? And if so, how does either rope “know” about the change in the other
rope? After neighbor discussion, be sure to emphasize that the answers to these
questions lie in the framework of the Equilibrium Rule: SF = 0.
Because there is no change in motion, the net force must be zero, which means
the upward support forces supplied by the ropes must add up to the downward
force of gravity on the two men and the rig. So a decrease in one rope must
necessarily be met with a corresponding increase in the other. (This example is
dear to my heart. Both Burl and I didn’t know the answer way back then—because neither he nor I had a model for
analyzing the problem. We didn’t know about Newton’s first law and the
Equilibrium Rule. How different one’s thinking is depends on whether there is a
model or guidance. If Burl and I had been mystical in our thinking, we might
have been more concerned with how each rope “knows” about the condition of the
other. This is the approach that intrigues many people with a nonscientific
view of the world.)
The
Support Force (Normal Force)
Ask
what forces act on a book at rest on your lecture table. Then discuss Figure
2.12, explaining that the atoms in the table behave like tiny springs. This
upward support force is equal and opposite to the weight of the book, as
evidenced by the book’s state of rest. The support force is a very real force.
Because it is always perpendicular to the surface, it is called a normal force. Without it, the book would
be in a state of free fall.
Friction—A Force That Affects Motion
Drag
a block at constant velocity across your lecture table. Acknowledge the force
of friction, and how it must exactly counter your pulling force. Show the
pulling force with a spring balance. Now, because the block moves without
accelerating, ask for the magnitude of the friction force. It must be equal and
opposite to your scale reading. Then the net force is zero. While sliding, the
block is in dynamic equilibrium. That is, SF = 0.
Equilibrium
of Moving Things
If
you’re in the car of a smoothly moving train and you balance a deck of cards on
a table, they are in equilibrium whether the train is in motion or not. If
there is no change in motion (acceleration), the cards don’t “know the difference.”
Speed
and Velocity
Define
speed, writing its equation in longhand form on the board while giving examples
(automobile speedometers, etc.). Similarly define velocity, citing how a race
car driver is interested in his speed,
whereas an airplane pilot is interested in her velocity (speed and direction). [More than enough information on
kinematic definitions is in Screencast #8.]
Motion
Is Relative
Acknowledge
that motion is relative to a frame of reference. When walking down the aisle of
a train at 1 m/s, your speed relative to the floor of the train is different
than your speed relative to the ground. If the train is moving at 50 m/s, then
your speed relative to the ground is 51 m/s if you’re walking forward, or 49
m/s if you’re walking toward the rear of the train. Tell your class that you’re
not going to make a big deal about distinguishing between speed and velocity,
but you are going to make a big deal of distinguishing between speed or
velocity and another concept—acceleration.
Galileo
and Acceleration
Define
acceleration, identifying it as a vector quantity, and cite the importance of change. That’s change in speed, or
change in direction. Hence, both are acknowledged by defining acceleration as a
rate of change in velocity rather than speed. Ask your students to identify the
three controls in an automobile that enable the auto to change its state of motion—that
produce acceleration (accelerator,
brakes, and steering wheel). State how one lurches in a vehicle that is
undergoing acceleration, especially for circular motion, and state why the
definition of velocity includes direction to make the definition of
acceleration all-encompassing. Talk of how without lurching one cannot sense
motion, giving examples of coin flipping in a high-speed aircraft versus doing
the same when the same aircraft is at rest on the runway.
Units
for Acceleration
Give
numerical examples of acceleration in units of kilometers/hour per second to
establish the idea of acceleration. Be sure that your students are working on
the examples with you. For example, ask them to find the acceleration of a car
that goes from rest to 100 km/h in 10 seconds. It is important that you not use
examples involving seconds twice until they taste success with the easier
kilometers/hour per second examples. Have them check their work with their
neighbors as you go along. Only after they get the hang of it, introduce
meters/second/second in your examples to develop a sense for the units m/s2.
[Screencast #18 covers this].
Falling
Objects
CHECK
YOUR NEIGHBOR: If an object is dropped from an initial position of rest from
the top of a cliff, how fast will it
be traveling at the end of 1 second? (You might add, “Write the answer on your
notepaper.” And then, “Look at your neighbor’s paper—if your neighbor doesn’t have the right answer, reach over and
help him or her—talk about it.”)
After
explaining the answer when class discussion dies down, repeat the process,
asking for the speed at the end of 2 seconds, and then for 10 seconds. This
leads you into stating the relationship v
= gt, which by now you can
express in shorthand notation. After any questions, discussion, and examples,
state that you are going to pose a different question—not asking for how fast,
but for how far. Ask how far the
object falls in 1 second.
Ask
for a written response and then ask if the students could explain to their
neighbors why the distance is only 5
m rather than 10 m. After they’ve discussed this for almost a minute or so,
ask, “If you maintain a speed of 60 km/h for 1 hour, how far do you go?”—then, “If you maintain a speed of 10 m/s
for 1 second, how far do you go?” Important
point: You’ll appreciably improve your instruction if you allow some
thinking time after you ask a question. Not doing so is the folly of too many
teachers. Then continue, “Then why is the answer to the first question not 10
meters?” After a suitable time, stress the idea of average velocity and the relation d = vt. [Screencast #12
treats Free Fall.]
For
accelerating objects that start from a rest position, the average velocity is
half the final velocity (average velocity = [initial velocity + final
velocity]/2).
CHECK
YOUR NEIGHBOR: How far will a freely falling object that is released from rest
fall in 2 seconds? In 10 seconds? (When your class is comfortable with
this, then ask how far in 1/2 second.)
Investigate
Figure 2.23 and have students complete the speed readings. Ask what odometer
readings (that measure distance) would be for the speeds shown. To avoid
information overload, we restrict all numerical examples of free fall to cases
that begin at rest. Why? Because it’s simpler that way. (We prefer our students
understand simple physics rather than be confused about not-so-simple physics!)
We do go this far with them:
Two-Track
Demo
Look
ahead at the two tracks shown in Exercise 79. With your hand, hold both balls
at the top end of the tracks and ask which will get to the end first. Or you
can quip, which will win the race, the slow one or the fast one? Or, the one
with the greatest average speed or the one with the smaller average speed?
Asked these latter ways, the question guides the answer. But be ready to find
that most students will intuitively know the balls will reach the end with the
same speed. (This is more obvious from a conservation of momentum point of
view.) But the question is not of speed, but of time—which gets there first. And that’s a
challenge to realize that! The speed gained by the ball on the lower part of
the dipped track is lost coming up the other side, so, yes, they reach the end
with the same speed. But the gained speed at the bottom of the dip means more
average speed overall. You’ll get a lot of discussion on this one. You can make
your own tracks quite simply. I got this idea from my friend and colleague,
Chelcie Liu, who simply bought a pair of equal length bookcase supports and
bent them by hand. They are more easily bent with the aid of a vice. [These tracks
make a concluding question in Screencast #31, when the conservation of energy
is discussed.]
Integrated
Science—Biology, Astronomy,
Chemistry, and Earth Science: Friction Is Universal
To
make the point that friction is indeed universal, break students into small
groups and ask them to list examples of friction that relate to each of the
major science subject areas—physics,
chemistry, biology, earth science, and astronomy. Have students state their
examples so all can appreciate the diversity of friction applications. Also,
you might have a brick available to students interested in verifying the
concept discussed in the Concept Check question for themselves.
Integrated
Science—Biology: Hang Time
This
fascinating idea completes the chapter. Most students (and other instructors)
are amazed that the best athletes cannot remain airborne for a second in a
standing jump. This prompts great class discussion. You can challenge your
students by saying you’ll award an A
to any student who can do a 1-second standing jump! You’ll have takers; but
you’ll award no A’s for this feat.
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