1. Observation-Based Thinking
Skills
Experimental activities can help students
learn to use observation-based logic and make mental connections
between different levels of thinking (macro,
micro, and symbolic). And
while they're doing this, they also learn chemistry concepts.
COMPETING REACTIONS (Using
Questions to Inspire Active Thinking):
This activity illustrates how a routine procedure becomes a minds-on
opportunity for learning. Students place solid Zn into a solution with
Cu+2 and H3O+
ions. If students are in a typical "going through the motions"
mode, their observations -- bubbles for awhile, a blue color in the solution
gradually disappears, a reddish-gold solid appears,... -- won't promote much
thinking. But when a teacher asks questions -- which chemicals are visible
(in what way) and invisible? what is reacting with what to produce what?
is there one reaction or two? are these reactions connected or competitive?
which chemicals are competing for what resource? can you write equations
for the net reactions? how do you know when each reaction is complete?
which reaction finishes first? how do you know which reactant is used
up and which is in excess? -- this routine task is transformed into a valuable
opportunity for learning. Students can learn about concepts (limiting
reactants,...) and a thinking process: using
observation-based logic to connect macro-level
observations (bubbles, blue color,...)
with micro-level events (interacting ions, atoms, and molecules)
and their symbolic
representations (as chemical symbols
and reaction equations).
CAUSING TROUBLE: An interesting twist is
to stir up controversy by giving groups differing instructions about how much
of each chemical to use, so their answers to "which finished first"
will be in conflict. :< )
USING THEORY: Students can do
calculations for each combination of chemicals in these "differing instructions"
runs, to determine whether there is a match between their theory-based calculations
and their reality-based observations.
PREPARATION: Students
can be prepared for this activity in several ways. They can react
copper wire with warm nitric acid, as discussed below. A simpler preliminary,
done as a demonstration in lecture or lab, is to show the gas-producing
reaction of HCl with Mg, along with a reaction equation and an explanation
of the "stealing electrons" mechanism. The concept of limiting
reactants can be discussed either before or after the lab.
updates in 2008:
RECOGNIZING A LIMITING REAGENT BY OBSERVING ITS ABSENCE: In
a
current
experiment
(being done at UW in recent years) students react Zn with I2 in
aqueous solution, and the
question is "how can you know when the reaction
is finished?" The
answer is that "it's finished when either the Zn is gone (could we
observe this?)
or the I2 is gone (could we observe this?)" and a key concept is the
importance of knowing what each chemical looks like, so they can observe
whether
it
is
or
isn't
still
present
in
their reaction beaker, and can logically conclude whether the reaction is
or isn't finished (whether the maximum possible amount of reaction has occurred)
and
which
chemical
was
the
limiting
reactant. {the
question in more detail} / You can see analogous supplementary
instructions (from Fall 2008) for
other current labs by looking for green text (it's
the color code for labs) in my schedule-page and
clicking the "instructions" links. These pages describe some
of the thinking
activities I use in labs; others are
in this "thinking
skills" page; but many activities are not described in print (here, there, or elsewhere) even though I
pre-plan them
and do them in lab, while other thinking activities (usually they're questions
or comments) are improvised during lab.
LIMITED KNOWLEDGE ABOUT A NON-LIMITING REAGENT: Another
important
"thinking
skills"
concept
(that is a key for experimental design
in
several labs during the
1990s and also now) is that if we want to measure the amount of a particular
chemical, it
MUST
be
the
limiting reagent in the reaction we're using. This concept is
important for experimental
design.
COPPER AND NITRIC ACID: Students observe this reaction, and think about questions: Has the copper wire disappeared? Have the copper atoms disappeared? Where are they: in the red-brown gas or the blue solution? Which color most closely matches that of copper? Is this significant? If copper is in the brown gas, in what form could it be: copper ions? {but these are strongly solvated by water, so are not likely to evaporate} copper atoms? {but neutral copper forms solid copper metal, not a gas} a copper compound? {but this would be either ionic or a metal alloy, and neither would evaporate} So where are the copper atoms now? / The teacher gets some copper sulfate (with Cu+2 ions), dissolves it in water, and asks students to compare this with the result of the copper/acid reaction.
TAKERS AND GIVERS (Halogens and Halides):
First, students observe mixtures of water and hexane and either Cl2
(the hexane layer is clear) or Br2 (this layer is now yellow/orange)
or I2 (it is pink/purple); then they observe the hexane layer
after mixing each of the six possible combinations of halogens (Cl2,
Br2, I2) with halides (Cl-, Br-,
I-). Based on their observations, students draw conclusions
about trends in reactivity among halogens and among halides.
This activity provides an opportunity
to practice observation-based logic. It also provides an opportunity
to think about the fundamental difference between reactions that involve
neutral halogens (which can react by gaining electrons to become negative
halides) and negative halides (which can lose electrons to become neutral
halogens), but only if questions provide a stimulation for thinking. One
result of this thinking is that students can decide, based on their observations,
what the reactivity trend is for halogens and for halides; typically they
think "Cl is more reactive than Br or I because Cl is more electronegative" but
this is true only for neutral halogens, while the trend is reversed for negative
halides; and
students should be able to explain, by
using
chemistry logic, why each trend should be expected.
Another way to help students "connect
ideas" is to show them a table of reduction potentials,
and ask them to find
the
value for each halogen (F2, Cl2, Br2, and I2 are +2.87, +1.36,
+1.08, and
+0.535 V)
and
ask them to explain
where the most reactive chemicals are — they are "high on the left" and "low
on
the
right"
so F2 is the most reactive halogen, but I- is the most reactive halide — and
ask whether this agrees with what they observed in their experiment.
As usual, students learn more when they
are challenged to think, when a teacher asks questions about what students
are observing and what they can logically conclude. This activity
can be done as either inquiry or confirmation, either before or
after
periodic
trends
in reactivity are studied in a lecture or textbook. As usual, of course,
questions and hints should be adjusted to match the students' foundation
of conceptual knowledge and thinking skills, which will differ in the inquiry
and confirmation modes.
CONVERTING PHYSICAL MODELS INTO MENTAL MODELS:
Students construct and study 3-D physical models
of chemical structures, in order to form their own mental
models. Usually, I'm interested in how chemistry labs can help
students learn thinking skills, or as a confirmation that will
help students master the concepts they are learning in lecture. But
this lab is a powerful way to let students learn chemistry concepts by a process
of inquiry.
During my lab introduction, to emphasize
that this lab is an opportunity for learning, I draw a crude picture of
a car, and ask students to imagine what this object looks like from the
front, side, rear, and diagonal. When I claim that they can do this
because my drawing is so good, they laugh because it isn't very sophisticated.
But it is good enough to let them know that it's a car, and from here their
"visual memories" can take over. They have seen lots of
3-D physical cars, so they've had plenty of practice forming 3-D mental
images of cars. By analogy, in this lab they should take advantage
of the opportunity to practice the art of converting the physical images
they can see into mental images they can imagine. They can also learn
how to use 2-D pictures they can see (in a textbook that is available in
lab) as a bridge between 3-D molecular models and 3-D mental images.
During the lab, students work in cooperative
groups, and for each structure (simple cubic, body-centered cubic, hexagonal
closest packing, cubic closest packing, face-centered cubic, CsCl, NaCl,
CaF2, diamond and graphite) they discuss questions from the lab
book (about coordination number, repeating patterns, physical properites,
the number of atoms in each unit cell and its relationship to the stoichiometry
of compounds, and more), first with each other, and then with me.
And I ask them other questions, such as whether they see a correlation between
coordination number and density, whether it is possible to have a coordination
number larger than 12, and what the term "closest packing" means.
The ionic compounds also offer an opportunity
to review principles (from earlier in the semester) about the size of ions,
and to think about thinking. We look at the CsCl structure, composed
of small spheres and large spheres, and I ask them to explain why they might
expect Cl- to be larger (because in an isoelectronic series,
negative ions are larger than positive ions, so Cl- is larger
than K+) and to give a counter-argument for why it should be
smaller (because Cl- has fewer electrons than Cs+,
as does K+). Then I ask them, "So which is larger?",
and we discuss the ways in which our situation (with principles indicating
that Cl- and Cs+ are both larger than K+)
is analogous to the question, "If Sue is taller than Tom, and Mary
is taller than Tom, who is taller, Sue or Mary?" This naturally
leads to a discussion of conflicting factors
and how we can cope with a situation where our logic seems inadequate for
reaching a conclusion. Then we do a "reality
check" using data about ionic sizes from the textbook.
In a similar process of thinking, we look at NaCl (now both factors agree
that Cl- is larger) and CaF2 (again the factors are
in conflict, but now the negative ion is slightly larger).
I also ask students to discuss and solve
geometry problems involving ionic radii and the length of a unit cell, or
the length of a "regular diagonal" (in 2 dimensions, for an FCC
structure) or a "long diagonal" (in 3 dimensions, for a BCC structure).
They also do a calculation for the densities of NaCl and CaF2,
using logic involving the number of each ion in a unit cell, atomic masses
(along with logic about the relative masses of nucleons and electrons, of
atoms and ions, plus the principle of electrical neutrality), Avagadro's
Number, and the length of a unit cell.
QUESTIONS ABOUT AIR:
Students blow up a balloon, cool it in liquid nitrogen, let it warm up, and
then discuss thought-stimulating questions: In what state (s, l, g)
is each component of air? {a table of freezing and boiling points is
provided} What is missing from the table? {it is a dry-air table
so we can talk about humidity,...} How does air in the balloon compare
with air in the room? {due to the body's metabolism, balloon-air contains
more H2O and CO2 but less O2 and the same
N2}
AUTOMATED SUBTRACTIONS:
Students weigh a block in four ways, with and without the taring
mechanism of the scale. Later in the semester, the analogous concept
of a blank stimulates thinking about the logical
functioning that is designed into spectrometers. { in each case,
the machine is designed to "subtract off" what you have defined
to be the zero-level amount (of mass or absorption) } In 2008
students measure the absorbance of complex (red) made by combining alcohol
(clear, 10% of mixture) with a reagent (orange, 90% of mixture) so they
use the orange mixture (it would be more correct to use a 90-10 mix of
the reagent + water, but...) to calibrate the spectrometer. I teach
the concept of automated subtraction, and the analogy between taring
and calibration, with these simple descriptions, with the math arranged
vertically in columns (as shown for "red + orange") to show "what
disappears during the subtraction"
more clearly, in a visually/logically obvious way:
• mass (beaker + block) - mass (beaker) = mass (block); in
2008 it's "mass (sugar water)"
• absorbance (complex + reagent) - absorbance (reagent) = absorbance (complex);
or, using colors that are
easier
for students to visualize,
A (red + orange) - A (orange) = A (red), or simply (red +
orange) - (orange) = (red),
| red + orange |
- orange |
red |
A MYSTERIOUS TREND: While they
are weighing a beaker containing liquid hexane, students see the weight steadily
decreasing. Is there something wrong with the scale? What
is happening? For determining an accurate weight, is this a random
error or systematic error? What
could be done to prevent or minimize the error? Would it be more serious
with 40.00 mL of hexane in a 50 mL beaker or in a 500 mL beaker?
CONCEPTUAL PICTURES: Students
draw pictures of molecules (liquid and gas) in a flask at different stages
of an experimental procedure. Drawing lets students experience the process
of translating "book-knowledge thinking" into practical lab thinking,
or for showing those who find this difficult (more students than I had expected)
that one way of thinking doesn't automatically lead to the other.
the questions and pictures
2. Thinking Skills for Data Analysis
To
help students learn the fundamentals of mathematical data analysis, I made
two handouts (the two links below will work by December 9, 2008)
for students to do as homework.
The first
handout (plus answers) contains a variety of questions and problems
about precision-and-accuracy, significant figures, finding standard deviations
(by
using an equation, and using their calculator's "statistical" mode),
strategies for identifying and handling "outliers" in a data
set, deciding if an error is random or systematic, and retroductively curve-fitting
data sets by using nonlinear relationships (logarithmic, square root,...).
The second
handout (plus answers) is more thematic. It asks students to explore
± uncertainties by using the logic of "worst-case scenarios"
to determine the minimum, maximum, and centered values for density, using
the data (for mass and volume) and uncertainties that are provided. This
illustrates the logical reasons behind the mathematical rules for processing
uncertainties (by + - x /), and the differences between absolute errors
(used
for + or -) and relative errors (for x or /).
This didn't cover everything in data analysis
(and neither does what's below) but it's a beginning.
Updates in 2008:
With experience, I've become more and more convinced
that almost all students need a much better understanding of the ideas-and-skills
used in data analysis. For example, most students usually:
• don't always include UNITS in their data,
and don't realize why this is a serious error.
• don't understand the differing strategies
that are used for multiplication-or-division (where sig figs are
used) and addition-or-subtraction (where decimal columns are used); or
they don't "match" the decimal columns after they have calculated a deviation,
by (for example) reporting a density as "1.046 ± .0026 g/mL"
instead of "1.046 ± .003 g/mL" with both to the nearest .001
g/mL.
• don't realize that sig figs are a simple,
unsophisticated measure of precision, so they overemphasize the statistical
significance of significant figures; the utility of other statistical
criteria is illustrated by a situation where students should
"break the rule" for sig figs and calculate density to 4 sig
figs when they divide "9.87 g / 9.73 mL" to
get 1.014 g/mL, even though their "sig fig rule" indicates
that only 3 sig figs are justified, because in this case percent error
(which justifies the use of 4 sig figs) is a better measure of precision than
sig figs.
• don't appreciate the difference between
4, 4.0, and 4.00, regarding what is being claimed: "4" is
a humble claim that the result is between 3.5 and 4.5 so it's rounded to 4,
the nearest whole number; but 4.00, confidently claims that the result
is between 3.995 and 4.005, with rounding to the nearest .01; of course,
"4.00" claims only that the calculation should be rounded
to .01, not that the result is necessarily accurate to .01, or is precisely
reproducible to .01.
• don't appreciate the
value of LARGE NUMBERS when collecting experimental data; in one
thinking activity, I ask them whether an Eppendorf Pipet (delivering 1.00
mL) must
be more precise than a 10 mL Volumetric Flask, to have the same
relative error in each measurement; (yes, it must be 10 times more precise,
by having 1/10 of the absolute error).
• don't re-calculate concentrations, based
on the actual amount of chemical used; for example, if they are told
to make 100.00 mL of .08103 M solution from CuCl2•2H2O
and they calculate that 1.3638 g is needed, if they actually weigh out
1.3814
g they must re-calculate the actual concentration as .08103 M, not .08000
M;
in this experiment, students now make a graph by Excel (not by hand drawing,
as in previous years) and for a computer .8103 is no more difficult than
.08000
/ In another lab, where they use a Mohr Pipet, students see why a
7-column table is helpful.
• don't think carefully enough about the
glassware they're using; thus, they sometimes measure volume using a
standard beaker (that is ± 5%) without realizing the lack of precision;
• don't know how to use equipment (especially
glassware) correctly, or they understand but they are not careful enough
in making their observations, when they adopt a "close enough for gen chem"
attitude; in these situations I often acknowledge, to students, that
it really doesn't matter (since we don't hold them responsible for precision/accuracy
by having
them get answers for quantitative unknowns) but I ask them to imagine themselves
in a situation where it really does matter, where they are in a research
lab, a police CSI lab, or a medical lab doing analyses for patients
whose health may depend on the accuracy of your results.
• don't ask themselves, often enough or
with sufficient skill, "does it matter?"; therefore,...
In one "thinking skills activity"
— motivated when I noticed that many students don't understand when
it's important for glassware to be initially dry, so they're either too careful
(when it doesn't matter) or too sloppy (when it does matter) — I ask
whether 1 mL of water that's initially in a 10 mL volumetric flask will cause
an error in 3 situations they have encountered during the semester:
it makes no difference when the flask is used for dilution, because
they eventually add water in "filling to the line" anyway;
it makes a small difference when they measure the absorbance of a red
complex (formed from alcohol, and used to determine the amount of alcohol)
for reasons that I won't describe here; and it makes a big difference
(10% less weight, plus 10% dilution) when they use "final weight - initial
weight" to find the mass of a sugar solution and then use this data to
calculate its density. { Earlier in the semester, I ask them to
"imagine that you know your volumetric flask in Part A begins with 0.40
mL of water on its walls (instead of being "clean and dry") and,
ignoring this knowledge, you calculate your solution density as 1.034 g/mL.
What is the "corrected density"? (i.e., what would the density be
if you had begun with a flask that really was clean and dry)" This
requires an if-then comparison of the actual/wet versus ideal/dry. }
/ And if a cuvet (used to measure absorbance) is not dry, if it
has not been rinsed with the solution whose absorbance they are measuring,
this would also cause a major error.
In another "does it matter?"
thinking activity, I ask whether it would be acceptable (without causing error)
if a particular Eppendorf Pipet consistently delivers a precise 1.175 mL (instead
of the 1.000 mL they expect) when they are using calibration
logic by "doing the same thing" to samples of knowns (to
make a calibration graph) and unknowns (to use the calibration graph).
Then I ask,
"How do you know if an Eppendorf Pipet is consistently precise, and (a
different question) if it's accurate?" Students can answer these
questions by doing calibration experiments if they know the density
of a liquid (like pure water, with d = .9982 g/mL at 20 C) and they repeatedly
deliver "1 mL" into a beaker, record the weight after each delivery,
and then analyze the data. In a similar way they can check the precision
and accuracy of several 10 mL volumetric flasks. They can compare their
own analyses with claims made by the manufacturers of the pipets and flasks.
In their first lab of the semester,
during a "cumulative
weighing" students see another example where "dry" matters
in one way but not in another way —
"The INSIDE of your beaker doesn't need
to
be dry
in
Part B, but the
beaker's OUTSIDE (especially the bottom) should stay dry, and (this is
very important for all data collected by everyone in lab) the top of the
balance-pan should stay dry. Do you understand why ‘initial
water’ inside the beaker doesn't matter, but getting water on the outside of
the beaker will cause experimental error in your data?" — and the
why-question
converts this opportunity (to use a thinking skill) into a
thinking activity.
more! — Data Analysis (re: accuracy & precision, random errors & systematic errors, and more) is also an important factor to consider in Designing Experiments.
ESTIMATING AMOUNTS
Here is a thinking
activity that would be useful (but currently is not done at UW) to help students
develop an intuitive feeling for "how much" and for
the size of metric units, which unfortunately
is necessary in the United States because we're the only non-metric
major country in the world. For
various objects, students measure amounts (mass,
length, volume) in metric units (g, mm and cm, mL), and convert these amounts
to American units (oz and lb, inch, fluid oz); then they estimate
amounts (mass, length, and/or volume) for various objects, as individuals
(first) and in groups (to "negotiate" about their differing estimates),
and we have a competitive
game to see which groups can make the best
estimates.
an option: This can also be done for ratios,
like density, although "supplied data" may be necessary to make this practical. Or,
when estimating densities, you can ask students to use their own observations
(from the past) in a variation of the game
asking "will it float?" on David Letterman.
3. Thinking Skills (logical and social) in The Process
of Science
As a prelab,
students do the first Data Analysis handout, described above. In lab
they measure the density of an unknown liquid (a mixture of ethylene glycol
and water), and we discuss precision and accuracy.
I ask them what precision is, what accuracy is,
and how these differ. We examine four sets of data that illustrate
all four combinations of precision and accuracy (both are high, both are
low, or one is high while the other low) and we discuss random
errors & systematic errors.
When I ask students about the accuracy
of their data, they should say (if they've been paying attention in our discussions
about precision and accuracy) that "We
can't
estimate
accuracy
because
we
don't
know the true value for the density of our
unknown liquid." Then I ask, "How did the values for density
(and Avagadro's Number, speed of light,...) get into the CRC Handbook?" Here,
the goal is to explore various perspectives on evaluations (and decisions & declarations)
that are made by a scientific community (or
sub-community or committee) or by an individual author or editor. What
are the criteria for developing a rationally
justified confidence in science?
Who did the work? Should we be more confident
about a value of Avagadro's Number based on a set of 5 experiments done by
one person,
by
a large research group, or by many large groups scattered around the world? We
discuss the process of creative and critical thinking in the context of
individuals, in-groups, and out-groups.
What was done? Should we
place more trust in a value of Avagadro's Number based on 5 similar experiments
that give the same value, or 5 different experiments that give the same
value? This lets us discuss systematic errors, background assumptions,
theoretical
and
experimental interdependencies, and the independent
confirmations that occur if we have many ways (not just one) to calculate
Avagadro's Number.
Objective criteria for evaluating the scientific
support for an
idea
include
experiments
(how many? done by different groups? are results reproducible? was there
good experimental design and data analysis?) and theory (logical coherence,...).
Subjective factors include questions about
the psychology
and
sociology
of critical
thinking,
in persuasion by logic, rhetoric, appeals to authority, and group politics
(personal
or institutional),
in
the
process
of achieving
a community consensus. How
do
scientists
respond
when
two
different
techniques
give different results? In their evaluations, can scientists be biased? We
discuss potential sources of bias, including "investments" of finances (such
as owning expensive instruments of one type but not the other), experience (knowing
how to perform and analyze one type of experiment better than the other),
or ego (when
there have been public declarations that one of the techniques is superior). Is
there anything scientists can do to minimize the effects of these biases?
These questions, and others that can
be planned or improvised, offer many opportunities for learning about the
logical-and-social process
of science, and the
"strategies for problem solving" used by scientists. For a teacher
with knowledge, imagination, and enthusiasm, many types of
discussions
(short or long, taking off in
many different directions) are possible. Case studies can be useful,
to provide concrete issues to think about and discuss.
Some
interesting ideas about scientific methods, both logical and social, are explored
in my model of Integrated
Scientific
Method, especially in Sections 1 & 2 (re: experimental observations
&
relationships with other theories) plus 3
& 8 (re: cultural-personal
factors & thought styles).
4. Logical Thinking Skills
used in Science
Students should have
opportunities
to use different kinds of scientific logic in labs.
HYPOTHETICO-DEDUCTIVE LOGIC
In science, an especially
valuable thinking skill is the hypothetico-deductive (HD) logic that
is the foundation of scientific method. Here are four activities involving
HD reasoning, selected from chemistry labs at UW.
• A written handout explains
the basic principles of mass spectrometry, provides mass-spec graphs for students
to analyze for
practice, then asks them to use another graph to determine the structure
of a C3H7Br compound. To solve this problem, students
must use HD logic: invent competitive theories
about the structure (i.e., use their imaginations to invent two structures
that are consistent with the principles that C forms 4 bonds, while H and
Br each form 1 bond); use each theory to predict the corresponding
graph;
compare these two sets of if-then predictions to see where they differ, to
find a "crucial
experiment" within the graph-data provided for them; do
a "reality
check" by observing the graph; compare these observations
with the predictions from each of the two competing theories (for the structure
of CH3H7Br), and draw a conclusion. Very few students have been able
to finish the entire process of HD logic, even after they were given an
explicit
step-by-step procedure for what to do first and what to do next until they
could reach a logical HD-conclusion. Obviously, students need more
experience with this thinking skill that is the foundation of scientific
method.
• In 2008 a computer lab (asking "what
is causing the fish to die") is intended to give students experience in
constructing a theory and testing it, but the construction/testing is trivially
easy, so
(unlike
the mass-spec example above, which is no longer done at UW) it doesn't provide
a useful experience with H-D Logic. But this lab is useful for teaching
other things, including Experimental Design. / To help
students experience the concept of a crucial experiment, I add an extra
question to another computer lab, in which they look at movies
of reactions and use calibration logic; I ask them (as in
the mass-spec lab above) to "explain
how you can distinguish between copper nitrate and copper sulfate" by
finding a crucial experiment so you can use tie-breaker logic to distinguish
between
the two blue solutions, to decide (for your blue "unknown solution")
whether it is copper nitrate or copper sulfate.
• In another
experiment in 2008,
students gain more experience with HYPOTHETICO-DEDUCTIVE LOGIC when
they develop
a theory (to
explain why a particular color is observed for the first of three solutions) and
test their theory (by
then applying it for the other two solutions).
THE LOGIC
OF LE CHATELIER
• In another opportunity for hypothetico-deductive
experience, students cause shifts in the equilibrium amounts of complex ions
(as shown in the reaction below) by adding chemicals and changing the temperature.
[Co(H2O)6]+2 + 4 Cl- --> [CoCl4]-2 + 6 H2O
First, students prepare and observe the complex ions: cobalt with water (pink) and cobalt with chloride (blue). Then, beginning with cobalt in water, they make a series of changes, shown by arrows in the diagram below. Before each change, they use Le Chatelier's Principle to predict the shift in equilibrium amounts (no change, to the right, or to the left) and circle the appropriate symbol in the PRED column. Then they use observations (is the color pink, blue, or an intermediate purple) and logic to estimate the relative amounts of left-side species (L) and right-side species (R) at each stage of the sequence (before and after every change) and in the bottom row they mark each equilibrium position. { For example, a mark is placed far to the left on the L-R bar if the "after HCl" solution is pink, in the middle for a violet color, 3/4 to the right for violet-blue, and far to the right if blue. } Based on their logically interpreted observations, they determine the observed before-to-after shift, mark the OBS column, then compare their predictions and observations.
For the temperature increase to 100 degrees, students cannot make a prediction because they don't know the reaction enthalpy. But after observing the equilibria (before and after) and determining the shift in equilibrium, they can retroductively infer whether the enthalpy is exothermic or endothermic, and mark this in the RETROD column. Then they can predict the equilibrium shift for the next change (when T drops to 0 in an ice bath), observe the before and after states to determine the shift, and compare predictions with observations.
Many concepts and thinking skills can be learned
in this lab. But without the diagram — which I developed to explicitly
promote logically organized hypothetico-deductive thinking — most students
will miss many of these opportunities for learning.
note: The diagram above is part of a 3-page
handout (plus notes) co-authored by Jacquie Scott (former Lab Director for General Chemistry at UW) and Craig Rusbult in 1995/1996, based on original ideas & diagrams by Craig Rusbult. The
handout contains diagrams (for this part of the lab and for similar sequences
involving other chemicals) along with explanations for how to use the diagrams,
plus thought-provoking questions.
CONFLICTING FACTORS
This situation occurs often in science, so students
should have experience with it, and they should know that scientists develop
criteria — mainly the observation-based "reality checks" of
scientific method
but also theory-based calculations — for coping with these situations.
Many lab experiments involve conflicting factors (and later you'll see them
here when this section is developed more fully) but the only one currently
written up is in "Errors & Conflicts" below:
EXPERIMENTAL DESIGN
Random Errors & Systematic Errors: Students
should know the difference; by analyzing some of the experiments they're
doing in lab, they can understand the importance for experimental design (in
strategies for designing an experiment to minimize systematic errors
and to keep random errors within reasonable limits); they can
also think about how to cope with random errors in their own data, and the
possibilities for systematic errors in their data.
Errors & Conflicts: In the current
Calorimetry Lab (using coffee cups), students are asked to keep their
T-changes in a range of 5-10 degrees,
and I ask them "Why? What bad things would happen if a solution
began at 20 C and the T-change was 90 C, or 70 C, or 1 C ?" They
know that the water will boil if T rises to 110 C after an increase of 90
C, and (if there are pockets of higher T due to uneven mixing) the cups
might even melt; with
a 70 C rise (and good mixing) the water won't boil, but the heat-insulation
will not be satisfactory if there is a 70 C difference between water (inside
the cup) and air (outside the cup) so their zero-sum assumption (that "Qreaction
+ Qsolution = 0") isn't valid, and they'll get bad data; by
contrast, if the T-change is 1 C the insulation will be acceptable, but
(with a thermometer that only reads to the nearest .1 degree) their precision
(the relative error) will be low because they are not using large numbers
(for example, a .2 degree error in "Tfinal - Tinitial" is a 20% error if
T-change
is
1
C,
but is only a 2% error if T-change is 10 C). / To
have good insulation the T-change should be small, but to have a low relative
error the T-change should be large; the
suggested range of 5-10 C is a compromise, in an effort to find an "optimum
balance" between these two conflicting factors. / There
was a similar compromise, in the "soda density lab" as it was done in 2007,
between large numbers (to calculate density from an arithmetic division
of mass by volume) and a range of numbers (when the data was graphed as
mass-versus-volume and the numerical value of the slope was density).
CALIBRATION
LOGIC
Students graphically
"calibrate" a new weighing scale based on data (provided for them)
about
the
digital-readout of the
new scale when various known masses are placed on it. Alternately, they
could use data from readouts of an old
scale (assumed to be accurate) and new scale when various "unknown masses" are
placed
on
each
of the scales. This experience shows students the logical process of thinking
(and use of data for reality checks) in a
calibration
procedure.
an example: I ask students to imagine that
a scale
(assumed
to
be accurate) measures the weight of five blocks to be 40.3, 49.9, 60.2, 70.1,
and 79.7 grams. Then
we imagine cross-checking experiments in which these
blocks (whose weights we assume are known) are weighed on a brand new scale to
gives results (38.5, 47.2, 57.0, 67.8, and 79.0 grams) that are consistently
precise (i.e., the first block always weighs 38.5, the second is always
47.2, and so
on) but
we have questions about its accuracy. Students can use these two
sets
of data
to
make
a calibration graph for the second scale, to adjust
for its inaccuracy and estimate the true weights.
update in 2008: In current labs for
Chem 103, we use similar quantitative calibration
logic in three experiments
throughout
the first
semester,
using calibration
graphs
drawn by hand or with Excel. In three labs, students measure a characteristic
of known samples
(to
make
the calibration graph) plus the same characteristic for an unknown sample, to
determine: the
sugar
concentration
of
a soda
sample; the concentration of alcohol in wine; the mass-% of copper
in a
compound. In each case we assume linearity; this
is an assumption for the soda, perhaps not justified, and for the wine and compound
it's theoretically justified by Beer's Law. Assuming linearity, students
use two techniques to move from a measured y-value (for the unknown) to a determined
x-value; 1) they do an "over and down" by drawing a horizontal
line rightward from y, then when it intersects the best-fit line for the graph
they drop this line straight down to find the corresponding value of x; 2)
they substitute y into the equation for "y = mx + b" calculated
by
Excel,
and
solve
for x. Then they compare the x-value they find visually (with over-and-down)
and mathematically (with y = mx + b). These techniques are described in
a supplementary
page I've made to accompany the lab manual, which links to a step-by-step
page for Making
Graphs by Using Excel.
Flame Tests (in the 1990s)
Using qualitative calibration logic (and I ask them to
think about the similarity
in logic)
students
do
flame
tests
for
solutions
of LiCl, Sr(NO3)2, KCl, CaBr2, and NaNO3,
and use logic to decide which chemical (assuming the cause is a single species)
produces each color. (*) In
a
second
run,
students
do
flame
tests
on
unknown solutions, and determine
the (probable) identity of an unknown chemical by using their observations plus calibration
logic. / * Students
could do additional experiments -- using the logic of Mill's Methods of Logical
Induction -- to determine whether each color is being caused by the positive
or negative ion, for example by testing LiCl, LiBr, LiI, LiNO3, and so on. A deductive conclusion
about causality is impossible,
but a "very high confidence" inductive conclusion
(the
metal
ion causes
the color) can be made rationally, using scientific logic.
questions for students: In your detective work
on the solutions, what assumptions did you make? { e.g., Is the stockroom
telling us the truth with their bottle labels? This is analogous to assuming,
in the first paragraph, that the first scale was accurate. For each experiment,
when declaring something "known" what assumptions are we making? } / Does
a violet
flame prove the solution contains KCl? { Could it be KBr or a substance
not contained in the known solutions? This illustrates the
asymmetry of if-then logic — "if
KCl, then violet" is
not
the same as "if violet, then KCl" — which is a very important principle
of
logic.
} Could
we
ever
conclude with certainty that "if violet, then K"? { What
additional information is needed? Is certainty possible in science? is
a high degree of confidence possible?
If we [somehow] know
the unknowns contain only Li, Sr, Na, K and Cu ions, can we be sure the solution
contains K? } If students observe a flame that is red and violet
and green,
what can they conclude? { We shouldn't place restrictions on theorizing. In
this case, is it justified to assume that a solution always contains ONLY one
metal
ion? } / Does
a yellow-orange flame always indicate Na+ in a solution? e.g., If
students repeat their flame tests for the known solutions in reverse order
they may (especially if they don't clean the test-wire thoroughly) see a yellow-orange
Na color, even in a solution that contains minimal Na. { This provides
an opportunity to discuss the concept of a false positive result,
and to ask what a false negative result would
be. }
Finally, students compare the two experiments:
the weighings (in two runs) and flame tests (in two runs). Between
the first and second runs of each experiment, what is constant & what is changing,
and what is known & what is unknown? What are the similarities and
differences in the logic used during the weighings and flame tests? In
what ways are we using "calibration logic" in each set, and how
is this logic similar and different
for
the
two
sets? { This lets
us discuss the usefulness and limitations of analogies. }
Update
in 2008: In 2000 the flame
tests were eliminated, and the lab involving "observation of reactions
to identify chemicals" was replaced by a computerized exercise using videotapes
of reactions. The
context of experience is now different, because students observe reactions
in movies instead of in lab, but the calibration logic is similar.
In 2008, students also use calibration logic
(but so far only in thought
experiments
not physical experiments) when they ask questions about the
precision and accuracy of glassware.
5. Using Guided Inquiry to teach Thinking Skills
Principles of Inquiry Teaching
Opportunities for inquiry
occur when gaps in knowledge (intentionally
designed into an activity) produce a situation in which students are required
to think, and are allowed to think, on their own.
During guided inquiry instruction the
teacher, like a writer of a good mystery story, should aim for a level of
challenge that is "just right" so students will not become bored
if a problem is too easy, or frustrated if it is too difficult. The
goal is to provide enough guidance but not too much. Ideally, students
will succeed, and in doing so they will feel genuine intellectual and emotional
satisfaction because their success is highly valued due to the obstacles
they overcame during the process of problem solving.
For most students, inquiry experience
will promote active thinking and motivation, if the instruction is well
designed. But if not, the inquiry is more frustrating than stimulating.
{ Some frustration can be beneficial, but usually it should be limited and
temporary. }
The level of challenge can be adjusted
by preparation before a problem begins
(by giving students prior experience in solving similar problems, by selecting
the phenomena to be studied and the problems to be solved, and by controlling
the conceptual knowledge and procedural information that is provided and
is withheld) and by coaching during the process
of problem solving (by observing students as they work, and providing
guidance by asking and answering questions, directing attention, and promoting
reflection).
A strategy for building skills:
If students are having trouble with a certain type of problem, activities
can be designed to help students gradually improve their skills in this
area, thereby allowing a gradually increasing level of difficulty for the
problems being solved.
Another teaching strategy is to set the
initial difficulty higher than most students can cope with, and then give
personally customized assistance when it is needed, while students are solving
the problems. These improvised coaching interactions let a teacher
adjust the level of difficulty, and also provide opportunities to facilitate
learning that is conceptual and procedural, intellectual and emotional.
One goal of this section is to illustrate the complexity of inquiry teaching, to emphasize the principle that inquiry should be done well or (for many students) it will be more frustrating than stimulating.
moderation in the use of inquiry:
I think every student should have many opportunities
for small-scale guided inquiry and at least one intensive
experience, as in the genetics course ,
because inquiry promotes experience that is productive (for
learning the process of science and how to cope with problem situations
in which "what to do next" is often not clear) yet
is unfortunately rare in conventional education.
But I don't think it would be beneficial
if every course was taught using inquiry methods, because even though
inquiry can help students learn scientific thinking skills (especially in their
first few experiences) and can improve motivation, usually it is not efficient
for learning the concepts of science. For a well-rounded approach to lifelong
education, we should encourage students to learn by active inquiry and also by
active reading, listening, and discussion. { Is "active reading" possible? }
a summary: In my opinion, some inquiry experience
is essential, but it should not be the main format for education.
MORE
The
second part of the appendix contains:
• another perspective on principles
of inquiry learning, a "cognitive apprenticeship" approach (Collins,
Newman & Brown, 1987) with six ways a teacher
can provide guidance: by modeling,
coaching, and scaffolding, and by encouraging articulation,
reflection, and exploration.
• two examples of inquiry instruction:
a) an in-depth analysis, using my
model of Integrated Scientific Method as the analytical framework, of an
innovative genetics course.
b) "An Inquiry
Lab" describes
an activity, formerly done at UW-Madison, in which students design an experiment.
|
Here are the five finished diagrams: |
|
Some techniques for guiding inquiry, from Collins, Brown & Newman (1987, pages
481-483): An Example of Guided
Inquiry Instruction For details about this fascinating course,
you can visit a web-page that describes THE COURSE AND ITS ANALYSIS and includes a
link to let you download my PhD dissertation, which had two main objectives: An Inquiry Lab The following discussion is in two parts: an equation that provides a framework for experimental design; and questions that show some possibilities for guiding students. An Equation
This equation is useful for experimental
design in Part 1, because students can solve for X (in J/mole) if they
have an equation containing X, and if they can fill every other blank
with a number. Possibilities for filling each blank in this X-equation are
shown in the diagram above, and are discussed below. Hints and Questions {and Answers} to
Use or Avoid 1. Should the X-equation be
provided for students? If yes, in how much detail? 2A. Give a hint/suggestion:
Think about the available RESOURCES and decide
how you can fill each blank in the X-equation. The bottom of the fraction is moles of reaction. 4A. If the AA is 5% by mass, what
is its molarity? If it is 5% by volume (with 5 mL pure AA diluted
to 100 mL), what is the molarity? { CRC info is needed, plus the
simplifying assumption that volumes are additive. } The X-equation has two volumes, mL (on top)
and L (on bottom). Students have trouble deciding which volume
to use for each blank, or even realizing that they must make a decision. miscellaneous questions: 7A. For Part 2, what experimental
modifications are needed? { Students can use the same equation,
but now X is [AA] so [AA] must be in the equation by making AA the limiting
reactant, and now J/mol is known from Part 1. Otherwise, everything
is similar. } CONCLUSION |
