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).
As a secondary benefit, students 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.
AN ALTERNATIVE: In a current experiment
(being done at UW in 2007) 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.
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) }
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. BASIC SKILLS
FOR DATA ANALYSIS: To
help students learn the fundamentals of mathematical data analysis, I make
handouts for students to do as homework.
The first handout 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 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 doesn't cover everything in data
analysis, but it's a start.
3. THE PROCESS
(LOGICAL AND SOCIAL) 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 and systematic errors.
When I ask students about the accuracy
of their data, they say "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,...) get into the CRC?" and we talk about the
evaluations (and decisions and declarations) made by a scientific community
or by an individual author.
Then we think about rationally
justified confidence: Should we be more confident about a value
of Avagadro's Number based on a set of 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. } / 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? { We discuss systematic errors, theoretical and experimental
interdependencies, and independent
confirmations. } What do scientists do if two different techniques
give different results? When they compare and evaluate, can scientists
be biased? What are some possible sources of bias,
and how might these be minimized?
These questions (and others that can
be planned or improvised) offer many opportunities for learning about the
"strategies for problem solving" used by scientists. /
Some interesting ideas about scientific methods, both logical and social,
are summarized in my model of Integrated Scientific Method
-- especially in Sections 2 (re: relationships between theories), 3 (cultural-personal
factors) and 8 (thought styles).
a few extra details
4. Hypothetico-Deductive
Logic
Students should have
opportunities
to use hypothetico-deductive (HD) logic.
Here are several activities involving HD reasoning, selected from chemistry
labs at UW:
USING SCIENTIFIC REASONING: 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.
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. Then
they
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. (*) {
For
calcium
bromide
a deductive
conclusion is impossible, but a rational inductive
guess can be made. comment: In looking at this "calcium bromide" statement later,
in 2007, I'm not sure what it means. } 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.
questions: In your detective work
on the solutions, what assumptions did you make? { Is the stockroom
telling us the truth with their bottle labels? } 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." } Could we ever
conclude with certainty that "if violet, then K"? { What
additional information is needed? Is certainty possible in science?
} If students observe a flame that is red and violet and green,
what can they conclude? { We shouldn't place restrictions on theorizing.
} Does a yellow-orange flame always indicate Na+
in a solution? { This lets us talk about false
positives and false negatives. }
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 or changing,
and what is known or unknown? What are the similarities and differences
in the logic used during the weighings and flame tests? { This lets
us discuss the usefulness and limitations of analogies. }
a few extra details
THE LOGIC
OF LE CHATELIER:
In another opportunity for HD 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 developed by myself and Jacquie Scott, a former lab
director at UW. 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. { Eventually,
these handouts will be available as PDF files. }
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.
conclusion and moderation in the use of inquiry
This website contains two examples of inquiry instruction:
1) On this page, "An Inquiry Lab" describes an activity in which students design an experiment.
2) An in-depth analysis, using my model of Integrated Scientific Method as the analytical framework, of an innovative genetics course.
For another perspective on principles of learning, a "cognitive apprenticeship" approach (Collins, Newman & Brown, 1987) describes six ways a teacher can provide guidance: by modeling, coaching, and scaffolding, and by encouraging articulation, reflection, and exploration.
An
Inquiry Lab
OBJECTIVES: In a lab
activity for General Chemistry at the University of Wisconsin in Madison,
students design experiments to determine the enthalpy change per mole of
acid-base reaction (in Part 1) and the precise concentration of a solution
of acetic acid (in Part 2).
RESOURCES that are available include:
a 25 mL graduated cylinder, thermometer (connected to computer for recording),
styrofoam coffee-cup calorimeter; .1 M NaOH (in lab the molarity will
be given to the nearest .001 M), 5% solution of Acetic Acid (AA);
and free information (from CRC, lab-book, textbook,...). / Also,
the weighing scales cannot be used for this experiment. (but this limitation
is optional)
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
Early in the semester I remind
students about a commonly used "miles per hour"
strategy: If they want to find the speed in miles per hour, they divide the miles traveled (for a certain part of
a trip) by the hours (for the same part of
the trip). In chemistry the first analogous application is a grams per mole strategy, dividing
the grams (for a certain amount of substance) by
the moles (for the same amount of substance). { A typical problem
that can be solved using this strategy is: If 973.0 g of a compound,
X2O, is heated in H2 gas and is converted into 864.2
g of pure X, what is the atomic weight and chemical symbol of X? }
For Part 1 of this experiment we can use a joules per mole strategy,
dividing the joules of reaction energy
(measured by observing its effect in producing a change of temperature)
by the moles of reaction (that produces
this change), as shown below.
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.
The following subsection shows, by describing
potential hints and questions and answers, some strategies a teacher might
use for adjusting the level of challenge in this inquiry lab. At one
extreme, we could just list the objectives and resources
and say "do it." Or, to make the problem easier, we could
ask every question below (and more), discuss each in detail, and explain
how to use "what can be learned from each question" in the experimental
design.
I don't make any claims about which questions
should be asked and discussed (and in what depth), because effective inquiry
teaching depends on the students (their abilities and experience, motivations
and attitudes), the context of instruction, and the goals of education.
The main purpose of the "Hints and Questions" section is to illustrate
the complexity of inquiry
teaching whose goal is an intermediate level
of challenge, in contrast with the simplicity
of direct teaching whose goal is a maximum level of clarity.
Hints and Questions {and Answers}
to Use or Avoid
comment: For some questions
below, an alternative is to suggest the study of specified sections or problems
in the textbook or lab-book.
1. Should the X-equation
be provided for students? If yes, in how much detail?
1A. Give a hint to "use the
miles-per-hour strategy"? Give this hint, plus a reminder that
"joules per mole" (or "joules of reaction energy per mole
of reaction") is the goal in Part 1? And a reminder that one
possible "effect" of energy transfer is calculated as (g)(J/gK)(K)?
1B. Give an equation with missing
details? For example,
X = (energy
of reaction) / (moles of reaction)
X J/mol = (joules
of heat produced) / (moles of reaction)
X = ( __ g ) ( __ J/g K
) ( __ K ) / ( __ L ) ( __ mol/L )
X = ( _ mL ) ( _ g/mL )
( _ J/g K ) ( Tf - Ti ) / (moles reaction)
1C. Give the hint(s) in 1A and
then say "Think about each unknown variable and how you can 'fill in
the blank' and whether modifying the equation (by using a
different level of detail) might help you fill all the blanks."
For example, moles can be expressed at a different
"level of detail" as (grams) / (grams/mole),
and you could decide to use either of these in an equation."
{ students should use (mL)(g/mL) instead of
(g) for the fraction-top,
and (L)(mol/L) instead of (mol)
for the fraction-bottom } To make things easier, you could use either
or both of these options -- (mL)(g/mL) or (g), and (L)(mol/L)
or (mol) -- in a "levels" hint instead
of the choice of "(moles) or (g)/(g/mol)"
suggested above. And we can remind students that a weighing scale
will not be available during lab.
2A. Give a hint/suggestion:
Think about the available RESOURCES and decide how
you can fill each blank in the X-equation.
2B. Which blanks can be filled
with free information you look up in CRC (or
lab-book, textbook,...) before lab? { g/mL, J/g K }
2C. What assumptions are necessary
when using the CRC-information for this lab? Does CRC have data for
.1 M NaOH? for 5% AA? { They must assume the actual values of
g/mL and J/gK for lab-solutions are approximately equal to the CRC
values for water. }
2D. What can be known by measurements you make in lab? { mL, L, change
of T }
2E. What can be known by other
observations you make in lab? { mol/L
from label on NaOH solution }
The bottom of the fraction is moles of reaction.
3A. How many moles of reaction
occur if you mix 2 mol HCl and 2 mol KOH? if you mix 3 mol HCl and
2 mol KOH? 3 mol HCl and 4 mol KOH?
3B. If you mix 6.0 L of .50 M HCl,
and 5.0 L of .40 M KOH, how much reaction occurs? { There is still
3 moles and 2 moles, as above, but this problem is cognitively closer to
the skills that will be used in experimental design. }
3C. What determines the moles of
reaction, the limiting reactant or the reactant in excess? Will the
X-equation contain information about the limiting reactant, excess reactant,
or both?
3D. In experimental design, is
it important to decide which reactant you want to be limiting? (The
important difference between asking about what "...you want to
be limiting" and what "...will be limiting" is discussed
in 3F.)
3E. To get a value for X that is
precise and accurate, what do you need? { All other blanks must be
filled with information that is precise and accurate. And the mol/L
is known more precisely for NaOH than for AA, so NaOH should be limiting.
}
3F-introduction. The first time
I taught this lab, even though everyone could answer the questions in 3A
(if 2 moles HCl and 2 moles KOH,...) many students didn't appreciate the
importance for experimental design, that only the limiting reactant appears
in the bottom of the fraction, as in Question 3C. They could run the
algorithm without understanding the significance, so when I asked "Which
reactant do you want to be limiting?" they were confused because
an authority (the instructor, TA, or textbook) had always decided how much
of each chemical to use, and now the student's role had changed.
3F. To help them prepare, I could
have asked Question 3C, and build-up problems such as these: If there
is 7.0 g of H2 (for "2 H2 + O2 -->
2 H2O"), how much O2 should be used if you want
H2 to be in excess by 20%? if you want H2 to
be limiting and O2 to be in excess by 20%? }
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. }
4B. After students have decided
that NaOH must be limiting, ask "If the AA is 5.0% plus-or-minus .5
%, what is the possible range in % and M, and which end of the range for
M (the extreme low or high value) is most critical, to be certain the NaOH
will be limiting? How much excess AA should there be: exactly
what is needed if AA is the critical value, or 10% more than needed, or
50% more, or...?
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.
5A. When determining the energy of reaction by the effect it produces, what
substance (and how much of it) is having its temperature changed?
{ the entire solution: mL of NaOH-solution + mL of AA-solution }
5B. When calculating moles
of reaction, what volume is important? { the volume of NaOH
solution, because NaOH is limiting and thus determines the moles of reaction
}
miscellaneous questions:
6A. What will you do with the solutions,
and how will you measure the initial and final temperatures? { measure
Ts, mix, measure T } How can you be certain that you are measuring
the average T of the solution? { mix well }
6B. How will you take into account
the heat-energy absorbed by the calorimeter? { The easiest way is
to assume it absorbs no heat. }
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. }
7B. Ask 4B again for Part 2.
{ The critical extreme changes; now it occurs if AA is 5.5%. }
CONCLUSION
As discussed above, the purpose of this section is
to illustrate the complexity of inquiry teaching, to accompany the principle
that inquiry should be done well or (for most 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.
APPENDIX
Here are the five finished diagrams:
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 two sets of questions: 1) What are your estimates for the precision of your measurements? 2) What are your estimates for the accuracy of your measurements?
To introduce these questions, I ask students for their definitions of precision, and how precision differs from accuracy. I provide four sets of data, and for each set I ask them to make a rough estimate (is it high or low) for precision and accuracy. { all four possible combinations are represented: high precision with high accuracy, high with low, low with high, and low with low } This provides an opportunity to discuss random errors and systematic errors. Then we look at their data.
The second set of questions, re: accuracy, is more interesting and challenging. My initial goal is to get students to say "We can't estimate accuracy because we don't know the true value for the density of our unknown liquid." Then I ask them about the values for density (and Avagadro's Number, the speed of light,...) in the CRC --- how did these values get into the CRC? Here, the goal is to develop the concept of evaluations (and decisions and declarations) that are made by a scientific community (or sub-community or committee) or by an individual author or editor.
This is followed by a series of questions about rationally justified confidence: Would you be more confident about a value based on 5 experiments done by the same person, or 5 experiments done by a large research group? What if these experiments were done by 4 large groups scattered around the world? { we develop the concept of creative and critical thinking by individuals, in-groups, and out-groups } / Would you be more confident if 5 similar experiments gave the same value, or if 5 different types of experiments gave the same value? { this lets us discuss several ideas, such as systematic errors, background assumptions, theoretical and experimental interdependencies, and we develop a concept of independent confirmation } At some point, before or after this lab, in lab or lecture, examples of independent confirmations (such as multiple ways to calculate Avagadro's Number, or...) are described, and interdependencies are discussed. / What do scientists do if two different techniques give different results? { we discuss experiments (reproducibility; analysis and design), critical thinking, arguments and consensus,... } When they compare and evaluate results, can scientists be biased? { we discuss potential sources of bias, including (but not limited to) "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?
This set of questions offers many opportunities for learning about the process of science (social and otherwise), about the wide variety of "strategies for problem solving" used by scientists. If a teacher has some knowledge and imagination, awareness and enthusiasm, many types of discussions (short or long, taking off in many different directions) are possible. / Some relevant concepts are discussed in my model of INTEGRATED SCIENTIFIC METHOD --- especially in Sections 2 (conceptual factors), 3 (cultural-personal factors) and 8 (thought styles). And on another web-page each concept (such as EXTERNAL RELATIONSHIPS BETWEEN THEORIES) is discussed in more detail.
In a logically analogous experiment, students first observe flame tests for solutions of LiCl, Sr(NO3)2, KCl, CaBr2, and NaNO3, and use cause-effect logic to decide which chemical (assuming the cause is a single species, not a combination) is producing each color. / This combination of chemicals provides an opportunity to show students different types of logic. For calcium bromide a deductive conclusion about causality is impossible, but a rational inductive guess (the metal ion causes the color) can be made. Following this is a second run, a "calibration" phase in which students do flame tests on unknown solutions.
This provides an opportunity for more thought-stimulating questions: What assumptions do we make when using results from the initial flame tests in our if-then calibrations? That the stockroom is telling us the truth about the known solutions. This is analogous to assuming, in the thought-experiment above, that the first scale was accurate. / Or we can ask, "Does a violet flame prove the solution contains KCl?" No, because it could be KBr or some other metal ion (besides the five tested above) or...; this shows that "if KCl, then violet" is not the same as "if violet, then KCl" thus illustrating the asymmetry of if-then logic. / When students observe a solution whose flame is red and violet and green, what can they conclude? That they shouldn't place restrictions on their theorizing, such as assuming that a solution contains only one ion. / What extra information do we need, to conclude with certainty that "if violet, then K"? 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 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 can compare the two sets of experiments: the weighings and the flame tests. Between the first and second runs in each set of experiments, what is constant and what changes? During each run, what is known and what is unknown? For each experiment, when declaring something "known" what assumptions are we making? Compare the logic used for weighing and flame testing. Do both sets involve calibrations? In what ways is the logic similar and different for the two sets?
An Example of Guided
Inquiry Instruction
In a conventional course,
students typically learn science as a body
of knowledge but not as a process of thinking,
and rarely do they have the opportunity to see how research science becomes
textbook science. A notable exception is a popular, innovative genetics
course taught at Monona Grove High School by Sue Johnson, who in 1990 was
named "Wisconsin Biology Teacher of the Year" by the National
Association of Biology Teachers, due in large part to her creative work
in developing and teaching this course. In her classroom, students
experience a wide range of problem-solving activities as they build and
test scientific theories and, when necessary, revise these theories.
After students have solved several problems that "follow the rules"
of a basic Mendelian theory of inheritance, they begin to encounter data
(generated by computer) that cannot be explained using their initial theory.
To solve this new type of problem the students, working in small "research
groups", must recognize the anomalies and revise their existing theory
in an effort to develop new theories that can be judged, on the basis of
the students' own evaluation criteria, to be capable of satisfactorily explaining
the anomalous data.
As these students generate and evaluate
theories, they are gaining first-hand experience
in the role of research scientists. They also gain second-hand
experience in the form of science history, by hearing or reading
stories about the adventures of research scientists zealously pursuing their
goal of advancing the frontiers of knowledge. A balanced combination
that skillfully blends both types of student experience can be used to more
effectively simulate the total experience of a scientist actively involved
in research. According to educators who have studied this classroom,
students often achieve a higher motivation level, improved problem-solving
skills, and an appreciation for science as an intellectual activity.
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:
to construct a model of INTEGRATED SCIENTIFIC METHOD and
to use this model as a framework for
the integrative analysis of Sue Johnson's innovative inquiry course.
Some techniques for guiding inquiry, from Collins, Brown & Newman (1987,
pages 481-483):
"Modeling involves an expert's
carrying out a task so that students can observe and build a conceptual
model of the processes that are required to accomplish the task. In cognitive
domains, this requires the externalization of usually internal (cognitive)
processes and activities -- specifically, the heuristics and control processes
by which experts make use of basic conceptual and procedural knowledge.
"Coaching consists of observing
students while they carry out a task and offering hints, scaffolding, feedback,
modeling, reminders, and new tasks aimed at bringing their performance closer
to expert performance. Coaching may serve to direct students' attention
to a previously unnoticed aspect of the task or simply to remind the student
of some aspect of the task that is known but has been temporarily overlooked.
"Scaffolding refers to the
supports the teacher provides to help the student carry out a task. These
supports can either take the forms of suggestions or help."
"Articulation includes any
method of getting students to articulate their knowledge, reasoning, or
problem-solving processes in a domain.
"Reflection enables students
to compare their own problem-solving processes with those of an expert,
another student, and ultimately, an internal cognitive model of expertise.
Reflection is enhanced by the use of various techniques for reproducing
or 'replaying' the performances of both expert and novice for comparison.
"Exploration involves pushing
students into a mode of problem solving on their own."
Can reading be active?
In her excellent book "On Becoming
an Educated Person," Virginia Voeks describes how you can learn more
when you read:
"Start with an intent to make the
very most you can from whatever you read. Treat the author as you
do your friends. When talking with a friend, you listen attentively
and eagerly. You watch for contributions of value and are sensitive
to them. You actively respond to his ideas with ones of your own.
Together you build new syntheses."
Yes, reading is more fun and more productive
when you approach it with an attitude of enthusiastic expectation.
Expect the author to share new ideas and fresh perspectives. When
you search with alert awareness for useful ideas, you will see them.
Reading then becomes refreshingly stimulating. Of course, you can
use this positive attitude to take full advantage of every opportunity for
learning, in all modes of experience in all areas of life.