Lecture 5
“The fatal pedagogical error is to throw answers like stones at the heads of those who have not yet asked the questions.” Paul Tillich
Review the pencil problem with emphasis on getting a total length distribution by taking either a sample and adding 100 such identical cylinders to generate a distribution or take 100 random samples and line them up. Review the problem of finding the diameter of the mechanical pencil so that 98 percent of the cylinders fit in the pencil.
Talk about critical thinking and how it is evaluated. Use Oxford and Cambridge links. Discuss some of the problems on the test, particularly the one on testing assumptions. Relate this to the RC assumptions.
https://www.oxford-royale.co.uk/articles/critical-thinking-skills-university.html
“Despite variation in definitions of critical thinking, there is significant agreement on its core compo- nents. The American Philosophical Association’s (1990) definition, which reflects the consensus of 200 policy makers, employers, and professors, describes critical thinking as: “purposeful, self-regulatory judgment which results in interpretation, analysis, evaluation, and inference as well as explanation of the evidential, conceptual and methodological considerations on which a judgment is based” (p. 2). Along these lines, Pascarella and Terenzini (2005) offer an operational definition of critical thinking largely based on the work of Erwin (2000):
“Most attempts to define and measure critical thinking operationally focus on an individual’s capability to do some or all of the following: identify central issues and assumptions in an argument, recognize important relationships, make correct references from the data, deduce conclusions from information or data provided, interpret whether conclusions are warranted based on given data, evaluate evidence of authority, make self-corrections, and solve problems (p. 156).”
Bok’s (2006) definition of critical thinking captures similar qualities: “The ability to think critically — ask pertinent questions, recognize and define problems, identify arguments on all sides of an issue, search for and use relevant data and arrive in the end at carefully reasoned judgments—is the indispensable means of making effective use of information and know- ledge (p. 109).”
From the Oxford critical thinking paper “Thinking skills test assessment (TSA) test specifications” at the bottom of page 10, critical thinking skills involve: drawing and summarising conclusions, applying principles, identifying assumptions and reasoning errors, and assessing the impact of additional evidence.”
Review the section “The importance of critical thinking” in the link above.
What are the pertinent questions based on? The model, heuristic, or pattern that is being discussed. What do you think is the biggest hindrance to critical thinking?
You don’t care because the things being taught are not important to you. You don’t have the time to critically evaluate the material, due to some deadline. You then rely on System 1 thinking. In business it is often the case that the most important thing is meeting a deadline rather than the quality of the work. Mines is good at training students to get the work in on time with less of an emphasis on truly understanding it, in my opinion.
Critical thinking in the RC lab.
Applying principles: conservation of energy in the form of Kirchhoff’s laws
Identifying assumptions and reasoning errors: -R and C are constant. -The battery does not affect the circuit (as shown in the circuit diagrams in textbooks). -The scope does not affect the circuit (its input impedance add at least a resistance in parallel). -Errors in C (number of sig figs printed on device) and R (depends slightly on temperature and therefore current through it)
Discuss how there are two ways to deal with the model. First does it decay exponentially and second how do we determine the effects of errors in R and C? To deal with the first plot data on semi-log scale. Expect straight line. Show data indicating that RC decay is not exponential. Mention that the error is in the A/D resolution of 8 bits which shows up on a log scale dramatically. Say the max voltage is 10. The 8 bit (.04 V resolution) will only register a max of 2.3 for 10 V (and for the next bit, 2.298 for 9.96 V). At the minimum, it registers -5 for 4 mV (and for the next bit -4.8 for 8 mV). Also note that no straight line can go through all data points within the 8 bit error. At the minimum voltage there is a fluctuation about the least significant bit which shows up as the jitter in the steps. look for the fundamental assumptions of the model then see what parts could be changed.
Drawing and summarising conclusions (the data do not support the model) -how do you determine the error in the data? -repeat the measurement! Trigger the voltmeter to acquire when the switch is opened. Add data for 10 runs at a given time delay to get mean and stnd dev. Does straight line go through all data within error?
Show ImportFitData.nb
How do you convince someone of your conclusions? Emphasis on supporting your conclusion with evidence.
Assessing the impact of additional evidence -try different values of R and C -REPEAT the measurement to get an idea of the error. -use a voltage standard or reference with a voltage divider to test the meter. -look at how C is measured (LC resonant circuit which specifies C at different frequencies).
Beyond being critical thinkers you need to be able to communicate your ideas both orally and in writing. You can be great at critical thinking but never be able to communicate it effectively.
That’s why you practice writing lab reports, giving oral presentations about your understanding of the labs and practicing positive and negative criticism. Take advantage of this opportunity to improve these skills.
Example of asking questions. How is this related to critical thinking. Informational: how do you know that? What are the assumptions and conditions for which the model is valid?
