Socratically drawing the laws of nature out of students’ brains rather than stuffing them in

My specialty in a classroom setting: What distinguishes my approach is the Socratic method of drawing laws of nature (for example Newton’s laws) out of students’ minds through guided classroom discussion rather than simply ‘lecturing’ (presenting the laws to them directly); in class we employ a combination of heuristic motivations and pre-lab hands-on experience to arrive heuristically at Hooke’s Law (F = – kx), the ideal gas law (PV = nRT), and relationships such as a = v2/r. (Further description of my approach, and references to videos of my teaching an actual class are included in the accompanying teaching statement.)

My expertise lies in crafting directed questions to draw out their initial assumptions, expectations and intuitions, and then guiding a classroom discussion meant to challenge these very expectations and assumptions, as a path to their discovery of the laws of physics. After this process, I seek their input in an attempt to construct the simplest equations which enshrine these conclusions mathematically.

A very good idea of my general teaching style and pedagogical technique can be gleaned from the videos of an “introduction to physics” course I taught to general-science majors some years ago, on my Youtube channel. The GR lectures on Youtube are another example, though time-limitations did not allow for the extensive back-and-forth I prefer.

 

Pedagogical approach (in teaching physics) –> Theory/speculation about the method
Recapitulating the mental process which led to present-day ideas, in other words the evolution of philosophy/science in regards to those specific concepts. Students will not really understand a new concept fully without having themselves gone through this process.
Bringing about a process whereby students ‘discover’ the laws of physics, via guided discussions in the classroom. (Rather than stuffing knowledge into students’ heads, drawing it out of their heads) Besides increasing their understanding and excitement, grants them a sense of ‘ownership’ of the ideasPerhaps this can also develop the brain-abilities useful for those who will go on to engage in research.
Stressing the ‘logicality’ of the equations given our experience, and clarifying (via the process of development) the complementary role of intuition, experience, experiment, logic, and then mathematical formalism. Gives students a sense of the scientific method, of the relationship of math and physics, and a view of physics as logical rather than received wisdom

 

Drawbacks of my method: 1. Not all students want to understand, some want to just know how to pass the exam, and will resist this method (perhaps one needs a two-tiered course?). 2. Given that the amount of time required for developing the ideas in the above manner is far greater than that which is required for simply writing equations on the board and explaining them, less material can be covered. 3. Some aspect of the exam will need either to be oral, or will involve mini-essays rather than equations/problem solving, and this will require more of the instructor’s time, either more time spent with individuals or more time spent on correcting/grading.

 

Tactics –> Purpose
Formulating periodic challenges/questions to students in terms sufficiently oblique, general or vague so as to not give away the answer, yet nevertheless sufficiently clear to elicit relevant suggestions. Helps maximize student contributions, and the level of thought required. Also: responses to carefully-crafted deliberately-vague questions can often illustrate basic misconception which would not be revealed when the question itself contains part of the answer.
Pretending that the intuitively-correct-seeming answer I offer or that a student proposes is correct when in fact it is not. This can encourage debate on the merits of an idea rather than automatically accepting my negation of its correctness.
Making it clear at the outset that when I challenge attendees, I am not seeking a display of previously-acquired knowledge (and actively discouraging any such volunteered information by cutting off the speaker in mid-sentence).During active classroom-discussion praising/validating reasonable speculations, honest grapplings with the conundrums I pose   even while pointing out why that particular idea is incorrect. Levels the playing field so that students who have taken prior courses do not have an overwhelming advantage, and indicates that science is more about reasoning than about received knowledge.Makes the point that students who were able to propose a reasonable hypothesis have succeeded at the appointed task of simulating the process of scientific discovery irrespective of whether or not the idea was in fact correct.
At various steps during the lecture challenging students to restate in their own words what I have taught. Forces students to follow the lecture as well as increasing their understanding.
Mining students’ misconceptions to inform the teaching process:  First identify students’ fundamental underlying misconceptions during classroom discussion, when answering student questions in class, or when grading exams.Use this insight to guide further classroom discussion, crafting an approach designed to overcome these misconceptions subtly, through the student’s guided self-discovery.Craft classroom and exam questions which will reveal whether a student has this misperception Instructors may understand the material too well to remember how confusing it may have been to them initially. Understanding the source of a student’s confusion can be helpful in preparing an explanation.The wording use by an instructor can be unintentionally ambiguous or unclear, leading to an incorrect understanding; if the instructor can trace a misunderstanding to its root in the lack of clarity or ambiguity in the instructor’s original explanation, this explanation can re revised/retracted, and a clearer one offered.

Lab: Just as diagrams help in ways that text cannot, so too experiment can grant intuitions that equations will not. Although expensive, complex, sophisticated up to date equipment for lab experiments have their place, I do not seek these for courses in basic physics for bright and already-motivated students. Instead, I try to have them come up with simple ways to examine phenomena, test hypotheses and compare predictions made via equations – even when it means to visualize a ‘gedanken-experiment’, for example imagining the use of a rocket in far empty space, and so on. When it is clear that ordinary things lying around and thought-experiments will not suffice, they are encouraged to mentally-design the least-complicated equipment that might do the job. Only then would I introduce the actual lab-equipment we will be using, and have students examine it to understand how it works and what it can measure.

What this means however is that there is less time available for the experiment itself and fiddling with often-recalcitrant or obscure equipment (as seen by the student). Within limits, and depending on the context (for example excluding engineering students, for whom lab and equipment are important in of themselves), it is less important to me whether the equipment worked as it was supposed to, and whether the measured numbers came out within the expected error margin, than whether the students acquired via their lab experience a deeper understanding of the phenomenon being studied, and an understanding of physics as inherently tied to experiment, both as verification of proposed theories or models and as a generator of unexpected and perhaps counterintuitive phenomena giving rise to new theories or models.

 

Understanding vs memorization: When students understand that physics is not intended as a compendium of received wisdom, but rather relies to a large degree on rational analysis (and of course experimental-verification), they can be empowered to see themselves as eminently qualified to participate in that endeavor.

Students in my class are led along a path enabling them to discover the laws of nature, seeing them as logical distillations of experiment (which can include ordinary experience) rather than as formulae to be memorized.

The laws of nature are however often counter-intuitive to the novice. In order to truly understand those which are, it is important first to engage the students’ intuition – to guide them to the realization how and why nature is not in accordance with it – and then hopefully towards a yet-deeper understanding and intuition.

 

Furthermore, when as part of a collaborative effort in the class we do formulate a law of physics, it is only after students have understood its logic and clearly grasped the meaning of the quantities represented in the formulae. Students will have arrived at “F = ma” , but also “a = F/m” and even “m = F/a”. They are able to articulate not just “a equals F over m” but rather “the amount of the acceleration of an object of mass-amount m due to the application on it of an external force of amount F, is given by (the amount, or the ratio) F/m”. “Learning a = F/m” means understanding why it makes sense, and the same for any other formula whether it is Bernoulli’s principle or kinematic equations or expressions of energy conservation.

 

Scientific model-building as a creative activity & appreciating the aesthetic aspects of physics: As physicists see it, practicing physics is not simply amassing greater knowledge of the workings of nature – as some students entering a physics course may misguidedly think – but rather, arriving at understanding of a law of nature and expressing it mathematically is to practice an art, engaging intuition, expressing an aesthetic. I make sure to impart an appreciation of this to students, via the process of arriving at equations in the classroom, as wells as by having them experience first-hand the simplicity of the equations we arrived at in comparison to potential competitors such as a = F/m vs a = F2 Volume/m3.  I also stress wherever possible fundamental aspects such as symmetry, unification (e.g. that the gravity acting to push us down also governs orbits), and ‘relativity’ (e.g. the relation of Galilean relativity, the law of inertia and a = F/m).

At the end of a course, students can understand what physicists mean when they say that the Einstein equations are a great cultural achievement for humanity.

 

Motivating classroom attendance: As an instructor, I am constantly aware of the need to maximize the benefits accruing to a student who attends my classes over just reading the text. One central benefit of attendance was mentioned above – the real-time Socratic back-and-forth student-teacher interaction. However an additional benefit of this type of interaction is the exposure of the students to the questions, insights and misunderstandings of their peers. Since it is inevitable that some students will ask or state what others could not articulate, or would never have thought of, students in a classroom of peers can benefit in ways that are impossible even from what would otherwise be optimal – an individual teacher-student interaction. My teaching method seeks to maximize this type of benefit by eliciting comments to my probing Socratic questioning from as many students as possible. I also make sure to encourage future participation by commending thoughtful contributions, and always make it clear that the purpose of their participation in these dialogues is not for students to show me that they already know the ‘correct’ answer.

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