How Deep is Deep Enough?

“Perfection is the enemy of the good”


Education is about depth. Generally, we start with overviews and the big picture. Then we move on filling in the gaps and providing additional information. To fulfill one of my general education requirements, I took an Introduction to Western Civilizations course. We covered the rise of western civilization from prehistory all the way up to the modern age. This course included only the most essential points.  If I had gone on and studied western history, we would have expanded on the main points covered in the Introduction to Western Civilizations course.

As an example, there were courses on the Middle Ages like The Medieval World and Introduction to Medieval People, and then going into more depth Medieval Women. Each course led to a narrower but deeper dive into the topic.

Another example of this depth occurred during my science education. In my Introductory Chemistry courses, we learned about the laws of thermodynamics; there are four laws if you include the zeroth law. The laws of thermodynamics were only a single chapter in my introductory textbook, covered in just a couple of class periods.

Several years later as part of physical chemistry, I took thermodynamics, a required course for chemistry and biochemistry majors.  We spent the entire course studying the laws of thermodynamics, including mathematically deriving all the laws from first principles.

While I have used a lot of my chemistry over the years, I’ve never used that deep dive into thermodynamics. There are fields and research areas where this information is needed, however, I wonder how many chemistry students need this deep a dive into thermodynamics.

Determining what to teach students and what depth they need to learn each of these topics is a critical point of the educational design process. There has recently been a change to a topic that all (US) science students need to cover, the International System of Units abbreviated SI for Système International d’unités or classically the metric system.

The SI system is the measurement system used in scientific research. The SI system has seven base units, and 22 (named) derived units (made by combine base units).   In the US we teach students the SI system because the US is one of three countries that didn’t adopt the SI system. Science students need to use the SI system; the question is how much they need to know about the system.

The French first established the original two unit’s, length (meter) and mass (kilogram) in 1795. The system was developed to replace the hundreds of local and regional systems of measurement that were hindering trade and commerce.  The idea was to create a system based on known physical properties that were easy to understand, this way anyone could create a reference standard.  The definition of the meter was 1/10,000,000 of the distance from the North Pole to the equator on the Meridian that ran through Paris. The Kilogram was the mass of 10cm³ or 1/1000 of a cubic meter of distilled water at 4°C.

Basing the units on physical properties was supposed to give everyone the ability to create standards, in practice difficulties in producing the standards meant the individually created standards varied widely.  In 1889 the definitions of the meter and kilogram were changed to an artifact standard; an artifact standard is a standard based on a physical object, in this case, a platinum-iridium rod and cylinder located just outside of Paris France.

The original Kilogram stored in several bell jars.
National Geographic magazine, Vol. 27, No.1 (January 1915), p. 154, on Google Books. Photo credited to US National Bureau of Standards, now National Institute of Standards and Technology (NIST).

The use of the artifact standers lasted for quite a while; however, as science progressed we needed more accurate standards and the definition’s changed again, the new idea was to define all the base units on universal physical constants.  Skipping over the krypton 86 definition, in the 1960s the definition of the meter was changed to the distance light travels in a vacuum in 1/299,792,458 of a second (3.3 nanoseconds).

The speed of light was chosen to define the meter because it contains the meter, the speed of light is 299,792,458 m/s. This definition might seem a little strange, but it makes a lot of sense.  The speed of light is a universal constant, no matter where you are the speed of light in a vacuum is the same. To determine the length of the meter, you measure how far light travels in 3.3 nanoseconds. If your scientific experiment requires higher precision, you can make a standard with higher accuracy, instead of using 3.3 nanoseconds you could measure how far light travel in 3.33564 nanoseconds.

On November 17, 2018, the definition of the kilogram changed at the 26th meeting of the General Conference on Weights and Measures. The new definition of the kilogram uses the Planck’s constant which is 6.62607015×10-34 Kg m2/s.  Like the meter, the definition of the kilogram applies a constant that contains the standard.  Just like the meter the determining the precision of the kilogram is dependent on the accuracy of the measurements.

Up to this point, we’ve taught the kilogram as an object; the definition of the kilogram was a cylinder just outside of Paris no matter what happened that cylinder was the kilogram. However, with these new definitions, it becomes possible for students to derive the standards themselves. Scientists at the National Institute of Standard and Technology (NIST) created a Kibble or watt balance, the device used to measure the Planck constant, built out of simple electronics and Legos.

It is surprisingly accurate (±1%) you can read about it here. Using the Kibble or watt balance, it would be possible to develop lab activities were students create a kilogram standard and then compare it to a high-quality purchased standard.

With the change to the kilogram standard, is now possible to use the metric system to teach universal constants and have the students derive all the SI standards based on observations and first principles. The real question is, should we? For the bulk of the science students and scientist for that matter, how deep does their knowledge of the SI system need to be? Most are not going to become metrologist’s the scientist that study measurements and measurement sciences. With the ever-growing amount of scientific information, we need to think about not only what we teach but how deep we teach. What do you think, students can now derive the standards of the SI system from first principles, should they? We can’t teach everything how do we determine what to teach and how much to teach?


Thanks for Listening to My Musings

The Teaching Cyborg

Obviously, They Should Read 40 Pages, Right?

“No two persons ever read the same book.”
Edmund Wilson


The designing of a course is about more than what happens in the classroom.  A course also includes homework, papers, and reading assignments to name a few.  According to the Carnegie unit recommendation, all the out of class work should fit into a period equal to two hours for ever credit.  Therefore a 3-credit course would have 6 hours of work outside classroom a week, how should that time be divided.  A question often asked is how much reading should I assign?

What this usually means is how much reading is reasonable considering all the other learning obligations the students have.  In the book, Academically Adrift: Limited Learning on College Campuses, Richard Arum, and Josipa Roksa state that students that have at least 40 pages of reading a week had more substantial gains on the College Learning Assessment. Since the information on the reading is self-reported, we don’t know what kind of reading this represents.  There are multiple types of reading, as an example, there is skimming, scanning, intensive, and extensive another set of options is surveying, understanding, and engaging used by the Center for Teaching Excellence at Rice University.

When students read for the survey, they are just trying to find the main points.  Reading for understanding requires the student to attempt to understand all the text down to the level of single sentences.  Finally Engaging with the book requires all the skills of reading for understanding while using the book to solve problems and build connections.

A book being viewed through a magnifying glass.
Book viewed through a magnifying glass. Image by Monica Velazquilo (CC BY-SA 3.0).

One way to estimate how much time it will take students to read a specific number of pages is a course workload calculator on the Reflections on Teaching & Learning blog on the Center for Teaching Excellence site at Rice University.  Using the workload calculator if the students reads 40 pages in a survey mode it takes 1.43 hours, Understanding takes 2.86 hours, while Engaging takes 5.71 hours.  If a three-credit class has an out of class workload of 6 hours, reading for engagement would take up all a student’s out of class time. Therefore if the point of your reading assignments is reading for engagement either 40 pages is too heavy, or it is the only thing the students should be doing.

There are other factors beyond the type of reading that affect how long the reading takes, like the complexity of the text.  The more significant the amount of new information in a book the longer it is going to take to read.

While the 40+ page suggestions from Academically Adrift is one of the few research-based examples I have seen there are additional suggestions.  In one case a course that meets on Tuesdays and Thursdays the instructor suggest assigning 80 – 120 pages for the period between Thursday and Tuesday and 30 – 40 pages for the period from Tuesday to Thursday.  The argument being that the weekend adds 48 hours, so the students have more time and can read more.

I don’t like this argument, the students have additional time, so they should do more reading.  The main point of the reading assignments is to get ready for in-class activities or to reinforce class activities.  In this example, the two class periods are the same length the amount of material used to prep for the class should be the same.

So, how many pages should be an assignment for each class period?  It should be clear that this is not a simple or straightforward issue.  Let’s start with a 3-credit class that meets Monday, Wednesday, and Friday, 3-credit hours times 2 hours per credit means this course has 6 hours per week for reading and assignments.  So, if we assume, we are talking about an introductory course that uses a textbook, and we devote half the total students time to reading (reading for understanding) then using the Rice tool the students would reading 42 pages in 3 hours. The 42 pages suggested by the tool match the reading recommendation from Academically Adrift.

Dividing the 42 pages by the three, students should read approximately 14 pages for each class period.  In a regular semester excluding exams and holidays, there are 40 class periods this gives us a maximum of 560 pages per semester.

How does 560 pages compare with what courses are doing? Looking at the reading list for some introductory science courses, the total number of pages assigned are 261, 256, 338, 463, 475, and 347.  The average page number is 375 ± 87. If we divide the average by the total number of class periods (40) that would mean students would be reading about 9.4 pages for each class or 28.1 pages per week.

So, what does this mean, are introductory science courses are underperforming?  I don’t think so.  For instance, the estimation tool I have been using lists different word densities for different types of books.  For a paperback book, it lists 450 words per page while a textbook has 750 words per page. If we went with word count, then 40 pages of a paperback equal 24 pages of a textbook.

Beyond word count, we should also ask about the number of new concepts? Additionally, is the student reading to prepare for a discussion, to get a general overview of a topic, or to gain a deeper understanding?  While I would love to have a rule or a set of rules that will help us design the best learning experiences, I don’t think we are there yet.

Is course design by word count the way we should go?  Again, I don’t think straight numbers whether pages or word count is the way to go. Because of variables like words per page, number of new concepts and types of reading I’m not sure we will ever have a single rule that determines the optimal number of pages to read.

Just using a number does not consider the reason for the reading assignment or the number of new topics in the text.  Since new concepts and long-term learning are impacted by things like working memory, and short- and long-term memory, I think the number of new ideas and the complexity of the text may end up being the most critical aspects when determining the length of reading assignments.

To determine the amount of reading appropriate for a course we defiantly need more research.  However, I’m not sure this is something that is really on the research radar.  If your students are having trouble do you ever think about changing the amount of reading?  How important do you think the reading assignments are to your students learning?  Do you think we are too concerned with how much reading we assign to students?


Thanks for Listening to My Musings

The Teaching Cyborg

It’s All in the Primes

“The greatest single achievement of nature to date was surely the invention of the molecule DNA.”
Lewis Thomas


When you’re an undergraduate student, two words mean a lot to you prerequisite and corequisite.  These two words let you know whether you must take courses one after the other or at the same time.  Ever since my undergraduate days, I have found these terms to be fascinating.  As a student, I often thought of the words differently.  Prerequisite meant we believe you need this information to understand our class, while corequisite indicated this information might be useful, but we don’t care.

That may seem a bit harsh, but that is the way it seemed to me when I was an undergraduate, and to be honest, it still seems that way to me. My experience for the first couple of years as a biology major was a little different than several of my classmates.  As a high school student, I had been fortunate enough to attend a school with a robust Advanced Placement (AP) and International Baccalaureate (IB) program, because of this I tested out of first-year biology and chemistry.  Then in a fit of madness, I took a full years’ worth of organic chemistry with labs over the summer.

Biology students would take organic chemistry the same time the would take the second year introductory biology courses, i.e., corequisite.  The first biology class I took was Molecular Biology, one day we were sitting in class, and the professor was talking about DNA replication.  If you know anything about DNA you know, the terms 5’ and 3’ (also written 5 prime and 3 prime) get used a lot.  DNA is composed of two directional strands if one strand is 5’ to 3’ left to right the other strand will be 3’ to 5’ left to right.  DNA replication is carried out by DNA Polymerase III which synthesizes new DNA from 5’ to 3’.  I could go on, but that should make the idea clear enough.

DNA replication or DNA synthesis is the process of copying a double-stranded DNA molecule. This process is paramount to all life as we know it.
DNA Replication Image by Mariana Ruiz

One day my classmate turned to me and said, “I don’t understand anything he’s talking about what the hell does all this 5’ and 3’ stuff mean.” It took me a second to figure out what my classmate was saying the terms had been obvious to me.  I told him the names came from organic chemistry; they are referencing the 3rd and 5th carbon on the deoxyribose ring. Specifically, the 5’ carbon on one nucleic acid binds to the 3’ carbon on another forming the DNA backbone. Didn’t they cover numbering carbons in your organic chemistry course I asked, it turns out they had not gotten to that yet?

Many times during my undergraduate education corequisite courses did not cover material before it was needed.  It was this tendency of separate classes not to line up that lead me to start thinking of corequisite courses as “we really don’t care.”  As a student, I usually assumed corequisite courses would be no help in a class I was taking.

As a professional, I understand the constraints that impact educational choices.  Ideally, we are trying to fit all the courses needed for a degree in four years, that is four years minus summers.  I suspect if we made every corequisite a prerequisite we would not fit all the courses into a four-year program.  Interestingly according to the Marian Webster’s dictionary, the first known use of corequisite as we use it in education was circa 1948.  The fact that corequisite didn’t exist until 1948 suggests to me that we used to fit all the courses into a four-year degree without corequisites, I wonder what changed? I would assume this has to do with the growth in the amount of material covered in a Bachler’s program while maintaining the time to degree.

The other impact on the usability of corequisite courses is that they are taught by different faculty sometimes in other departments.  We hire faculty because of their experts in a field, to take full advantage of this expertise faculty are given the freedom to design and teach subject matter in the method they determine is best.  I wonder if schools are doing enough to promote communication between faculty members that teach courses related by corequisites.

Then again is a corequisite essential enough for a faculty member to change how they teach their course?  When thinking about curriculum design and degrees, I often think where is the line between the needs of the degree and the design freedom of a faculty member, is there a line? With the constant changes in many if not most fields and the growing amount of knowledge we must teach, we must rely on the experts in the field to keep the content of individual courses relevant.  With the continual work to keep course content relevant is it even possible to create a completely unified curriculum?

It may be that corequisite is the best we can do with respects to a degree’s curriculum.  However, I do know that anytime I deal with the curriculum of either a single course or a whole degree, I always remember “about what the hell does all this 5’ and 3’ stuff mean.”


Thanks for Listing To my Musings

The Teaching Cyborg

Abracadabra: Your number is 7 Sort of or is it?

“Science is magic that works.”
Kurt Vonnegut

In 1956 George A Miller’s paper “The Magical Number Seven Plus Or Minus 2 Some Limits On Our Capacity For Processing Information” was published in Psychological Review. This paper would go on to be one of the most cited psychology papers. The article starts with Miller talking about being persecuted by a number.

My problem is that I have been persecuted by an integer. For seven years this number has followed me around, has intruded in my most private data, and has assaulted me from the pages of our most public journals. This number assumes a variety of disguises, being sometimes a little larger and sometimes a little smaller than usual, but never changing so much as to be unrecognizable. The persistence with which this number plagues me is far more than a random accident. There is, to quote a famous senator, a design behind it, some pattern governing its appearances. Either there really is something unusual about the number or else I am suffering from delusions of persecution.

George A. Miller

This paper has to do with the similarity in a person’s performance on one-dimensional judgment tasks and memory span. In one-dimensional judgment tasks, individuals are asked to discriminate between items that differ only by one characteristic. The frequency or loudness of a tone or the saltiness of a solution. While there are some variations in different types of items individuals can distinguish about seven (plus or minus) different objects correctly. Memory span is the maximum number of things a person can recite back correctly immediately after being exposed (hearing, feeling, or seeing) to them. Again, the memory span is about seven. The similarity of these two items led to the obvious question, are they related? Was there something magical about the number seven, especially as Miller says since we see seven everywhere.

What about the magical number seven? What about the seven wonders of the world, the seven seas, the seven deadly sins, the seven daughters of Atlas in the Pleiades, the seven ages of man, the seven levels of hell, the seven primary colors, the seven notes of the musical scale, and the seven days of the week? What about the seven-point rating scale, the seven categories for absolute judgment, the seven objects in the span of attention, and the seven digits in the span of immediate memory? For the present, I propose to withhold judgment. Perhaps there is something deep and profound behind all these sevens, something just calling out for us to discover it. But I suspect that it is only a pernicious, Pythagorean coincidence.

George A. Miller

You may ask “why do we even care”? I first heard about the magic number in a teaching workshop years ago. Where it was being used to define the number of things you could present in a lecture. However, from a practical point of view, we care about memory span because it is a component of short-term memory and working memory. In education to “learn something,” the information needs to move into long-term memory. Information can’t reach long-term memory without passing through short-term memory. Working memory interacts with both short-term and long-term memory since working memory is the place where we do things with information; compute, analyze, and modify information.

The process of conversion to long-term from short-term memory requires reinforcement of the neural pathways, which is accomplished by repetition or reloading of the information into short-term memory. Repetition and reloading of information is where the capacity limit becomes essential. If we are teaching and we keep bumping information out or filling the short-term memory than the new information cannot be reloaded and reinforced.

In Miller’s law capacity is 7 + or -2 or 5 to 9 chunks. So, if we use this as part of a lesson plan do we teach five or seven or nine new things? I would argue the answer should be the lowest number since that gives the best chance for all the students to learn. Some people say we should teach seven or nine because that lets us identify the “best” students. I think this is incorrect because it fails to acknowledge one of the fundamental differences between short-term and long-term memory. Short-term memory has a capacity limit while long-term memory does not. So as long as there’s sufficient reinforcement every student in the class can learn (transfer to long-term memory) all the information regardless of what their memory span is.

Now I’m going to drop the other shoe the magic number seven was published 62 years ago it was a review of the research as it stood at that time. In 2010 Cowan published a new review titled “The magic mystery four: how is working memory capacity limited and why.” In this paper, Cowan goes on to show how research since Miller’s work has demonstrated chunking and multivariable decision-making shows a wide range of capacity limits that seem to be dependent on the type of information. However, working memory does seem to have restrictions, and moreover, these limits can be used to predict mistakes and failures in information processing. This limit on working memory is 3 – 5 or 4 + or -1.

I like this number a lot better, why? Not because of any research. The reason is that of course design. If I use the argument from earlier, I would “teach” three new concepts at a time. It’s that number “three” that makes me like the research better. Instead of saying I’m pursued and persecuted by a number, perhaps I will say three has been my companion.

Man with the number three
Man with the number three.

A story has three parts, the beginning, middle, and the end. When I write a proposal, I include three goals. The three primary colors in the RGB spectrum. I know these are just coincidences there’s no real meaning behind it. I also suspect if I’m aware of it and willing to think logically when the need is there, there is no actual harm in my companionable number three, for the time being at least I have some research to back me up.

How much do “magic” numbers influence course design? How much should they change course design? In the teaching is an art or science debate I’m on the science side, so I like research. What are you? The critical thing about Miller’s review is that he eventually concluded that the capacities of memory span and one-dimensional judgment were, in fact, nothing more than a coincidence, memory span is still essential to course design.


Thanks for listening to my musings

The teaching cyborg

Clear and Obvious Facts

“There is nothing more deceptive than an obvious fact.”
Arthur Conan Doyle, The Boscombe Valley Mystery


I have watched or been a student in a lot of biology classes over the years.  I sometimes think we take a lot for granted when we teach students. Not only in biology but in many of the STEM fields. We have the advantage of teaching science on the shoulders of all the greats that came before us.  Sometimes I think we forget how long it took to answer questions and just how smart the people that figure them out were. Also, we forget how fast things change, in biology we have something called The Central Dogma. Simply it states that DNA goes to RNA goes to protein. It’s as simple as that; we know proteins are not made directly from DNA and RNA is not made from proteins.

The funny thing about The Central Dogma’s place in modern biology is that it’s relatively new. We’ve been studying biology for a long time; Van Leeuwenhoek discovered single-cell organisms in 1670,  Hooke coined the term cell in 1665.  Macromolecules came later; Proteins in 1838, DNA in 1869, and RNA between 1890 and 1950, RNA was initially thought to be the same as DNA. However, we didn’t know whether DNA or proteins were the sources of genetic inheritance until 1952. We didn’t know the structure of DNA until 1953. Meselson and Stahl published the proof of semi-conservative replication of DNA in 1958.

In 2018 most of The Central Dogma is less than 70 years old. There are a substantial number of people alive that are older than The Central Dogma. This information is only old because of the speed at which biology has been progressing over the last century.

When teaching facts In STEM education we often run into a severe problem, students can often give us the “correct” answer on a test.  However, if you dig a little deeper, they don’t understand what that answer means.

I have often thought that teaching biology (or any STEM field) through an understanding of the foundational experiments would help students understand the facts. Imagine going through these experiments; What was the question?, Why did they do this?, Why didn’t they do that?, What do the results show?, and What do they do next?. Teaching these experiments to students would explain not only what we know but why we know it.

Let’s look at a couple of examples. We know that DNA is the molecule responsible for genetic inheritance. How do we know? For many years scientists thought proteins had to be the source of genetic inheritance because DNA was just too simple.  In 1952 Alfred Hershey and Martha Chase conducted an experiment that provided some of the most persuasive evidence that DNA was the source of genetic inheritance.

Hershey and Chase use T2 bacteriophage for their experiment, T2 phage reproduced by infecting a bacterial cell. The bacterial cell produces new phage that would be released when the cell lysed. While the mechanism of T2 phage reproductions was not known, the process required the transfer of “genetic material” from the phage to the bacteria. The T2 phage is composed of two components a protein shell and DNA core. The researchers needed to determine what part of the T2 phage entered the bacterial cell.

The researchers needed a way to label proteins and DNA independently of each other.  Two atoms helped sulfur and phosphorus. Proteins use sulfur while DNA does not. DNA uses phosphorus while proteins do not. They grew phage with radioactive sulfur or radioactive phosphorus. These radioactive phages infected cells, after infection, the phage and cells were separated, and the location of the radioactivity was determined.

They found the radioactive DNA was always with the bacteria (Figure 1B) while none of the radioactive protein was with the bacteria (Figure 1A). They also showed that radioactive DNA could get incorporated into the bacterial DNA. While other scientists conducted additional experiments, this experiment showed it was the DNA, which carried the genetic information.

Cartoon depiction of the Hershey Chase Experiment
Hershey Chase Experiment, Derived from Hershey Chase experiment.png by Thomasione from Wikimedia Commons

Your students can probably (we hope) tell you that DNA replicates semiconservatively.  However, if you asked them to prove semiconservative replication of DNA, could they do it? Without looking up the Meselson and Stahl experiment. In the late 1950s when Matthew Meselson and Franklin Stahl conducted their research, we already knew the structure of DNA. It was immediately clear from the structure that DNA could serve as a template for its replication.

Early on there were three competing models for DNA replication; conservative replication (Figure 2A), semiconservative replication (Figure 2B), and dispersive replication (Figure 2C). The differences in these models can be described based on where the new and old DNA strands are after replication. In conservative replication after one round, you end up with one DNA molecule composed entirely of new DNA and one molecule composed entirely of old DNA. After two rounds of replication, you now have three new DNA molecules and one old DNA molecule. In semiconservative replication after the first round, you get two molecules that both contain one new and one old strand of DNA. After two rounds you get two molecules composed entirely of new DNA and two molecules composed of one new and one old strand. In disrupted replication, the DNA molecule was cut every ten base pairs on alternating strands, and then new DNA would fill in the gaps. After one round you get molecules that are 50-50 old versus new DNA. After two rounds of replication, you get four strands that would have somewhere between 50-50 and 75-25 new versus old DNA.

Cartoon representation of 3 different modes of DNA replication tested in the Meselson and Stahl Experiment.
3 different modes of DNA replication, Dertived from DNAreplicationModes.png by Adenosine from Wikimedia Commons.

The beauty of these models is that if you can follow the new and the old DNA you can distinguish between all models. Meselson and Stahl marked new and old DNA with nitrogen isotopes specifically N14 and N15 these isotopes differ by one neutron. Which turns out is enough to separate DNA by density in a cesium chloride gradient.

They grew bacteria on media which contained N15 then allowed the cells to grow on media containing N14 for 0, 1, or 2 cycles of replication. The DNA was then isolated from the cells and density was used to separate the DNA molecules.  After zero rounds of replication, there was a single band lower than cells grown only on N14 (Figure 3 N15 0). After one round of DNA replication, there was a single band between the N15 and N14 bands (Figure 3 N15 1). This result ruled out conservative replication since conservative replication should have produced one heavy (N15) and one light (N14) band. However, both semiconservative and disrupted replication should produce 50-50 molecules at round one. After two rounds of replication, we get two band’s one at the 50-50 spot the second at the light (N14) position (Figure 3 N15 3). This position of bands is what you’d expect from semiconservative replication but not dispersive replication. Dispersive replication would have produced a band between the 50-50 and the N14 band. Therefore, DNA replicated semiconservative.

Cartoon representation of the Results from the Meselson Stahl Experiment.
Meselson Stahl Experiment, Derived from Meselson-stahl_experiment_diagram_en.svg: LadyofHats, Wikimedia Commons

Even if you don’t need this experiment to teach your students how semiconservative replication works, the Meselson and Stahl experiment is often referred to as one of the most elegant experiments ever conducted in biology and is worth studying to learning experimental design.

Up until these experiments were conducted the information that we teach as clear and obvious facts was up for debate. While we probably can’t go over every single fundamental experiment in enough details, so our students understand them, because of the total amount of material we need to cover, foundational experiments can be useful. If there’s a topic that your students are having trouble grasping maybe take the students through the experiments that demonstrated the facts. Perhaps the solution is a one-credit recitation that covers the experiments in conjunction with the lector.  That might solve all our problems (shakes head ruefully).  One last thought, if students are having trouble grasping that clear and obvious fact maybe stop and ask if it is clear and obvious?


Thanks for listening to my musings

The teaching cyborg