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

Is It in the Syllabus?

Directions are instructions given to explain how.
Direction is a vision offered to explain why.
Simon Sinek

The course syllabus is the backbone of many courses; the syllabus is the means by which the teachers deliver their expectations and policies to students. However, getting students to read the syllabus has become such a common problem that it has entered popular culture. A quick search of the international net turned up over 50 memes, mugs, T-shirts, and posters all was some variation of the phrase “it’s in the syllabus.” My favorite being “It was in the syllabus it’s still in the syllabus it’s always in the syllabus” There are a lot of web pages written about the topic of the syllabus Amy Baldwin’s website is called “it’s in the syllabus.”  Austin Community College professor David Lydic has a unique approach to students asking him questions that are in the syllabus.

David Lydic using his t shirt, that reads it's in the syllabus, to answer a student question that is in the syllabus.
David Lydic showing his It’s in the syllabus t shirt. Image source Imgur

The funny thing is I had not planned on writing about the syllabus. However, I recently collected course syllabi for another project. I collected 20 syllabi for first-year majors biology courses and ten each from chemistry and physics. When I started looking at the syllabi and noticed something interesting, the only thing that was in all of them was the course name.

Five of the 40 syllabi did not list the course instructor, only 12 of them listed learning goals, ten didn’t even list course schedules. With all this emphasis on it’s in the syllabus, I was quite surprised to find that when you go and look at syllabus well, it’s not in the syllabus. Since a lot of schools or at least departments require course syllabi coupled with the fact that syllabi are generally regarded as legal contracts why is so much missing?

My guess is a lack of training and models. I’ve previously talked about out why I use models in my work and so I won’t go into it. If you want to read about it, you can review my earlier blog post here. For this blog, I’m going to use the recommended checklist from “the course syllabi: a learning-centered approach” second edition. When I used this checklist to examine all 40 syllabi, this is what I found.

Syllabi Checklist Table

Biology (n=20)
Chemistry (n=10)
Physics (n=10)
Total
(n=40)
table of contents

0

0 0 0
instructor information 17 8 10 35
student information form (not needed anymore) 0 0 0 0
letters to the student or teaching philosophy statement 0 0 0 0
purpose of the course 0 0 0 0
course description 8 8 6 22
course objectives (learning goals) 4 4 4 12
readings 17 8 5 30
resources 16 9 8 33
course calendar 17 8 5 30
course requirements 0 0 0 0
policies and expectations (Instructor/Course):
attendance 0 0 0 0
late papers 0 0 0 0
missed tests 1 1 0 2
class behaviors 1 2 2 5
civility 0 0 0 0
policies and expectations (University/College):
academic honesty 9 4 7 20
disability access 7 5 7 19
safety 0 1 0 1
evaluation 0 0 0 0
grading procedures 13 7 9 29
how to succeed in this course: tools for study and work 0 0 1 1

There are a few things on this list that are not relevant anymore; student information systems replaced student information forms.  I generally include the purpose of the course with the course description.  So, what do you think of this list?  Is it too much, not enough, should it just be different? There are two things that each appeared only once in a syllabus that I think I would add; one is a list of FAQs and other while I don’t necessarily like what it suggests. I understand its presence, and that is an escape plan.  Though in all honesty, it should be the responsibility of the school to have escape plans for all its buildings.

Course syllabi are the perfect example of where schools could and should help their teachers. With today’s learning management systems school should be able to create a page template for the syllabus. The advantages a lot of the information could be auto-populated, for example when the course is assigned the syllabus page auto-populates the course title, description, room and meeting times from the course catalog. Appointing the professor can automatically populate contact information. Additionally, programs could automatically fill school policies like; disability policy, honor code, harassment, and safety. A form that could be used to add all the additional information that faculty added themselves. Imagine having a form that auto-populates with a schedule of dates that you could add readings and assignments without figuring out the calendar.  Not only would this help save time, but it would also lead to consistency and support both new and experienced faculty include all the necessary components of a syllabus. Since schools write many of these components, the school should be responsible for their upkeep and consistency among syllabi.

Is there anything else you think should be in a syllabus? Anything you would leave out? Would a syllabus creation tool be something you would like to see? What do you think about the syllabus? Whatever you think about the syllabus as a group I think we need to think a little bit before we go into “It’s in the syllabus.”

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

Why I Use Models

“We all have mental models: the lens through which we see the world that drive our responses to everything we experience. Being aware of your mental models is key to being objective.”
Elizabeth Thornton

I like using models when designing courses and instructional interventions. When I say models, I mean a structured guide that help you build or develop components of a class. In general, I just like models, I generally believe the ability to create a model is strong evidence that not only do you have a deep understanding of the subject, but you can tell a complete story. Educational models have been around for a long time, The Socratic Method anyone? You could even say the Rosetta Stone was a model for teaching language. We might not have ever translated some writing without it.

An image of the front Rosetta Stone.
An image of the front Rosetta Stone.

One of the problems with educational models is that there are so many of them and they can be controversial. For example, the number of things written in favor of and opposition to learning styles fills more space than the learning styles themselves. Additionally, there are a lot of learning styles according to Coffield et al. 2004 there are more than 70 learning styles just a partial list is

  • Neil Fleming’s Visual, Aural, Reading/Writing and Kinesthetics (VARK)
  • Felder and Silverman’s Index of Learning Styles
  • David Kolb’s Learning Style Inventory (LSI)
  • Myers-Briggs Type Indicator (MBTI)
  • Allinson and Hayes Cognitive Style Index (CSI)

I have in fact taught and used the Kolb learning style, and I think it can be helpful if used correctly, “i.e., the way I use it :)” but that is a discussion for another time.

So, with all the mind-numbing options why do I like models? It’s not because I believe there is a single silver bullet model. I don’t believe in the silver bullet, the idea that one thing can solve all our problems. That there is no one-size-fits-all solution to everything in education? Why? The process of teaching and learning is not one discrete whole it is tens, hundreds, thousands of little interacting pieces. Each of these pieces has their own specific needs requirements and issues. Therefore, I use different models for different things, some of the models I use are:

  • For Rubrics
    • Effective Grading: A Tool for Learning and Assessment in College, 2nd Edition
      Barbara E. Walvoord, Virginia Johnson Anderson
      Nov 2009, Jossey-Bass
  • Question Design
    • Taxonomy of Educational Objectives Handbook I: The Cognitive Domain
      Benjamin Bloom, M.D. Englehart, E.J. Furst, W.H. Hill, David Krathwohl
      1956 Longmans, New York, NY, USA
  • Syllabus Design
    • The Course Syllabus: A Learning-Centered Approach
      Judith Grunert O’Brien and Barbara J. Millis
      March 2008, Jossey-Bass
  • Per-Per Instruction and Student Response System
    • Clickers in the Classroom: How to Enhance Science Teaching Using Classroom Response Systems
      Douglas Duncan
      September 2004, Pearson
  • Course Design
    • Understanding by Design
      Grant P. Wiggins and Jay McTighe
      January 2005, Heinle ELT

I chose these models because they work with my internal model of education. Even when I am working with groups that have different focuses I still like using models. The first thing I like about models is that I am often working on courses that will be taught at multiple locations or by various instructors. Models allow for a consistency that can be reinforced by existing materials.

Consistency across courses, both from year to year and across multiple sections within the same year. Consistency can be especially useful if you have courses with different instructors. Consistency is also helpful internally in a class. Internal consistency frees up working memory for the students. The less students must focus on structure or course layout the more they can focus on content.

Models are also a great way to introduce new instructors to the art and craft of teaching. Models give them guides to follow. Having models for things like syllabi, rubrics, and question writing helps new instructors focus their time and energy on lesson planning and content.

Another advantage of remaining consistent over time is to improve your teaching. When you encounter a problem with your teaching, more specifically your students learning, you’ll want to try and find a way to solve the problem. Even if you’re only doing this for your class, this is educational research which means human research. One of the most challenging things with human research is controlling all the variables. In fact, many people will tell you it’s impossible to control for every single variable. Using models to support the design of your course means that your courses are going to be consistent from year to year and you can have a greater belief that the interventions you created made the difference in the student learning.

What do you think about models? Do you use models? What models do you use?

 

Thanks for listening to my musings

The Teaching Cyborg

So, you think you can’t do Inquiry-based Learning: Better ask the gnome

“Scientific inquiry starts with observation. The more one can see, the more one can investigate.”
Martin Chalfie

In 1995 the National Research Council published the National Science Education Standards in which they recommended as one of its central point’s learning science through inquiry. As defined in the National Science Education Standards inquiry has two meanings:

Scientific inquiry refers to the diverse ways in which scientists study the natural world and propose explanations based on the evidence derived from their work. Inquiry also refers to the activities of students in which they develop knowledge and understanding of scientific ideas, as well as an understanding of how scientists study the natural world. (p23)

Five years later a companion book Inquiry and the National Science Education Standards: A Guide for Teaching and Learning was released. The purpose of this companion book was to help teachers understand and implement inquiry in their classrooms. In 2018 almost, a quarter of a century later implementation is still let’s be kind and say incomplete.

If we teach science as a method of looking at the world and asking questions Which is what science is instead of a collection of facts, principles, and ideas that many people view it as then the inquiry-based teaching method is critically important. So why isn’t inquiry-based STEM education universal?

The most common answer I hear is “I can’t do inquiry my class is too big.”  In my mind, this means you can collect bigger data sets. Followed closely by “My students aren’t ready for inquiry,” well instead of full inquiry try guided inquiry.  Lastly, “I have too much material to cover there is no time for inquiry.”  There might be something to say for that last statement, but that is a soapbox for another time, but I would say design your learning goals into the inquiry tasks.

Another way to address these questions, is to ask the question, does inquiry require complicated questions with lots of complicated equipment? Let’s ask a Gnome.

The Gnome Experiment

KERN the gnome in a case with his digital scale
Kern the gnome packed with his scale. Image: Gnome Experiment

The humble garden gnome is practically a cultural icon. To some garden gnomes are a passionate collectible, to others a novelty, and to still others the butt of the joke. However, there is one gnome that taught us about gravity while researching the physical makeup of our planet.

I think I first heard of the Gnome Experiment from a TED talk. The question proposed was could you measure the difference in gravity around the earth on a basic scale. To test their scales the Kern company got one of their scales a garden gnome and started shipping them around the world where the gnome’s recording weight and a picture at each stop. Here are some of the places the gnome has been

KERN the Gnome photographed in four different locations around the world.
Kern the gnome packed with his scale. Image: Gnome Experiment

The result of the experiment is a resounding yes. Kern the gnome weighed different amounts in different places.  Using a similar process what could you teach your students. While the phenomenon of gravity is simple to describe, it’s a difficult concept to grasp in real life.  Weight is dependent on gravity, and the amount of gravitational attraction on the surface of the Earth is dependent on the distance to the center of the planet and mass (density) of the material underneath you.  Apply this information correctly, and it can teach you about gravity and the earth.

For instance, suppose we were to conduct this experiment again.  Only this time in addition to the gnome and scale we also included a GPS/altimeter. I live in Colorado a quick search gives us a list of 20 roads that have an elevation over 12,000ft.  Suppose we took our gnome on a road trip and used our altimeter to measure the weight at 12,000ft on each of these roads. Since we have now controlled for elevation, what would it mean if we got different results?

As a teaching aid, the gnome experiment can be quite fun and useful. The idea that a garden gnome can be used to conduct science is a great icebreaker. More importantly, the Gnome Experiment shows how you can ask a genuine inquiry with a simple experiment and only a little bit of equipment. Stop and think about experiments you can ask you’re not asking your students to win the Nobel prize.  Think up some simple experiments and have your class address them.  I suspect what we need is a database of inquiry-based experiments for education, like the database of test and exam questions that are out there.

 

Thanks for listening to my musings

The Teaching Cyborg