Critical ThinkingEducationLesson PlansPedagogy

Teaching the nuance of “wrong”

I teach children aged 12-15.  This borderland between childhood and adulthood is filled with both physical and mental upheavals. Mentally it is a transition from thinking in a concrete manner to thinking in a more abstract and nuanced manner.  Into this quagmire I step boldly and try to teach science and a nuanced definition of the word wrong.

Why do I need to teach about wrongness? because I teach that science is dynamic.  It changes as new information is gathered about a topic. Science as a human endeavor creates theories, develops models that illustrate those theories, and continually tests those explanations as new data is generated.  So when I say that science changes, my students often only hear that science is wrong.  The concepts of refining and clarifying ideas are too subtle for some of my concrete thinkers and so in addition to illustrating those I lay siege to their concept of wrong.

Most of my students see the concept of wrong as a clear and distinct line.  This is right and that is wrong.  They are a dichotomy.  2 x 6 = 12 it never equals 10.  They are happy in their little black and white world and are extremely uncomfortable when I explain that there are degrees of wrongness.  For example: when I begin talking about significant figures and error in measurements the hypothetical pure number correctness 2 x 6 = 12 does not hold sway because in terms of measurement 2 cm x 6 cm = 10 cm2.  (See below for a more complete explaination)

This has been known to cause panic attacks in a certain type of person.

Over the past few years I have worked on different ways to add nuance to my student’s personal definition of wrongness. My goal is for them to see that there are things that are more wrong than others.  That we often are perfectly happy using tools and models that objectively have a high level of wrongness, but are useful in certain contexts.

I start with cows.

“What’s this?”  I ask.

Simple Cow Drawing

IMG_0414 by Chris Ray

  A cow my class responds.

“Then what is this?”

detailed sketch of a cow

Cow by Ivan Salas


Still a cow

Which is a better model of a cow? Which one is less wrong?  Through class discussion we rank the relative wrongness of cow pictures.  We talk about how even a simple drawing of a cow that shows a cow is on a farm, and not in a forest can be useful when describing where different animals are found, or which animals are domesticated.  There is of course a point where a model is so wrong that it is no longer useful, for instance this chicken cow.

We need to use a model that is good enough for the task, but is not weighed down by so much extra information that it becomes equally as useless as a chicken cow.  Maps and globes are a great example of this.  If we are travelling from one town to another we use a flat map.  We do not use a globe.  The globe does not have enough detail, but it is very useful when seeing where continents and countries can be found.  Globes also do not distort the land masses of the earth to the extent of the map known as the Mercator projection.

By Strebe (Own work) [CC-BY-SA-3.0 (], via Wikimedia Commons

By Strebe (Own work) [CC-BY-SA-3.0 (], via Wikimedia Commons

The Mercator projection is a nice lead-in to the importance of knowing the wrongness of your model.  A map that is a nice tool for navigation does a terrible job of showing the size of continents and countries.  The sizes of places that are far from the equator are exaggerated.  Alaska (663,300 square miles) is represented as being about the same size as Brazil (3.288 million square miles).  This is not a low level of wrongness, but it does not make the map useless.  It just increases the importance of knowing where the wrongness lies.

I recently read a post on overcoming student misconceptions which can seem like a Sisyphean task.  It seems to me that while we might not be able to overcome all misconceptions, it is at least possible to not create any new ones by talking about the strengths and weaknesses of the models we use.  I do this when I teach about the atom and elements.  It is easy here because there are so many models that we use and we use them for different purposes.  When you sit multiple models of the same thing next to each other it makes it easier to see the strengths and weaknesses.

My final tool for talking about wrongness is Isaac Asimov’s essay The Relativity of Wrong.  Its reading level is a bit high for younger students, but the science, humor and snark makes it worth the time to read and discuss it in class.

A good portion of the essay is devoted to the shape of the earth and one of the benefits is that it hits people right between the eyes with the common misconception that the earth is a sphere, but it does not stop there as shown by this quote:

 To put it another way, on a flat surface, curvature is 0 per mile everywhere. On the earth’s spherical surface, curvature is 0.000126 per mile everywhere (or 8 inches per mile). On the earth’s oblate spheroidal surface, the curvature varies from 7.973 inches to the mile to 8.027 inches to the mile.

This demonstrates how the article highlights that science is not wrongity wrong wrong, but is more of an incomplete picture.  Over time our pixilated view of the world becomes clearer as knowledge increases our resolution. We grow from a fuzzy understanding to clarity.


A quick explanation of why 2cm x 6 cm= 10 cm2 in significant figures:  The use of significant figures is really a grammar applied to numbers, where the number of decimal places tells you the level of possible error in your measurement.   In the grammar:

  • 2 cm means 2 cm + or – 1 cm
  • 2.0 cm means 2 cm + or – 0.1 cm
  • With that in mind around 2 cm x around 6 cm gives you around 10 cm2

Featured Image Mercator projection SW by Strebe

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Jennifer teaches science in a public school in Pennsylvania. She lives there with her husband and two dogs.


  1. October 28, 2014 at 9:23 pm —

    This is a very useful approach to a difficult problem. Even my college students still have the black and white right vs wrong approach. I may “borrow” this to remind them that it’s not that simple! Thanks!

  2. November 4, 2014 at 5:12 pm —

    Thank you for introducing me to The Relativity of Wrong! In teaching students ages 20+ how to evaluate information, I have to emphasize that reliability and accuracy run along a continuum most of the time. Government websites might be generally considered trustworthy sources, but even they have biases, such as a state health department that advertises crisis pregnancy centers or when the U.S. Dept of Ed stripped its site of research that contradicted No Child Left Behind. Or peer-reviewed study indexed in PubMed about a medical device may have been funded in large part by a manufacturer. This is why critical thinking skills are so important.

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