Relativity in a Canoe

September 29, 2014

The world moves around the canoe.

The world moves around the canoe.

Perhaps not surprisingly, my middle school students have a difficult time wrapping their heads around the idea of multiple frames of reference. We were in a canoe on the Current River and I asked the student paddling in the rear of the boat to look at me and answer the question, “Are we in the canoe moving, or are we steady in one spot and everything around us moving?”

This resulted in some serious cognitive processing. And she still has not gotten back to me with an answer.

Another student, faced with the same question, thought it over overnight and concluded that it was a riddle. He figured the correct answer was that the canoe was moving and the land was still. I asked him to think about it a little more (because he was only half right).

Interestingly enough, I’ll be teaching my Advanced Physics class this block, and the first chapter has a neat little section on coordinate systems. I’m curious to see if the 11th and 12th graders have an easier time with the concept.

The canoe moves.

The canoe moves.

Citing this post: Urbano, L., 2014. Relativity in a Canoe, Retrieved September 25th, 2017, from Montessori Muddle: .
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Gum: “a functional food with function but no food”

December 4, 2011

Gum is an effective booster of mental performance, conferring all sorts of benefits without any side effects. … chewing gum is often a better test aid than caffeine. [However] gum chewers only showed an increase in performance during the first 20 minutes of testing.

— Lehrer, 2011: The Cognitive Benefits of Chewing Gum in Wired.

Jonah Lehrer has a fascinating article on, how chewing gum improves mental performance“. It does not seem to matter what type of gum, just as long as you’re chewing.

The benefits (briefly and probably overly simplified) of chewing gum:

On the other hand, while chewing might be good for most types of memory, one study found that chewing, and other rhythmic tasks reduces short-term recall of long lists (Kozlov et al., 2011).

Lehrer cites a 2004 review of the research on gum and memory, which describes chewing gum as, “a functional food with function but no food” (Scholey, 2004).

The takehome message for using gum while taking tests:

When taking a test, save the gum for the hardest part, or for those questions when you feel your focus flagging. The gum will help you concentrate, but the help won’t last long.

— Lehrer, 2011: The Cognitive Benefits of Chewing Gum in Wired.

Image via

Citing this post: Urbano, L., 2011. Gum: "a functional food with function but no food", Retrieved September 25th, 2017, from Montessori Muddle: .
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Doodling is Good!

October 22, 2011

To Doodle: to make spontaneous marks to help yourself think.
–Sunni Brown (2011): Doodlers, unite! (at 3:19) in TED.

Unfortunately, teachers are usually opposed to doodling in class. (Image from Sunni Brown's TED talk.)

Doodling on a notepad is often seen as evidence that a student is not paying attention. Very much to the contrary, argues Sunni Brown in this TED talk:

Studies show that sketching and doodling improve our comprehension — and our creative thinking.
— TEDtalksDirector: Sunni Brown: Doodlers, unite! on YouTube.

She describes doodling as a, “preemptive measure to stop you from loosing focus.” In addition, doodling helps integrate all four modes of learning (visual, auditory, reading/writing, kinesthetic) as well as helps provoke an emotional response, all of which greatly aid retention of information and creative thinking. Finally, doodling is most useful when we’re trying to process a heavy, dense load of information.

Brown has more details in her article in .net, Why the Doodle Matters.

(hat tip: The Dish)

Citing this post: Urbano, L., 2011. Doodling is Good!, Retrieved September 25th, 2017, from Montessori Muddle: .
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Multiple Intelligences

August 22, 2010

The cycle of work. Within each subject area there are different types of assignments designed to provoke learning in many different styles.

The lessons, the individual works, the different group works, the reading; they’re all set up in this elaborate combination so that different students with different learning styles can get the information they need in the way that’s most meaningful to them. But the students also get to experience a wide range of learning styles so that they can become acclimatized to the different styles while actually figuring out which ones work best for them.

The logic behind this approach comes from Howard Gardner’s ideas on multiple intelligences. He argues that we have aptitudes for different ways of learning, and learning is easier and faster if students take advantage of their preferred learning styles. Whether we acquire these preferences through nature or nurture is an intriguing question, but by middle school I’ve found that it does not take long to recognize that some students have rather strong preferences.

[T]here exists a multitude of intelligences, quite independent of each other; that each intelligence has its own strengths and constraints; that the mind is far from unencumbered at birth; and that it is unexpectedly difficult to teach things that go against early ‘naive’ theories of that challenge the natural lines of force within an intelligence and its matching domains. – Gardner (1993) p. xix.

The learning intelligences have been defined in a number of different ways (see Smith, 2008 and BGfL for examples). We parse them like this:

  • Linguistic intelligence – learning from the written word or hearing words (auditory).
  • Logical/Math – using numbers and logical reasoning.
  • Bodily-kinesthetic – learning from doing.
  • Visual/Spatial – emphasizes images and relationships in space.
  • Interpersonal – learning from/with others.
  • Intrapersonal – introspective learning.
  • Musical – rhythm is important
  • Naturalistic – comprehending of the environment.

I prefer students to discover their preferred intelligences via the variations convolved into the curriculum, however, the BGfL has an online, multiple intelligences test that I’ve used in the past. However, as with standardized tests, you don’t want to stereotype students or have them stereotype themselves. All the intelligences interact. Different challenges force us to take different approaches, using different combinations of our intelligences to best effect. As always, a growth mindset is best. With their mental plasticity, adolescence is the best time to explore different learning approaches.

Citing this post: Urbano, L., 2010. Multiple Intelligences, Retrieved September 25th, 2017, from Montessori Muddle: .
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WEIRD behavior

August 22, 2010

San foragers of the Kalahari would probably look at these two red lines and say they were the same length. (Image adapted from Fibonacci on Wikipedia)

The small window into the effects of modern life on the way we think was opened just a little wider recently by an interesting article by Joseph Heinrich and others. They sift through a large number of studies of people living the industrialized life and their more rural counterparts to find real differences in they way these different groups think.

San village

In the image above, the San foragers would be right, the two lines are the same length, but your typical Western, Educated, Industrialized, Rich, and Democratic (WEIRD) person would need to the left line to be about 20% longer for them to say they were identical. Why this is, I can’t say, but it might be that our visual perception is colored at an early age by the carpentered edges we see around us. Or maybe not.

And it’s not just in vision. WEIRD people think of fairness and co-operation in decision-making, and where things are relative to the self differently too, and their kids tend not to be able to identify easily with other species. The latter result is likely because of the “nature deficit“. The article clearly demonstrates that people think very differently, in very fundamental ways, if they come from modern environments.

The paper, found via Big Questions Online and Edge, is a fascinating read, and not too bad coming from a technical journal. There are a lot of interesting results summarizing a lot of behavioral science research. As a reminder to remember that one scientific article, no matter how good it is, remains just one perspective. the paper’s pdf has a number of commentaries and criticisms attached from other behavioral science researchers.

Where the WIERD people are. (Image from Wikipedia)

What I’m still trying to process, are the implications for Montessori educational philosophy. Because there are these significant, large differences in the way people see the world, we need to be aware of the perspectives of our audience. Students also need to appreciate how cultural differences affect the way we think and see the world that influence how we argue and how we behave. Yet they also need to recognize the there are some subjects, say the physical sciences, that are objective; there is a single, definite truth (for some value of definite) about the composition of a water molecule.

Citing this post: Urbano, L., 2010. WEIRD behavior, Retrieved September 25th, 2017, from Montessori Muddle: .
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Optical Illusions

August 17, 2010

Look at the figure on the right. Stare at the black dot without moving your eyes. The smudge will miraculously disappear! Try the same experiment again with the smudge on the left. This time the smudge does not disappear. What is going on here? Why does the smudge disappear in one instance and not the other? (Illusion from the Wilderdom Store. Use under Creative Commons Attribution License)

Wilderdom has a wonderful set of cooperative games and icebreaking games that they share for free. They also have a book of optical illusions that would work well for a challenge during morning community meetings.

Their material is copyleft so as along as you attribute them and use the same licensing terms (and cite their Creative Commons License) . You are free to use their stuff as you like.

Citing this post: Urbano, L., 2010. Optical Illusions, Retrieved September 25th, 2017, from Montessori Muddle: .
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Getting the mind to wander

April 16, 2010

The mind tend to wander when working at repetitive tasks that don’t require much brain processing. So the brain just switches over to thinking about long-term things. There is even a specific part of the brain, called the “default network” that starts up when we zone-out. That, at least, is what I summarize from looking at some neuroscience research by Malia Mason and others (2007) on wandering minds.

What’s interesting is that the default network tends to be used for “certain kinds of self-referential thinking, such as reflecting on personal experiences or picturing yourself in the future” (Zimmer, 2010). That means introspection. Introspection is the point of Personal World, so it follows that we should want our students’ minds to wander during Personal World.

So how do we design the Personal World time and environment to encourage daydreaming? Repetitive tasks aid mind-wandering, as will anything that is rote that does not require acute cognitive focus. Raking the garden, doodling should be encouraged, in fact, anything that encourages boredom.

I would think also, that reducing the cognitive load would also be beneficial, which might also mean no music. Yet music helps isolate the individual, particularly when they’re using ear buds. Perhaps quiet, “boring” sounds would be best, coming a shared radio so students can’t choose to listen to something else. Of course, if you’re listening to the music on your mp3 player then you tend to tune out the songs anyway so maybe it all falls out in the wash.

Of course this could all be malarkey, based as it is on a single study, so I’ll end with the words of caution that coms at the end of the article:

Although the thoughts the mind produces when wandering are at times useful, such instances do not prove that that the mind wanders because these thoughts are adaptive; on the contrary the mind may wander simply because it can. – Mason et al., 2007.

Citing this post: Urbano, L., 2010. Getting the mind to wander, Retrieved September 25th, 2017, from Montessori Muddle: .
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Daydreaming …

April 15, 2010

Focused work. We like to see our students focused on their work and we give them long blocks of time to do so. It is hard, however, for anyone to stay on task for two hours straight. You have to allow for a certain amount of mind wandering and daydreaming. What a lot of neurologic research is uncovering is that zoning-out is an essential part of putting the pieces together and helps with learning.

When we are no longer even aware that our minds are wandering, we may be able to think most deeply about the big picture. – Zimmer (2010)

Daydreaming by Edward Harrison May (1876) (from Wikimedia Commons).

While we sleep the brain assembles information into coherent patterns, helping us learn and process emotions. Carl Zimmer has an article in Discover Magazine on how unfocused daydreaming accomplishes the same thing.

Citing this post: Urbano, L., 2010. Daydreaming ..., Retrieved September 25th, 2017, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

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