Making mistakes, accidentally or on purpose

[Maria Droujkova]

"Bearded Math" blog by Pete Horne has an essay about the value of mistakes in mathematics http://beardedmath.blogspot.com/2009/08/lets-make-some-mistakes.html A quote:

"Too often, students see mistakes as tantamount to failure; however, mistakes are an inevitable and necessary part of the learning process. Marvin Minsky, the Toshiba Professor of Media Arts and Sciences at MIT has noted, “We tend to think of knowledge in positive terms—and of experts as people who know exactly what to do. But one could argue that much of an expert’s competence stems from having learned to avoid the most common bugs.”1 Innovation also hinges on making mistakes and learning from the errors, be it realizing that a process will not work, or examining how an unanticipated result could be used to solve another problem."

~*~*~*~*~*
Here is my reply, about math anxiety reducing activities:

Once in a while, I invite my students to make mistakes on purpose. Activities I've done so far:

- Make as many mistakes as you can in solving this problem!
Works better in groups, as a collaborative task. Leads to students analyzing "all possible" mistakes. Relies on the "catch them all" (collector) game mechanic for fun value.

- Make the silliest/weirdest mistake possible!
This relies on comparing mistakes. Again, it's a high order (creating/evaluating) task, because students have to compare their mistakes and judge which are silliest, and why.

An activity I want to try:
- Make mistakes that are hard to notice!
For example, the (in)famous proof that 1=2 has a relatively subtle mistake, at least for the beginning algebra level.

Cheers,
Maria Droujkova
http://www.naturalmath.com

Make math your own, to make your own math.

[anirban chaudhuri]

This is an excellent idea.

Children commonly display a "fear" for mathematics because of the mistakes they commit.This fear for mathematics is much greater than a generalised lack of interest for a particular subject e.g. history or geography,and this fear factor is such an important issue when we consider the psychological make-up of a child. Sometimes this fear becomes deeply embedded in the subconscious mind and manifests itself as insecurities,lack of self-confidence and mental inhibitions when the child grows up into an adult,and at that stage it is difficult to trace a psychological deficiency or a personality handicap back to the original root-a fear for mathematics which a person might have had in childhood.
One of the definite causes for this fear for mathematics is that making a mistake in mathematics has got a more prominent and immediate reflection which a child identifies as Failure, which might not be the case in other subjects where the result of making a mistake while learning is much less direct.

This is further compounded by parent (and peer) pressure.
Parents generally misinterpret a lower grade in mathematics in the report-card of a child as they too,errandously,associate it directly with Failure or a Weakness,and their reactions create more unwanted pressure in the child's mind who develops a feeling of 'letting down' or 'disappointing' the parents.This frequently creates a subconscious antipathy for the subject as a child would normally want to avoid situations where he feels that he has let his parents down or disappointed them.And these subconscious repurcussions have a more pronounced manifest when the child grows up even to the point of displaying aberrant social interactions.

Maria's thought-process and the resultant endeavour is particularly significant in this aspect. Children should be encouraged by teachers in school and by parents at home alike to accept the fact that making mistakes is a part of learning,growing up and living life in general and mistakes in mathematics do not signify any potential failure or inability.

Though times have changed and so have people's outlook in general,a certain lack of a similar awareness at the parent and teacher level,is still strongly perceived universally across all communities and societies.This awareness still remains to be vastly improved.A child should be let free to approach and learn the intricacies of mathematics in his own way under proper,understanding guidance.Mathematics is an integral part of everyday life.It is important that a child learns mathematics in the proper way without inhibitions and fear of failures so his life can be more healthy and productive-an effect leading to better community psychology and interaction which is so significant in today's Life in a broader perspective.

Cheers Maria.

Anirban.

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[Maria Droujkova]

I think there is some sort of deep "existential dread" inherent in mathematics.

I used to blame all math anxiety on poor social practices, grades, timed tests, ridiculing mistakes and so on. Enter my daughter Katya...

We are unschoolers, which is a type of homeschooling that does not typically involve any of these anxiety-producing practices Anirban mentions. Katya has never had a grade in her life. We seem to be celebrating mistakes and exploration when doing mathematics. Math is definitely a part of our everyday life, with both parents working and playing with it daily. Yet once in a while, Katya gets severe bouts of math anxiety.

None of us know why. It usually comes when there is a fear that a problem will take "forever," or understanding of a concept will "never" come - though we frequently spend days on problems and have fun with that. So this is probably the general dread of human limitations in the face of mathematics. Or maybe it's just me putting some subconscious pressure on the kid!

Cheers,
Maria Droujkova
http://www.naturalmath.com

Make math your own, to make your own math.

[Loren BRAUNER]

Thank you for the great suggestions! Much appreciated : )

---

From: Maria Droujkova <drou...@gmail.com>
Sent: Monday, August 24, 2009 11:58 AM
To: natur...@googlegroups.com
Cc: pho...@bridgtonacademy.org
Subject: [NaturalMath] Making mistakes, accidentally or on purpose

"Bearded Math" blog by Pete Horne has an essay about the value of mistakes in mathematics http://beardedmath.blogspot.com/2009/08/lets-make-some-mistakes.html A quote:

"Too often, students see mistakes as tantamount to failure; however, mistakes are an inevitable and necessary part of the learning process. Marvin Minsky, the Toshiba Professor of Media Arts and Sciences at MIT has noted, “We tend to think of knowledge in positive terms—and of experts as people who know exactly what to do. But one could argue that much of an expert’s competence stems from having learned to avoid the most common bugs.”1 Innovation also hinges on making mistakes and learning from the errors, be it realizing that a process will not work, or examining how an unanticipated result could be used to solve another problem."

~*~*~*~*~*
Here is my reply, about math anxiety reducing activities:

Once in a while, I invite my students to make mistakes on purpose. Activities I've done so far:

- Make as many mistakes as you can in solving this problem!
Works better in groups, as a collaborative task. Leads to students analyzing "all possible" mistakes. Relies on the "catch them all" (collector) game mechanic for fun value.

- Make the silliest/weirdest mistake possible!
This relies on comparing mistakes. Again, it's a high order (creating/evaluating) task, because students have to compare their mistakes and judge which are silliest, and why.

An activity I want to try:
- Make mistakes that are hard to notice!
For example, the (in)famous proof that 1=2 has a relatively subtle mistake, at least for the beginning algebra level.

Cheers,
Maria Droujkova
http://www.naturalmath.com

Make math your own, to make your own

[The entire original message is not included]

=

[Sue VanHattum]

If you're thinking about this problem, it's important to know that the host wil *always* open another door and will always ask if you want to switch. (At least, it was important for me.)

Warmly,
Sue

>
> Suppose you're on a game show, and you're given the choice of three
> doors. Behind one door is a car, behind the others, goats. You pick a
> door, say #1, and the host, who knows what's behind the doors, opens
> another door, say #3, which has a goat. He says to you, "Do you want
> to pick door #2?" Is it to your advantage to switch your choice of
> doors?

---

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[Maria Droujkova]

Another great idea from Pete, on his "Bearded Math" blog post:
http://beardedmath.blogspot.com/2009/08/lets-make-some-mistakes.html
~*~*~*~*~*

Thanks Maria for the good ideas. Students often overlook the value in mistakes. Another useful exercise is to have students create a multiple choice test where the alternate answers represent common mistakes. This can also be done collaboratively with students voting on what they see as likely mistakes on a particular problem. Great practice before standardized tests.

Pete Horne
Bridgton Academy 
~*~*~*~*~*

[Maria Droujkova]

Another GRAND mistake resource: http://threesixty360.wordpress.com/category/math-mistakes/ This one is great for activities where students search for mistakes in "official"-looking sources.

I am reading "Amazon is non-transitive" right now. Fun fun fun: http://threesixty360.wordpress.com/2009/09/02/amazon-isnt-transitive/ "These are frequently bought together: bed pillow A, lap desk B, bed pillow C." The search system, apparently, thinks that since A and B make good bedfellows, and so do B and C, all three of them go together.

Making more horrible puns,