BABEL, the Basic Automatic B.S. Essay Language generator, is software created by Les Perelman and others [chronicle.com] at MIT. Perelman was a "Director of Undergraduate Writing" at MIT. He has used BABEL to generate nonsense essays and feed them to automated essay grading software. The BABEL output gets high marks with sentences like "Privateness has not been and undoubtedly never will be lauded, precarious, and decent." I think Perelman has a point here. Clever students will no doubt learn to game any such grading system to their benefit. Teachers must question what, if any, benefit an automated essay grading system has.
Back in 2005, Perelman discovered an excellent predictor of score [nytimes.com] on an SAT essay test. It was the length of the essay. No other variable he examined correlated nearly as well with the score. The top scoring essays had many factual errors, too. No matter, according to SAT. The writing quality depends not on the correctness of any facts, according to SAT. Perelman's advice for scoring well is to practice writing fast and make up facts. Perhaps the high scorers can land a job with Fox News?
A paper by Perelman in the Journal of Writing Assessment critiques automatic scoring of essays.
4 out of 5 flipped classroom instructors recommend this blog.
Showing posts with label pedagogy. Show all posts
Showing posts with label pedagogy. Show all posts
Thursday, May 1, 2014
Monday, April 21, 2014
Hybrid Pedagogy
Earlier today I stumbled onto hybrid pedagogy, a website for the eponymous open access journal, while reading a post from Rebecca Schuman, a blogger at Slate who covers education. The director, Jesse Stommel, is an assistant professor at UW-Madison. Give their site a whirl if you're into hybrid learning and pedagogy.
Friday, April 4, 2014
Flipped Learning Guidelines
The Flipped Learning Network (FLN) has announced [pdf] a formal definition of the term "flipped learning" on March 12, 2014, Two things immediately catch my attention here. First, they do not say "flipped classroom." The other attention-getter is who is the FLN? It is interesting that they do not use the more common "flipped classroom" term. They take care to draw a distinction between flipped learning and the flipped classroom. Until I chanced upon this announcement, I was unaware of any controversy or distinction that involved a definition of the concept.
If you are unfamiliar with the flipped classroom concept, head over to youtube and do a search. Their are many videos on this topic.
The FLN bill themselves as a group of experienced flipped learning educators. Their website is attractive and well-organized. Aaron Sams is at the top of their board members page. I believe he is the creator of the flipped learning model of instruction.
The flipped learning definition is published under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, from the non-profit Creative Commons organization. Whoever the FLN is, they are clearly interested in openly sharing their ideas and standards. This is commendable. They do not want others creating derivative works of their standard, so they want to keep control of it. They also do not want others deriving works and selling them for profit. Having looked and worked in the education field, I cannot help but notice all the for-profit enterprises (ETS, MetaMetrics, textbook publishers, Pearson Education, Charter Schools, ad infinitum). But, as I scrutinize the FLN website, I notice ads at the bottom of the page. There's Pearson, Sophia Learning, Cisco, Adobe, etc. This non-profit organization has some deep-pocketed corporations backing them.
A tip of the hat to Casting out Nines, a blog that posted on this new definition.
If you are unfamiliar with the flipped classroom concept, head over to youtube and do a search. Their are many videos on this topic.
The FLN bill themselves as a group of experienced flipped learning educators. Their website is attractive and well-organized. Aaron Sams is at the top of their board members page. I believe he is the creator of the flipped learning model of instruction.
The flipped learning definition is published under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, from the non-profit Creative Commons organization. Whoever the FLN is, they are clearly interested in openly sharing their ideas and standards. This is commendable. They do not want others creating derivative works of their standard, so they want to keep control of it. They also do not want others deriving works and selling them for profit. Having looked and worked in the education field, I cannot help but notice all the for-profit enterprises (ETS, MetaMetrics, textbook publishers, Pearson Education, Charter Schools, ad infinitum). But, as I scrutinize the FLN website, I notice ads at the bottom of the page. There's Pearson, Sophia Learning, Cisco, Adobe, etc. This non-profit organization has some deep-pocketed corporations backing them.
A tip of the hat to Casting out Nines, a blog that posted on this new definition.
Sunday, March 2, 2014
Hyperreal Numbers and Calculus without Limits
Once upon a time, I stumbled into a hyperreal number field on the internet when searching for something related to calculus. Maybe I was calculating the volume of a Steinmetz Solid? The so-called hyperreals can be used to develop the calculus without limits. The claim is made that, perhaps, the use of "infinitesimals" is less confusing than the concept of the limit for struggling calculus students. In fact, there is a calculus text using this approach that one can download for free from this page. The author, H. Jerome Keisler, is a professor emeritus of mathematics at UW-Madison.
What are the hyperreals? They are an extension R* of the field of real numbers, which is usually denoted by R. R is a subset of R*. Without going in to too much detail, R* is obtained from R by adding in infinitesimals and infinitely large numbers. An infinitesimal number is infinitely small. What does this mean? For every real number a, a number ε > 0 is infinitesimal if -a < ε < a. That's it. In contrast, 1/ε is infinitely large (a "hyperinteger"). Conceptually, hyperreals are similar to complex numbers. However, unlike the complex numbers, they are depicted in one linear dimension, not a two-dimensional plane. The nitty gritty is all in Keisler's book. With the concept of the infinitesimal available, we can have the hyperreal quantity x + ε that is infinitely near x. This hyperreal x + ε can then be used to formulate the derivative, which won't be surprising to anyone who has studied calculus.
Here's figure 1.4.3 from Keisler's book. An "infinitesimal microscope" has been used to zoom in on the hyperreal number line:
The infinitesimal microscope is a captivating pedagogical concept. I claim that it's easier to grasp than the concept of a limit. Children learn about microscopes in grade school. Maybe they learn about it nowadays by zooming in on their iPads. In any case, R* is a useful mathematical concept that can be used to formulate the calculus without that ungainly Σ thing. All you need is a little ε guy. :-) Keisler's book provides more than 800 pages of evidence.
The history of infinitesimals is interesting. The epilogue [pdf] to the aforementioned calculus text lays out the story. Archimedes anticipated both infinitesimals and the ε, δ approach of limits in some of his proofs. In the 17th century, the modern calculus was developed independently by Newton and Leibniz. In his reasoning, Newton used both infinitesimals and the concept of a limit as well as the so-called velocity method. Leibniz used infinitesimals. So there were three competing methods for doing calculus: infinitesimals, limits, and the velocity method. Jumping ahead (see Keisler's epilogue for whole story), the first truly rigorous treatment of calculus was formulated by Karl Weierstrass in the 1870's. I believe it was Weierstrass who introduced the ε, δ notation that we still use today.
There can be little doubt that the limit approach is firmly entrenched in the current pedagogy. Other than Keisler's book, I am unaware of any other textbook that uses this approach. I never heard it in Altgeld Hall or Van Vleck. Mathematics teachers should be aware of this alternative approach and should consider using it to introduce students to derivatives and integrals.
What are the hyperreals? They are an extension R* of the field of real numbers, which is usually denoted by R. R is a subset of R*. Without going in to too much detail, R* is obtained from R by adding in infinitesimals and infinitely large numbers. An infinitesimal number is infinitely small. What does this mean? For every real number a, a number ε > 0 is infinitesimal if -a < ε < a. That's it. In contrast, 1/ε is infinitely large (a "hyperinteger"). Conceptually, hyperreals are similar to complex numbers. However, unlike the complex numbers, they are depicted in one linear dimension, not a two-dimensional plane. The nitty gritty is all in Keisler's book. With the concept of the infinitesimal available, we can have the hyperreal quantity x + ε that is infinitely near x. This hyperreal x + ε can then be used to formulate the derivative, which won't be surprising to anyone who has studied calculus.
Here's figure 1.4.3 from Keisler's book. An "infinitesimal microscope" has been used to zoom in on the hyperreal number line:
The infinitesimal microscope is a captivating pedagogical concept. I claim that it's easier to grasp than the concept of a limit. Children learn about microscopes in grade school. Maybe they learn about it nowadays by zooming in on their iPads. In any case, R* is a useful mathematical concept that can be used to formulate the calculus without that ungainly Σ thing. All you need is a little ε guy. :-) Keisler's book provides more than 800 pages of evidence.
The history of infinitesimals is interesting. The epilogue [pdf] to the aforementioned calculus text lays out the story. Archimedes anticipated both infinitesimals and the ε, δ approach of limits in some of his proofs. In the 17th century, the modern calculus was developed independently by Newton and Leibniz. In his reasoning, Newton used both infinitesimals and the concept of a limit as well as the so-called velocity method. Leibniz used infinitesimals. So there were three competing methods for doing calculus: infinitesimals, limits, and the velocity method. Jumping ahead (see Keisler's epilogue for whole story), the first truly rigorous treatment of calculus was formulated by Karl Weierstrass in the 1870's. I believe it was Weierstrass who introduced the ε, δ notation that we still use today.
There can be little doubt that the limit approach is firmly entrenched in the current pedagogy. Other than Keisler's book, I am unaware of any other textbook that uses this approach. I never heard it in Altgeld Hall or Van Vleck. Mathematics teachers should be aware of this alternative approach and should consider using it to introduce students to derivatives and integrals.
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