How to be Exceptionally Wrong

Introduction

Being wrong is an easy task. Being wrong consistently and when hundreds of people are actively trying to make you less wrong is a work of art mastered by few groups as well as our school. Over my next few posts, I will discuss some of the more egregious mistakes that our school has made, and explain their relationship to common fallacious reasoning.

Measurement Bias

Measurement bias is often harder to spot than other forms of bias. It comes in two forms: well meaning people who choose a bad way of measuring data that leads to incorrect conclusions, and people that purposefully manipulate what information they disclose in order to deliberately misinform outside groups.

Confirmation Bias

Confirmation bias is one of the most pernicious forms of bias in logical reasoning. It is caused by starting with strong preconceived notions about how the world is or should be, and forcing evidence to fit with your position, or simply disregarding it because it must be wrong as it disagrees with you.

Our School

In 2011-2012, administration in our school decided that a Diversity and Equity Task Force was necessary to address the challenge that an increasingly diverse Burlington High School would create for creating an effective curriculum. This report had several severe problems in how it was set up.

1. It did not include teachers or students, the two groups that know most about how teachers are affecting students.
2. It did not account for differences in socio-economic class, despite the fact that numerous studies have shown class to have a much larger effect on achievement than race, and the strong correlation between class and race in Burlington

This led to a slew of bad measurements that did not accurately reflect student performance.

1.  Consort rates (students who did not complete high school in 4 years) were misreported as drop-out rates, despite the fact that 4 year graduation rates are a particularly poor measure when looking at large populations of refugee students who enter the school system far below grade level. 
2. Lying about graduation rates: it was reported that there was a 20% difference in graduation rates between students who received free and reduced lunch and those who did not. Both groups have 95% or greater graduation rates.
3. Looking at static measures of student performance rather than growth from year to year to account for the fact that students enter high school at different academic levels.

The 31 page paper published by the task force was largely filled with these sorts of errors (I have selected some of the first as properly refuting all of the claims takes at least 10 pages, more on that later). These statistics were badly chosen that misrepresented what Burlington High School was doing about race. Either due toward incompetency caused by only one of their advisory council having a background in maths or statistics (David Rome), or they purposefully chose statistics that showed Burlington in a bad light.  Although it is unfortunate that such a widely anticipated report was constructed so shoddily, the worst was still to come. After the report was released, David Rome (the only maths or statistics person on the task force), published a 15 page rebuttal to the formation, methods, and conclusions of the task force. Rather than respond maturely by talking about the errors the task force made, and how to update the data used by the task force to better reflect reality, the school district called Mr. Rome a racist, called for his removal from the school, and protested his report. This shows the categorical disinterest our school district has toward data that contradicts the gut feelings of administrators, and an inability to acknowledge mistakes that mean that (among other things) the only question asked of potential job canidates is

The Burlington School District is especially interested in candidates who can contribute to the diversity... of the District and community through their teaching and/or service. How can you, as a paraeducator, help the district to further this goal.

 In other words, the only thing the school district cares about for hiring purposes is diversity. There are no questions asked about style of education, no questions about how they would handle difficult situation. This creates an environment where the way to get a job at our school is not to be well qualified for the job, smart, or hard working, but simply to be a member of a race or ethnicity that is currently under-represented in Burlington High School's staff.

Works Cited

"Equity Audits at the School District Level." Using Equity Audits to Create Equitable and Excellent Schools (2009): 57-66. Burlington School Board, 13 Apr. 2013. Web. 19 Oct. 2015.

"PARAEDUCATOR." Burlington School District: Jobs. N.p., n.d. Web. 19 Oct. 2015.

Rome, David. "1 Response to the “Task Force Report on Diversity, Equity and Inclusion”." (n.d.): n. pag. 30 Jan. 2012. Web. 19 Oct. 2015.

What I Believe but Can Not Prove

One of my biggest unprovable beliefs is that individuals have an effect on the shape of history. This "Great Man" theory of history opposes the Marxist theory which says that societal change is dictated by social and economic conditions and that individuals have little freedom to make meaningful decisions

The cover to Thomas Hobbes book, Leviathan showing a ruler made of the bodies of the masses

 

This is a basically unprovable belief because our records  of the past are not of sufficient to undergo a full analysis as to which is a better method. More importantly, this is unproven because it isn't an especially useful question. Both theories at times, provide useful ways of looking at the past, and there really is no reason for them to be in conflict.

Unproven Belief

I read the article on page 174-175 by Leo M. Chalupa. This article is about three of the authors beliefs: that the human brain is the most complex entity in the
known universe, that we will eventually succeed in discovering all there is to discover about the world if we live long enough, and that science provides the best means of understanding the world. I will address each of these claims separately. The first statement would be fairly easy to disprove, but is very hard to prove. To prove this false, all that is necessary is finding an object in the universe more complicated than our brain. To prove it true, it would be necessary to observe every object in the universe. The second statement is provably false. Given the uncertainties inherent in logic itself, it is impossible to have a complete understanding of the world. The third part of this statement is the only one that is truly unprovable. I agree that, of the methods we have found, there appears that science is the best for finding the truth, but there very well may be a better one out there.

xkcd comic by Randal Monroe

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Idealogical Immunity

All systems of belief have axioms. These are statements that are hopefully both obvious and fundamental. If chosen well, a simple set of axioms allows one to build up a consistent and powerful system of logic. The problem comes when these axioms are wrong. In formally defining geometry, Euclid based the field off of the following axioms:

1.  A straight line segment can be drawn joining any two points.
2.  Any straight line segment can be extended indefinitely in a straight line.
3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.
4. All right angles are congruent.
5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.

These mostly worked, but as Gauss showed, the fifth is not always true (specifically in spherical or hyperbolic geometries). Euclid's problem wasn't being wrong, but rather creating unnecessary restrictions that narrowed his world view.

Since the beginning of history, humans have tried to create systems of axioms that do not lead to contradictions, and that allow all knowledge to be either proven or disproven. Thanks to Kurt Gödel, one of the best mathematicians of all time, we now know that this is impossible. Any system of logic will, by necessity, either be incomplete, or be completely wrong. I think that the ideas I am ideologically immune to are those that are my axioms for understanding the world. For me, these tenets are:

• For a theory to be true, it must be the one to best explain what is observed.
• If  two theories produce the same results under all circumstances, they are equally valid (and whichever is simpler should be used).
• If something is not measurable (measurable here meaning having definite state), it is not real.

These beliefs are fundamental to the way I approach the world, and I can not think of any evidence that would cause me to change them, because without them I would have no way to interpret other evidence.