Quantitative Methods

“Quantitative Methods” is a term that encompasses mathematical methods that model and predict observable and unobservable phenomena from engineering to financial valuations.

The NEW mathematical tools of Education Administration

The NEW mathematical tools of Education Administration

Research in education is finally approaching the next level, and judging by my graduate classes in statistics, we’re going to need some incredible brain power to use these new methodologies.

First and foremost on the VAM (Value-Added Modeling) for evaluating teachers, schools, and districts, the premiere tool is called HLM (Hierarchical Linear Modeling). To use this software reasonably well, you need about two courses in basic statistics, a course of linear regression, and another course of multi-level modeling. It’s a pain in the arse to interpret the numbers that come out of these models, but if you can do it, you can probably work for anyone from Operations Research departments to Goldman Sachs. As a quick summary, if you input last year’s scores, students’ socioeconomic status, gender, race, parents’ education, etc. then you should be able to predict a student’s score the following year. In companies if you plot the productivity vs. sick days used, chances are you’ll see a relationship in the data. If you’re working through multi-level regression work, I’ve found these resources that carried me through a few homework assignments as well as a midterm:

Multilevel Regression Modeling Resources

Probability has also become a major focal point for estimating how random characteristics of schools, teachers, and students can be modeled. For a great introduction to probability theory, Ross is the major book that all beginners seem to find the most appropriate:A First Course in Probability (8th Edition). The major takeaway from probability theory is the “probability distribution.” For the best possible overview of the interconnectedness of this (insanely) difficult topic (well, at first…), this paper is a beautiful graphical organizer. Anyone who begins this little tumble down the rabbit hole will also be drawn to Bayesian Data Analysis. You’ll also probably need to get a good grip on R (the programming language) as well… So, if this is you and you’re trying to figure out this mess of Bayesian analysis (also related to Artificial Intelligence, Neural Networks, and forecasting), you’ll probably want this book with the cute little puppies on the front:

Finally, IRT (also known as Item Response Theory) is how they grade the SATs. CDM (Cognitive Diagnosis Modeling) is an evolution of IRT and is the umbrella concept of the multifaceted models that have arisen to explain the ways we can test for specific skills. It is extremely complex and requires algorithms such as the Expectation-Maximization Method or Maximum Likelihook methods (which again, require insane amounts of statistics training in probability and inference).

If you’re looking into developing a strong program in statistical analysis in education, this is your foundation. Policy and management aside, this is how to extract the data that is required to make policy arguments. If your superintendent isn’t aware of these tools, it’s time to go to a board meeting.

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Transitions…

Transitions…

This day is usually filled with brooding…

Strolling back into a high school after a 2 month vacation and seeing your coworkers is a happy occasion that gets quickly thrown to the side as socially ardent teenagers quickly smash through the doors and shout to their supporting cast of boisterous pseudo-hooligans while we make our opening speeches. Teaching is honorable… and our abilities of crowd control are rarely acknowledged.

Today, for me, began with a text from my coworkers… cursing me from their annual re-insertion into public sector protocol while I lay in bed thinking about how best to mentally prepare for my 6:30-9:30pm graduate class on Probability. My daily stress level during the “school year” has officially plummeted from an 60/100 to a 20/100. My advisor has even shunned my overzealous work ethic and told me to “settle in” to my schedule. Wanna know my schedule that needs settling into? M 4:30-7:30pm, T 6:30-9:30pm, W 4:30-7:30pm, & Th 4:30-7:30pm. I think I’ll hit the gym during the days that I work on my comfort level.

Now, it’s not all easy. Specifically, I have very little experience with this new form of statistical mathematical notation. The language of math of physics is much more visual and robust. We don’t randomly insert a vector term unless there is a physical property that includes direction… whereas, statisticians can randomly insert and fit an extra nominal term within a model that has no physical interpretation; it’s just data. It is data that may or may not be important. Rarely do physicists do anything “extra.” We are barebones, brute force mathematicians that learn the elegant tricks when we have to. So my prediction is that this change in philosophy is going to carry my forehead into the figurative brick wall as I glean the nuances of Item Response Theory and Hierarchical Multilevel Analysis.

On another note, my fourth class in “Teacher Evaluation” is going to require a great deal of empathy. Subjective/Qualitative Evaluation is farthest thing I’ve ever witnessed from a hard science that attempts to portray itself as an evolved, structured analysis. I have a feeling that I’ll be making hand waving arguments and laughing at the false pretenses of administrators. Nearly every paper on teacher evaluation that I have ever seen, shows that local administrators show extreme bias in their evaluations… so much so that third-party university professionals are usually called in to “correct” for the skew in qualitative data. Sadly, qualitative data is still the only evaluation method my former colleagues and I have ever been subjected to.

 

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My psychometric training

My psychometric training

I’ll be blogging about my graduate training in psychometrics at Rutgers Graduate School of Education under the direction of Dr. Jimmy de la Torre.

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Applied Science and Math…

Applied Science and Math…

I earned a Ph.D. in Physics in May, 2007. I applied extensive analysis to nuclear scattering data in collaboration with international scientists in the federally funded BLAST experiment which took place at MIT.

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