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.

Read More