What makes better mathematics teachers? A Cross sectional analysis of the United States

A student of economic history will tell you that a fall in technological advancement is foreshadowing for the collapse of the empire. While today the US remains a world leader in technological advancement, there is a fear that over time this will change due to the US falling behind the rest of the world’s ability to innovate. This is a threat to the US’s economy and public safety In 2013 The Program for International Student Assessment (PISA) released data comparing the academic achievement in math, science and language of 15-year-old students in 65 countries. While most of the countries have improved their scores from the previous test time (2009), U.S. students’ performance stayed flat – they were ranked 36th in math, 28th in science and 24th in language. This is below most of the advanced and some developing economies, and significantly below the OECD average (PISA benchmark). Yet, according to The National Center for Education Statistics, the United States spends well above the OECD average level of expenditures per student for all levels of education. A burning question that many politicians, educators, and researchers ask nowadays is: why is such an advanced country not performing up to par? In addition many fear that this decline in academic achievement is foreshadowing a decline in the US as a world leading innovator and super power.

The purpose of my research is to discover what works in regards to teachers in bettering the mathematics education of students. This research will study the effects of teacher’s certifications and licensing on mathematics performance. In addition it will examine the effects various government actions and requirements on a state-by-state level. The goal of this research is to understand what is working in the US, in the hopes that it can shed light on ways that the US can reform its education system in order to maintain itself as a world’s innovator.

A study by Dan D. Goldhaber and Dominic J. Brewer shows that there was no statistically significant difference between student mathematic achievement taught by teachers with a MA or PhD, however there was a significant, positive difference between students taught by teachers with a degree in mathematics and those taught by teachers whose degree was outside of mathematics. In addition they found that “mathematics students who have teachers with emergency credentials do no worse than students whose teachers have standard teaching credentials, all else being equal.” This suggests that standard certification may not be effective in raising mathematics achievement.

However a study by Linda Darling Hammond at Stanford University suggests that there is a positive correlation between masters degrees (or higher) on student performance. This study also found similar results to the Goldhaber and Brewer study, that students with teachers who have a degree in mathematics experience an increase in their scores. In fact they found a significantly stronger correlation for students taught by teacher with extensive mathematics coursework.

This study will be a cross sectional multiple regression analysis of the United States using mathematics achievement as the dependent variable. I intend in using SAT math scores, so long as College Board accepts my request for the data. If not I have found suitable back up data (from the NCES), although it may limit my study due to the fact that is it only available at the state level, unlike the SAT data that could be available by county, which would allow me to analyze significantly more variation.

Some possible independent variables for the model are teachers with a masters degree or higher, teachers with an education degree, and teachers with a degree in mathematics. In addition dummy variables will be created to measure the effects of different state requirements for teachers. I will control for gender, ethnicity, family income if possible, student teacher ratios, and expenditure per student and various other factors data permitting. It is important to note that all studies that I have encountered have found significant differences in performances of various races, genders and family incomes, thus justifying my control variables.

I believe students taught by teachers who hold graduate degrees (masters or higher) will not out perform other students in mathematics. Instead I believe that students taught by teachers with a specialization in mathematics will out perform those who are not. Additionally I believe that students in states with stricter requirements for teacher’s certification will perform better.


Blog Post #1: The Implications of a Global Financial System

Today we live in a global society.  The Internet allows us to communicate instantly from anywhere around the world and people and goods can be moved around the earth at speeds unfathomable by people just one century ago. With this comes a global economy. There are trade connections all around the world that are growing increasingly stronger, and human society is becoming increasingly dependent on this. This leads me to the topic of my research, The Implications of a Global Financial System. I raise the questions, if financial institutions are so interconnected, what risks does this pose to the systemic health of the global financial system? What can the bankruptcy of one “Systemically Important Financial Institution” or SIFI, mean for the overall Financial System? I plan to answer these questions using network analysis derived from graph theory and game theory.

Graph theory is the study of how connections between things can be visually structured and their properties can be measured. It is useful in network analysis in order to view the structure of the network and how it affects the other members of the network. Graph theory has been the epicenter of the research done by my advisors Prof. Quintas and Prof. DuCasse for many years now.

Game theory the analysis of strategies for dealing with competitive situations where the outcome of a participant’s choice of action depends critically on the actions of other participants. Game theory will help us better understand how different financial institutions will act in the network they create.

By understanding the structure of the network created by financial institutions, and the way they interact with each other I am developing a model of the global nature of the financial system. Through this cross discipline analysis I believe it is possible to better understand how financial system functions as an aggregate and potentially discover a way to create a safer financial network.

I am conducting my research currently by studying more advanced topics in graph theory and game theory in order to expand the depth of my knowledge. This will help me model the financial system in the most articulate and accurate way.  I am also studying the different methods in which economists measure exposure amongst financial institutions. Ultimately the plan for my model will be creating a graph where the nodes are financial institutions and the edges are weighted based on financial exposure. I will use this model to study the implications of exposure in the financial system and to discover how this can affect the health of the overall financial system.

In order to supplement my research with an example, I plan on conducting a case study using my model based upon The 2008 Financial Crisis, arguably triggered by the collapse of Lehman Brothers. I plan to evaluate the interconnected nature of Lehman Brothers and model the contagion their collapse caused in the financial system.