The Great Math Mystery

March 23, 2015 1 comment

This is the title of an upcoming NOVA special. The question in the tag line: Is math invented by humans, or is it the language of the universe? It will be interesting to see how they answer that question. My best guess is that the program will conclude by saying that it is a little of both, but the journey to getting there should be interesting.

Here is a video preview and description of the show from PBS, airing April 15, 2015 at 9 pm.

Program Description:

Join NOVA on a mathematical mystery tour—a provocative exploration of math’s astonishing power across the centuries. We discover math’s signature in the swirl of a nautilus shell, the whirlpool of a galaxy, and the spiral in the center of a sunflower. Math was essential to everything from the first wireless radio transmissions to the prediction and discovery of the Higgs boson and the successful landing of rovers on Mars. Astrophysicist and writer Mario Livio, along with a colorful cast of mathematicians, physicists, and engineers, follow math from Pythagoras to Einstein and beyond. It all leads to the ultimate riddle: Is math a human invention or the discovery of the language of the universe?

Enjoy the Pi Day of the Century!

Today, on 3/14/15 at 9:26:53, we celebrate the beauty of God’s creation and his infinite, irrational love for us.

pi day

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The Form of Teaching Matters

January 25, 2015 Leave a comment

A recent article in the Economist entitled “Falling Away” stated the following

Just one extra year of schooling makes someone 10% less likely to attend a church, mosque or temple, pray alone or describe himself as religious, concludes a paper published on October 6th that looks at the relationship between religiosity and the length of time spent in school. Its uses changes in the compulsory school-leaving age in 11 European countries between 1960 and 1985 to tease out the impact of time spent in school on belief and practice among respondents to the European Social Survey, a long-running research project.

By comparing people of similar backgrounds who were among the first to stay on longer, the authors could be reasonably certain that the extra schooling actually caused religiosity to fall, rather than merely being correlated with the decline. During those extra years mathematics and science classes typically become more rigorous, points out Naci Mocan, one of the authors—and increased exposure to analytical thinking may weaken the tendency to believe.

This article summarizes the results of a paper “Compulsory schooling laws and formation of beliefs: education, religion and superstition”, by Naci Mocan and Luiza Pogorelova. National Bureau of Economic Research, October 2014.

There are a number of things of interest in this report. On one level there is the analysis of the impact of schooling on religious belief that speaks to the impact of the formational power educational institutions have on all aspects of our lives, not just our cognitive growth. On another level is the fact that the authors of this report use mathematical and statistical analysis to report their findings and communicate the message that “school causes religiosity to fall” (emphasis added).

In regards to that second level, I make it a point to teach my AP Stats students that correlation does not imply causation. We even have some fun looking at spurious correlations put together by tylervigen.com. That fact is that from a statistical perspective causation has nothing do with the results of the study, but rather the design of the study. The results of this particular study are achieved through the European Social Survey, which is an observational study, thereby lacking the control/treatment groups necessary to conclude causation.

So then, if the researchers are reporting that they believe school causes religiosity to fall, it is because they want the data to indicate that. That fact should be very instructive to us as Christian educators: there is no way to separate your worldview from mathematics, in this case the interpretation of data analysis. Our students need to be brought up with an understanding that this is largely how the discipline of statistics is undertaken, especially in studies reported on in popular media. My hope and prayer is that my students will be more thoughtful consumers of data – that they would have both the Christian wisdom and the statistical tools to truly understand what a study is trying to communicate.

Returning to the first level, that of recognizing the formative power of educational institutions, I would like to share the thoughts of Albert Mohler as he addressed the article on his Briefing Podcast.

This report makes no distinction between the impact of education and the impact of school, now that’s a crucial issue. Those are two different things. Education is about learning, school is about the institutional context in which that takes place. I think there is no reason to doubt that the longer one is in one of the secular school systems of Europe the less likely one is to be referenced as a believer. But the big issue here that isn’t even confronted in this story is the fact that those schools, those institutional contexts, become the very engines for the secularism their here trying to report on and trying to track and measure.

I recently completed a course in my doctoral studies on curriculum development and Dr. Mohler makes a point that seemed to be the theme of my course: there is a difference between schooling and education. Much of what we refer today as education, is really just schooling – the day to day routines and practices of an institutions – and that schooling is what shapes us at a deeper level than simply informing us on what we need to know. I believe Dr. Mohler is right in pointing out that the institutional contexts of education are driving secularism rather than the content that is taught.

The article indicates that as mathematics and science classes become more rigorous, increased exposure to analytical thinking may weaken the tendency to believe. I have written before about the myth of critical thinking in mathematics and I believe that applies here. I truly feel that any mathematician who is honest will tell you that as rigor and analytical thinking increase, the need to believe actually deepens, not weakens. I have even heard this point made by mathematicians who are decidedly not Christian. The more we learn the more we realize what we don’t know, what we can’t know, and we gain a deeper appreciation of the beauty and mystery of the discipline of mathematics.

As Christian educators I hope that what we take from this article is the realization that the form of teaching matters. The practices, routines, and habits of the classroom and the school at large go farther in impacting students than the content that we attempt to pass along. This notion forms the basis of my forthcoming dissertation, so I anticipate writing about it in much greater detail in the months to come. For now let me close with a quote from James K.A. Smith’s book Desiring the Kingdom which has gone a long way in shaping my thoughts on this issue of education v. schooling:

Education is not primarily a heady project concerned with providing information; rather, education is most fundamentally a matter of formation, a task of shaping and creating a certain kind of people. What makes them a distinctive kind of people is what they love or desire – what they envision as “the good life” or the ideal picture of human flourishing. An education, then, is a constellation of practices, rituals, and routines that inculcates a particular vision of the good life by inscribing or infusing that vision into the heart (the gut) by means of material, embodied practices. And this will be true even of the most instrumentalist, pragmatic programs of education (such as those that now tend to dominate public schools and universities bent on churning out “skilled workers”) that see their task primarily as providing information, because behind this is a vision of the good life that understands human flourishing primarily in terms of production and consumption. Behind the veneer of a “value-free” education concerned with providing skills, knowledge, and information is an educational vision that remains formative. There is no neutral, nonformative education; in short, there is no such thing as a “secular” education.

I have a forthcoming article entitled “Cultivating Mathematical Affections: The Influence of Christian Faith on Mathematics Pedagogy,” that will be published in a Perspectives on Science and Christian Faith theme issue on the matter of mathematics that goes into more depth on this topic. I will link to it and share some more thoughts here once it publishes, but for now, I would love to hear your thoughts.

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