Serving Through Statistics

Whoever wishes to become great among you shall be your servant, and whoever wishes to be first among you shall be your slave; just as the Son of Man did not come to be served, but to serve, and to give His life a ransom for many.

~ Matthew 20:26-28

I wanted to do things a little differently with my AP Statistics spring project this year. I found in the past that the cumulative project I assigned in the spring (where students designed an experiment, collected data, and used a statistical inference procedure to draw conclusions) just didn’t hold their interest, and therefore the projects didn’t reflect the students’ best work. You have to keep in mind these are high school seniors getting ready to graduate, their GPA is pretty much set in stone regardless of their grade on this project, and they have already taken (and passed, I hope) the AP Stat exam. For some reason they didn’t want to go the extra mile on this stat project simply because it was an interesting application of statistics. Weird right?

Wrong.

Looking back, as a student I would probably approach the project with the same indifferent attitude. The solution? Make the project something truly meaningful that the students have a vested interest in. Of course this is easier said than done. As I racked my brain thinking of ideas I was blessed to receive this notice from PRIMUS (which I posted here on GodandMath):

The journal  PRIMUS announces a special issue on Service-Learning. Kelly Black, Karl-Dieter Crisman, and Dick Jardine will be guest editing the special issue, inspired by a MAA Contributed Paper Session on this topic at the Joint Meetings in 2011.

Service-Learning connects service to the community with academically-based learning. This is a growing concern on college campuses, sometimes even a mandate, but the mathematical sciences are often seen as a more challenging environment to bring service into the classroom.  In particular, there are only a few resources widely available on this topic specifically geared toward collegiate mathematics.  This PRIMUS special issue aims to provide a significant addition to this literature, with a number of tested ideas in a single volume as a pedagogical resource.

I thought a service-learning project would a be a great way for students to apply what they have learned in the classroom to their local community, and all in the context of serving – a Christian maxim that is easy to sell in a public school environment.

After a quick Google search I cam across the National Service-Learning Clearinghouse and their Mathematics resources. This was a valuable resource for me in planning out this project (especially Mark C. Hampton’s Introduction to Statistics syllabus).

I presented the idea to my students and I was amazed to see how excited they became over the project. They quickly determined the focus of their study: evaluating the aid provided to victims of Texas wildfires from last summer. The wildfires had come through our county and affected the lives of many of the students, their family, and their friends. I believe the ownership the students felt in selecting a topic so close to their hearts, as well as the incentive of presenting their results publicly (a commitment was made at the beginning of the project to present the results before the city council and to publish them in the local paper), truly made the project more meaningful. This resulted in motivated and dedicated students, new and interesting learning opportunities, and one amazed teacher.

I knew my students were awesome, but this brought it to a whole new level.

For more details on the organization and implementation of the project I invite you to visit Navasota ISD’s Teaching and Learning Blog for a nice write-up. Below is a video that the district so graciously put together:

I also had the fortune of being a finalist for the HEB Excellence in Education Awards. As part of the awards program, a film crew surprised me in my classroom and did an impromptu interview on this project. Below is their completed video:

If you would like more details, I will be giving a presentation over this project at CAMT (Conference for Advancement in Mathematics Teaching) this summer. Here is a link to the online catalog with the description of “Serving through Statistics.” Below are the mathematical/pedagogical goals of this presentation:

The goal of this presentation is to equip participants with the tools to successfully implement a project that synthesizes the major concepts of AP Statistics: experimental design, data analysis, and statistical inference. Through this project students will integrate their conceptual understanding of statistics with the practical functioning of their local community, ultimately gaining a deeper appreciation for the role statistics plays in the organization and evaluation of service societies.

My hope is to implement more projects like this next year and to begin expanding them to the other subjects I teach.

Geometry, I have you in my sights…with this idea.

Black Swans and God Incarnate

Image from Black Swan Ministries

Black Swan as a term derives from a Latin expression that characterizes something as being  “a rare bird in the lands, and very like a black swan.” When the phrase was coined, the black swan was presumed not to exist. The importance of the simile lies in its analogy to the fragility of any system of thought. A set of conclusions is potentially undone once any of its fundamental postulates is disproved. In this case, the observation of a single black swan would be the undoing of the phrase’s underlying logic, as well as any reasoning that followed from that underlying logic.

This Latin phrase was a common expression in 16th century London as a statement of impossibility. For a long time Europeans believed that all swans were white. That notion only held true as long as their discovered world contained only white swans. At the time,  all historical records of swans reported that they had white feathers. In that context, a black swan was impossible or at least nonexistent. Then Australia was discovered and along with it, the existence of the black swan. The term metamorphosed to connote that a perceived impossibility might later be disproven.

Upon this event, perceptions of the world and what swans were had to change.

A Black Swan event is any event that occurs outside the realm of expectations. Black Swan events were characterized by Nassim Nicholas Taleb in his book, The Black Swan. Taleb regards almost all major scientific discoveries, historical events, and artistic accomplishments as “black swans”—undirected and unpredicted. Taleb asserts in the New York Times:

What we call here a Black Swan (and capitalize it) is an event with the following three attributes. First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Second, it carries an extreme impact. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable.

I stop and summarize the triplet: rarity, extreme impact, and retrospective (though not prospective) predictability. A small number of Black Swans explains almost everything in our world, from the success of ideas and religions, to the dynamics of historical events, to elements of our own personal lives

Black Swan seems to be a relatively apt statistical description of the incarnation. When gathering resources for this post I even came across Black Swan Ministries who also recognize this connection. I’d briefly like to address Taleb’s three criteria for categorizing something as a Black Swan (with a slight change in wording on the last point).

Rarity

Obviously the incarnation is an extremely rare event: having occurred once in history. To further discuss this point, I’d like to make mention of The Logic of God Incarnate, a work by Tom Morris.

This work is a response to John Hick’s Myth of God Incarnate. Hick attacks a Chalcedonian Christology which affirms that Jesus is fully divine and fully human: two natures, one person. Hick’s objection falls along these lines: God is omnipotent, omniscient, omnibenevolent, eternal, immutable. Humans are limited in power, limited in knowledge, limited in goodness, temporally constrained, changeable. God is perfect. Humans are imperfect. Therefore it is logically incoherent to say that Jesus is God incarnate – no being could be both perfect and imperfect, both fully divine and fully human.

On Hick’s view it is not possible to have the two natures of the divine and human because they comprise incompatible attributes. If his premises are right, then his argument is true. But since the conclusion of his argument is false, there must be something wrong with his premise.

Hick’s argument begins by assuming being perfect is essential to divinity. God could not have failed to be perfect. This is true.

His argument also assumes that imperfection is essential to humanity, but is it? Morris argues this is wrongheaded. The essence of a “thing” is the set of properties which are individually necessary and jointly sufficient for being that thing; if you lack any one of those properties then you are not that thing. Hick assumes that the each of the properties listed under being human are part of the set of properties that are essential to being human and this is what Morris attacks.

Morris makes a difference between nearly universal properties and essential properties. Nearly universal property is one that almost every member of a kind possesses, but isn’t necessary for that thing. Case in point: having white feathers was a nearly universal property of swans, but it wasn’t essential to being a swan. Being limited in power, limited in knowledge, limited in goodness, etc. are nearly universal properties: Christians believe there is one human being in history who was human but lacked the property of being limited in power, limited in knowledge, limited in goodness, etc. Jesus of Nazareth.

Impact

To Christians, this category goes without explanation. But let’s try anyway…

As purposed by God, the eternal Son of God (Isa 9:6; John 1:1-2; 8:58; Col 1:17; Heb 1:10-12; Rev 1:8; 21:6) came into this world that He might manifest God to men, fulfill prophecy, and become the Redeemer of a lost world. To this end He was born of the virgin, and received a human body and a sinless human nature (Luke 1:30-35; John 1:18; 3:16; Heb 4:15). He was completely, 100% deity (John 1:1, 18; 10:30-33; 20:28; Rom 1:3-4; 9:5; 1 Cor 15:45-49; Phil 2:6-8; Titus 2:13; Pet 1:1). He was also completely, 100% human (Matt 13:55; John 1:14, 19:5; 1 Tim 2:5; Heb 2:14).

Jesus Christ was incarnate. The eternal second person of the Godhead entered space and time and became man for us and for our salvation (John 1:1, 14; 2 Cor 8:9; Phil 2:6-8; 1 Tim 3:16). He was miraculously born of a Virgin and the Holy Spirit (Matt 1:18-25; Luke 1:26-38). He led a sinless life (2 Cor 5:21; 1 Pet 2:22; 1 John 3:5) of perfect obedience to the Father (John 6:38; Rom 5:18-19; Phil 2:8). He spent His life preaching, teaching and performing miraculous wonders to evidence His divine mission and to proclaim the new advent of God’s kingdom (Matt 4:23-24; 7:28-29; 9:35-36; John 20:30-31). In the fulfillment of prophecy, He came first to Israel as her Messiah-King, was rejected of that nation (John 1:11; Acts 2:22-24), and gave His life as a ransom for all (1 Tim 2:6).

Jesus Christ was crucified as a substitutionary atonement for sin. On the cross in Christ, God bore the just penalty for the world’s sin, satisfied His justice, and thus made a way for reconciliation (Isa 53:4-12; John 3:15-17; Rom 3:21-26; 5:6-11; Heb 2:14-17). It was necessary for Him to be both true God and true man in order to redeem (1 Tim 2:5). As man, He represent us (Heb 4:15) and as God He saves us (Heb 7:24-25).

Belief in the divinity of Christ is a prerequisite of salvation (Rom 10:9; 2 Peter 1:3) and to deny His humanity is to be labeled the antichrist (2 John 7).

Retrospective Recognition

Gospel writers quote the Old Testament to show how Jesus in his life and ministry fulfilled the Old Testament Scriptures (Mat 21:4-9; Mar 11:7-10; Luk 19:35-38; Joh 12:12-15). Matthew includes nine additional proof texts (1:22-23; 2:15, 17-18, 23; 4:14-16; 8:17; 12:17-21; 13:35; 27:9-10) to drive home his basic theme: Jesus is the fulfillment of the Old Testament predictions of the Messiah.

Jesus himself makes this clear:

Beginning with Moses and with all the prophets, (Jesus) explained to them the things concerning Himself in all the Scriptures (Luke 24:27).

All the Scriptures center about the Lord Jesus Christ in His person and work in His first and second coming, and hence no portion, even of the Old Testament, is properly read, or understood, until it leads to Him.