Latest Event Updates

The Schedule Makers

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http://espn.go.com/video/clip?id=9897968

I always assumed Major League Baseball’s schedule was constructed using some intense algorithm. It seems that for twenty-five years MLB used human intuition to construct their elaborate schedule. It seems like now programming and computer programming sophistication has caught up.

This is a worthwhile twelve minute video by ESPN’s 30 for 30 series (directed by Joseph Garner). Also a worthwhile graph theory application.

New website: withrespecttox.com

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My new website geared primarily towards math education has launched: withrespecttox.com

The title is With Respect to x, which references differential calculus (take a derivative with respect to x).  It also alludes to one of Algebra’s primary concepts: the variable. Respect the variable! 

I will continue to use this site for economic, education, and sports commentary.  Most of my site’s traffic is on math resource sites and it is easier for me to update a site based on my profession.  So, please visit my new site: www.withrespecttox.com.

WRTx

Hashtag Math

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Last year as a test review, I asked my students to categorize problems.  Beyond knowing the mechanics, I want my students to know the when and why. Thus I asked them to tell me what “big theme” each problem represented.  With a set of review problems, I began to #hashtag the problems. Two examples are shown below:

Screen Shot 2013-11-14 at 8.23.38 AM

Screen Shot 2013-11-14 at 8.25.28 AMI have no scientific research showing that this helps my students make connections and categorize concepts, but they certainly remembered and enjoyed hashtagging math problems!  This is a technique I plan on continuing and is worth considering beyond just review.  At minimum, hashtagging in class was unique, so it stood out as something special.  Their favorite was #factoredform, so I wonder how long until its trending?

Challenging Routine

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Two months ago, as the school year was beginning, I read a handful of articles discussing the correlation between productivity and routine.  Business journals, blogs, tweets, and newspapers praise the importance of routine.  Wake early, exercise, browse headlines before leaving for work.  Work on creative tasks in the morning and mechanical tasks later in the day.  Make lists and wind down before sleep.  Setting a routine and completing tasks based on that routine would certainly make anyone more productive.

Whether we consciously follow a routine or not, we all have daily patterns.  As a teacher, my class has a routine; over time patterns emerge and habits form.  Deviations from our routine signal importance. We are doing something different for a reason.  I hope to encourage my students to realize that changes signal importance.  I hope to say: “Hey look, we are doing we are doing something different!”

Those moments only happen when the routine is broken.  This past summer, my day-to-day routine changed as I worked for a summer program on a rural college campus.  I had to run at different times of the day and worked until later in the evening.  My entire routine- mental and physical- changed and my body responded as if to say: “Hey look, we are doing we are doing something different!”Image

Ultimately, a routine will put us into a position to complete our daily tasks and be productive.  But those moments of innovation or ideas sparking in our minds will only happen if we consciously break our routine.  Consider Google’s “20% time,” which is the one day per week that employees spend time working on side projects. This time is a structured (our routine) break of routine.  This time has been lauded as the nest egg of innovation.

Personally, this blog is my opportunity to break away from my day-to-day routine of teaching, coaching, and economic researching.  I need to make this break of routine a common activity; it is an opportunity for me to think through issues and current events and put my thoughts on “paper.”

Breaking away from our day-to-day habits gives us opportunity and the signal that our task is worth the time.  Within the framework of the routine encouraged by productivity experts, we can incorporate intentional breaks to signal importance and generate opportunities for growth.

An Election: Heads vs. Tails

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Yesterday during a tangent in my Algebra 2 class I realized how little understanding my students had about the voting process as well as how predictions are made and how, when, and why networks announce winners without all of the votes counted.

Today, I ran an activity that pitted Heads vs. Tails. Each student received a penny and flipped the coin to determine their vote: Heads or Tails.  The class consisted of 19 students.

In our first election, we strictly counted votes- a popular election.  Tails beat heads 10-9.

In our second election (everyone re-flipped their coin), the girls announced first: tails 6 and heads 5.  I asked our students, what do we EXPECT to happen with the remaining 8 votes?  Assuming fair coins, we expect 4 for heads and 4 for tails.  So if we had to bet, would we bet that heads would win or tails? Since tails already had a 1 vote lead, tails was most likely to win.  In fact, the scenario most likely to result in a win for heads was 5 heads and 3 tails.  This was not a probability class, but with some basic concepts we could have given percentages to each outcome.

Back to this specific election:  With only the girls reporting, the vote was 6 for tails and 5 for heads.  I asked one boy to announce his result.  He flipped tails, so the vote count was 7 for tails and 5 for heads.  I declared, “I am ready to call the election for tails!”  The students protested; there were 7 students still left to vote.  Could heads have come back and won?  Yes, but this was unlikely since 5 of the 7 remaining flips would need to be heads.  We counted the votes and tails won 10-9 (4 of the 7 remaining flips went to heads).  I did not have a specific percentage in mind when I “called” the election (the real chance when I declared tails victorious was around 75%, but I wanted to make a point).  We discussed how, when, why (and the implications) newspapers and television stations “call elections.”

In our third election, I told the class that the front row (5 students) always voted heads and were going to vote for heads again.  With 14 students left to flip, I said that I had enough information to call the election and was sure heads would win.  Again, with the likelihood around 75% that heads would win, there was a decent chance tails could come back, but again, I was making a point.  We then discussed how this activity mirrored the Electoral College with states like California consistently voting democrat.

Finally (and I did not have time to do this election), I was going to weight each row differently.  The first row would vote and their winner would receive 4 votes, the winner of the second row would receive 3 votes, the 3rd row two votes and the back row one vote.  I was going to have each row announce in order 1-4, then redo this system with the back row announcing first.

Please leave a comment if you have any ideas on improving this exercise or need any help implementing it in your class.

The Role of Gender and Tracking in Student Achievement at the Extremes

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The following is the abstract of a recent paper I wrote analyzing student performance data. Here is a link to the entire paper.

http://dl.dropbox.com/u/33186846/Student%20Achievement%20at%20Extremes.pdf

Measurement of student achievement is at the heart of educational policy and standardized testing has been both supported and contested as a genuine representation of student achievement. This study shows that the interpretations of standardized testing may have starkly contrasting meanings for different cohorts of students. By using quantile regression to account for conditional PSAT scores, educational factors such as gender and tracking are shown to effect students in varying ways. For the students in this study, gender was a significant indicator of performance on the PSAT test, with being male accounting for more than a five point “bump.” The conclusion from the quantile regressions is that students with extreme PSAT scores are outliers based on ability or inability, not because of their gender. Meanwhile, students that participated in the “honors” tracking system had more of an increase in their predicted score the higher their conditional PSAT score.

Education: Skills or Signals?

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It’s that time of year when almost 100 million Americans go back to school.  Yes, approximately 25% of the US population is enrolled at least part-time as a student at some level of kindergarten through graduate programs.  My question is whether these students are learning skills applicable outside of the classroom or are they just earning credentials for their resume?

The easy answer is both, but I would argue that after initial universal skills are learned, education acts as a signal of ability to comprehend and analyze. It is important to distinguish between learning a skill, such as the ability to problem solve, versus signaling that you have the ability to problem solve. Before going too deep, an example should clarify the difference.

Consider high school math, in Algebra or Geometry a student may learn the skill of deductive reasoning and problem solving. Then a few years later in Calculus, the students signal that they have the requisite skills needed to comprehend Calculus concepts. Note that this signal (the ability to understand Calculus) may not be an applicable “life skill,” but if you ask a college admissions officer they would tell you it is quite valuable to signal to colleges that you are able to complete a Calculus course.

What skills will be acquired in schools this fall that will be applicable? Obviously basic reading, writing, and arithmetic are necessary skills learned in the lower grade levels. Once these skills are mastered, the second level of thinking comes into play. That is, using factual knowledge to solve problems.  Finally third level thinking, including synthesizing (or combining) knowledge from various sources to derive original thoughts and conclusions. The last two “levels of thinking” are not necessarily taught on their own, yet students acquire these skills through high school and these attributes are the base argument for a “liberal arts education” promoted by colleges.

So, when does education stop being skill based and start becoming a signaling device? My conclusion is that this balance transfer occurs in the midst of the traditional high school years. The American high school curriculum (including calendar and schedule), include many requirements that act as hurdles. Also, many advanced graduate programs fail to provide students with necessary skills. These degrees simply act as acknowledgement that a student has read the core literature of a field and does not enable students to go out into the world ready to produce original ideas.

Below are two graphs that I believe represent traditional educational paths for American students and the subsequent returns of skill development from that education. The first graph represents a student whose returns to schooling are negative, that is each year fewer skills are acquired.  Unfortunately, I believe this is the path of the majority of American students.  The second graph represents a student that take a career orientated path and ends their education in a trade school or college or graduate program that gives the student real skills to be applied outside of the classroom.

If we want education to have meaning for our students, we should gear curriculum to achieve the second path shown above.  Ideally, we could create a skill development graph that is a horizontal line where students are constantly acquiring applicable skills. This may seem far off, but if we want our future citizens to be equipped to face the challenges of an ever-changing economy and job market, we need to be sure that they are prepared with applicable skills, not a diploma that recognizes that they jumped through the appropriate hoops.