# Education

### NCTM Presentation: Integrating Authentic Economics Applications into the Math Classroom

These are the resources that will be presented on Saturday at 11:00 (room 108 in BCEC).

Handout: Economic Applications NCTM

Slides: NCTM economic applications

Extra Resources:

### Creating a projectile motion still

As a class project, a student wanted to calculate the velocity of a marker being thrown into the trash. He calculated the time it took the marker to hit the trash after he released the marker and the distance to the trash. This is the horizontal average velocity, so I asked him to go further. The image below is a projectile motion still and a quick desmos graph of a parabola of best fit. Now he has an equation for height… his task is to determine the vertical velocity.

Below is a link to a video of how I created this image.

### Hybrid Microeconomics Part 2 of 3: Early Reflections

Five week into my hybrid AP Microeconomics course, we had our first major test. Having only met in person four times, I was anxious to see the results. The test was marginally more difficult than the same one given to my “face-to-face” AP Microeconomics course this fall. The results were better than my students from the fall!

My first major realization is that the students are very much actively engaged with the material; there are readings, workbook activities, videos, and online quizzes. In a traditional class, students may have been able to not thoroughly complete their reading or problems, then coast through a 40-minute class. During our in-person sessions, the students have more thoughtful questions because they have confronted the material on their own; they make connections, ask insightful questions, and anticipate concepts.

I used a LMS (Canvas) in the fall with my face-to-face course, but students rarely used the resources- Canvas tracks student hours logged on and it was minimal in the fall. This spring, the online resources have been more robust and students need to take online quizzes, so inevitably the usage will be more, but its not that I notice increased usage, I notice increased engagement. An example is an discussion board thread that was complete (students were asked to define some vocab words and did), then a week later I noticed that it was highlighted as “unread.” When I looked, a handful of students continued the conversation. They were asking about subtleties from the text and how some definitions seeming contradicted each other. Granted this was a subset of the class, but these five students were going beyond

their required engagement with the concepts and really wrestling with ideas that can be difficult and deepening their understanding by explaining examples and different ways of thinking about a problem or idea.

So the quantifiable results are at minimum on par (probably better, but small sample size), but the student engagement with Microeconomics is clearly through the roof. These students are becoming *active* learners; a skill as useful as the economics they are learning.

### Hybrid Microeconomics Part 1 of 3: About the Course

I am teaching a hybrid AP Microeconomics course this spring. This is the first of three posts describing my experience teaching this course. The first is the basics about the course. Attached is a FAQ that I sent to students before the class began.

**About the Course: AP Microeconomics**

- This is a one-semester course.
- It is a hybrid course where students meet once every six school days and complete online readings, activities, and assessments.
- The goal was to add the opportunity for students to fit the course into their schedule and to add the flexibility to students’ workload.
- Students are expected to complete about an hour’s worth of work each day (equivalent of 40 minute class plus 20 minute homework).

**Resources**

- Students use the Learning Management System Canvas.
- Students read from Mankiw’s Principles of Economics textbook.
- Students complete workbook activities from Stone’s AP Microeconomics Resource Manual.

**Course Meetings**

- Students meet in small groups in occasionally non-traditional locations (ie. library or breakout room)
- The schedule was challenging to coordinate everyone’s availability, given that we did not have a dedicated meeting time.

**Assignments**

- There are five major resources that we use:
- Videos (short bursts of information)
- Textbook (longer and more theoretical)
- Workbook & Handouts (focusing on mechanics)
- Class (connecting dots and filling in the blanks)
- Discussion Board (with threaded answers to questions, both conceptual and vocabulary)

**Assessments**

- Students take online quizzes to test for basic comprehension and completion
- Students take in-person quizzes and tests by scheduling a convenient time.

### An Election: Heads vs. Tails

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 3^{rd} 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

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?

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.