### NCTM Presentation: Assessing Conceptual Understanding

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Below are resources related to NCTM Presentation: Assessing Conceptual Understanding (# 457; room 258B, BCEC)

Editable .docx: Conceptual Questions NCTM

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

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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:

demand

Making Airplanes

### Creating a projectile motion still

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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.

http://youtu.be/eXJ-nc2AJb4

### What Is My Main Goal of My Calculus Course

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I recently ran into a student that I taught during my first year of teaching (ten years ago) what he remembered from my Calculus course. He remembered the word derivative and that we had to do problem sets and if he did well on those he would do well on the tests. But he didn’t really remember any “Calculus”. He works in marketing and- I assume- does not need to use any of the rules, theorems, or formulas particular to Calculus. But, I bet he has a better appreciation of the concept of change because of my course, even though he might not attribute it to my course; at least I hope he does.

So, What do I want my students to remember five or ten years after they leave my course? Really the question I am asking is “What is my main goal in my calculus course?”

For me, the answer is change. Algebra 2 and PreCalculus are about functions and points on a graph (I don’t love that description, but its serves my purpose), while Calculus is about the change at those points. Imagine Algebra 2 is about the point, and Calculus is about the slope at that point. So, as we returned from Spring Break- and were technically in the middle of our unit on the Fundamental Theorem of Calculus- I tried to gauge what my students remembered about Calculus after ten days away…

They looked in their notes and said things like chain rule, fundamental theorem of calculus, derivatives, and change. They also have every standard example in their notes (think volume of a balloon for related rates) that they can use in future Calculus courses as a resource (I have anecdotal evidence that they refer to these notes in college), but as I tried to dig deeper into what this course engrained in them, I was not sure that more than a few understood what I meant by change.

SO, I talked to a physics teacher who was excited to collaborate. I borrowed some “logger pros” and Vernier sensors to begin a two-day task/project/lab/experiment. Here it is:

The outcome of this “task” will be to:

• describe a movement in words
• By hand, graph:
• distance vs. time graph of the movement
• velocity vs. time graph of the movement
• acceleration vs. time graph of the movement
• demonstrate the movement
• use the “logger sensors” to create an actual capture of the movement, including distance, velocity, and acceleration graphs
• verify that the description, movement, and graphs all correspond
• determine a means to present this information

We are going to spend two days on this task, then return to our normal progression of finding area between two curves. But for these two days we’re going to try to see if we can reinforce what I believe to be the central theme to Calculus.

Maybe in ten years, they’ll remember this.

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

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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

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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.

• 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.

### Disruptive Innovation Transforms

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“There is an indirect relationship between the number of times an institution uses the term Innovation and how innovative the institution actually is.”

I came across a New Yorker article from the summer (linked here) that applied concepts from Clayton M. Christensen’s 1997 book “The Innovator’s Dilema” to the current culture of technology, start-ups, and education. Christensen’s premise is that innovation takes two forms: sustaining innovation and disruptive innovation. Sustaining innovation is analogous to R&D- it is based on improving the current product. Disruptive innovation is blowing up the system; it means starting from scratch or reinventing.

The article, written by Jill Lepore, briefly discusses the history of Harvard University and the introduction of Massive Open Online Courses. These courses were thought to open up opportunities for anyone not able to attend Harvard, and to be substitutes for the courses taught there. But are MOOCS, or online learning in general disruptive? Is teaching a hybrid class disruptive? Or are current trends innovating education simply sustaining innovation?

What would a true disruptive innovation to education look like?