Sig Harden - Academia.edu (original) (raw)

Papers by Sig Harden

The American Biology Teacher, 2014

Optimal foraging theory is a principle that is often presented in the community ecology section o... more Optimal foraging theory is a principle that is often presented in the community ecology section of biology textbooks, but also can be demonstrated in the laboratory. We introduce a lab activity that uses an interactive strategy to teach high school and/or college students about this ecological concept. The activity is ideal because it engages students in a hands-on activity that teaches them a fundamental ecological principle; it can be completed in a short class period; and it utilizes a few inexpensive, easy-to-purchase supplies.

Journal of the Alabama Academy of Science, 2009

The American Biology Teacher, 2014

In 1858, Darwin published On the Origin of Species by Means of Natural Selection. His explanation... more In 1858, Darwin published On the Origin of Species by Means of Natural Selection. His explanation of evolution by natural selection has become the unifying theme of biology. We have found that many students do not fully comprehend the process of evolution by natural selection. We discuss a few simple games that incorporate hands-on activities to demonstrate to students this important aspect of biology.

At some point in their mathematical training, most teachers encounter the Witch of Agnesi. The Wi... more At some point in their mathematical training, most teachers encounter the Witch of Agnesi. The Witch, a plane curve named and studied in the mid-1700s by the Italian mathematician Maria Agnesi, is constructed as follows: Center a circle with radius a at the point (0,a). Choose any point A on the line y=2a and connect it to the origin O with a line segment. Label the point where the line segment OA intersects the circle as B. Let P be the point whose x-coordinate is the same as point A and whose y-coordinate is the same as point B.

The International Journal of Interdisciplinary Educational Studies, 2014

Interdisciplinary endeavors, those that cross traditional academic boundaries, are burgeoning, as... more Interdisciplinary endeavors, those that cross traditional academic boundaries, are burgeoning, as the benefits of teaching across the curriculum, collaborating across disciplines, and addressing subject matter from multiple perspectives increasingly are recognized. Overcoming administrative and structural constraints, such as allocation of faculty workloads and course length, are challenges that require creative solutions. Our approach incorporated expertise from three departments, psychology, biology, and history, which produced a biopsychosociohistorical perspective that was interdisciplinary with transdisciplinary features. An undergraduate student's A/V presentation in one class formed the basis for an applied group project in another class, and included a pilot study. Our approach and example are described, as well as benefits to students, faculty, and administrators, and pedagogical implications.

Australian Senior Mathematics Journal, Jul 1, 2010

Australian Senior Mathematics Journal, 2009

A s teachers of first-year college mathematics and science students, we are constantly on the loo... more A s teachers of first-year college mathematics and science students, we are constantly on the lookout for simple classroom exercises that improve our students' analytical and computational skills. One such project, Predicting Precipitation in Darwin, is outlined below. In this project, students: • analyze and manipulate raw precipitation data; • build a prediction model using a Markov chain; • predict the long term distribution of precipitation-free and rainy days in Darwin, Northern Territory, Australia; • use a chi-square test to evaluate the effectiveness of the model they have constructed; • improve their prediction model. Beyond access to the Internet (to obtain the raw data) and a computer spreadsheet program or calculator, no special equipment is required. If the data is downloaded in advance, a well-prepared junior or senior high-school mathematics (or science) class should be able to perform this exercise in approximately 30-45 minutes of class time. Mathematical preliminaries: Markov chains A Markov chain is a sequence of identical trials, each of which can result in exactly one of a finite number of outcomes, called states. As the trials progress, the probability of moving from one state to another depends only on the state in which you are currently found. In most applications, Markov chains are represented by a state transition matrix, P. In this matrix, the entry in the (i,j)th position (row i, column j) is the probability that you will move to state j in the next trial if you are currently in state i. Properly constructed, the sum of each row in the matrix is one. Due to the properties of matrix multiplication, the (i,j)th entry in the matrix P 2 is the probability that you will move from state i to state j over the course of two trials; the (i,j)th entry in P 3 is the probability you will move from state i to state j in three trials, and so on.

The American Biology Teacher, 2014

Optimal foraging theory is a principle that is often presented in the community ecology section o... more Optimal foraging theory is a principle that is often presented in the community ecology section of biology textbooks, but also can be demonstrated in the laboratory. We introduce a lab activity that uses an interactive strategy to teach high school and/or college students about this ecological concept. The activity is ideal because it engages students in a hands-on activity that teaches them a fundamental ecological principle; it can be completed in a short class period; and it utilizes a few inexpensive, easy-to-purchase supplies.

Journal of the Alabama Academy of Science, 2009

The American Biology Teacher, 2014

In 1858, Darwin published On the Origin of Species by Means of Natural Selection. His explanation... more In 1858, Darwin published On the Origin of Species by Means of Natural Selection. His explanation of evolution by natural selection has become the unifying theme of biology. We have found that many students do not fully comprehend the process of evolution by natural selection. We discuss a few simple games that incorporate hands-on activities to demonstrate to students this important aspect of biology.

At some point in their mathematical training, most teachers encounter the Witch of Agnesi. The Wi... more At some point in their mathematical training, most teachers encounter the Witch of Agnesi. The Witch, a plane curve named and studied in the mid-1700s by the Italian mathematician Maria Agnesi, is constructed as follows: Center a circle with radius a at the point (0,a). Choose any point A on the line y=2a and connect it to the origin O with a line segment. Label the point where the line segment OA intersects the circle as B. Let P be the point whose x-coordinate is the same as point A and whose y-coordinate is the same as point B.

The International Journal of Interdisciplinary Educational Studies, 2014

Interdisciplinary endeavors, those that cross traditional academic boundaries, are burgeoning, as... more Interdisciplinary endeavors, those that cross traditional academic boundaries, are burgeoning, as the benefits of teaching across the curriculum, collaborating across disciplines, and addressing subject matter from multiple perspectives increasingly are recognized. Overcoming administrative and structural constraints, such as allocation of faculty workloads and course length, are challenges that require creative solutions. Our approach incorporated expertise from three departments, psychology, biology, and history, which produced a biopsychosociohistorical perspective that was interdisciplinary with transdisciplinary features. An undergraduate student's A/V presentation in one class formed the basis for an applied group project in another class, and included a pilot study. Our approach and example are described, as well as benefits to students, faculty, and administrators, and pedagogical implications.

Australian Senior Mathematics Journal, Jul 1, 2010

Australian Senior Mathematics Journal, 2009

A s teachers of first-year college mathematics and science students, we are constantly on the loo... more A s teachers of first-year college mathematics and science students, we are constantly on the lookout for simple classroom exercises that improve our students' analytical and computational skills. One such project, Predicting Precipitation in Darwin, is outlined below. In this project, students: • analyze and manipulate raw precipitation data; • build a prediction model using a Markov chain; • predict the long term distribution of precipitation-free and rainy days in Darwin, Northern Territory, Australia; • use a chi-square test to evaluate the effectiveness of the model they have constructed; • improve their prediction model. Beyond access to the Internet (to obtain the raw data) and a computer spreadsheet program or calculator, no special equipment is required. If the data is downloaded in advance, a well-prepared junior or senior high-school mathematics (or science) class should be able to perform this exercise in approximately 30-45 minutes of class time. Mathematical preliminaries: Markov chains A Markov chain is a sequence of identical trials, each of which can result in exactly one of a finite number of outcomes, called states. As the trials progress, the probability of moving from one state to another depends only on the state in which you are currently found. In most applications, Markov chains are represented by a state transition matrix, P. In this matrix, the entry in the (i,j)th position (row i, column j) is the probability that you will move to state j in the next trial if you are currently in state i. Properly constructed, the sum of each row in the matrix is one. Due to the properties of matrix multiplication, the (i,j)th entry in the matrix P 2 is the probability that you will move from state i to state j over the course of two trials; the (i,j)th entry in P 3 is the probability you will move from state i to state j in three trials, and so on.