{"id":29128,"date":"2020-10-09T05:30:26","date_gmt":"2020-10-09T10:30:26","guid":{"rendered":"http:\/\/www.discoverclarksville.com\/articles\/?p=29128"},"modified":"2020-10-09T00:07:31","modified_gmt":"2020-10-09T05:07:31","slug":"austin-peay-state-university-statistics-instructor-builds-real-world-models-to-help-students-grasp-math-concepts","status":"publish","type":"post","link":"https:\/\/www.discoverclarksville.com\/articles\/2020\/10\/09\/austin-peay-state-university-statistics-instructor-builds-real-world-models-to-help-students-grasp-math-concepts\/","title":{"rendered":"Austin Peay State University statistics instructor builds real-world models to help students grasp math concepts"},"content":{"rendered":"

\"AustinClarksville, TN<\/strong> –  Austin Peay State University statistics instructor Sam Ligo for years has used his woodworking skills and engineering know-how to build mathematical models \u2013 real-world 3D representations of the math \u2013 to help his students learn.<\/p>\n

And over the summer, he built his latest learning tool \u2013 a Galton Board.<\/p>\n

\"Austin<\/a>

Austin Peay State University’s Sam Ligo sits with some of the models he has created for his students. (APSU)<\/p><\/div>\n

<\/p>\n

\u201cI\u2019ve always sought out the physical representation of the math as a learner, so I started thinking about these things, about how I can make the concept more physical for the students,\u201d said Ligo, who has taught in Austin Peay State University\u2019s Department of Mathematics and Statistics since he retired as an Army colonel in 2012.<\/p>\n

\u201cI think we all teach in the way we like to learn, and I like to learn by seeing and hearing and feeling the concepts,\u201d Ligo stated.<\/p>\n

The Galton Board \u2013 also known as a bean machine \u2013 helps to demonstrate how random samples of a population tend to fall in a normal distribution (creating a bell curve). The mathematical concept is called the central limit theorem. You can see a Galton Board in action here<\/a>.<\/p>\n

The Galton Board, however, is just the latest of the mathematical gadgets that Ligo has built for his students over the years.<\/p>\n

\"Ligo<\/a>

Ligo is a math instructor for the Austin Peay State University Department of Mathematics and Statistics. (APSU)<\/p><\/div>\n

\u201cIt\u2019s where my teaching and my profession come together, so as an engineer, it\u2019s all about the application of the math,\u201d he said. \u201cThe answer to that in my mind is, \u2018Let\u2019s make a three-dimensional model.\u2019\u201d<\/p>\n

During Ligo\u2019s 26-year Army career, he was a U.S. Military Academy at West Point-trained engineer. He also led the ROTC program at Austin Peay for four years as the professor of military science and taught statistics \u2013 similar to courses he now teaches at APSU \u2013 at West Point for more than three years.<\/p>\n

He teaches non-mathematics majors at Austin Peay, and the models help his students grasp the concepts. Colleagues in the department also borrow the models for their classes.<\/p>\n

\u201cAll of these models came as I taught one semester to the next and saw the points where the students really struggled with the abstractness of the concepts,\u201d Ligo said.<\/p>\n

 <\/p>\n

[470center]<\/p>\n

Teaching during a pandemic<\/h3>\n

Ligo has 191 students in four classes this semester, and only about 50 of those are attending his lectures in person. A typical class has 12 students in the classroom and 30-40 watching via Zoom, he said.<\/p>\n

He devoted much of his summer to making his fall classes as normal as possible, even if most the students had to watch his lectures online.<\/p>\n

\"Ligo<\/a>

Ligo built this model to teach linear regression. (APSU)<\/p><\/div>\n

\u201cThere was the thought process of how much am I going to try to replicate normalcy versus how much am I going to go to be an online instructor,\u201d Ligo said. \u201cI decided to stay as close to normal as possible and yet still do everything possible to give the students in the classroom and out of the classroom pretty much the same experience.\u201d<\/p>\n

As the math models show, Ligo\u2019s teaching style revolves around his working through problems by hand. He relies little on slides and spends most of his lectures working problems on a whiteboard or on paper under a camera, both broadcast over Zoom.<\/p>\n

\u201cI hope that the experience isn\u2019t much different (than before the pandemic), because there\u2019s the problem statement and there\u2019s my hand and my voice working the problem statement,\u201d he said.<\/p>\n

He credits the department\u2019s teaching assistants who help him monitor the class experience and questions \u2013 in-person and online \u2013 for making the fall classes a success.<\/p>\n

\u201cI\u2019m blessed that I have those teaching assistants. I have one for each of my four sections that do that job for me, which is key for this whole thing to work.\u201d<\/p>\n

 <\/p>\n

[470center]<\/p>\n

Bringing tools to the classroom<\/h3>\n

The first model that Ligo created to demonstrate a mathematical principle was a board that uses thumb tacks and rubber bands to show linear regression. Linear regression is a way to show the relationship between two or more variables.<\/p>\n

\u201cThese rubber bands are fighting each other and stretching each other until you get this equilibrium,\u201d he said as he moved the tacks around the board, showing how the rubber bands stretch between the points. \u201cAnd that is exactly what the math is doing when you conduct a linear regression, the math at this point is struggling against that one, and there is the equilibrium.\u201d<\/p>\n

\"Ligo's<\/a>

Ligo’s Galton Board. (APSU)<\/p><\/div>\n

Ligo has built other teaching tools during his time as a teacher, including during his time in the Army when he used models to help teach aspiring soldiers how to navigate with maps. He has also built such tools as catapults, an Egyptian chain<\/a> (used to measure right-angle triangles) and a marble board to show skew distribution.<\/p>\n

The Galton Board idea came to Ligo in spring 2019.<\/p>\n

\u201cI\u2019ve always been intrigued by these,\u201d he said.<\/p>\n

[320left]During AP Day (an event for prospective students to visit Austin Peay) that spring, he and his colleagues noticed prospective students were drawn to the flashier demos at other departmental tables.<\/p>\n

\u201cPhysics has all their cool stuff, and health and human sciences has their skeletons,\u201d he said. \u201cEverybody has something that they can literally bring to the table except math. One of the things we came up with was making a big and noisy Galton Board. It was conceived on AP Day, and then it had to cook for a long time before I could come up with a design that I could build that wasn\u2019t terribly technical or too terribly fancy that I could build given the tools that I have in my garage.\u201d<\/p>\n

To learn more<\/h3>\n

For more about the Department of Mathematics and Statistics at Austin Peay, visit https:\/\/apsu.edu\/mathematics<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

Clarksville, TN –  Austin Peay State University statistics instructor Sam Ligo for years has used his woodworking skills and engineering know-how to build mathematical models \u2013 real-world 3D representations of the math \u2013 to help his students learn. And over the summer, he built his latest learning tool \u2013 a Galton Board.<\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[5],"tags":[23,8199,262,512,825,4445,1275,34961,12621,11894],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4xGYI-7zO","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.discoverclarksville.com\/articles\/wp-json\/wp\/v2\/posts\/29128"}],"collection":[{"href":"https:\/\/www.discoverclarksville.com\/articles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.discoverclarksville.com\/articles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.discoverclarksville.com\/articles\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.discoverclarksville.com\/articles\/wp-json\/wp\/v2\/comments?post=29128"}],"version-history":[{"count":1,"href":"https:\/\/www.discoverclarksville.com\/articles\/wp-json\/wp\/v2\/posts\/29128\/revisions"}],"predecessor-version":[{"id":29129,"href":"https:\/\/www.discoverclarksville.com\/articles\/wp-json\/wp\/v2\/posts\/29128\/revisions\/29129"}],"wp:attachment":[{"href":"https:\/\/www.discoverclarksville.com\/articles\/wp-json\/wp\/v2\/media?parent=29128"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.discoverclarksville.com\/articles\/wp-json\/wp\/v2\/categories?post=29128"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.discoverclarksville.com\/articles\/wp-json\/wp\/v2\/tags?post=29128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}