Don Ploger | Florida Atlantic University (original) (raw)
Papers by Don Ploger
The Journal of Mathematical Behavior, 1991
In 1968, Douglas Engelbart gave "The Mother of All Demos”, showing a computer with a graphic... more In 1968, Douglas Engelbart gave "The Mother of All Demos”, showing a computer with a graphical interface controlled by a pointing device. Those experimental technologies of 1968 have become part of every day life, as have speech recognition and computer translation. This case study follows the progress of a man learning a second language using readily available technology. When J spoke his native English, Google Translate achieved an accuracy rate greater than 95%. When J spoke Mandarin words that a native Chinese speaker could easily understand, Google Translate had an accuracy rate less than 40%. Using this feedback, J decided to learn French. In the beginning, there were many false negatives, words that a sympathetic native speaker understood, but the computer program did not. Despite these setbacks, there was long-term progress, and the methods are described. These results provide some evidence to guide engineering practice. The human translator succeeded because she knew t...
This presentation combines two theoretical perspectives. The first perspective, from engineering ... more This presentation combines two theoretical perspectives. The first perspective, from engineering education, emphasizes the importance of communicating essential knowledge to non-engineers. The second theoretical perspective comes from the mathematics education research literature. It is well established that students may be able to recall certain facts, but fail to use those facts in solving novel problems. In many cases, students do not even recognize that solving such problems is important. This presentation describes how undergraduate engineering majors designed robots for a class project. These robots are low cost, built with mass produced low precision parts. Calibration and error-correction techniques in software and hardware are used to enhance their precision. These robots are designed to draw geometric art, and in the process, teach Mathematics to high school students. A detailed analysis of the necessary subject matter knowledge is provided here. Furthermore, a high school...
Teaching Children Mathematics, 1997
Young children are fascinated by the concept of impossible, and that interest can lead to an exte... more Young children are fascinated by the concept of impossible, and that interest can lead to an extended exploration in mathematical reasoning. This article describes a set of class-room-tested activities that help children develop convincing arguments by building on their intuitive ideas about what is impossible.
Teaching children mathematics, 2005
computing with fractions. What can the concerned teacher do to help? Fortunately, many resources ... more computing with fractions. What can the concerned teacher do to help? Fortunately, many resources are available. Mathematics education textbooks, such as those by Cathcart et al. (2003) and by Reys et al. (2003), provide a useful overview of models and methods to help teachers. In addition, various studies offer more detailed descriptions to help the classroom teacher bring powerful fraction ideas into the classroom. Riddle and Rodzwell (2000) found that young children have a beginning understanding of fraction concepts. In many instances, however, educators ignore this powerful intuitive knowledge, and as a result, students learn computation of fractions by rote. The authors conclude that although students must eventually understand the standard algorithms, “children should start by using their understanding of fractions to develop procedures that make sense to them” (p. 206). Although young children have useful ideas about fractions, these intuitions do not automatically develop in...
Teaching Children Mathematics, 1997
This article describes the results of a fifth-grade class using spreadsheets to investigate chall... more This article describes the results of a fifth-grade class using spreadsheets to investigate challenging mathematical topics. Consistent with the Curricu-lum and Evaluation Standards for School Mathe-matics, children are encouraged to recognize, de-scribe, extend, and create a ...
2013 ASEE Annual Conference & Exposition Proceedings
2013 ASEE Annual Conference & Exposition Proceedings
2013 ASEE Annual Conference & Exposition Proceedings
The Mathematics Teacher
Cryptography is the art and science of encoding and decoding messages. It plays an important role... more Cryptography is the art and science of encoding and decoding messages. It plays an important role in business as a means to protect corporate secrets, in banking to secure accounts, in the military to protect information, and in personal security devices to protect individuals. (See Kahn [1967] for a review of cryptography.) In this activity we introduce cryptography into the high school classroom as a context for doing mathematics.
Journal of Mathematical Behavior, 1991
Journal of Experimental Psychology General, 1991
ABSTRACT
Journal of Mathematical Behavior, 1991
Http Dx Doi Org 10 1080 00094056 2012 682550, Apr 30, 2012
2015 ASEE Annual Conference and Exposition Proceedings, 2015
The Journal of Mathematical Behavior, 1991
In 1968, Douglas Engelbart gave "The Mother of All Demos”, showing a computer with a graphic... more In 1968, Douglas Engelbart gave "The Mother of All Demos”, showing a computer with a graphical interface controlled by a pointing device. Those experimental technologies of 1968 have become part of every day life, as have speech recognition and computer translation. This case study follows the progress of a man learning a second language using readily available technology. When J spoke his native English, Google Translate achieved an accuracy rate greater than 95%. When J spoke Mandarin words that a native Chinese speaker could easily understand, Google Translate had an accuracy rate less than 40%. Using this feedback, J decided to learn French. In the beginning, there were many false negatives, words that a sympathetic native speaker understood, but the computer program did not. Despite these setbacks, there was long-term progress, and the methods are described. These results provide some evidence to guide engineering practice. The human translator succeeded because she knew t...
This presentation combines two theoretical perspectives. The first perspective, from engineering ... more This presentation combines two theoretical perspectives. The first perspective, from engineering education, emphasizes the importance of communicating essential knowledge to non-engineers. The second theoretical perspective comes from the mathematics education research literature. It is well established that students may be able to recall certain facts, but fail to use those facts in solving novel problems. In many cases, students do not even recognize that solving such problems is important. This presentation describes how undergraduate engineering majors designed robots for a class project. These robots are low cost, built with mass produced low precision parts. Calibration and error-correction techniques in software and hardware are used to enhance their precision. These robots are designed to draw geometric art, and in the process, teach Mathematics to high school students. A detailed analysis of the necessary subject matter knowledge is provided here. Furthermore, a high school...
Teaching Children Mathematics, 1997
Young children are fascinated by the concept of impossible, and that interest can lead to an exte... more Young children are fascinated by the concept of impossible, and that interest can lead to an extended exploration in mathematical reasoning. This article describes a set of class-room-tested activities that help children develop convincing arguments by building on their intuitive ideas about what is impossible.
Teaching children mathematics, 2005
computing with fractions. What can the concerned teacher do to help? Fortunately, many resources ... more computing with fractions. What can the concerned teacher do to help? Fortunately, many resources are available. Mathematics education textbooks, such as those by Cathcart et al. (2003) and by Reys et al. (2003), provide a useful overview of models and methods to help teachers. In addition, various studies offer more detailed descriptions to help the classroom teacher bring powerful fraction ideas into the classroom. Riddle and Rodzwell (2000) found that young children have a beginning understanding of fraction concepts. In many instances, however, educators ignore this powerful intuitive knowledge, and as a result, students learn computation of fractions by rote. The authors conclude that although students must eventually understand the standard algorithms, “children should start by using their understanding of fractions to develop procedures that make sense to them” (p. 206). Although young children have useful ideas about fractions, these intuitions do not automatically develop in...
Teaching Children Mathematics, 1997
This article describes the results of a fifth-grade class using spreadsheets to investigate chall... more This article describes the results of a fifth-grade class using spreadsheets to investigate challenging mathematical topics. Consistent with the Curricu-lum and Evaluation Standards for School Mathe-matics, children are encouraged to recognize, de-scribe, extend, and create a ...
2013 ASEE Annual Conference & Exposition Proceedings
2013 ASEE Annual Conference & Exposition Proceedings
2013 ASEE Annual Conference & Exposition Proceedings
The Mathematics Teacher
Cryptography is the art and science of encoding and decoding messages. It plays an important role... more Cryptography is the art and science of encoding and decoding messages. It plays an important role in business as a means to protect corporate secrets, in banking to secure accounts, in the military to protect information, and in personal security devices to protect individuals. (See Kahn [1967] for a review of cryptography.) In this activity we introduce cryptography into the high school classroom as a context for doing mathematics.
Journal of Mathematical Behavior, 1991
Journal of Experimental Psychology General, 1991
ABSTRACT
Journal of Mathematical Behavior, 1991
Http Dx Doi Org 10 1080 00094056 2012 682550, Apr 30, 2012
2015 ASEE Annual Conference and Exposition Proceedings, 2015