Sharing Teaching Ideas: If the Product of Two Numbers Is Zero…

1994 ◽  
Vol 87 (2) ◽  
pp. 89
Author(s):  
Richard Forringer
Keyword(s):  
Problem Solving ◽  
First Year ◽  
The Real ◽  
Quadratic Equations ◽  
Knowing That ◽  
Way Of Knowing ◽  
Factoring Polynomials ◽  
To Come ◽  
Teaching Ideas ◽  
Algebra Class

My first-year-algebra class has just finished the topic of factoring polynomials. The groundwork has been laid for problem solving with quadratic equations, one of the real eye-openers in the course. I look forward to teaching this topic with the excitement and anticipation of knowing what is to come. My students sense my excitement but do not fully understand it and have not experienced it for themselves. As Confucius once observed, “Everything has its beauty, but not everyone sees it!” Many students have no way of knowing that this part of algebra is incredibly significant. A short, simple statement, “If the product of two numbers is zero, then one of those numbers must be zero,” seems too easy, too self-evident, and too obvious to be so important!

Sharing Teaching Ideas: If Distance = Rate × Time, Then Where Am I?

1989 ◽  
Vol 82 (2) ◽  
pp. 108-109
Keyword(s):  
Class I ◽  
First Year ◽  
Standard Practice ◽  
The Subject ◽  
Set Up ◽  
Teaching Ideas ◽  
Algebra Class

In working with an average first-year algebra class, I noticed that the students sometimes got so wrapped up in solving for that pesky x that we often forgot the practical uses of the subject. A perfect opportunity came up as we began a section on distance problems. The standard practice is to analyze the problem by putting into a chart the information found by using the formula distance = rate × time to set up the equations.

Sharing Teaching Ideas: Table Tennis, Anyone? Using Ping-Pong to Teach the Coordinate Plane

1997 ◽  
Vol 90 (9) ◽  
pp. 712-714
Author(s):  
John D. Foshay ◽  
Wendy L. Wells
Keyword(s):  
First Year ◽  
Table Tennis ◽  
Coordinate Plane ◽  
Ping Pong ◽  
Teaching Ideas ◽  
Coordinate Geometry ◽  
Algebra Class

During a first-year-algebra class, tenth- and eleventh-grade students, overhearing the sounds of a Ping-Pong game from downstairs, voiced a strong desire to play. This incident led the authors to stumble onto the idea of using Ping-Pong to teach coordinate geometry. From this inquiry by interested students came the idea of using a Ping-Pong table as the visual anchor on which to situate the coordinate plane.

Equilibrium models vs. realistic understanding

2017 ◽  
Author(s):  
Lawrence A. Boland
Keyword(s):  
Real World ◽  
Stable Equilibrium ◽  
Decision Makers ◽  
Equilibrium Models ◽  
The Real ◽  
Knowing That ◽  
Equilibrium Process ◽  
Way Of Knowing

In the real world, the process of reaching the assumed equilibrium involves decision makers’ knowledge and their awareness of any disequilibrium. Equilibrium attainment also requires their making the correct decisions required for a ‘stable’ equilibrium. Any model which fails to explicitly address the equilibrium process and its requirements is vulnerable to criticism of the model’s realism. This chapter explores, specifically, whether the knowledge required to reach equilibrium can ever be attained by participants, whether the process of obtaining that knowledge can be consistent with the requirements of achieving an equilibrium. It also explores the ‘ignorant consumer’ who has no way of knowing that he or she is not maximizing.

Reflections: A Lesson in Related Rates

1996 ◽  
Vol 89 (5) ◽  
pp. 390-393
Author(s):  
Joe D. Nichols
Keyword(s):  
Problem Solving ◽  
Advanced Placement ◽  
Real World ◽  
Basic Concept ◽  
First Year ◽  
General Application ◽  
The Real ◽  
Calculus Students ◽  
Real World Applications

My objective in teaching an Advanced Placement calculus course is not only to help students pass the AP examination each spring but also to help them develop insights into advanced problem solving and real-world applications. I continually search for examples in my students' daily environment that can help them make a tangible connection from the classroom textbook to the real world. In this article, I discuss a general application of a basic concept with which all first-year-calculus students must contend: the problem of related rates.

First-Year Engineering Computing Courses in Canadian Engineering Programs

1969 ◽  
Author(s):  
Sean Maw ◽  
Janice Miller Young ◽  
Alexis Morris
Keyword(s):  
Problem Solving ◽  
Engineering Students ◽  
Expected Value ◽  
Knowledge Development ◽  
First Year ◽  
Recent Past ◽  
Engineering Programs ◽  
Digital Computation ◽  
Pedagogical Philosophies ◽  
Introductory Computing

Most Canadian engineering students take a computing course in their first year that introduces them to digital computation. The Canadian Engineering Accreditation Board does not specify the language(s) that can or should be used for instruction. As a result, a variety of languages are used across Canada. This study examines which languages are used in degree-granting institutions, currently and in the recent past. It also examines why institutions have chosen the languages that they currently use. In addition to the language used in instruction, the types and hours of instruction are also analyzed. Methods of instruction and evaluation are compared, as well as the pedagogical philosophies of the different programs with respect to introductory computing. Finally, a comparison of the expected value of this course to graduates is also presented. We found a more diverse landscape for introductory computing courses than anticipated, in most respects. The guiding ethos at most institutions is skill and knowledge development, especially around problem solving in an engineering context. The methods to achieve this are quite varied, and so are the languages employed in such courses. Most programs currently use C/C++, Matlab, VB and/or Python.

scholarly journals Study of Live Lecture Attendance, Student Perceptions and Expectations

2021 ◽  
Author(s):  
Johnathan Emahiser ◽  
John Nguyen ◽  
Cheryl Vanier ◽  
Amina Sadik
Keyword(s):  
Student Perceptions ◽  
Teaching Practices ◽  
First Year ◽  
First Year Students ◽  
Study Materials ◽  
Class B ◽  
Second Year ◽  
To Come ◽  
Perceptions And Expectations ◽  
Insight Into

AbstractDeclining lecture attendance has been an ongoing concern for educators involved in undergraduate medical education. A survey was developed (a) to gain insight into the reasons students skipped class, (b) to identify the type of study materials they were using, and (c) to determine what they thought would motivate them to come to class. The survey was sent to 317 first-year and second-year medical students, and 145 (45%) responded. Only 63% of first-year students and 53% of second-year students attended any lectures that were not mandatory. The attendance was higher for students who aspired to less competitive specialties such as pediatrics and family medicine. The most popular reasons for not coming to class were related to the efficiency of information intake and instructor or class style. The most heavily used resources (> 60%) were materials or recorded lectures provided by the instructor. The second-year students also heavily used outside study materials for Board exams, such as Pathoma (50%). Students’ ideas for what might increase their attendance suggest that they perceive that the lectures may not prepare them for Board exams, and they would like faculty to address Board related content more often in class and on assessments. Respondents also suggested that teaching practices might be improved through faculty development. Faculty awareness of and references to Board exam content, embedded in strong teaching practices, may help students find more value in live lectures. Carefully designed active learning sessions may change students’ minds regarding the relevance and value of these sessions.

MOORE ON THE SCEPTICAL PHILOSOPHER

Think ◽  
2021 ◽  
Vol 20 (57) ◽  
pp. 69-87
Author(s):  
Guy Longworth
Keyword(s):  
Knowing That ◽  
Dear Reader ◽  
Way Of Knowing

1. Since I don't know who you are, dear reader, and since I know that some people don't have hands, I don't know whether you have hands. Probably you do, but knowing that something is probable is rarely, if ever, a way of knowing that thing. By contrast, I know that I have hands. Let me check. Yes, here is one of my hands; and here is another. Since I know that here is one of my hands and that here is another, and since I know that it follows from those two claims that I have hands, I can deduce that I have hands. So, I know that I have hands.

Alice in the Real World

2012 ◽  
Vol 17 (7) ◽  
pp. 410-416 ◽  
Author(s):  
Tom Parker
Keyword(s):  
Problem Solving ◽  
Real World ◽  
Mathematical Problem ◽  
Computer Application ◽  
Mathematical Problem Solving ◽  
The Real ◽  
Programming Knowledge

A computer application promotes programming knowledge and allows students to create their own worlds through mathematical problem solving.

Teaching Enterprise — Can it Be Done in Large Groups?

2003 ◽  
Vol 17 (1) ◽  
pp. 37-44
Author(s):  
Raymond D. Donnelly
Keyword(s):  
Market Research ◽  
Business Plan ◽  
Management Programme ◽  
First Year ◽  
Large Numbers ◽  
Commercial Sources ◽  
To Come ◽  
The University ◽  
Large Groups

This paper reports on work carried out in the School of Management at Heriot-Watt University in Edinburgh. Following a wide-ranging review of the first-year management programme, a module on enterprise was introduced. As part of that module students had to compete in a game, the object of which was to come up with a business idea, conduct market research and present a business plan and proposal to a panel of judges. The number of students was 225 in year one but reached around 500 within five years. The module has generated many good ideas and has attracted sponsorship from commercial sources. As yet the university has been unable to take the ideas further. It is possible that enterprise can be learned by people in large numbers, but perhaps universities are not the places in which to attempt such work.

Tracing the Rift: Heidegger, Hölderlin, and “The Origin of the Work of Art”

2019 ◽  
Vol 53 ◽  
pp. 295-307
Author(s):  
Will McNeill ◽  
Keyword(s):  
Central Concept ◽  
Work Of Art ◽  
The Real ◽  
Philosophical Significance ◽  
To Come ◽  
Central Claim ◽  
Do So

Heidegger’s 1936 essay “The Origin of the Work of Art” is notoriously dense and difficult. In part this is because it appears to come almost from nowhere, given that Heidegger has relatively little to say about art in his earlier work. Yet the essay can only be adequately understood, I would argue, in concert with Heidegger’s essay on Hölderlin from the same year, “Hölderlin and the Essence of Poetizing.” Without the Hölderlin essay, for instance, the central claim of “The Origin of the Work of Art” to the effect that all art is in essence poetizing, Dichtung, can hardly be appreciated in its philosophical significance without the discussions of both essence and poetizing that appear in the Hölderlin essay. This is true of other concepts also. The central concept of the rift (Riß)—the fissure or tear—that appears in “The Origin of the Work of Art” might readily be assumed to be adopted from Albrecht Dürer, whose use of the term Heidegger cites at a key point in the 1936 essay. Here, however, I argue that the real source of the concept for Heidegger is Hölderlin, and that the Riß is, moreover—quite literally—an inscription of originary, ekstatic temporality; that is, of temporality as the “origin” of Being and as the poetic or poetizing essence of art. I do so, first, by briefly considering Heidegger’s references to Dürer in “The Origin of the Work of Art” and other texts from the period, as well as his understanding of the Riß and of the tearing of the Riß in that essay and in its two earlier versions. I then turn to Heidegger’s 1936 Rome lecture “Hölderlin and the Essence of Poetizing,” in order to show the Hölderlinian origins of this concept for Heidegger.

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