Serendipitous Discovery of Pascal’s Triangle

1975 ◽  
Vol 68 (2) ◽  
pp. 95-98
Author(s):  
Francis W. Stanley
Keyword(s):  
First Year ◽  
Pascal’S Triangle ◽  
The Subject ◽  
Pascal's Triangle ◽  
Algebra Class

Teachers often welcome questions from students—especially if the questions were anticipated in preparing the lesson. But unanticipated questions may not be so eagerly received. Some of these are motivated by a student’s desire to divert the teacher from the subject at hand; others, by honest curiosity. Regardless of their motivation, there are those occasional questions that fit naturally into the discussion. Many of these may well be worth the price of preempting a carefully planned lesson to search out a reasonable conclusion with the students. Such a question was responsible for a serendipitous digression in our first-year algebra class.

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.

THE APPLICATION OF PREVIEW, READ, WRITE, AND RECITE (PRWR) METHOD TO IMPROVE STUDENT’S ACHIEVEMENT IN READING RECOUNT TEXT

2014 ◽  
Vol 3 (2) ◽  
Author(s):  
Rahmat Nasution And Rahmah
Keyword(s):  
Secondary Data ◽  
Analysis Data ◽  
Primary Data ◽  
Average Score ◽  
First Year ◽  
Generic Structure ◽  
The Subject ◽  
Minimum Criteria ◽  
Main Ideas ◽  
Orientation Test

The objective of this research is to find out whether the application Preview, Read,Write, and Recite (PRWR) method improve student’s achievement in readingrecount text. This research applied classroom action research model. This studywas done in six meetings. The subject of this study was first year of SMAN 1Delitua. Primary data were collected by giving 20 questions of multiple-choicetest, the aspects contained in the tests focused on generic structure, main ideas,factual information, and Secondary data were collected by (interview, observationsheet, and questionnaire sheet. Based on analysis data, it was found that thestudent’s achievement improved. It could be seen from the comparison of result inthe orientation test and the cycle test I and II. There were only 9 students who hadpassed minimum criteria KKM in orientation test (75). The improvement showedthat in cycle I and II, based on the total average score it was 16 (42,4%) up to 26(78,7%) in cycle II, The secondary data gathered from interview, observationsheet, and questionnaire sheet, showed that students’ expression and enthusiasticalso improved. Thus, it was found that the applications of Preview, Read, Write,and Recite (PRWR) method in process of teaching improved students’achievement in reading recount text. It is suggested that English teachers applyPRWR method in teaching reading recount text.

Pascal's Prism

2012 ◽  
Vol 96 (536) ◽  
pp. 213-220
Author(s):  
Harlan J. Brothers
Keyword(s):  
Probability Theory ◽  
Fractal Geometry ◽  
Euclidean Geometry ◽  
Fibonacci Series ◽  
Pascal’S Triangle ◽  
Number Sequences ◽  
Definition Of ◽  
Image Position ◽  
Pascal's Triangle

Pascal's triangle is well known for its numerous connections to probability theory [1], combinatorics, Euclidean geometry, fractal geometry, and many number sequences including the Fibonacci series [2,3,4]. It also has a deep connection to the base of natural logarithms, e [5]. This link to e can be used as a springboard for generating a family of related triangles that together create a rich combinatoric object.2. From Pascal to LeibnizIn Brothers [5], the author shows that the growth of Pascal's triangle is related to the limit definition of e.Specifically, we define the sequence sn; as follows [6]:

3057. A Note on Pascal's Triangle

1963 ◽  
Vol 47 (359) ◽  
pp. 57
Author(s):  
Robert Croasdale
Keyword(s):  
Pascal’S Triangle ◽  
Pascal's Triangle

scholarly journals The Fibonacci p-numbers and Pascal’s triangle

2016 ◽  
Vol 3 (1) ◽  
pp. 1264176 ◽  
Author(s):  
Kantaphon Kuhapatanakul ◽  
Lishan Liu
Keyword(s):  
Pascal’S Triangle ◽  
Pascal's Triangle

Peer instruction improves performance on quizzes.

2000 ◽  
Vol 24 (1) ◽  
pp. 51-55 ◽  
Author(s):  
S P Rao ◽  
S E DiCarlo
Keyword(s):  
Decision Making ◽  
Peer Instruction ◽  
First Year ◽  
First Response ◽  
Learning Technique ◽  
Testing Complex ◽  
The Subject ◽  
Level Of Understanding ◽  
First Year Medical Students ◽  
Intellectual Activities

Peer instruction is a cooperative-learning technique that promotes critical thinking, problem solving, and decision-making skills. Benson's think-pair-share and Mazur's peer-instruction techniques are simple cooperative exercises that promote student's participation in class and increase student's interaction with each other and with the instructor in a large classroom. We borrowed concepts from Benson and Mazur and applied these concepts to enhance student involvement during the respiratory component of the medical physiology class. The medical physiology class consisted of 256 first-year medical students. The peer-instruction technique was used for 10 classes. Each class of 50 min was divided into three or four short presentations of 12-20 min. Each presentation was followed by a one-question, multiple-choice quiz on the subject discussed. Questions ranged from simple recall to those testing complex intellectual activities. Students were given 1 min to think and to record their first answer. Subsequently, students were allowed 1 min to discuss their answers with their classmates and possibly correct their first response. The percentage of correct answers increased significantly (P < 0.05) after discussion for both recall and intellectual questions. These data demonstrate that pausing three to four times during a 50-min class to allow discussion of concepts enhanced the students level of understanding and ability to synthesize and integrate material.

scholarly journals Arithmetic Triangle

2017 ◽  
Vol 9 (2) ◽  
pp. 100
Author(s):  
Luis Dias Ferreira
Keyword(s):  
Arithmetic Progression ◽  
Modus Operandi ◽  
Interesting Point ◽  
Pascal’S Triangle ◽  
Initial Term ◽  
The Common ◽  
Pascal's Triangle

The product of the first $n$ terms of an arithmetic progression may be developed in a polynomial of $n$ terms. Each one of them presents a coefficient $C_{nk}$ that is independent from the initial term and the common difference of the progression. The most interesting point is that one may construct an "Arithmetic Triangle'', displaying these coefficients, in a similar way one does with Pascal's Triangle. Moreover, some remarkable properties, mainly concerning factorials, characterize the Triangle. Other related `triangles' -- eventually treated as matrices -- also display curious facts, in their linear \emph{modus operandi}, such as successive "descendances''.

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