Algebra and the Development of Reason

1931 ◽  
Vol 24 (5) ◽  
pp. 285-297
Author(s):  
Susanne K. Langer
Keyword(s):  
High School ◽  
Secondary School ◽  
The Other ◽  
Human Reason ◽  
High School Algebra ◽  
School Teaching ◽  
The Subject ◽  
The Mean ◽  
Points Of View

What I wish to say to you today is a general reflection on the subject of high-school algebra. As a layman both in mathematics and in secondary school teaching, I can speak only from two lay points of view—that of the pupil, which meets you at one end of your activity, and that of the philosopher, which you encounter at the other. Consequently I shall begin by talking about the futility and barren, ness of algebra, and end, I hope, by reviewing with you its importance, interess and charm. For it is a peculiarity of the subject that an uninitiate mind can usually see nothing in it but a dry, lifeless discipline, whereas the adept sees in it the apotheosis of human reason. The mean from the former outlook to the latter is your ministry.

Classics in Mathematics Education: Algebra and the Development of Reason

1966 ◽  
Vol 59 (2) ◽  
pp. 158-166
Author(s):  
Susanne K. Langer
Keyword(s):  
High School ◽  
Mathematics Education ◽  
Secondary School ◽  
The Other ◽  
Human Reason ◽  
High School Algebra ◽  
School Teaching ◽  
The Subject ◽  
Points Of View

WHAT I wish to say to you today is a general reflection on the subject of high school algebra. As a layman both in mathematics and in secondary school teaching, I can speak only from two lay points of view—that of the pupil, which meets you at one end of your activity, and that of the philosopher, which you encounter at the other. Consequently, I shall begin by talking about the futility and barrenness of algebra, and end, I hope, by reviewing with you its importance, interest, and charm. For it is a peculiarity of the subject that an uninitiate mind can usually see nothing in it but a dry, lifeless discipline, whereas the adept sees in it the apotheosis of human reason.

scholarly journals The Effectiveness of a Program Based on the Theory of TRIZ in the Subject of Physics to Develop the Skills of Creative Thinking and Critical Thinking Among the Secondary School Students of the Southern Al-Mazar

2020 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
Itimad Jamil Al-Jaafreh Jamil Aljaafreh
Keyword(s):  
High School ◽  
High School Students ◽  
Critical Thinking ◽  
Secondary School ◽  
Creative Thinking ◽  
Secondary School Students ◽  
The Other ◽  
School Students ◽  
The Subject ◽  
Experimental Group

Purpose: The study aimed to learn about the effectiveness of a program based on the Theory of TRIZ in the subject of physics to develop the skills of creative thinking and critical thinking among the high school students of the Southern al-Mazar Brigade, the study used the design like experimental, and was represented the tools of study in the Torrance test for creative thinking and the test of California for critical thinking, as a training program was built based on the theory of creative solution to problems.Methodology: The sample of the study consisted of ( 81) students of the first high school scientific which was chosen in the method of intent and the students are distributed on two randomly assigned school divisions as exacts and pilots, one (40) students and the exact group, and the other (41) students represented the experimental group.Findings: The results of the study showed that there are statistically significant differences in favor of the experimental group that indicates the effectiveness of the program in developing the skills of creative thinking and Critical thinking  among the students.

scholarly journals Observations on the Fat Globules in Milk

1913 ◽  
Vol 5 (3) ◽  
pp. 331-356 ◽  
Author(s):  
W. F Cooper ◽  
W. H Nuttall ◽  
G. A Freak
Keyword(s):  
Annual Report ◽  
The Other ◽  
Optimum Temperature ◽  
Fat Globules ◽  
Chief Factors ◽  
Mean Size ◽  
The Subject ◽  
The Mean ◽  
Definite Result

Results of our previous work were published in the Journ. of Agric. Sri., IV, 1911. There, also, a brief summary of the chief papers published on the subject of the fat globules was given, to which it is unnecessary to refer in detail here.When the work was first commenced in 1909, the problem before us was the consideration of the variation in the size of the fat globules, with relation to churning, as regards the different breeds of cattle. The breed was considered because it was usually supposed that this was one of the chief factors which influenced churning. The most definite result of our work was that it was shown that consideration must be given to the character of the milk, irrespective of the breed. This conclusion is quite contrary to that of other workers, but an examination of their figures shows, undoubtedly, that this is actually the case: the results given by Woll (Digestion Expts., Seventh Annual Report, Agric. Expt. Stat, Wisconsin, 1890, 238; also Agric. Sci., 1892, vi, 445) emphasise this point particularly. It is also shown by this year's work, as may be seen from Tables V–XI.The comparative size of the globules has been worked out very thoroughly by Gutzeit, who measured the mean volume of the globule. Other workers give their results as “relative sizes.” In our work we attempted to ascertain the distribution of the fat in the globules, and to this end the number of globules of each size was determined, and curves were drawn. The result of this, however, was negative. At that time we were considering the breeds of the cows from which the milks were obtained; had we considered them solely as milks of a certain mean size of globule, much more might have been achieved.An apparatus was devised to give an absolute figure for the churnability of any cream, but, until the effect of the other factors has been determined, it is impossible to interpret the results. Some experiments to ascertain the optimum temperature were described also.

scholarly journals STUDENT’S MATHEMATICAL VALUE IN MATHEMATICS LEARNING USING NON-ROUTINE PROBLEM

2018 ◽  
Vol 37 (3) ◽  
Author(s):  
Nurul Ain Safura ◽  
Nyimas Aisyah ◽  
Cecil Hiltrimartin ◽  
Indaryanti Indaryanti
Keyword(s):  
High School ◽  
Mathematics Learning ◽  
The Other ◽  
Control Value ◽  
Learning Mathematics ◽  
The Subject

Abstract: This study aims to determine the ability of students in solving non-routine problems in learning mathematics in high school. The focus of the study is the ability of students in solving non-routine problems that include the value of objectism, value of control, value of mystery, value of progress, value of rationalism, and value of openness. The subject of this study was determined purposively, that was based on the diversity of answers. The selected subject was six students of class X SMA in Palembang. The data were collected using observation, test, and interview which were then analyzed descriptively. The results show that in general the ability of students in solving non-routine problems is dominated by the value of objectism, control, rationalism, and progress. The other two values which did not dominantly appear were mystery and openness. Keywords: mathematical value, non-routine problemNILAI MATEMATIKA (MATHEMATICAL VALUE) SISWA PADA PEMBELAJARAN MATEMATIKA MENGGUNAKAN SOAL NON RUTIN Abstrak: Penelitian ini bertujuan untuk mengetahui kemampuan siswa dalam menyelesaikan soal non rutin pada pembelajaran matematika di SMA. Fokus penelitian adalah kemampuan siswa dalam menyelesaikan soal non rutin yang meliputi nilai objektisme, nilai kontrol, nilai misteri, nilai kemajuan, nilai rasionalisme, dan nilai keterbukaan. Adapun subjek penelitian ini dipilih secara purposive, berdasarkan keberagaman jawaban. Subjek yang terpilih adalah enam orang siswa kelas X SMA di Palembang. Data dikumpulkan menggunakan observasi, tes, dan juga wawancara, yang kemudian di analisis secara deskriptif.  Hasil penelitian menunjukkan bahwa secara umum kemampuan siswa dalam menyelesaikan soal non rutin masih didominasi pada nilai objektisme, nilai kontrol, nilai rasionalisme, dan nilai kemajuan. Dua nilai lain yang tidak dominan muncul adalah nilai misteri dan nilai keterbukaan.Kata Kunci: nilai matematika, soal non rutin

The Effect of Waking Suggestion on Post-Hypnotic Amnesia

1981 ◽  
Vol 11 (1) ◽  
pp. 44-46 ◽  
Author(s):  
D.P. Fourie
Keyword(s):  
Point Of View ◽  
The Other ◽  
Hypnotic Susceptibility ◽  
The Subject ◽  
The Mean ◽  
The Difference ◽  
The One ◽  
The Relationship ◽  
Female Subjects

It is increasingly realized that hypnosis may be seen from an interpersonal point of view, meaning that it forms part of the relationship between the hypnotist and the subject. From this premise it follows that what goes on in the relationship prior to hypnosis probably has an influence on the hypnosis. Certain of these prior occurences can then be seen as waking suggestionns (however implicitly given) that the subject should behave in a certain way with regard to the subsequent hypnosis. A study was conducted to test the hypothesis that waking suggestions regarding post-hypnotic amnesia are effective. Eighteen female subjects were randomly divided into two groups. The groups listened to a tape-recorded talk on hypnosis in which for the one group amnesia for the subsequent hypnotic experience and for the other group no such amnesia was suggested. Thereafter the Stanford Hypnotic Susceptibility Scale was administered to all subjects. Only the interrogation part of the amnesia item of the scale was administered. The subjects to whom post-hypnotic amnesia was suggested tended to score lower on the amnesia item than the other subjects, as was expected, but the difference between the mean amnesia scores of the two groups was not significant.

Development of Blue-Yellow and Red-Green Discriminations in Infants during the First Year of Life

Perception ◽  
1997 ◽  
Vol 26 (1_suppl) ◽  
pp. 235-235
Author(s):  
L I Leushina ◽  
V M Bondarko ◽  
A A Nevskaya
Keyword(s):  
Healthy Subjects ◽  
Risk Group ◽  
Emotional Reaction ◽  
Mean Difference ◽  
The Other ◽  
First Year ◽  
Colour Discrimination ◽  
The Subject ◽  
The Mean ◽  
First Year Of Life

Colour discrimination was investigated in infants aged 4 – 14 months. 250 healthy subjects and 80 subjects with slight defects in basic visual functions (the risk group) participated. A coloured toy was moved in front of the subject and disappeared behind a screen, reappearing after 2 – 3 s at the other side. Sometimes when the toy was hidden, the experimenter replaced it with another one that differed only in colour: yellow was replaced by blue or vice versa (Y/B switch), or red by green or vice versa (R/G switch). The form and size of the toy remained constant. The emotional reaction of surprise showed whether the infant discriminated these colour pairs. The brightness of the stimuli was slightly varied make sure that the infant reacted to the change in colour rather than brightness. About 75% of healthy 4 – 5-month-olds showed good expressive reactions to the Y/B switch, and practically all children did so at 7 – 8 months. The discrimination of red and green develops more slowly: only at 12 months did practically all children show good reactions to the R/G switch. In all children, Y/B discrimination preceded R/G discrimination. The mean difference between the numbers of children discriminating these two pairs was 7.6%. The infants of the risk group were as good as their healthy age-mates in Y/B discrimination, but performed significantly less well on R/G: the mean difference between the numbers discriminating the former but not the latter was 17.0%. Possible reasons for the retardation of chromatic discrimination in the risk group are discussed.

Aspects of Teacher Discourse and Student Achievement in Mathematics

1977 ◽  
Vol 8 (3) ◽  
pp. 195-204
Author(s):  
Lyle R. Smith
Keyword(s):  
High School ◽  
Student Achievement ◽  
First Year ◽  
Teacher Discourse ◽  
High School Algebra ◽  
Several Variables ◽  
The Mean ◽  
Achievement In Mathematics ◽  
Algebra Class

Each of 20 high school algebra teachers taught a lesson on direct variation to one first-year algebra class. The students (N=455) had not previously been taught this topic in class. Before the lessons were taught, each teacher was given a list of lesson objectives. Immediately after each lesson, a posttest that focused on the lesson objectives was administered. The teachers were not shown the posttest before they taught their lessons. Correlations were found between the mean posttest scores for the classes and several variables pertaining to teacher discourse.

An Achievement test in Solid Geometry

1928 ◽  
Vol 21 (3) ◽  
pp. 151-162
Author(s):  
Louis A. McCoy
Keyword(s):  
Secondary School ◽  
Subject Matter ◽  
Achievement Test ◽  
School Mathematics ◽  
The Other ◽  
Good Teacher ◽  
Secondary School Mathematics ◽  
Solid Geometry ◽  
The Subject ◽  
The Right

In the work of teaching secondary school mathematics in a large school where there are as many as twelve different divisions of the same subject, it would be very interesting and indeed very enlightening to see the different grades of work being done. Different teachers have their own pet ways of doing things, of presenting new matter, of conducting recitations, of drilling on old matter, of developing mathematical power in their pupils, etc. And yet they are all striving for the same results. The fact that one teacher's pupils consistently attain better results naturally should put a premium on that teacher's methods, and the work of the department would be improved if some of the other teachers would take a leaf out of the successful teacher's book. Students will often remark “So and So is a good teacher; I get a lot out of his class; he makes things clear; he has good discipline; he certainly gets the stuff over, etc.”An inspector visits the class, notes the attitude of the pupils, the personality and skill of the teacher, and oftentimes is familiar enough with the subject matter of the recitation to see if the pupils are catching and giving back the right things, and then grades the teacher as an Al man, for example. But does the opinion of the boys themselves or the visitor answer the question whether or not the teacher is successful in giving his subject to the pupils? Don't we need something more objective, more tangible, more exact on which to pin our faith? In general the supervisors are hitting it right, also the students, but we think we can do better.

Fixed Point Theorems in Euclidean Geometry

1973 ◽  
Vol 66 (4) ◽  
pp. 324-330
Author(s):  
Stanley R. Clemens
Keyword(s):  
High School ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Euclidean Geometry ◽  
Transformation Theory ◽  
High School Geometry ◽  
School Geometry ◽  
The Subject ◽  
Points Of View ◽  
Modern Mathematics

The direction of future high school geometry courses is currently the subject of much discussion. One frequent suggestion is that high school geometry should be presented with transformation theory as the unifying theme. In support of this new direction, we shall illustrate that transformations can be employed to bring theorems from classical synthetic geometry into the so-called mainstream of modern mathematics. The thread tying these two points of view together will be the application of fixed point theorems.

Perception of Illness among Secondary School Pupils in South Africa: Malaria, Tuberculosis, HIV/AIDS, and Alcoholism

2001 ◽  
Vol 88 (3) ◽  
pp. 847-848 ◽  
Author(s):  
Karl Peltzer
Keyword(s):  
South Africa ◽  
High School ◽  
High School Students ◽  
Secondary School ◽  
Secondary Schools ◽  
The Other ◽  
Northern Province ◽  
School Students ◽  
Gradual Onset ◽  
Hiv Aids

The study investigated beliefs of 121 high school students in Grade 11 about people who are ill with malaria, tuberculosis, HIV/AIDS, and alcoholism. The sample of Black pupils were chosen at random from two rural secondary schools in one region in the Northern Province of South Africa. Analysis indicated that HIV/AIDS was clearly distinguished from the other three illnesses by being seen as the least easily cured, having the most gradual onset, being the most contagious, showing the least look of illness, and the patients being likely those most blamed for their illness.

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