scholarly journals The Road of the German Book Praktische Analysis into Japanese Secondary School Mathematics Textbooks (1943–1944): An Influence of the Felix Klein Movement on the Far East

2018 ◽  
pp. 117-129
Author(s):  
Masami Isoda
Keyword(s):  
Secondary School ◽  
Far East ◽  
School Mathematics ◽  
Mathematics Textbooks ◽  
Secondary School Mathematics ◽  
The Road ◽  
Felix Klein ◽  
The Far East

Graphs in Real Time

1999 ◽  
Vol 5 (2) ◽  
pp. 92-99
Author(s):  
Charlene E. Beckmann ◽  
Kara Rozanski
Keyword(s):  
Secondary School ◽  
Real Time ◽  
School Mathematics ◽  
Mathematics Textbooks ◽  
Constant Ratio ◽  
Secondary School Mathematics

Slope is introduced in various ways in current middle and secondary school mathematics textbooks. In one approach, students graph a line and determine the vertical and horizontal distances from the axes to a point on the line, determining the coordinates of the point. Students then calculate the ratio of vertical distances to horizontal distances for several pairs of points on the line and discover that the ratio is always the same. At this point, this constant ratio is defined as the slope of a line. Students are then asked to determine to what aspect of the graph the slope corresponds and how it relates to the equation of the line (Phillips 1991, 55–57).

scholarly journals CAS Assisted Proofs in Upper Secondary School Mathematics Textbooks

2019 ◽  
Vol 8 (3) ◽  
pp. 232
Author(s):  
Uffe Thomas Jankvist ◽  
Morten Misfeldt
Keyword(s):  
Secondary School ◽  
Teaching And Learning ◽  
School Mathematics ◽  
Upper Secondary School ◽  
Mathematics Textbooks ◽  
Secondary School Mathematics ◽  
Proof Schemes ◽  
Mathematical Proofs ◽  
Upper Secondary ◽  
Upper Secondary Level

This article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics textbooks, 38 instances of CAS assisted proofs are identified in ten different textbooks. The CAS based proofs in these textbooks are of three types: complete outsourcing of the proof to CAS; partial outsourcing of the proof to CAS; and additional verification of the proof’ correctness by CAS. Analyses of examples of each of these types are provided. The analyses draw on theoretical constructs related to both proofs and proving (e.g. proof schemes) and to use of digital technologies in mathematics education (lever potential, blackboxing, instrumental genesis). In particular, the analyses make use of a distinction between epistemic, pragmatic and justificational mediations. Results suggest both potential problems with using CAS as an integrated part of deductive mathematical proofs in textbooks, since it appears to promote undesired proof schemes with the students, and difficulties with understanding these problems using the constructs of epistemic and pragmatic mediations that are often adopted in the literature regarding CAS use in mathematics teaching and learning.

Experimental Courses in Secondary School Mathematics

1922 ◽  
Vol 15 (2) ◽  
pp. 63-78
Author(s):  
Raleigh Schorling
Keyword(s):  
Secondary School ◽  
School Mathematics ◽  
National Committee ◽  
Secondary School Mathematics ◽  
The Road ◽  
Mathematical Association ◽  
Committee Work ◽  
On The Road ◽  
Class Room

The National Committee on Mathematical Requirements, working under the auspices of the Mathematical Association of America, and numerous cooperating organizations, has prepared various reports dealing with the reorganization problems of secondary school mathematics. There is a growing sentiment against accepting materials of instruction or even outlines of courses that express merely an individual's opinion, especially if that opinion is not based upon class-room experience. Rut it is equally important to realize that a curriculum constructed in committee sessions, differs only in degree, not in kind. Fortunately, a milestone on the road of progress in education has been reached, which indicates that committee work that would eventuate, must be prefaced and supplemented by carefully made inventories of the experience that bears upon the problems studied. In consequence, a number of sub-committees have made studies of some of the details involved in the fundamental recommendations of the National Committee. One of these investigations deals with experimental courses in mathematics.

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