An Analysis of Addition and Subtraction Word Problems in American and Soviet Elementary Mathematics Textbooks

1986 ◽  
Vol 3 (3) ◽  
pp. 153-171 ◽  
Author(s):  
James W. Stigler ◽  
Karen C. Fuson ◽  
Mark Ham ◽  
Myong Sook Kim
Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2123
Author(s):  
Raúl Tárraga-Mínguez ◽  
Julio Tarín-Ibáñez ◽  
Irene Lacruz-Pérez

A textbook constitutes the hegemonic material of the educational institution. It acts as a mediator between the official curriculum and the educational practice. Given its potential influence in the classroom, this study analyzes the treatment of word problems included in the mathematics textbooks published by the publishing houses with the greatest diffusion in Spain at every primary education grade. Three variables were analyzed: their semantic structure, their degree of challenge, and their situational context. The results indicate that most of the problems included in textbooks are characterized by low complexity and variability regarding their semantic structure. They are also characterized by a limited degree of challenge and by being presented in highly standardized situational contexts. Likewise, it is found that there is no evolution in the treatment of these problems with respect to previous studies carried out in the Spanish context. Therefore, it is concluded that the mathematics textbooks currently used in schools are not effective tools to address the process of teaching-learning problem solving.


Author(s):  
Rik Koncel-Kedziorski ◽  
Hannaneh Hajishirzi ◽  
Ashish Sabharwal ◽  
Oren Etzioni ◽  
Siena Dumas Ang

This paper formalizes the problem of solving multi-sentence algebraic word problems as that of generating and scoring equation trees. We use integer linear programming to generate equation trees and score their likelihood by learning local and global discriminative models. These models are trained on a small set of word problems and their answers, without any manual annotation, in order to choose the equation that best matches the problem text. We refer to the overall system as Alges.We compare Alges with previous work and show that it covers the full gamut of arithmetic operations whereas Hosseini et al. (2014) only handle addition and subtraction. In addition, Alges overcomes the brittleness of the Kushman et al. (2014) approach on single-equation problems, yielding a 15% to 50% reduction in error.


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