高中数学教材中数学建模问题情境的比较研究——以人教A版、苏教版和鄂教版为例

A Comparative Study of Mathematical Modelling Problems in High School Mathematics Textbooks—Taking People’s Education Edition A, Jiangsu Education Edition and Hubei Education Edition as Examples

摘要: 高中数学改革发展的重要变革的一方面是数学建模，而高中数学教材中的数学建模内容都以问题情境为载体。研究从内容分布及编排、类型及数量、真实性水平与表征特征为维度，对人教A版、苏教版及鄂教版必修部分数学建模问题情境进行统计分析。得出的主要结论是：三版教材内容及编排虽有差异，但整体呈现循序渐进的特点；文化情境较少，对数学史和数学文化的重视不够；均注重真实性水平；综合型表征较少。本研究据此对教材编写、教材开发以及教师教学提出一些启示。

Abstract: One of the important changes in the reform and development of high school mathematics is mathematical modelling, and the mathematical modelling content in high school mathematics textbooks takes the problem situation as the carrier. The study conducts statistical analysis of the mathematical modelling problems of the compulsory part of People’s Education Edition A, Jiangsu Education Edition and Hubei Education Edition from the dimensions of content distribution and arrangement, type and quantity, authenticity level and characterisation characteristics. The main conclusions drawn are: although the content and arrangement of the three editions of the textbook are different, the overall characteristics are step-by-step; the cultural situation is less, and the mathematical history and the mathematical culture are not enough; both pay attention to the level of authenticity; and the comprehensive representation is less. Based on this, some inspirations are put forward for textbook writing, textbook development and teacher teaching.