High Efficiency Of The High School Mathematics Learning To The Construction Of Evaluation Index System

As a kind of tools used for mathematical educational evaluation, the Evaluation System of High Efficient Mathematical Learning for High School (ESHEMLHS) are beneficial for improving the theoretical studies of mathematics education, for orientating students toward high efficient mathematical learning, and for contributing to the comparative research in mathematics education.The paper firstly shows the background and the significance of this research; then gives the literature review, combing the evolution of relative research on ESHEMLHS vertically and combing main research directions in this area horizontally; then defines the core concepts and states the theoretical basis of this research in terms of brain science, consciousness theory, learning theory and metacognitive theory.The ESHEMLHS are constructed by using methods of literature research, interviews and questionnaire survey. First, the hypothesis of ESHEMLHS is put forward on the basis of literature research. And then, amends the hypothesis by case interviews, expert consultation to form the ESHEMLHS. Finally, examine the rationality of the evaluation system by collecting data from questionnaire survey, processing them with software of Excel and SPSS, taking statistical description and so on.Through theoretical analysis and empirical research, four first-level indexes of ESHEMLHS are determined. They are:mathematical cognition, mathematical meta-cognition, the non-cognitive factors in mathematical learning, consciousness in mathematical learning. On that basis,18 second-level indexes are identified, among which seven for mathematical cognition:(1) Mathematics Cognitive Structure-mathematical knowledge is relatively complete, grasping multiple representations of mathematical knowledge; (2) Mathematics Cognitive Structure-having the ability of transferring mathematical knowledge, grasping the connection of knowledge; (3) Mathematical Understanding-persisting in independent, in-depth thinking and understanding mathematical knowledge deeply; (4) Mathematical Ability-having a strong mathematical capacity, such as mathematics thinking, mathematics application, mathematics communication, mathematics representation; (5) Mathematical Thought and Method-emphasizing on the comprehension and acquisition of mathematical ideas and methods; (6) being engrossed in mathematics learning, being positive thinking during mathematics classes, taking notes timely and questioning when you do not understand something; (7) having perspicacity during the process of mathematics problem-solving; (8) math score. There also are four second-level indexes for mathematical metacognition, four for the non-cognitive factors in mathematical learning and three for consciousness in mathematical learning.