Research On Grade 10 Students’ Algebraic Thinking Ability ——Taking A High School In Shanghai For Example

In recent decades,the importance of algebra has been widely recognized in the reform of mathematics education in various countries.However,there are still many obstacles in teaching and learning algebra.Many students have difficulty transitioning from arithmetic thinking to algebraic thinking,and the term‘algebraic thinking’has attracted a great deal of attention from researchers.China’s high school mathematics curriculum takes Function as a mainline,and students will learn an abstract definition of Function in Grade 10.Meanwhile,mathematics in high school covers Set,Inequality,and Sequence,requiring students to have a higher level of mathematical literacy.In order to ensure students’ readiness for high school algebra and Function,it is necessary to investigate the current state of their algebraic thinking ability.Based on the theory of algebraic thinking proposed by Kaput,the researcher constructs a framework which includes four content elements of algebraic thinking and investigates Grade 10 students’ algebraic thinking ability through a test.The research questions are as follows.（1）How is the overall performance of Grade 10 students’ algebraic thinking ability?（2）How is the performance of Grade 10 students’ algebraic thinking ability in each content element?（3）Is there any gender difference in the algebraic thinking ability of Grade 10students?（4）Is there a positive relationship between the performance of Grade 10 students’ algebraic thinking ability and their academic performance in mathematics?The results of the study demonstrate that:（1）The overall performance of Grade10 students’ algebraic thinking ability is at a moderate level,and 40% of them excel in using algebraic thinking to solve problems;（2）The students perform well in functional thinking,generalized arithmetic,and modeling language,but not in algebraic proof.For functional thinking,the students are able to discover figural patterns,but they have problems representing the patterns symbolically.For generalized arithmetic,the students are proficient in the properties of numbers and their operations,and have a sense of structure in recognizing relationships between variables.For modeling language,60% of the students are capable of extracting mathematical relationships from real-world contexts,and constructing mathematical models to solve practical problems.For algebraic proof,70% of the students have difficulty in using symbols flexibly to make logically rigorous proofs.（3）The students perform rather well in generalization and operation,but they still have much room for improvement in representation and argumentation;（4）The overall performance of male students is better than that of female students in the test,but there is no statistically significant difference between them;（5）There is a significant positive correlation between students’ performance in the test of algebraic thinking ability and their academic performance in mathematics.Given the research results,several suggestions are proposed for the cultivation and development of students’ algebraic thinking ability:（1）Inspire students to express themselves,and enhance their capability of using symbolic representation;（2）Integrate mathematical thinking and methods into class,and cultivate students’ sense of structure;（3）Focus on the preciseness of students’ thinking and strengthen the training of algebraic proof skills;（4）Pay attention to individual differences and encourage students to explore new ideas and methods.