Canadian Elementary Teachers' Conceptions And Practices In Catering For Students' Individual Differences In Mathematics Teaching

The Ministry of Education in Ontario,Canada,has implemented curriculum and teaching reform that encourages “Support every child,reach every student”.As teachers are the practitioners of the reformation of teaching,it is particularly important for teachers to catering to students' individual differences in classroom teaching.The purpose of this study is to explore the teaching conceptions and teaching practice of Canadian elementary teachers in catering for students' individual differences in the teaching of mathematics and to explore the factors that affect their conceptions of teaching and their teaching practices.This study adopted the orientation of the qualitative research and instrumental case study and the multiple case study were both used as the research strategies.The participants included four teachers,two principals and two coaches at these two public elementary schools in Toronto,Canada.The data collection included classroom observation and interview with the four teachers,and some interviews with the principals and the coaches.The source of data also includes the teaching materials,which were collected during the observations and interviews with teachers,the relevant data of the school curriculum and the teaching plans.I observed the teachers in the classroom and then conducted the interviews with the teachers based on the observations.The overall idea is observing the teachers' teaching first and then from this entry point to conduct interviews and more follow-up questions with the teachers based on the discovery from the observations.And then to reveal the teachers' conceptions of teaching from teachers' description in catering to students' individual differences in the teaching of mathematics.The study found that the common features of the teaching practice of these four teachers in catering to students' individual differences in the teaching of mathematics are as follows:(1)open-ended questions and parallel tasks were designed to enable all students can have the opportunities to participate in learning;(2)Canadian teachers' mathematics examples tended to be based on the real life situation,these teachers paid attention to the students' level of preparation,learning style,and the way of learning,manipulatives were important to help students understanding mathematical concepts and visualizing thinking,what's more,technology such as math games and coding were integrated into mathematics teaching to engage students;(3)students were encouraged to use a variety of ways to express their learning products,and teachers used observation,communication,discussion,and other ways to conduct ongoing formative assessment of students throughout the teaching process;(4)Canadian teachers tended to pay attention to the arrangement of classroom physical space in order to promote students to become independent learners,and teachers focused on creating a safe learning environment for students to feel free to take risks and make mistakes.The study also found that the teaching conceptions of the four teachers showed some common characteristics:(1)they firmly believe that there are some individual differences between students,and that every student can achieve his or her potential within their zone of proximal development;(2)how teachers teach is the most important factor affecting students' mathematics learning,teachers should pay attention to students' preparation level of learning,learning style and interest in mathematics teaching,and teachers should learn with students with a growth mindset;(3)teachers indicated that learning expectations should take into account the students' ability and level,their preparation levels and also learning styles,and attach importance to the cultivation of mathematics application ability;(4)the flexible use of curriculum is an effective teaching practice,teachers should help students to find mathematics in students' real life situations;(5)teachers advocated that teaching should be adjusted according to students' learning needs,and a safe learning environment should be created so that students can feel free to take risks and have a try;and(6)Canadian teachers emphasize that there are various ways to assess students' mathematical learning in daily teaching.The study further found that teachers' beliefs and values of teaching,teachers' teaching experience,teachers' pedagogical knowledge and ability,the personal experience,teachers' learning and self-reflection and other personal characters are the important personal factors that influence teachers' practices and conceptions in catering for students' individual difference in mathematics teaching.The beliefs of teaching,the teaching experience and their personal experience determine how the teachers think about students' mathematics learning and the nature of mathematics teaching.The teacher's pedagogical knowledge is the ability of the teachers in catering to students individual differences.The teacher's learning and self-reflection are the endogenous power to promote the interaction of other factors.At the same time,how teachers cater to students' individual differences is also influenced by the factors from school that include the school culture,the principals,the organized professional activities in the school and also the students.There is a certain degree of interaction between the school situation factors and teachers' practices in catering to students' individual differences.In addition,the educational policy of Ontario,organized professional activities out-ofschool,group support,and individual support out-of-school are other factors that have a certain impact on the teachers' catering for students individual differences.Based on the analysis and discussion of the above research findings,and combined with the present situation and existing problems of taking care of students' individual differences in elementary mathematics teaching in China,this study puts forward some suggestions for mathematics teachers and some departments of the Ministry of Education.It is suggested that teachers should design open-ended questions and parallel tasks to cater to the different learning needs of students,and change their own roles in the classroom to help students to become independent learners.Building a safe learning environment to build students' self-confidence in mathematics learning is also needed,and teachers need to assist in differentiated instruction through the deep integration of technology and mathematics curriculum.It is also important for teachers to pay more attention to students' real-life experience when they make lesson plans,and build students' skills of using mathematics through interdisciplinary inquiry projects.It is also a good idea to combine assessment with the process of teaching by using the ongoing formative assessment and so on.At the same time,it is hoped that some departments of the Ministry of Education can help teachers to plan their professional development in an autonomous and active way instead of the passive way,and increase supports for teachers in caring for students' individual differences with a professional expert in differentiated instruction.