According to Shulman, he has list seven types of knowledge which are important and necessary for teaching.
In my opinion, I will say that content knowledge is the most important knowledge a mathematics teacher must have. Content knowledge means the concepts, principles, relationships, processes, and applications a person should know within a given academic subject, appropriate for his/her developmental age/grade level. Teachers must have a broad and comprehensive understanding of the subject and they must be able to deliver subject content in a competent and confident manner. By having an in depth knowledge of content, teachers will be able to cater for all ranges of ability with their student groups. Other than that, they can help the students to create useful cognitive maps, relate one idea to another, and address misconceptions. This is very important as we are looking on the knowledge necessary for teaching in mathematics. A mathematics teacher must fluency and care with mathematical language and notation. I have been told by my mathematics’ teacher that mathematics is a subject of concepts and logics when I’m in secondary school and I still remember it until today.
After a teacher having the content knowledge, he or she must have general pedagogical knowledge. Teach not only involves learning content and how to translate that subject matter into an understandable form. It also requires knowledge about the process to teaching itself. Pedagogical knowledge involves the classroom management and control. A teacher must have its own style in teaching that can attract the student to listen to the taught. As we know there are some students who scare of mathematics and think that mathematics is very hard. So teacher must motivate the students and tell them to be friend with mathematics. Since mathematics is a subject of concepts and logics, a teacher must has knowledge on how to deliver the concepts or theories to students so that they will have better understanding and know how or when to use it.
Teaching any subject in our country must follow the curriculum that has been plan by our government. So there are some particular materials like text books or any others materials that are suitable to use as the teaching materials. Every subject has its own syllabus and it is a need in the education of our country. Thus, a teacher must have the knowledge of curriculum.
Another type of knowledge that I also agree with Shulman is the knowledge of learner and their characteristics. Being a teacher, he or she must have self awareness on their behaviour. Why am I saying so? People always saying that parent should act as a role model to their children. Parents always being blame of the delinquency of teenagers. Since students spend almost half of the day in the school, so we cannot denied that the teachers also play an important role. Thus, teachers should aware of their behaviour in the classroom because it will affect how individuals learn.
Lastly, I would like to conclude that a mathematics teacher must able:
• Design mathematically accurate explanations that are comprehensible and useful for students
• Use mathematically appropriate and comprehensible definitions
• Represent ideas carefully, mapping between a physical or graphical model, the symbolic notation, and the operation or process
• Interpret and make mathematical and pedagogical judgments about students’ questions, solutions, problems, and insights (both predictable and unusual)
• Be able to respond productively to students’ mathematical questions and curiosities
• Make judgments about the mathematical quality of instructional materials and modify as necessary
• Be able to pose good mathematical questions and problems that are productive for students’ learning
• Assess students’ mathematics learning and take next steps
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