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Preparing Students for High School Mathematics – A High School Maths Teacher’s Wish List
During many years of my teaching career in high school mathematics, I heard many older teachers complain that elementary teachers do not prepare their students well for high school mathematics. They complained about the different maths standards of students from different primary schools that fed into their high school. So, in my role as head of a high school Mathematics department, I decide to present a workshop for elementary teachers to explain what my teachers and I would like to see in our new students. You could call it the “High School Math Teacher’s Wish List.”
Here is the wish list:
• Develop a work ethic as part of normal classroom culture I. e. students continue with work immediately. (Time is a big issue in secondary school where, especially in upper school, the required work to be covered for school accreditation is imposed and checked annually)
• Develop a homework ethic where homework is set nightly and reviewed daily. (In most elementary schools, homework is set weekly. In core high school subjects, homework is often done daily or set several times a week.)
• Develop a study ethic. Homework does not = study. (The study must consolidate the fundamentals of the subject that the student must know to be successful and those areas that the student finds difficult).
• Develop the belief that all students can do some math. Debunk the myth that math is hard. (It’s important to teach your students to think of all math problems as easy. This will encourage them to at least try the problem.)
• Develop an understanding that mathematics is an essential part of life and that we make mathematical decisions every day without realizing that we are doing so.
• Instill in students the belief that asking questions is a “cool” thing to do.
• Inculcate in students the belief that mathematics is not for boys but is unisexual.
• Give students a taste of a high school-type lesson.
o Chalk and conversation lessons;
o Formal exams
o Textbook exercises.
In addition to teaching the content of their curriculum, I would like elementary teachers to introduce these ideas to their students below if it is not part of their teaching regime. Most of these ideas are designed to improve math results for all students. They reduce errors, reduce time spent on individual exercises, increase work performance and result in better exam results. This creates happier students who will see Mathematics as a discipline in which they can be more successful.
These ideas (with some explanations) include:
• Order agreement; (The student’s understanding of this is often poor by the time they reach high school. They often use the BOMDAS or BODMAS method.)
• Examination technique; (This leads to less fear of exams – more questions attempted and better results).
• A verification procedure; (This will reduce careless mistakes and increase confidence).
• How to solve problems; approach exercises in unfamiliar and practical situations/contexts; (Problem-solving strategies will reduce fear of these problems. Teachers should model these strategies for their students often.)
• Estimation as a form of verification; (This should be done at the beginning of the solution and serve to check that the answer is what was expected).
• A fixation procedure; (This allows the student to communicate their solution mathematically while allowing for easy checking as the student works through the problem.)
• That an answer is not enough. They must explain in written mathematical language how they arrived at the answer.
• That there is often more than one way to solve a problem.
• Estimation is “integral” to solving real problems.
• Teach them to work around the page rather than through the page. (This allows the eye to easily check as the eye moves down instead of traversing the page over many symbols that can confuse the eye).
This “Wish List” could be a “Pie in the Sky” wish. But the ideas it contains are worth expressing.
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