I need guidance on the dual requirements in high school of: 1) using calculators to solve realistic problems but 2) the need of students to reinforce (practice, learn) mental and pencil arithmetic.
I believe that students need to understand how to multiply by 10,100 & 5. They need to completely understand that 3/3 = 1, 1 * x = x, 1 + 0 = 1, 5 -5 = 0, 50 * 89 = 89 * 50 ect. I don't believe that students can grasp an understanding of algebra without this type of arithmetic knowledge - not the type of understanding where they memorize a rule long enough to pass a test - the type of understanding where it is an integral part of their permanent thought processes. My concern is trying to teach Algebra to students who have used calculators so much that they have never developed this comprehension.
How does a teacher develop this type of understanding when the student knows that "THE ANSWER" is simply a couple of button pushes away? Yet text books are written with the intent that students will be using calculators.