So to continue with yesterday's discussion, I wondered what skills do most people consider necessary so a student will not struggle when they take Algebra I. Algebra I is the class that moves students from straight calculations to working with more abstract computations. It requires students to develop deeper thinking skills and learn more in depth problem solving skills.
Students need to have a strong foundation in the standard four operations and they should know their times tables up to 10 x 10. I realize we have calculators now but if a student does not know these items, they won't know if they have a reasonable answer.
They should also be familiar with using signed numbers with normal operations of addition, subtraction, multiplication or division. They need to understand that -10 - 10 has the same answer as -10 + (-10). They need to have developed a number sense for signed numbers.
In addition, it would helpful for students to have a good foundation with fractions because they will be dealing with algebraic fractions at some point in Algebra I. They need to know the process for finding a common denominator when adding fractions with different denominators. They should be fluent in using exponents and the rules associated with them. Exponents are used throughout Algebra I and without that knowledge, they will struggle.
As far as other skills, it helps to have a good grasp of certain basic properties such as the commutative, associative, or distributive property. These three properties are used in one way or another to solve algebraic equations. Students don't need to name them, just how to apply them.
In addition, they need to have the ability to turn a word problem into an algebraic expression or equation so they can solve it. I've found when I worked in industry, I spent a lot of time working from word problems either in the form that my boss was telling me the end result. This is a skill that is not as well developed by many students because their elementary teachers are not good at it so they don't focus on it.
As I stated yesterday, when I was in middle school, we had to take a test to see if we had the necessary skills to succeed in Algebra I. Why don't we forget this race to get students taking higher levels of math before they are ready and concentrate on making sure they have the skills they need as they are developmentally ready