The ABC's of the Math123's
3 Essential Tools for Every Student of Mathematics
A – the answer. When adding in mathematics, the answer is called the sum. When subtracting, it’s called the difference; the quotient when dividing, and the product when multiplying. Getting to the correct answer is the ultimate goal in mathematics. Whether solving an equation, evaluating an expression, writing an algebraic expression, simplifying a fraction, finding the sum, difference, quotient, or product, or problem solving, the goal does not change: finding the correct answer . Once students understand the ultimate goal, they can take ownership of finding the correct answer through brainstorming, strategizing, discoveries, and application.
B – basics (fundamentals). Students of mathematics must be equipped with basic mathematical fundamentals for reaching the ultimate goal of finding correct answers. Consider this goal their job. Just like on a real job, if workers are to perform their jobs well, they must be trained and provided the proper resources and skills for meeting goals. This same concept applies to learners of mathematics. Students must be equipped with the basics and fundamentals necessary for finding correct answers when working mathematics. Students should know how to
1) add, subtract, multiply, and divide and relate the operations accordingly
2) choose appropriate problem solving strategies
3) choose correct operation(s)
4) model problems
5) check their work and answers for accuracy (determining reasonableness)
6) connect prior knowledge to new knowledge
7) apply new knowledge in different formats and contexts
8) defend their answers (developing their thought process)
9) discover, model, and adopt strategies that work for them
10) discover or be shown more than one way to get to correct answers
C – confidence. Now that the ultimate goal (finding the correct answer) and the tools for accomplishing this goal have been identified, the last essential resource for every math student is confidence. A student’s confidence in their ability to attain the ultimate goal is developed carefully and thoughtfully through teacher, parent, and peer encouragement, student discoveries, and classroom opportunities for success through modeling, teaching, learning, and the equipping of students with the necessary fundamentals for finding correct answers.