Fast, Correct Answers Do Matter in Mathematics

In mathematics, developing automaticity in low-level skills is crucial for freeing up mental resources needed for higher-level thinking. Fast and correct answers are essential, as they allow students to focus on complex problem-solving without being bogged down by basic calculations. A case study illustrates this concept through three students—Otto, Rica, and Finn—who demonstrate varying levels of automaticity in multiplication. Otto, who has mastered multiplication, solves problems quickly and confidently, while Rica and Finn struggle due to their lack of automaticity, leading to frustration and fatigue. The article emphasizes that building automaticity requires consistent practice, starting with understanding the underlying concepts, followed by untimed practice, and finally timed exercises. It argues against the false dichotomy of teaching concepts versus procedures, asserting that both must be taught in tandem to support each other as students progress in mathematics. The author concludes that memorization should come after students have a solid grasp of the concepts and procedures, as this approach enhances retention and understanding.

- Automaticity in basic math skills is essential for higher-level problem-solving.

- Students with strong automaticity perform better and feel more confident in math.

- Consistent practice is necessary to develop automaticity in mathematical skills.

- Concepts and procedures in math should be taught together for effective learning.

- Memorization should follow a solid understanding of concepts and procedures.