Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.

“Fluency in each grade involves a mixture of just knowing some answers, knowing some answers from patterns (e.g., “adding 0 yields the same number”), and knowing some answers from the use of strategies. It is important to push sensitively and encouragingly toward fluency of the designated numbers at each grade level, recognizing that fluency will be a mixture of these kinds of thinking which may differ across students.”

“Low achievers are often low achievers not because they know less but because they don’t use numbers flexibly – they have been set on the wrong path, often from an early age, of trying to memorize methods instead of interacting with numbers flexibly (Boaler, 2009). This incorrect pathway means that they are often learning a harder mathematics and sadly, they often face a lifetime of mathematics problems.

Number sense is the foundation for all higher-level mathematics and when students fail algebra it is often because they don’t have number sense. (Feikes & Schwingendorf, 2008)

When students focus on memorizing times tables they often memorize facts without number sense, which means they are very limited in what they can do and are prone to making errors

For about one third of students the onset of timed testing is the beginning of math anxiety (Boaler, 2014). When students are stressed, such as when they are taking math questions under time pressure, the working memory becomes blocked and students cannot access math facts they know (Beilock, 2011; Ramirez, et al, 2013). As students realize they cannot perform well on timed tests they start to develop anxiety and their mathematical confidence erodes. It is important when teaching students number sense and number facts never to emphasize speed. In fact this is true for all mathematics. The fact of being quick or slow isn’t really relevant.’ (Schwartz, 2001). Sadly speed and test driven math classrooms lead many students who are slow and deep thinkers to believe that they cannot be good at math.”

“Premature [fact] drill, however, will certainly be ineffective, waste valuable time, and for many students contribute to a strong distaste for and a faulty view of learning mathematics.” (Van de Walle, 2007). “Drilling inefficient methods does not produce mastery.” (Van de Walle, 2014).

Some of our best mathematical thinkers are often those most negatively influenced by timed testing. National Council of Mathematics Teachers, April 2014