When teachers emphasize the memorization of facts, and give tests to measure number facts students suffer in two important ways. For about one third of students the onset of timed testing is the beginning of math anxiety (Boaler, 2014)

In recent years brain researchers have found that the students who are most successful with number problems are those who are using different brain pathways – one that is numerical and symbolic and the other that involves more intuitive and spatial reasoning

activities that encourage visual understanding of number facts

In order to learn to be a good English student, to read and understand novels, or poetry, students need to have memorized the meanings of many words. But no English student would say or think that learning about English is about the fast memorization and fast recall of words.

The core of mathematics is reasoning – thinking through why methods make sense and talking about reasons for the use of different methods (Boaler, 2013). Math facts are a small part of mathematics and probably the least interesting part at that.

stop seeing mathematics as calculating

Conrad Wolfram

students need to learn calculating through number sense

links the memorization of number facts to students’ understanding of more complex functions, which is not supported by research evidence.

What research tells us is that students understand more complex functions when they have num- ber sense and deep understanding of numerical principles, not blind memorization or fast recall (Boaler, 2009).

the lowest achieving students are those who focus on memorization and who believe that memorizing is important when studying for mathematics (Boaler & Zoido, in press).

PISA

The highest achievers in the world are those who focus on big ideas in mathematics, and connections between ideas.

One of the best methods for teaching number sense and math facts at the same time is a teaching strategy called ‘number talks’

Two books, one by Cathy Humphreys and Ruth Parker (in press) and another by Sherry Parish (2014) illustrate many different number talks to work on with secondary and elementary students, respectively.

Research tells us that the best mathematics classrooms are those in which students learn number facts and number sense through engaging activities that focus on mathematical understanding rather than rote memorization.