What was missing from Sadlier and where are the math facts?
What was missing from Sadlier is a clear emphasis on students understanding not only how to perform computation but how to apply the math they are learning.
Mathematics facts are important but the memorization of math facts through repetition, practice and timed testing is unnecessary and damaging.
Math facts are a small part of mathematics and are best learned through the use of numbers in different ways and situations.
An outsized focus on math facts gives students the false impression that math facts are the essence of mathematics, and, even worse that the fast recall of math facts is what it means to be a strong mathematics student.
High achieving math students approach problems such as 19 + 7 by changing the problem into, for example, 20 + 6.Or, 21 - 16 into 20 - 15. Low achieving students do not use number sense. 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 of trying to memorize methods instead of interacting with numbers flexibly. This incorrect pathway means that they are often learning a harder mathematics and sadly, they often face a lifetime of mathematics challenges.
Number sense is the foundation for all higher-level mathematics. When students fail algebra it is often because they don’t have number sense. When students work on rich mathematics problems they develop number sense and they also learn and remember math facts.
When students focus on memorizing they often memorize facts without number sense, which means they are very limited in what they can do and are prone to making errors. https://www.youcubed.org/wp-content/uploads/2017/09/Fluency-Without-Fear-1.28.15.pdf
When your student spends multiple lessons learning different methods for addition and subtraction, remember, they are developing the ability to use numbers flexibly and to apply what they have learned to new situations, not just learning to add and subtract.