Success in math fact fluency is driven by delivery of facts and operations. Each operation has a prerequisite. For example, success in addition is prerequisite to both subtraction and multiplication. After years of working with students with learning disabilities and students identified as gifted and talented, it is no longer a surprise that most students will learn addition and multiplication facts much faster than multiplication alone.
In teaching fact fluency, delivery of content in a specific sequence is foremost in the success of your students. Once you recognize sequential delivery is primary to fact fluency success, the methods you choose can be much broader.
Studies including brain scans of young learners practicing facts indicate that subtraction and division are not stored in the same location in long-term memory as addition and multiplication. Therefore, students are not as able to "flip" the answers as we expect them to. Just because a student knows 6+7=13 does not mean he/she knows 13-7=6. Subtraction and division will not be caught unless taught.
Addition is prerequisite to subtraction and multiplication is prerequisite to division. Therefore, the sooner you teach the inverse of a known fact equation, the better the results regarding fact fluency. Including communicative facts in the same group and then following them with groups including their inverse is most effective in helping students fully grasp the fact family concept. Conceptualizing fact families will assist in understanding the communicative properties of addition and multiplication and their relationship with inverse equations. A comprehensive understanding of fact families is prerequisite to computational fluency.
Computational fluency and fact fluency are used as though they are interchangeable terms. They are not. Computational fluency is our ultimate goal and includes, among many things, a students ability to rapidly and fluently travel the number line both forward and backward. It also, includes an innate understanding of the operational symbols and when to move forward or backward on the number line. Computational fluency is most apt to follow fact fluency; therefore, fact fluency is prerequisite to computational fluency for most learners of mathematics.
Rapid fact recall from long term memory provides learners with a fluid ability to break down incremental parts and use them interactively within mathematical concepts. The more rapidly early mathematicians recall facts the less taxation on cognitive memory required for learning mathematics. Therefore, the more fluent learners compute known facts the greater the relativity of the fact in whole or in part within conceptual understanding of high rigor mathematical processes.
Math fact fluency is a necessary prerequisite to success in mathematics, and your sequential delivery of facts and operations will impede or enrich the retrieval of facts from long-term memory. Check out the suggested sequence of deliver in Math Facts Matter. Use this system with materials, methods and strategies you already have or consider some of the Math Facts Matter materials prepared for your convenience.