Every year I talk with parents who want to help their child memorize ‘math facts’. Why do we teach it differently now? If my middle school child did not develop fact fluency in elementary school, is it too late? Most importantly, how can I help my child? It is never too late to develop these skills! It is essential that teachers and parents work together. Let’s discuss why we teach it differently and ways you can help at home.
Multiplication Fact Fluency vs Procedural Fluency
Yes, your child is learning differently. This is a great change; it promotes better thinking skills and builds a stronger mathematical foundation! Experts agree it is very important for students to have a thorough understanding of concepts rather than memorizing and practicing procedures they do not understand. In fact, research shows students who are exposed to the reasoning after first learning a procedure do not do as well or remember it as long as students who are first taught conceptually.
Fluency in mathematics is important, and procedural fluency (including basic facts) affects many areas of mathematics. Students do not have to answer more quickly than anyone else to be fluent, but they should be able to determine an accurate answer using a variety of strategies in an appropriate amount of time. Students should also be able to apply these procedures to a variety of problems and situations.
Do you remember what you wore last Tuesday? Do you remember what you had for lunch last Monday? Remembering random facts is not something most of us even try to do. It is not an indication of intelligence—no critical thinking is required! How is this related to fact fluency? Just memorizing facts without meaning is not helpful. It is the equivalent of memorizing what you wear each day! The National Council of Teachers of Mathematics explains it well in their position statement on procedural fluency. We don’t want students to just memorize facts or formulas; we want students to understand the concepts so they can apply them in a variety of situations. Practice is essential for building multiplication fluency, but it should be engaging and purposeful!
How to Practice Multiplication Fact Fluency at Home
Is your child still counting to find the product of 6 x 7? Using an area model can help improve procedural fluency! We use Color Tiles, but you can modify this at home with anything that will create an array. Check out our math manipulatives products for inspiration!
Before beginning, ask your child to build an array that represents a challenging fact, such as 6 x 7. If your child understands the concept and is able to build this array, then s/he is ready to begin using strategies to improve multiplication fluency!
Ask your child to determine the number of tiles without counting every square. What strategy is used? Is there a more efficient way? One goal for all students K–12 is to look for and make use of structure. By focusing on what students know and using those skills to build new understanding, you are building both fluency and confidence! Students can quickly determine multiples of 1, 2, 5, and 10. How does that help them? What if you had a candy bar, broke it into pieces, and ate all the pieces? How much of the candy bar did you eat? The picture below shows some examples of how this idea (the distributive property) helps students. Notice that each section represents an easier problem! Then students find the sum of the parts. (Is your child struggling with addition? We’ll discuss that in a future post.)
Parents have told me this appears to be a lot of work. Yes, it does require more thinking and time. It also has many more benefits! This type of thinking is used to solve multiplication of multi-digit numbers. In middle and high school, this model helps students understand how to multiply polynomials! It is a foundational concept and is worth the effort!
The tiles are easy to use anywhere. Your child could even use them on a cookie sheet while in the car. Is your child more interested in a digital resource? Try Brainingcamp.com!
The next step is for your child to draw a representation of this rather than building it. Older students may move to this stage quickly. Finally, practice is still important, but when your child is able to do this mentally, there are ways to practice that are meaningful and engaging. We will discuss those ways in another blog!
Leanne Luttrell strongly believes mathematics is so much more than basic computation, formulas, and memorization! In her 30 years of experience in education, has had a variety of roles, including elementary and middle school teacher, math coach, K-12 gifted endorsement instructor, professional development leader, curriculum developer, author, and grades 3-9 tutor. In addition to other awards and honors, Leanne received the Presidential Award for Excellence in Mathematics and Science Teaching in 2004. She is excited to be part of the hand2mind team!