The article, Multiplication Fact Fluency: Using Doubles by Judith Flowers and Rheta Rubenstein discusses approaches that use and develop problem solving, reasoning and confidence in learners. Multiplication fact fluency is part of an elementary curriculum, but is a skill many middle students continue to struggle with.
“Not knowing multiplication facts creates a gap in a student’s mathematics development and undermines confidence and disposition toward further mathematical learning
(Wallace and Gurganus 2005).”
We associate learning multiplication facts with drills, skip counting, practice and tools for memorization, such as flashcards. Flowers and Rubenstein suggest approaches that apply number relationships, base-ten structures of our place value system, decomposing and recomposing numbers. These strategies build on the process of doubling. Ultimately, we want to give students more opportunity to use a variety of strategies.
“Students are asked to identify what they know and to reason their way from using familiar facts to accumulating new ones. The process exploits the idea of doubling, a natural and energizing process
that many students already have mastered and which helps to initiate a learning strand that leads to proportional reasoning.”
The doubling process is broken down into stages called problem sets. It develops a sequence of mental math from simple doubling problems to more complex. This can be done through individual, small group, or whole class instruction. Once doubling is mastered, the connection to multiplication can be introduced.
When teaching facts of 3, Flowers and Rubenstein relate doubling and repeated addition. For example, the fact 3 x 7 = 7 + 7 and add from there. When those mental math skills are strengthened, students think to decompose the number. For example, 7 as (6 + 1) or (5 + 2).
Another suggestion is to take inventory and record of “facts I know” and “facts I need to learn.” Using this data, arrays can be constructed to visualize properties. This strategy will also build upon the concept of area.
“These activities strengthen and continue to build on an understanding of useful mathematical concepts, such as the place-value structure of our base-ten numeration system, the distributive
property, and decomposing and recomposing. For future learning, these activities pave the way for such important work ahead as multiplicative comparisons, rational numbers, probability, exponential growth, and proportional reasoning.”
After reading this article, it assured me even though I thought I was spending too much time reviewing basic math facts in the beginning of the year, I was effectively strengthening my students mathematic reasoning skills. Having taught third grade for six years, in September I spend a solid week or two on basic math facts. I expose them to mental math skills such as, doubling, doubling +1, doubling -1, addends of 10, etc. Multiplication is a major part of the third grade math curriculum. I don’t really emphasize on the memorization of facts as I do on the multiplication concept. I break down the concept by using precise wording, repeated addition, pictures of grouping, and constructing arrays. I assess my students on the concept as well as their facts (not timed). After completing our multiplication unit, I know my students are able to compute any multiplication problem they are given with a variety of strategies.
How this will help me to teach a math class?:
I was always a struggling student throughout my schooling. I believe my disability benefits me when instructing my students. When I teach certain concepts, I find myself teaching outside the text to relate concepts as I would comprehend them if I were the student. The article assured me to continue to build my students reasoning and problem solving skills when teaching math. It’s okay to spend an extra day on certain concepts on building a “foundation” because it will ultimately benefit my students down the road when learning more complex topics.