Teaching multiplication concepts: how language influences outcomes
In part 1 of this post on language in mathematics, I shared some observations of two vastly different approaches to teaching the concept of multiplication. To recap, I provided a case study of my own two children: Alexander (aged 9) and Isabelle (aged 7). Alexander had learned multiplication the traditional way and relied heavily on skip counting and memorization. Isabelle had taken the conceptual route, an approach that placed greater emphasis on modeling multiplication with objects and pictures and relating the concept of multiplication to repeated addition.
Unfortunately, neither approach provided the “full package.” Isabelle lacked fluency of recall, and Alexander lacked understanding of what multiplication really means. I concluded part 1 with a promise to try and right these wrongs. I hope I’ve delivered on that promise below, organized as a continuation of each case study.
Multiplication Concepts Case study 1: Alexander (continued)
Alexander’s interests include nerf guns, army, and motorbikes. So, it comes as little surprise that talking about math is low on his list of priorities! At the risk of sounding unethical, deception is necessary to engage Alexander with math. He needs to do math without realizing he’s doing it. This approach to language in mathematics requires me to “see the math” in everyday activities. For Alexander, I choose to “see the math” in the army games we play each night before bed. For example, I might stipulate that we each receive the same number of foot soldiers and that these foot soldiers can only be arranged into equal rows on the battlefield. The conditions I place upon the game make Alexander think about math and unknowingly solve the problem (as I said, deception is key). The challenge for me as a parent is to keep up the charade. In short, I have to resist the temptation to teach math in the traditional sense. I don’t ask him to write a multiplication fact to match their arrangement for the battle, but instead question if a 2 x 10 arrangement is the most suitable formation.
Multiplication Concepts Case study 2: Isabelle (continued)
Isabelle is easier to teach than Alexander because at least she’s willing to listen! Isabelle will sit down with you and do her homework without any need for bribery or coercion. However, she still doesn’t enjoy it, so I’m always looking for ways to motivate her. Recently, we gave Isabelle her first iPad, which overtime has become an actual extension of her biological arm. Given Isabelle’s willingness to learn and her love of technology, it made sense to me to impose a set time each day to play an educational game. For Isabelle, this was the car trip to and from school. I’ll refrain from recommending any one mathematics app, but I encourage you to think carefully about the app you choose for your child. Motivation is important, but so to is a sound developmental sequence of the content.
In this post, I’ve shared a practical approach to developing conceptual understanding and fluency that has worked for me and my kids. The reality is there’s no quick fix. You have to know your own child, be pragmatic, and go with whatever works for you. If your child doesn’t like doing math in the traditional sense, try to “see the math” in what they enjoy doing and engage them that way. For Alexander, seeing the math involved my own immersion into the games he likes to play. For Isabelle, seeing the math involved some guidelines around the use of her iPad. Try to “see the math” in what your child likes to do and you’ll have greater success in engaging them in. And, if you do have any innovative methods of using language in mathematics to reinforce multiplication concepts that have worked for you, please do share them in the comments section below.
About the Author
Peter Stowasser has been researching and writing for ORIGO Education since late 2009. He has contributed to the development of both national and international mathematic programs and authored several ORIGO Big Books. Peter has spoken at numerous mathematic conferences within Australia and abroad (United States of America) covering a range of topics across all primary year levels. Peter is now midway through his PhD in mathematics education. His area of interest: Student epistemic cognitions about different mathematic topics.
About ORIGO Education
ORIGO Education is dedicated to making learning mathematics meaningful, enjoyable and accessible for all, offering Pre-K through Grade 6 instructional materials, and professional learning.