Language about multiplication can be confusing
The mathematical language we use to describe multiplication can present particular difficulties to some learners. As Kathy Richardson observes, many children “simply don’t understand what the teacher is saying when she uses the word ‘times’.” (Richardson, 2012, p. 160) Linguists use the term mathematics register to talk about the meanings of words like “times” when these words are being used for specialized mathematical purposes (Halliday, 1978, p. 195).
Games and activities teach the mathematical language explicitly
Children benefit when they are given opportunities to learn the meanings of words in the mathematics register, as well as how and why people choose to use these words this way (Schleppegrell, 2007; Riccomini et al., 2015).
That is the main purpose of the activity and game series at the beginning of the Multiplication section. The discussion activity “Think about what multiplication is” connects the mathematical meaning of “times” to the meaning learners already know.
The game “This many stars, that many times” is adapted from the classic “Circles and Stars” by Marilyn Burns (1991), itself similar to “Star Count” by Peggy Kaye (1987). “This many stars, that many times” is conceptually novel in that it focuses attention on the word “times” to reinforce the connection between the mathematical and the familiar meanings of the word.
The discussion activity “Writing number sentences about multiplication helps learners gain comfort with the way “times” is used in number sentences, and the writing activity “Write your own number sentences about multiplication” relates “times” number sentences to a variety of English phrases about rectangular arrays. Rectangular arrays are often used to illustrate multiplication visually and with manipulatives (Bruni and Silverman, 1976; Richardson, 2012, p. 172-174), but many children need explicit assistance to see the relationship between multiplication and arrays (Richardson, 2012, p. 171).
In each of these games and activities, the language is informal, as recommended by M. A. K. Halliday for teaching children about terms in the mathematical register (Halliday, 1978, p. 202-204).
Next section: Earlier games cover needed knowledge
Back to Why the games work
References
Bruni, James V., and Helene J. Silverman. 1976. “The Multiplication Facts: Once More, With Understanding.” The Arithmetic Teacher 23(6): 402-409.
Burns, Marilyn. 1991. Math By All Means: Multiplication, Grade 3. Sausalito, CA: Math Solutions.
Halliday, Michael Alexander Kirkwood. 1978. Language as Social Semiotic. London: Edward Arnold.
Kaye, Peggy. 1987. Games for Math. New York: Pantheon Books.
Schleppegrell, Mary J. 2007. “The Linguistic Challenges of Mathematics Teaching and Learning: A Research Review.” Reading & Writing Quarterly 23(2): 139-159.
Richardson, Kathy. 2012. How Children Learn Number Concepts: A Guide to the Critical Learning Phases. Rowley, MA: Didax, Inc.
Riccomini, Paul J., Gregory W. Smith, Elizabeth M. Hughes, and Karen M. Fries. 2015. “The Language of Mathematics: The Importance of Teaching and Learning Mathematical Vocabulary.” Reading & Writing Quarterly 31(3): 235-252.
July 14, 2020