As a non-math major (heck, I’m not even a math minor… and never been asked to teach mathematics in my practicums, which is why I am taking this class), I am often reminded that mathematics possesses its own language and specialized vocabulary that students almost entirely learn at school. The same is true for English. Synecdoche and metonymy, anyone? The chapter says that studies show there is a lack of opportunities for students to learn mathematics at home, especially compared to opportunities in language and literacy development (120). Children need to learn how to speak to communicate and their caregivers speak around and to them all the time, so it’s not surprising that youngsters pick up language, but I’m interested in knowing the reasons why parents do not teach their children mathematics to the same degree. Is it cultural? After all, mathematics is all around us. However, I digress from the list of prescribed topics I am supposed to write about this week.
Concerning number sense, the chapter defines this as students’ fluidity and flexibility with numbers, and connecting those numbers to real-life experiences. I found it interesting that the “evolving number sense typically comes as a by-product of learning rather than through direct instruction” (126). This certainly makes a case for rich, hands-on tasks over teacher-led lectures. It also means that students do not best learn number sense through memorization. The chapter suggests several ways to incorporate number sense in a typical school day: circle time, attendance, lining up, and more (136). It is a seamless way to connect numbers to real-life experiences, and students think mathematically probably without even realizing that they are participating in mathematics.
As for the part-part-whole relationships, the chapter does not mention “math stories,” but this is what my son calls them in Grade 1 or 2 when he was asked to look at or come up with combinations that make x. The chapter’s suggestion makes sense to keep x a constant number throughout the activities so as to not confuse the students.
Moving on to Chapter 10, the text defines mastery of basic math facts as when a student can give “quick response (about three seconds) without resorting to inefficient means, such as counting by ones” (162). Again, the text says that memorization is not the way to go (162) because it is inefficient, inflexible, and can lead to students misapplying facts (163). There is a development process that goes along with basic fact mastery for addition and subtraction with “retrieval from long-term memory” as the last part of the process (163). Two other approaches to fact mastery get thumbs up: Explicit strategy and guided invention. The key to both is to present students with a collection of strategies, or what I like to think as a toolbox, and allow students to practise them, and then stick with the ones that work for them. As teachers, we lesson plan with kinesthetic, auditory and visual learners in mind, so it does not seem that much of a stretch to allow students to approach mathematics with the reasoning strategies that make sense to them. But first, the teacher must have a “command of as many successful strategies as possible” (164) in order to recognize effective ones and aid students.