This article stresses the importance of teaching early childhood teachers (preK and K) how to relearn and what it means to really know and teach math. They state that teachers should consider how we teach reading through decoding and then attach meaning and apply this to how we teach mathematics. So as we try to decode what “3” means, it can’t just mean the quantity three, and it is not just a word T-H-R-E-E. Representing “3” with three dots would be more accurate but still not complete. Teachers must build MEANING and UNDERSTANDING for the abstract number symbol by developing background knowledge.
To begin, teachers must practice at an early age with SUBTIZING, to instantly “see how many” and see the different sets of units that the number can be broken into. For example: 8 is really 5 and 3, 7 and 1, 6 and 2, 4 and 4, it is not must ONE NUMBER. As children learn number in this way, they will understand and not just call out from rote memorization, but will rather understand the relationship among these numbers. The authors state that the reason the concepts are not being taught properly is that the teachers were not taught properly when they were students are do not “reflect on these deeper number sense connections.”
Build Quantity and Magnitude: Teachers must start with verbal counting, one-to-one correspondence, subitizing, and counting within a set for cardinality. So, for example the teacher would teach “3” by: writing it on the board, giving 3 manipulatives to each students, and discuss that the symbol “3” represents the number of objects in the set. Then, to enrich the understanding, the teacher would show “3” objects in one set and “0” in another set, 2 and 1, and 1 and 2.
Numbers in Context: Now the teacher should give meaning to numbers and show relationships on a number line. So with our previous example using “3” the teacher will show this number on a number line and demonstrate the relationships it has with the numbers around it; 3 is one larger than 2 and it is 1 smaller than 4. Magnitude will be developed when the students understand the relative size of 3 on the number line and understand it’s “place” or “where it lives.” Another example: a teacher can have the class count boys and girls in the class and represent each of these on a number line. Then the teacher must use the numbers on the number line to talk about the relationships. Number line play will also develop math understanding of before, after, more than, less than, and equal to.
This article has has taught me that children do not innately “understand” number just like they do not initially understand letters and words either. This skill must be taught in a comprehensive way so that true meaning is achieved rather than mere memorization and rote use of number. I will use the methods of this article, verbal counting, one-to-one correspondence, subitizing and counting for the “set,” grouping, demonstrating relationships, showing on a number line and making games of counting and showing relationships with number.
Katie – You said that you thought some of this was too complex for such young students. I disagree. I think that teaching children the meaning of “3” and showing relationships and building connections seems simple. Are you just talking about how they discussed the process? Because, if so, I agree …. you wouldn’t say to Kinders “We are going to learn that the orthographic symbol 3 represents more than just a number, or a group of items, or a word …..” Some of their wording was truly complex and confusing.