In thinking about the math courses, I
wanted to ask each of you to consider thinking about one concept such as
multiplication or fractions. Begin to think about how that concept
appears at various levels of instruction. What would be the earliest
exposure a student might have? What vocabulary is essential for the child
to comprehend the concept? How could a child experience the concept,
practice the concept and demonstrate proficiency at an early level?
Then, I would like you to jump ahead
several levels and years. How is this concept applied at higher levels of
math? How does the early vocabulary continue to be important in concept
formation and application? How does one expand this concept to extremely
abstract levels?
As primary grade teachers, we need to
understand how what we do at basic levels forms the foundation of what is to
come. As secondary teachers, we need to understand the basic
concepts instruction and vocabulary so that we may go back to fill in gaps for
those who need remedial instruction.
You might also choose a concept such as
division or multiplication. Try to spend a few moments considering the
various levels and applications. Think about the skills that form the
basis of these operations. A student's knowledge of fractions for example
has ramification throughout high school and college math; yet, it is often the
least developed of math skills as student’s progress
In thinking about multiplication, early exposure seems to come with skip counting and addition word problems involving repeat addends. I appreciate your point about using vocabulary that promotes understanding of concepts to come from early on, such as "3 + 3 + 3 + 3 is 4 times the number 3!" The same language cacn be used later on to introduce the concept of multiplication, including multi-digit. At more abstract levels, 4P can be seen as "4 times P." The same terminology should be used throughout to link the concept across levels.
ReplyDeleteGraham Fletcher has made some great videos that illustrate the progression of math concepts from the early years through advanced levels. He shows exactly how the things taught in the early grades build and remain valuable throughout a child's math education. The videos are found on his website, gfletchy.com .
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