Background
I have several reasons for wanting to write this unit on utilizing place value to understand multiplication. First, I want my students to know how to use the basic principles of number sense to assist them in solving more complex problems and to demonstrate how that understanding is a driving force in their overall understanding of mathematics in their future courses. Number sense can be defined as:
A person's ability to use and understand numbers:
- knowing their relative values,
- how to use them to make judgments,
- how to use them in flexible ways when adding, subtracting, multiplying or dividing
- how to develop useful strategies when counting, measuring or estimating.2
My students have an extremely difficult time with all aspects of number sense. It seems that students move from one grade level to the next without a clear understanding of the basics which only serves to increase their overall deficits in mathematics. These deficits include, but are not limited to, computation with basic addition, subtracting across zeros, and knowing the basic multiplication and division facts. With such deficits in their foundation, how can they progress with success to more challenging or grade level expectations? A student can read a book fluently, memorize the historical contributions to the arrival of Africans in the Jamestown Settlement, and even carry out the steps of the scientific method, but as Paul Halmos3 expresses it, “the only way to learn mathematics is to do mathematics.”
Secondly, it is also of vital importance to me that my students begin to feel that math is indeed something that they can do and that we can have some fun while doing it. In my nine years of teaching, I have had the pleasure of teaching, mentoring, and interacting with hundreds of students yearly on multiple levels inside and outside of the classroom, but I cannot recall one student who has simply said, “I get math, it comes easy to me.” I have many students say, “I like math but I simply do not get it.” The most common statement is, “Math is too hard so I don’t like it.” Personally, I receive all three statements as they are and I am grateful that the student would share their thought with me. But in doing so they knew that I would do something with the information. I am 100% confident in knowing that my students trust that I care about them and want them to do well, and that is a great honor that I will always cherish. This level of trust also allows me to take them to a place of discomfort in regard to mathematics.
Third, for far too long students have been given math instruction based on simply arriving at a solution without an understanding as to how they arrived at the solution, and more importantly, what the solution means in terms of the initial problem given. In this unit, my desire is to take these components to bring my students’ understanding and application of number sense full circle.
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