Introduction
Many educators today would agree to some extent that there has been a shift in mathematics education on many levels and across all grade levels. As a student, one must demonstrate understanding of concepts in mathematics often before one’s brain is developmentally able to comprehend that mathematics is more than procedures or a set of rules to reach a specific solution. The brain of an elementary school student is still being formed, it is constantly absorbing the information around it. Thus, a child’s response to a mathematical inquiry is generally based on his or her current information that can also vary with the activity.
In my experience as a fourth-grade math teacher, the majority of my students have a strong dislike of all things related to multiplication. I am accustomed to the moans and groans as well as the “it’s too hard” or “it takes too long” cries from my students. I often wonder, why do my students feel this way? More importantly, how can I help them feel more confident in their ability to solve problems that involve multiplication? What makes it too hard or too long? What does “too long” even mean? Are my students referring to the number of procedural steps needed to arrive at the product? Realistically, some of their feelings regarding these skills can be linked to their overall feelings about mathematics which could have been damaged by negative experiences with a previous teacher, a parent/guardian’s view on mathematics or lack of support, or even past performance in math class in earlier grades. There could also be some elements of low self-esteem and lack of confidence wrapped up into these feelings. Fourth graders can be a very peer approval seeking group of impressionable minds.
When I think about my personal experiences in elementary school, I distinctly recall the teacher standing in front of the classroom giving directions, showing us the steps to solve the math problem of the day and then giving the class problems to solve on their own. There was little to no small group instruction, movement around the classroom, or technology usage. There was, however, an adult in the classroom who I truly believed cared about my success in her classroom as well as for my overall growth as a child. I could go on and on about the importance of how a student’s perspective regarding how the teacher feels about him or her can affect the student’s performance in the classroom, but that would lead into a completely different unit.
I hope that the curriculum unit I have created will lessen the anxieties of my future students as we delve into how the basic principles of place value can help us understand and solve multiplication problems. We will explore the Base 10 Number System, the role of place value within that system, and how a clear and complete understanding of both are needed to conceptualize multiplication parameters before one can thoroughly apply the procedures needed to investigate and solve multi-digit equations, as called for in the state guidelines, by demonstrating to the students that multiplication is an extension of the skills they already possess for addition. I will also demonstrate how numbers can be broken up into more manageable pieces to arrive at the product sought in the problem, which will help my students to better visualize the end result. I believe that a greater understanding of the concepts behind the algorithms will increase their overall confidence, foster a growth mindset, and increase their degree of inquiry.
Once a clear foundation has been laid, I will focus on the Virginia Standards of Learning requirements for third graders including both single and multi-digit multiplication. Although my focus is not the Standards of Learning or Common Core mathematics standards for third graders, I do believe that looking at the objectives of the previous year, as well as more widely used standards could prove beneficial in showing how the objectives shift from year to year and what the students should have been exposed to prior to arriving in fourth grade. Having this information gives me a frame of reference to access the student’s prior knowledge as well as gauge their retention of the previous year’s learning.
As we move from conceptualizing multiplication to application and computation, I will dig deeper into several multiplication algorithms. I will discuss three methods for multiplying whole numbers: Area Models, the Box Method, and the traditional U.S. multiplication algorithm (which I generally call Old School in my classroom as it pays homage to the way my students’ parents and I learned multiplication). Each of the methods will be modeled for the students, with emphasis on the role place value plays and what the digits really mean once the algorithm is put in place and solved.
Because I want my students to truly understand that math connections can be made everywhere, I also plan to incorporate math related picture books into the introduction of each skill. For example, the book, Two Ways to Count to Ten: A Liberian Folktale1 retold by Ruby Dee illustrates to the audience that it is easier and quicker to skip count, i.e. use multiplication, instead of counting by ones. I can use the text to address my students’ complaint that “it takes too long” to solve multiplication problems. Many of the inquiry-based questions we will solve in class will focus on everyday occurrences that my students will come across throughout the school year. (Sample questions are listed in the resources section)
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