#### Title

Investigate Students’ Understanding of the Prime Factorization and Use of Prime Numbers in Regards to the Fundamental Theorem of Arithmetic

#### Presentation Type

Poster

#### Faculty Mentor’s Full Name

Matt Roscoe

#### Faculty Mentor’s Department

Mathematical Sciences

#### Abstract

In the field of education, we are facing a dilemma of having a large number of struggling students in the field of math. Research has been done on both middle school students and pre-service elementary school teachers’ understanding of the multiplicative structure of the natural numbers. Research demonstrates an under-utilization of unique prime factorization (30=2x3x5;primes) in the identification of a number’s factors (30=1,2,3,5,6,10,15,30; all the factors). However, research methods have not been applied to elementary school student even though Common Core State Standards (CCSS) require that 4th graders attain this understanding in the following standard: CCSS.Math.Content.4.OA.B.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. The question of distinguishing prime numbers as a base for students to better understand multiplication has been widely debated with scholars such as Rina Zazkis and Peter Liljedahl. Recent studies (i.e. Roscoe & Feldman, in press) have shown that teachers’ understanding of factor can be strengthened by engaging in a sequence of instructional tasks that explore the relationship between a number’s prime factorization and its factors. Our groups’ study sought to extend the scope of investigation in this area to the population of elementary school students, with a goal of observing whether the methods we implemented had a successful student gains by measuring pre and post-tests. The CCSS are requiring that students explain their understanding of mathematical methods and logic, and we have found, in students post-tests, that our method of instruction helped bridge the gap for students to solidify their understanding and students explanations improved in both visual and written planation.

#### Category

Social Sciences

Investigate Students’ Understanding of the Prime Factorization and Use of Prime Numbers in Regards to the Fundamental Theorem of Arithmetic

South UC Ballroom

In the field of education, we are facing a dilemma of having a large number of struggling students in the field of math. Research has been done on both middle school students and pre-service elementary school teachers’ understanding of the multiplicative structure of the natural numbers. Research demonstrates an under-utilization of unique prime factorization (30=2x3x5;primes) in the identification of a number’s factors (30=1,2,3,5,6,10,15,30; all the factors). However, research methods have not been applied to elementary school student even though Common Core State Standards (CCSS) require that 4th graders attain this understanding in the following standard: CCSS.Math.Content.4.OA.B.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. The question of distinguishing prime numbers as a base for students to better understand multiplication has been widely debated with scholars such as Rina Zazkis and Peter Liljedahl. Recent studies (i.e. Roscoe & Feldman, in press) have shown that teachers’ understanding of factor can be strengthened by engaging in a sequence of instructional tasks that explore the relationship between a number’s prime factorization and its factors. Our groups’ study sought to extend the scope of investigation in this area to the population of elementary school students, with a goal of observing whether the methods we implemented had a successful student gains by measuring pre and post-tests. The CCSS are requiring that students explain their understanding of mathematical methods and logic, and we have found, in students post-tests, that our method of instruction helped bridge the gap for students to solidify their understanding and students explanations improved in both visual and written planation.