Date of Award


Degree Type

Creative Project

Degree Name

Master of Education (MEd)



First Advisor

Beth L. MacDonald

Second Advisor

Patricia S. Moyer-Packenham

Third Advisor

Kerry Jordan


Through my experience I have found students often rely on concrete or pictorial strategies to solve mathematical problems. These strategies are great to build an understanding in mathematical concepts. However, using these strategies becomes a tedious task when working with multi-digit numbers to solve problems involving mathematical operations. For example, a student who relies on drawing base ten blocks to solve three-digit addition problems may experience fatigue, as this is not the most efficient means to solve problems everyday. Through my experience I have found that these strategies may hinder students' abilities to solve a problem correctly because they focus on their drawing and become overwhelmed with how many blocks they have to draw.

Concrete manipulatives allow students opportunities to manipulate concrete objects, which help build a strong foundational understanding of mathematical concepts, such as place value (Wai Lan Chan, Au, & Tang, 2014). When students use their understanding of place value with concrete manipulatives they are able to extend this understanding in their mental math abilities, which will help them abstractly compute problems correctly (Bobis, 2008). If students are able to abstractly solve a problem they would then be able to mentally compute a problem, instead of having to use concrete objects or draw a picture. This would help students be able to focus on what a problem features instead of focusing on drawing a picture.

The purpose of this study was to help me understand how my students’ flexible engagement with concrete experiences can help construct flexibility abstractly. Furthermore, I wondered if this flexibility would help improve students’ problem-solving abilities in mathematical experiences. Specifically, the purpose of this project was to determine how third grade students (ages 8-9 years old), identified as struggling, flexibly used their concrete experiences to construct flexible abstract strategies when solving mathematical problems involving addition, subtraction, and estimation. Student flexibility was measured through assessments given that involved story problems and numbers lines. It was also measured by student dialogue (Shumway, 2011; Yang & Wu, 2010), whole class counting routines (Shumway, 2011), and number line tasks (Siegler & Booth, 2004.)

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