Since 2016, third to fifth-grade students at a Title I elementary school have not met adequate yearly progress because 70% of students have not scored proficient on the end-of-grade mathematics assessment. The purpose of this qualitative case study was to explore the instructional approaches that elementary school teachers use to teach mathematics to students at the Title I school and to investigate which instructional strategies teachers believed to be the most effective in improving mathematics test scores. This study was grounded in social constructivism, based on the impression that the individual creates knowledge based on mental ability. Data for this study consisted of interviews with 10 third- to fifth-grade mathematics teachers and one instructional lead teacher from a Title I elementary school and the review of two lesson plans from each participant except the lead teacher. The interviews were analyzed by coding the unstructured text, leading to two themes: Grade 3-5 mathematics teachers used the Concrete Representational Abstract (CRA) model and Universal Design for Learning (UDL) approach to teach elementary students and Grade 3-5 mathematics teachers used differentiation, experiential learning, mnemonics, and mathematics fluency to teach elementary students. The lesson plans aligned with the themes. Teachers wanted more professional development in effective district-recommended mathematics strategies to improve students' mathematics achievement. A 3-day professional development training was designed to strengthen the mathematics instructional strategies mentioned by participants in this study. This study may contribute to the school district by providing useful information to administrators and teachers seeking effective mathematics instruction techniques to improve student achievement. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]