Abstract Students in grades 3 and 4 attending a traditional public elementary school in a northeastern state did not meet proficiency levels in mathematics as measured by the state's assessment system. Published reports indicated that students attending the Montessori programs were more proficient in solving math problems compared to students in traditional schools. However, researchers had not compared Montessori and traditional teachers' perceptions of teaching elementary mathematics. The purpose of this qualitative case study was to explore the perceptions of traditional and Montessori teachers regarding teaching basic problem solving skills in mathematics. Koehler and Grouws' model provided the theoretical framework. Data collection included semistructured interviews with 6 traditional and 4 Montessori elementary teachers, field notes, and journaling. Data were analyzed using a coding scheme that incorporated the theoretical model's categories. Findings indicated that both groups of teachers reported that concrete (manipulatives) to abstract (pen and paper) learning was an effective approach to teaching basic math concepts and problem-solving skills. Social change will be realized when struggling elementary students in both Montessori and traditional settings begin to meet proficiency levels in mathematics and benefit from instruction that balances concrete and abstract learning skills. As such, students will be able to explore, develop, and become more actively engaged in learning math and problem solving in all elementary grades. The project deliverable, a position paper supporting the principal theme of concrete to abstract learning, may be used to promote effective instructional practices in mathematics, hence, positive social change.