This case study focuses on a team of teachers and students in a Lesson Study, focused on using mathematical modeling (MM) to make significant decisions to design and plan for a sustainable edible garden in their community. We examined (a) how teachers develop students’ capacity to engage in mathematical modeling, while attending to equitable teaching practices; and (b) how teachers’ view of teaching through mathematics modeling changed after unit implementation. We found that teachers were deliberate in employing specific structures, routines, and tools to attend to equitable participation, when eliciting student thinking in the modeling process. We found that teachers’ view of mathematics modeling changed as they recognized how MM allowed for (a) integration of important mathematics concepts while giving students ownership of the mathematics; (b) opportunity to assess both content and 21st century process skills; and (c) positive energy that came from both students and teachers when teaching through the use of mathematical modeling. A promising strategy for preparing our youth for rigorous mathematics and skills to solve ill-structured problems is by integrating mathematical modeling in early elementary grades to develop critical 21st century skills and a productive disposition towards problem posing and problem solving.

The abstract nature of mathematics requires the communication of mathematical ideas through multiple representations, such as words, symbols, pictures, objects, or actions. Building representational fluency involves using mathematical representations flexibly and being able to interpret and translate among these different models and mathematical concepts. This article shares a collaborative lesson study experience in planning and teaching a unit on decimals. Participants included fifth- and sixth-grade teachers and lesson study facilitators, including a university mathematics educator, a doctoral student, and a school mathematics specialist. The lesson was taught in a fifth-grade class with a high population of English language learners (ELL) and special needs students. The overarching goal of the lesson study was to develop students' representational fluency and mathematical proficiency with decimals. While working with teachers, the lesson study facilitators shared related research on representations and the importance of selecting and evaluating effective mathematical models to give the diverse population access to decimal concepts. The lesson study facilitators' goal was to heighten teachers' awareness of the importance of multiple representations and introduce a planning process that allows teachers to select models in a thoughtful and critical way that would facilitate the teaching and learning of a mathematics concept.

This study examined a focused remediation and enrichment effort among school and university faculty to affect the mathematics achievement of a group of third-grade students in a Title I elementary school. A total of 87 students participated in the Code RED (Remediation and Enrichment Days) Project. During the Code RED Project, student assessment data were used to identify high-need areas for mathematics instruction. The Code RED Project sessions occurred in small groups over a 10-week period. Pre- and posttest assessments, as well as state-standardized tests, were used for data gathering during the project. Pre- and posttest data indicate that students made significant gains in mathematics achievement during the Code RED Project overall, in different ability groups, and in different subgroup populations. In addition, during the Code RED Project, 100% of the third-grade class passed the end-of-grade state-standardized testing. A comparison of the pass rates for the state-standardized test for third-grade students before and during the Code RED Project indicates a significant increase in students labeled in the pass-proficient and pass-advanced categories. In addition to the students' increasing their achievement results, teachers adopted new instructional practices, and preservice teachers participated in the inquiry culture of the school.