The primary aim of Project M 3 : Mentoring Mathematical Minds was to develop and field test advanced units for mathematically promising elementary students based on exemplary practices in gifted and mathematics education. This article describes the development of the units and reports on mathematics achievement results for students in Grades 3 to 5 from 11 urban and suburban schools after exposure to the curriculum. Data analyses indicate statistically significant differences favoring each of the experimental groups over the comparison group on the ITBS (Iowa Tests of Basic Skills) Concepts and Estimation Test and on Open-Response Assessments at all three grade levels. Furthermore, the effect sizes range from 0.29 to 0.59 on the ITBS Concepts and Estimation Scale and 0.69 to 0.97 on the Open-Response Assessments. These results indicate that these units, designed to address the needs of mathematically promising students, positively affected their achievement.Putting the Research to Use: To date, there is a paucity of research-based, challenging mathematics curriculum units designed specifically for mathematically promising elementary students. As a result, gifted programming for these students, if it exists within a district, often involves a collection of assorted math puzzles and problems or an above-grade-level textbook that was written for the average student. The findings from this curriculum study suggest to practitioners that mathematics curriculum units that are challenging and engaging with a focus on important math concepts and that encourage students to think and act like practicing mathematicians contribute to students' math achievement. The fact that this study was replicated with a second cohort strengthens the result. In addition, since almost 50% of the students came from economically disadvantaged backgrounds, the study illustrates that the curriculum was highly effective with this special population, while meeting the needs of all talented students.

To date, there has been very little research-based mathematics curriculum for talented elementary students. Yet the gifted education and mathematics literature suggest support for curriculum that is both enriched and accelerated with a focus on developing conceptual understanding and mathematical thinking. Project M3: Mentoring Mathematical Minds is a 5-year Javits research grant project designed to create curriculum units with these essential elements for talented elementary students. These units combine exemplary teaching practices of gifted education with the content and process standards promoted by the National Council of Teachers of Mathematics. The content at each level is at least one to two grade levels above the regular curriculum and includes number and operations, algebra, geometry and measurement, and data analysis and probability. The focus of the pedagogy encourages students to act as practicing professionals by emphasizing verbal and written communication. Research was conducted on the implementation of 12 units in 11 different schools, 9 in Connecticut and 2 in Kentucky. The sample consisted of approximately 200 mathematically talented students entering third grade, most of whom remained in the project through fifth grade. Students in this study demonstrated a significant increase in understanding across all mathematical concepts in each unit from pre- to posttesting. Thus, Project M3 materials may help fill a curriculum void by providing appropriate accelerated and enriched units to meet the needs of mathematically talented elementary students.

The goal of Project M2 was to develop and field-test challenging geometry and measurement units for K-2 students. The units were developed using recommendations from gifted, mathematics, and early childhood education. This article reports on achievement results for students in Grade 1 at 12 diverse sites in four states using the Iowa Tests of Basic Skills (ITBS) mathematics concepts subtest and an open-response assessment. Using HLM, as expected there were no statistical differences between the experimental (n = 186) and comparison (n = 174) groups on the ITBS (91% of the items focused on number). Statistically significant differences (p < .001) favoring the experimental group were found on the open-response assessment with a large effect size (d = 1.88). Thus the experimental group exhibited a deeper understanding of geometry and measurement concepts on the open-response assessment while performing as well on a traditional measure that covered all Grade 1 mathematics.

Developing mathematical talent in our students should be of primary consideration in education today as nations respond to the challenges of economic crises and ever-changing technological advances. This paper describes two U.S. federally funded curriculum projects, Project M 3 , Mentoring Mathematical Minds, and Project M 2 , Mentoring Young Mathematicians for students ages 5 through 12. These projects foster in-depth understanding of advanced mathematical concepts by challenging and motivating students to solve and discuss high-level problems in a fashion similar to practicing mathematicians. The curricula have undergone national field tests with proven research results showing significant achievement gains for students studying the curricula over a comparison group of like-ability students. This paper outlines the philosophy behind each program and its connection to the literature and best practices in the fields of gifted education and mathematics education. Next, specific instructional strategies integral to both curricula are outlined. These strategies help teachers establish a community of learners that promotes rich discussions as a platform for posing and solving interesting problems, constructing viable arguments, and defending as well as critiquing solutions. Finally, strategies to help young student mathematicians develop clear and logical written justifications for their mathematical reasoning and share their creative insights are described.

This study compared the characteristics of second graders' mathematical writing between an intervention and comparison group. Two six-week Project M2 units were implemented with students in the intervention group. The units position students to communicate in ways similar to mathematicians, including engaging in verbal discourse where they themselves make sense of the mathematics through discussion and debate, writing about their reasoning on an ongoing basis, and utilizing mathematical vocabulary while communicating in any medium. Students in the comparison group learned from the regular school curriculum. Students in both the intervention and comparison groups conveyed high and low levels of content knowledge as indicated in archived data from an open-response end-of-the-year assessment. A multivariate analysis of variance indicated several differences favoring the intervention group. Both the high-and low-level intervention subgroups outperformed the comparison group in their ability to (a) provide reasoning, (b) attempt to use formal mathematical vocabulary, and (c) correctly use formal mathematical vocabulary in their writing.The low-level intervention subgroup also outperformed the respective comparison subgroup in their use of (a) complete sentences and (b) linking words. There were no differences between groups in their attempt at writing and attempts at and usage of informal mathematical vocabulary.