*Math Trailblazers* is a national curriculum based on 30 years of research and development by a team of mathematicians, scientists, education researchers, teachers, and teacher developers who are part of the Teaching Integrated Mathematics and Science (TIMS) Project at the University of Illinois at Chicago (UIC). (Read more about early editions and the history of *Math Trailblazers*.)

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# Research and Development of *Math Trailblazers*, 4^{th} edition

The 4^{th} Edition of *Math Trailblazers* embodies current thinking about how students develop conceptual understanding of mathematics and become productive problem-solvers and communicators of their reasoning. It is a significant revision of previous editions informed by the results of funding from the National Science Foundation (NSF) of a multi-year grant (NSF-0242704). This research in *Math Trailblazers* classrooms included a whole number study, video study, implementation study, fraction and proportionality study, a content review, an external analysis of the geometry strand, and an extensive field test in all grades. (Read the report here.)

The research teams learned much about how teachers use curriculum, how curriculum can support teachers as learners, and how curriculum supports the learning of students. For example, in classrooms where the observed lessons had high fidelity to the intended curriculum, a clear majority (60%) of the students were able to use multiple external representations and make connections among them. In contrast, where low fidelity to the intended curriculum was observed, a little over 90% of the students were able to use at least one external representation to support their thinking when problem solving, but these students were not able to make connections across the representations. The results of this collection of research led to significant revisions, a field test, and a final round of revisions to respond to the findings. (See the research studies and personnel.)

While maintaining successful curriculum components of the previous editions, the author team revised those lessons and units that needed improvement based on their own research, alignment to the Common Core State Standards, and advances in understandings within the math education community. For example, successful field test classrooms encouraged students to represent strategic thinking using a variety of quantitative and procedural representations (i.e., number lines, counters, arrays, area models, diagrams, algorithms, expressions, equations). Revisions paid particular attention to the development of mental math strategies along with multiple algorithms. Students organize these strategies into menus, so students can more flexibly choose efficient strategies and move from less efficient to more efficient procedures. The authors engineered tasks to encourage students to make connections among representations and strategies. These connections facilitate the development of deep and flexible understanding of concepts.

Based on the NSF-funded research, advances in the mathematics education community, and an assessment study (Pellegrino and Goldman, 2007), the authors paid particular attention to the assessment structure of the program, including teachers’ formative assessment practices and their ability to support student discourse and inquiry, particularly during open-response problem solving.

In 2012, Anna Bargagliotti analyzed *Math Trailblazers* for its alignment with the Guidelines for Assessment and Instruction in Statistics Education (GAISE) (Bargagliotti, 2012). The TIMS Laboratory method was recognized as a method that captures the statistical thinking put forth by GAISE. The curriculum was also recognized for including tasks that illicit deep understanding of not only the mathematics but also the variability involved in the data. See What’s New in MTB4? for more details.

In writing *Math Trailblazers*, 4^{th} edition, the authors followed recommendations by the National Research Council (NRC, 2001), and more current findings by other researchers such as those at the Rational Number Project and the Cognitively Guided Instruction professional development program. The new edition is also based on the research of experts at UIC’s Learning Sciences Research Institute (LSRI) , who work to identify and solve critical learning and instructional challenges and design and test innovative models, tools, and technologies to support teachers and students. Learn more about the *Math Trailblazers* 4th Edition Research and Development team.

**Publications and Resources**

- Bargagliotti, A. “How well do the NSF Funded Elementary Mathematics Curricula align with the GAISE report recommendations?”
*Journal of Statistics Education.*20 (3), 2012.

- Brown, S., Pitvorec, K., Ditto, C. and C.R. Kelso, “Reconceiving the Intended Curriculum: An Investigation of Elementary Whole Number Lessons.”
*Journal for Research in Mathematics Education*, vol. 40, (2009). - Castro-Superfine, A., Canty, R., and Marshall, A., “Translating Between Representation Systems: All-Or-None or Skill Conglomerate?”
*Journal of Mathematical Behavior*, p. 217, vol. 28, (2009). - Castro-Superfine, A., Kelso, C., and S. Beal, “Examining the Process of Developing a Research-based Mathematics Curriculum and Its Policy Implications.”
*Educational Policy*(online), (2009). - Cramer, K and T. Wyberg, “Efficacy of Different Concrete Models for Teaching the Part-whole Construct for Fractions.”
*Mathematical Thinking and Learning*, p. 226, vol. 11, (2009). - Flevares, L.M., N. Noronha, M. Perry, L.M. Sims, and M.R. Schleppenbach, “Voices on a Standards-Based Mathematics Curriculum: Envisioning a Conversation among Teachers, Curriculum Writers, and Educational Researchers.”
*Journal of Curriculum Studies*, (2009). Submitted

- National Research Council.
*Adding It Up: Helping Children Learn Mathematics.*J. Kilpatrick, J. Swafford, and B. Findell, Eds. National Academy Press, Washington, DC, 2001. - Pellegrino, J.W., and S.R. Goldman. (2007). “Beyond rhetoric: Realities and complexities of integrating assessment into teaching and learning.” In
*The future of assessment: Shaping teaching and learning*. C. Dwyer (Ed.). Mahwah, NJ: Erlbaum. - Sconiers, S., McBride, J., Isaacs, A., Randall Kelso, C. and T. Higgins.
*The ARC Center Tri-State Student Achievement Study: A Report of the ARC Center at The Consortium for Mathematics and Its Applications (COMAP)*. National Science Foundation, 2003. *UIC-Harvey Local Systemic Change Project: Summary of a Student Outcomes Study*(Kelso, C.R., and S. Zhao)*Washington State Math Trailblazers Student Achievement Report*(Kelso, C.R., B. Booton, and D. Majumdar)