Cynthia O Anhalt

Interests

Research

Mathematics Education: teacher preparation, student learning, K-12 curriculum, assessment, issues of language and mathematics teaching and learning, mathematical modeling in K-12 and for teacher preparation

Teaching

Mathematics Education: undergraduate mathematics teacher preparation courses, graduate research mathematics education courses

Courses

Scholarly Contributions

Books

• Anhalt, C. O. (2020). Access to mathematics by opening doors for students currently excluded from mathematics.
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  Anhalt, C. (2020). Access to mathematics by opening doors for students currently excluded from mathematics, Critical Issues in Mathematics Education (CIME) 2018 Workshop Report, Mathematical Sciences Research Institute (MSRI), Berkeley, CA. MSRI Library publication.
• Goffney, I., Gutierrez, R., Anhalt, C. O., Aguirrre, J., Berry, R. Q., Brown, K., Bullock, E., Celedon-Pattichis, S., Gholson, M., Myers, M., & Song, E. (2018). Annual Perspectives in Mathematics Education 2018 Volume: Rehumanizing Mathematics for Students who are Black, Latin@, and or Indigenous. National Council of Teachers of Mathematics.
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  Annual Perspectives in Mathematics Education (APME) 2018 Volume: Rehumanizing Mathematics for Students who are Black, Latin@, and or Indigenous. Rochelle Gutierrez & Imani Goffney (Co-Editors), Editorial Panel members: Julia Aguirre, University of Washington Tacoma; Cynthia Anhalt, University of Arizona; Sylvia Celedon-Pattichis, University of New Mexico; Erika Bullock, University of Wisconsin Madison; Robert Berry, University of Virgina; Kyndall Brown, University of California, Los Angeles; Maisie Gholson, University of Michigan; Marrielle Myers, Kennesaw State University; Esther Song, Lindblom Math & Science Academy, Chicago Public Schools.

Chapters

• Anhalt, C. O. (2021). Dr. Cynthia Oropesa Anhalt. In “Testimonios: Stories of Latinx and Hispanic Mathematicians"(pp pp. 155-164). AMS.org: https://bookstore.ams.org/clrm-67/: American Mathematical Society.
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  Life stories of Latinx and Hispanics in the mathematical sciences, "testimonios" from Latinx mathematics and mathematics education faculty.
• Anhalt, C. O., Cortez, R., & Aguirre, J. (2021). Mathematical modeling thinking: A construct for developing competency across grades. In Exploring the nature of mathematical modeling in the early grades, Early Mathematics Learning and Development Series(pp pp. 45-66). New York: Springer International Publisher. doi:https://doi.org/10.1007/978-3-030-63900-6
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  Anhalt, C., Cortez, R. & Aguirre, M. Mathematical modeling thinking: A construct for developing competency across grades. In J. Suh, M. Wickstrom & L. English (Eds.) Exploring the nature of mathematical modeling in the early grades, Early Mathematics Learning and Development Series, New York: Springer International Publisher.
• Lischka, A., Lai, Y., Strayer, J., & Anhalt, C. O. (2020). Developing mathematical knowledge in and for teaching in content courses. In The mathematics teacher education partnership: The power of a networked improvement community to transform secondary mathematics teacher preparation(pp 119-141). Charlotte, NC: Information Age Publishing.
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  Lischka, A., Lai, Y., Strayer, J., Anhalt, C. (2020) Developing mathematical knowledge in and for teaching in content courses. In (Eds.) The mathematics teacher education partnership: The power of a networked improvement community to transform secondary mathematics teacher preparation, pp. 119-141, Information Age Publishing: Charlotte, NC.
• Anhalt, C. O., Civil, M., McGraw, R. H., & Eli, J. A. (2019). Stronger together: The AZ mathematics teaching (MaTh) Noyce program’s collaborative model for secondary teacher preparation. . In Recruiting, preparing, and retaining STEM teachers for a global generation. The Netherlands: Sense Publishers. doi:10.1163/9789004399990_002
• Civil, M., Civil, M., Anhalt, C. O., Anhalt, C. O., Mcgraw, R. H., Mcgraw, R. H., Eli, J. A., Eli, J. A., Civil, M., Anhalt, C. O., Mcgraw, R. H., & Eli, J. A. (2019). Stronger together: The Arizona Mathematics Teaching (MaTh) Noyce Program’s Collaborative Model for Secondary Teacher Preparation. In Recruiting, retaining, and preparing STEM teachers for a global generation. Rotterdam, Netherlands: Sense.
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  Eli, J., McGraw R., Anhalt, C., & Civil, M. (2019). Stronger Together: The AZ Mathematics Teaching (MaTh) Noyce Program’s Collaborative Model for Secondary Teacher Preparation. Book chapter in J. Leonard, A. Burrows, and R. Kitchen (Eds.), Recruiting, Preparing, and Retaining STEM Teachers for a Global Generation. Sense Publishers, The Netherlands.
• Anhalt, C. O., Staats, S., Cortez, R., & Civil, M. (2018). Mathematical Modeling and Culturally Relevant Pedagogy. In Cognition, Metacognition, and Culture in STEM Education. The Netherlands.: Springer: the language of science, Publishing Editor Education.
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  Anhalt, C., Staats, S., Civil, M., & Cortez, R. (invited, accepted). Mathematical Modeling and Culturally Relevant Pedagogy. Book chapter in Yehudit Judy Dori, Zemira Mevarech, and Dale Baker (Eds.), Cognition, Metacognition, and Culture in STEM Education. Springer: the language of science, Publishing Editor Education, The Netherlands.
• Cortez, R., Anhalt, C. O., Staats, S. K., & Civil, M. (2018). Mathematical Modeling and Culturally Relevant Pedagogy. In Cognition, Metacognition, and Culture in STEM Education(pp 307-330). Switzerland: Springer. doi:10.1007/978-3-319-66659-4
• Anhalt, C. O., Cortez, R., & Smith, A. (2017). Mathematical Modeling: Creating Opportunities for Participation in Mathematics. In Access and Equity: Promoting High Quality Mathematics in Grades 6-8(pp 105-119). National Council of Teachers of Mathematics.
• Anhalt, C. O. (2016). Acknowledging Personal Perspectives to Build Mathematical Understandings, A Commentary. In Cases for Teacher Educators: Facilitating Conversations about Inequities in Mathematics Classrooms(pp 47-51). The Association of Mathematics Teacher Educators (AMTE) Professional Book Series.
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  Anhalt, C. (2016) Acknowledging Personal Perspectives to Build Mathematical Understandings, A commentary to understanding White privilege: When a good task is not enough by Kristen Bieda in Cases for Teacher Educators: Facilitating Conversations about Inequities in Mathematics Classrooms, Dorothy White, Sandra Crespo, Matt Felton, Imani Goffney, Joi Spencer and Marta Civil (Eds.).
• Anhalt, C. O. (2014). Scaffolding in Mathematical Modeling for ELLs. In The Common Core State Standards in Mathematics for English Language Learners: Grades K-8(pp 111-126). Maryland, USA: Teaching English to Speakers of Other Languages (TESOL) International Association Publications.
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  Anhalt, C. (2014). Scaffolding in Mathematical Modeling for ELLs. Book chapter in Marta Civil and Erin Turner (Eds.) The Common Core State Standards in Mathematics for English Language Learners: Grades K-8, pp. 111-126. Book series: The Common Core State Standards and English Language Learners, Series Editor: Luciana C. de Oliveira, Teachers College, Columbia University. Teaching English to Speakers of Other Languages (TESOL) International Association Publications.
• Anhalt, C. O., Eli, J. A., Eli, J. A., & Anhalt, C. O. (2012). Building connections from whole number to polynomial long division: Teaching English language learners. In Beyond good teaching: Advancing Mathematics Education for ELLs(pp 96-103). Reston, VA: National Council of Teachers of Mathematics.
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  English language learners share a basic need: to engage, and be engaged, in meaningful mathematics. Through guiding principles and instructional tools, together with classroom vignettes and video clips, this book shows how to go beyond good teaching to support ELLs in learning challenging mathematics while developing language skill.Position your students to share the valuable knowledge that they bring to the classroom as they actively build and communicate their understanding.The design of this book is interactive and requires the reader to move back and forth between the chapters and online resources at www.nctm.org/more4u. Occasionally, the reader is asked to stop and reflect before reading further in a chapter. At other times, the reader is asked to view video clips of teaching practices for ELLs or to refer to graphic organizers, observation and analysis protocols, links to resources, and other supplementary materials. The authors encourage the reader to use this resource in professional development.
• Anhalt, C. O., & Matthew, O. (2011). Algebraic and geometric representations of perimeter with algebra blocks: Professional development for teachers of English language learner in the U.S.. In Latinos and mathematics education: Research on learning and teaching in classrooms and communities(pp 195-214). Charlotte, NC, USA: Information Age Publishers.
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  Anhalt, C., & Ondrus, M. (2011). Algebraic and geometric representations of perimeter with algebra blocks: Professional development for teachers of English language learner in the U.S., pp. 195-214. Book chapter in Téllez, K., Moschkovich, J.N., & Civil, M. (Eds.) Latinos and mathematics education: Research on learning and teaching in classrooms and communities. Charlotte, NC: Information Age Publishers. Book review by Cecilia Henríquez Fernández, Journal of Urban Mathematics Education December 2011, Vol. 4, No. 2, pp. 131–139.
• Anhalt, C. O., Karp, K., & Minerva, L. (2010). Facilitator’s guide questions. In Models of intervention in mathematics: Reweaving the tapestry. Reston, VA, USA: National Council of Teachers of Mathematics (NCTM).
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  Anhalt, C., Karp, K., & Minerva, L. (2010). Facilitator’s guide questions. In C. Fosnot (Ed.) Models of intervention in mathematics: Reweaving the tapestry. Reston, VA: National Council of Teachers of Mathematics.
• Anhalt, C. O., Ward, R., & Vinson, K. (2004). The mathematics curriculum: Prosecution, defense, verdict. In Defending public schools: Curriculum(pp 47-60). Praeger: Greenwood Publishing Group.
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  Anhalt, C., Ward, R., & Vinson, K. (2004). The mathematics curriculum: Prosecution, defense, verdict. Book chapter in Vinson, K. and Ross, W. (Eds.), Defending public schools: Curriculum. Greenwood Publishing Group, Praeger, pp. 47-60.

Journals/Publications

• Tidwell, W., Anhalt, C. O., Cortez, R., & Kohler, B. (2022). Modeling memorization: A data collection and mathematical modeling experience. Problems, Resources, and Issues in Mathematics Undergraduate Studies (PRIMUS).
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  This article presents a mathematical modeling activity for students related to the process of memorization in which students collect their own data to drive their model development, model parameterization, and validation. Engaging in the data collection gives them insight to critique and evaluate various models. This task is a low floor, high ceiling problem that offers both a relatable context and a window to quantitative approaches in cognitive science. A detailed analysis of the situation is provided, including several mathematical approaches to model the memorization process in the activity that highlight the richness of the problem. Experimental results from students participating in this activity are also discussed. Instructors can adapt and implement this modeling exploration for use in various undergraduate courses, from introductory to advanced, depending on the emphasis of the lesson. In addition, pedagogical recommendations with a focus on fostering equitable teaching practices are offered.
• Anhalt, C. O., Tidwell, W., Cortez, R., & Kohler, B. R. (2021). Development of prospective elementary teachers' mathematical modelling competencies and conceptions. International Journal of Mathematical Education in Science and Technology, 1-21. doi:10.1080/0020739x.2021.2005170
• William, T., Anhalt, C. O., Ricardo, C., & Brynja, K. (2021). Development of prospective elementary teachers' mathematical modeling competencies and conceptions. International Journal of Mathematics Education in Science and Technology (IJMEST). doi:10.1080/0020739X.2021.2005170
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  This study examines prospective elementary teachers' growth and development of competencies, conceptions, and perceptions of mathematical modeling in a mathematics content course for elementary teachers. A series of three lessons in mathematical modeling were implemented over nine class sessions at a large university in the western United States that engaged students in modeling tasks and in the modeling process. The goal was to capture prospective teachers' thoughts and perceptions on the meaning of mathematical modeling and their conceptions of teaching and learning modeling at the elementary and middle school level. The research questionswere: (1) How do prospective teachers translate the mathematical modeling cycle into their own practice of doing modeling? and (2) How do prospective teachers' conceptions of modeling and teaching and learning modeling evolve throughout the implementation of a series of mathematical modeling lessons? Data sources included posters, modeling reports, responses to a pre- and post-intervention questionnaire, and semi-structured interview dialogue. Data analyses included mixed methods using provisional coding, open coding, and a categorical rubric. Findings from this study indicate that (1) Prospective elementary teachers translated the mathematical modeling cycle into their own practice by developing their range of modeling competencies including numerous components of the modeling cycle, and (2) They developed a professionally appropriate conception of mathematical modeling along with productive perceptions of the benefits of teaching and learning modeling.
• Aguirre, J. M., Anhalt, C. O., Turner, E. E., Foote, M. Q., & Roth McDuffie, A. (2020). Engaging children’s mathematical knowledge bases with math modeling tasks in elementary classrooms. Quaderni di Ricerca in Didattica (Mathematics), 7, 463-472.
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  Aguirre, J.M., Anhalt, C.O., Turner, E.E., Foote, M.Q., & Roth McDuffie, A. (2020) Engaging children’s mathematical knowledge bases with math modeling tasks in elementary classrooms. Quaderni di Ricerca in Didattica (Mathematics). 7, 463-472. http://math.unipa.it/%7Egrim/quaderno_2020_numspec_7.htm
• Guzman, L., Anhalt, C. O., & Sheldon, J. (2020). Complex Competencies in Mathematics Teacher Education: Prospective Teachers Unpacking Mathematics and Mathematics Teacher Identities. Quaderni di Ricerca in Didattica (Mathematics), 7, 235-238.
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  Guzman, L., Anhalt, C. & Sheldon, J. (2020). Complex Competencies in Mathematics Teacher Education: Prospective Teachers Unpacking Mathematics and Mathematics Teacher Identities. Quaderni di Ricerca in Didattica (Mathematics). 7, 235-238. http://math.unipa.it/%7Egrim/quaderno_2020_numspec_7.htm
• Aguirre, J. M., Anhalt, C. O., Cortez, R., Simic Muller, K., & Turner, E. (2019). Engaging teachers in the powerful combination of mathematical modeling and social justice: The Flint water crisis task. Mathematics Teacher Educator, 7(2), 7-20.
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  Aguirre, J.M., Anhalt, C., Cortez, R., Simic Muller, K. & Turner, E. (2019). Engaging teachers in the powerful combination of mathematical modeling and social justice: The Flint water crisis task, Mathematics Teacher Educator, 7(2), 7-20.
• Aguirre, J., Yanisko, E., Wickstrom, M. H., Turner, E. E., Suh, J. M., Seshaiyer, P., Osana, H. P., Mcduffie, A. R., Matson, K., Lee, D. H., Gallagher, M. A., Carlson, M. A., Birkhead, S., Bennett, A. B., Anhalt, C. O., & Aguirre, J. M. (2019). Exploring the Nature of Mathematical Modeling in the Early Grades.. International Group for the Psychology of Mathematics Education, 1478-1486.
• Anhalt, C. O. (2019). Engaging teachers in the powerful combination of mathematical modeling and social justice: The Flint Water crisis task. Mathematics Teacher Educator Journal.
• Anhalt, C. O., Aguirre, J. M., Cortez, R., Turner, E. E., & Simic-Muller, K. (2019). Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task. Mathematics Teacher Educator, 7(2), 7-26. doi:10.5951/mathteaceduc.7.2.0007
• Anhalt, C. O. (2018). Forming Culturally Responsive Mathematics Teachers. University of Arizona Department of Mathematics Newsletter, 10-11.
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  Anhalt, C. AZ Nyce: Forming Culturally Responsive Mathematics Teachers, pp. 10-11. University of Arizona Department of Mathematics Newsletter, Fall 2018.Article is based on the Noyce Scholars who are part of a new generation of teachers in the mathematics teaching field.
• Anhalt, C. O., & Cortez, R. (2018). Mathematics Education as a Mathematician’s Research Area: An Invitation for Collaboration. Notices of the American Mathematics Society, 65(8), 1007-1010.
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  Anhalt, C. & Cortez (2018). Mathematics Education as a Mathematician’s Research Area: An Invitation for Collaboration, Notices of the American Mathematics Society, Volume 65, Number 8, September, pp 1007-1010.
• Anhalt, C. O., Cortez, R., & Been Bennett, A. (2018). The Emergence of Mathematical Modeling Competencies: An Investigation of Prospective Secondary Mathematics Teachers. Mathematical Thinking and Learning.
• Anhalt, C. O., Cortez, R., & Bennett, A. B. (2018). The Emergence of Mathematical Modeling Competencies: An Investigation of Prospective Secondary Mathematics Teachers. Mathematical Thinking and Learning, 20(3), 202-221. doi:10.1080/10986065.2018.1474532
• Anhalt, C. O., & Cortez, R. (2016). Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation. Journal of Mathematics Teacher Education (JMTE), Volume 19(Issue 6), 523-545. doi:10.1007/s10857-015-9309-8
• Anhalt, C. O., & Cortez, R. (2015). Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation. Journal of Mathematics Teacher Education (JMTE).
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  Anhalt, C. & Cortez, R. (revising & resubmitting per editor request). Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation, Journal of Mathematics Teacher Education (JMTE).
• Anhalt, C. O., & Cortez, R. (2015). Mathematical Modeling: A Structured Process.. Mathematics Teacher, 108(6), 446-452.
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  Anhalt, C. & Cortez, R. (2015). Mathematical Modeling: A Structured Process. Article featured on cover of the Focus Issue on Mathematical Modeling, Mathematics Teacher, 108(6), February, pp. 446-452, National Council of Teachers of Mathematics.
• Felton, M., Anhalt, C. O., & Cortez, R. (2015). Going with the Flow: Challenging Students to Make Assumptions. Mathematics Teaching in the Middle School, 20(6), 342-349.
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  Felton, M., Anhalt, C., & Cortez, R. (2015). Going with the Flow: Challenging Students to Make Assumptions. Focus Issue on Mathematical Modeling, Mathematics Teaching in the Middle School (MTMS), 20(6), February, pp. 342-349, National Council of Teachers of Mathematics.
• Anhalt, C. O., & Rodriguez, M. E. (2013). K-8 Teachers’ Concerns about Teaching Latino/a Students. Journal of Urban Mathematics Education, 6(2), 42-61.
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  Anhalt, C. & Rodriguez, M. (2013). K-8 Teachers’ Concerns about Teaching Latino/a Students, Journal of Urban Mathematics Education, Vol. 6, No. 2, pp. 42–61, ©JUME,
• M., I., Hockenberry, M. J., Anhalt, C., Mccarthy, K., & Krull, K. R. (2011). Mathematics intervention for prevention of neurocognitive deficits in childhood leukemia. Pediatric Blood and Cancer, 59(2), 278-284.
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  PMID: 21938763;PMCID: PMC3246526;Abstract: Background: Despite evidence that CNS treatment is associated with cognitive and academic impairment, interventions to prevent or mitigate these problems are limited. The purpose was to determine if early intervention can prevent declines in mathematics abilities. Procedures: Fifty-seven children with ALL were enrolled and randomized to a Mathematics Intervention or Standard Care. Subjects completed neurocognitive assessments prior to the intervention, post-intervention, and 1 year later. Parents received written results and recommendations for use with their school. The Mathematics Intervention was based on Multiple Representation Theory and delivered individually over 1 year. Results: Thirty-two of 57 subjects completed the study and were included in data analyses. These 32 subjects completed all neurocognitive assessments and, for those in the Intervention Group, 40-50hours of the Mathematics Intervention. There were no group differences on relevant demographic variables; risk stratification; number of intrathecal methotrexate injections; or high dose systemic methotrexate. Significant improvements in calculation and applied mathematics from Baseline to Post-Intervention (P=0.003 and 0.002, respectively) and in visual working memory from Baseline to 1 year Follow-up (P=0.02) were observed in the Intervention but not the Standard Care Group. Results from repeated measures ANOVA demonstrated significant between group differences for applied mathematics [F(2,29)=12.47, P
• Fernandes, A., Anhalt, C. O., & Civil, M. (2010). Going beyond ‘multiple choice’: Probing Mexican-American students’ thinking and communicating on assessment items in measurement. TODOS Research Monograph II, Assessment of Hispanic/Latino Students in Mathematics, 2(1).
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  Fernandes, A., Anhalt, C., & Civil, M. (2010). Going beyond ‘multiple choice’: Probing Mexican-American students’ thinking and communicating on assessment items in measurement. TODOS Research Monograph II, Assessment of Hispanic/Latino Students in Mathematics.
• Fernandes, A., Civil, M., Anhalt, C. O., Fernandes, A., Civil, M., & Anhalt, C. O. (2009). Mathematical Interviews to Assess Latino Students.. Teaching children mathematics, 16(3), 162-169. doi:10.5951/tcm.16.3.0162
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  Teachers' use of appropriate questioning strategies illustrates the interplay between language and math as English Language Learners describe their understanding of measurement in one-on-one interviews
• Anhalt, C. O., Civil, M., & Fernandes, A. (2008). Exploring alternative mathematics assessments with Latino/a students. Teaching Children Mathematics.
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  This study explores the wealth of student thinking generated by the task-based interviews of 15 Latino/a students as they solve measurement items from NAEP. We conjecture that these interviews could be used to complement paper-and-pencil assessments, especially in the case of Latino/a students who have been known to struggle to comprehend the language in the questions. The paper discusses three major themes namely, issues of language, use of visual cues, and mathematical communication from our interviews. Further, key factors in designing and conducting task-based interviews with students and the benefits and challenges of this form of assessment are also discussed.
• Ondrus, M., Horak, V. M., Anhalt, C. O., Ondrus, M., Horak, V. M., & Anhalt, C. O. (2007). Issues of Language: Teacher Insights from Mathematics Lessons in Chinese.. Mathematics Teaching in the Middle School, 13(1), 18-23. doi:10.5951/mtms.13.1.0018
• Ward, R. A., Vinson, K. D., & Anhalt, C. O. (2006). Teacher candidates' growth in designing mathematical tasks as exhibited in their lesson planning. The Teacher Educator, 41(3), 172-186. doi:10.1080/08878730609555382
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  In order to gain insight into preservice teachers' beliefs about planning for mathematics instruction, a study was carried out involving K‐8 teacher candidates enrolled in an elementary mathematics methods course. Doyle's (1992) notion of academic task and the research on pedagogical content knowledge served as the theoretical framework for this study. The teacher candidates submitted lesson plans at three intervals during a semester‐long methods course; the lesson plans were then coded based on candidates' planned uses of academic tasks. Analyses of the data revealed trends in these teacher candidates' design of academic tasks over the course of the semester. Recommendations and implications are pre‐sented highlighting the benefits of incorporating the knowledge base on academic task into a mathematics methods course as a means to con‐tribute to teacher candidates' developing pedagogical content knowledge via their designing of academic tasks in lesson planning.
• Ward, R. A., Vinson, K. D., & Anhalt, C. O. (2004). K-8 Teacher Candidates' Use of Mathematical Representations and the Development of Their Pedagogical Content Knowledge as Exhibited in Their Lesson Planning. Focus on learning problems in mathematics, 26(3).
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  Abstract A study was carried out involving thirty-one K-8 teacher candidates enrolled in an elementary mathematics methods course to investigate and document their thinking as they plan for mathematics instruction. The teacher candidates submitted lesson plans at three intervals during a semester-long methods course which were coded based on the planned uses of mathematical representations. Analysis of the data revealed trends in the choices of representations. Recommendations are presented highlighting the potential benefits of incorporating the knowledge base on mathematical representations into a mathematics methods course and a discussion ensues on the development of these teacher candidates' pedagogical content knowledge through their choices of mathematical representations in their lesson planning. ********** Introduction A primary goal of a methods course is to prepare future teachers to teach the subject matter in effective and engaging ways such that student understanding is maximized. In other words, the authors posit that methods courses provide opportunities for teacher candidates to develop and further their pedagogical content knowledge. In an attempt to document and explore how K-8 teacher candidates represent mathematical ideas in ways that are understandable to students, a study was carried out in which K-8 teacher candidates submitted lesson plans at three intervals during a semester. Serving as a lens during the coding and analyses of these lesson plans were the five representations defined by Lesh, Post, & Behr (1987). Of interest to the authors were the representations these teacher candidates might choose to use as they plan for teaching a mathematics topic in the most effective way as possible; that is, so that student understanding is maximized. Also of interest was the potential emergence of trends in these K-8 teacher candidates' choices of representations in their lesson planning as they progressed through their semester-long elementary mathematics methods course. After analyzing the lesson plans of these teacher candidates at three intervals, the authors were able to document the planned choices of and trends in both teacher and student use of various representations within their lesson plans. These choices and trends will be described and a discussion will follow presenting the potential benefits of incorporating the knowledge base on mathematical representations into a mathematics methods course to contribute to the development of K-8 teacher candidates' pedagogical content knowledge. Research on pedagogical content knowledge Many researchers have described the various types of knowledge that are needed by teachers. In particular, Shulman (1986) defines pedagogical content knowledge as the ability to represent ideas in ways that are understandable to students. Shulman argues that teachers need to know things such as what topics children find interesting or difficult and what the representations are that are most useful for teaching a specific content idea. Shulman (1987) further elaborates on pedagogical content knowledge as the capacity "to transform the content knowledge he or she possesses into forms that are pedagogically powerful and yet adaptive to the variations in ability and background presented by the students" (p. 15). For Carter (1990), pedagogical content knowledge represents an attempt to determine what teachers know about their subject matter and how they translate that knowledge into classroom curricular events. Doyle (1992) contents that this ability distinguishes a teacher from a non-teaching specialist; for example, "Knowing biology is necessary, but certainly not sufficient, to know how to represent biological content to students in a teaching situation" (p. 498). Kennedy (1998) offers that recitational knowledge; that is, the traditional mode of defining facts and terminology is not sufficient for teaching. …
• Anhalt, C. O., Vinson, K. D., & Ward, R. A. (2003). Mathematical Representations and Pedagogical Content Knowledge: An Investigation of Prospective Teachers' Development.. FOCUS on Learning Problems in Mathematics., 26(3), 1-11.
• Civil, M., Anhalt, C. O., & Allexsaht-snider, M. (2002). Middle School Mathematics Classrooms: A Place for Latina Parents' Involvement. Journal of Latinos and Education, 1(4), 255-262. doi:10.1207/s1532771xjle0104_5
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  The study is of 3 Latina parents of children in an Arizona middle school in which parents made observations and participated in three different reform mathematics classrooms. The parents' expectations, concerns, and reactions to the observations of the lessons were discussed and recorded. The goal of the study was to better understand the Latina parents' perspectives about their children's mathematics education. The findings from this study can be used to guide teachers' and parents' efforts to develop effective programs for educating parents about mathematics education reform.
• Ward, R. A., & Anhalt, C. O. (2002). An Investigation of Preservice Teachers' Understanding of the Area of a Parallelogram.. Issues in Teacher Education, 11(2), 43-52.
• Fernandez, M. L., Anhalt, C. O., Fernandez, M. L., & Anhalt, C. O. (2001). Transition toward Algebra.. Mathematics Teaching in the Middle School, 7(4), 236-241. doi:10.5951/mtms.7.4.0236

Proceedings Publications

• Anhalt, C. O., Cortez, R., Kohler, B., & Tidwell, W. (2022, August). Interrogation of Social Justice Contexts in Mathematical Modeling: The use of Simulations of Practice in the Mathematical Preparation of Teachers.. In 16th International Conference of the Mathematics Education for the Future Project.
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  Research in prospective teachers’ development of mathematical modeling knowledge for teaching is gaining momentum. The MODULE(S)2* project developed curriculum in modeling for teacher education that includes simulations of practice. Through simulations of practice, prospective teachers reflect on and plan a discussion around student thinking, their models, and the contextualization of their results. We present an analysis of prospective teachers’ modeling work on the decreasing area of Indigenous reservation land in the U.S., and a simulation of practice which explores different methods for finding the area of land in connection to the injustice deeply rooted in the treatment of indigenous people. This problem explores a critical social issue and calls for explicit attention to pedagogical knowledge in structuring discussions around the contextualization of the mathematical results.
• Anhalt, C. O., & Cortez, R. (2021, January). Examining MKT in Mathematical Modeling through PSTs’ Participation in Simulations of Practice. In Joint Mathematics Meetings, Washington DC, Virtual.
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  Anhalt, C., & Cortez, R., Examining MKT in Mathematical Modeling through PSTs’ Participation in Simulations of Practice. Invited Special Session of the AMS of the Joint Mathematics Meetings, Mathematics Courses Designed to Develop Mathematical Knowledge for Teaching (MKT) High School, JMM Virtual Conference, January 6-8, 2021.
• Anhalt, C. O., Kohler, B., & Cortez, R. (2020, Fall). Mathematical Modeling Modules: Curriculum Material for Secondary Teacher Education. In Mathematics Teacher Education Partnership (MTEP).
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  Anhalt, C., Kohler, B., Cortez, B. (2020). Mathematical Modeling Modules: Curriculum Material for Secondary Teacher Education, Proceedings of the Mathematics Teacher Education Partnership (MTEP) annual conference (virtual). https://www.aplu.org/projects-and-initiatives/stem-education/mathematics-teacher-education-partnership/mtep-conferences-meetings/mtep9.html
• Lai, Y., Strayer, J., Lischka, A., Anhalt, C. O., Quinn, C., & Reed, S. (2020, fall). Theoretical report: A framework for examining prospective teachers’ use of mathematical knowledge for teaching in mathematics courses.. In In A. Weinberg, D. Moore-Russo, H. Soto, & M. Wawro (Eds.), Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education, 765-773.
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  Lai, Y., Strayer, J., Lischka, A., Anhalt, C., Quinn, C. & Reed, S. (2019). Theoretical report: A framework for examining prospective teachers’ use of mathematical knowledge for teaching in mathematics courses. In A. Weinberg, D. Moore-Russo, H. Soto, & M. Wawro (Eds.), Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education (pp.765-773). Oklahoma City, Oklahoma.
• Aguirre, J., Anhalt, C. O., Turner, E. E., Foote, M., & Roth McDuffy, A. (2019, July). Engaging Children’s Multiple Mathematical Knowledge Bases with Mathematics Modeling Tasks in Elementary Classrooms. In International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71).
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  Aguirre, J., Anhalt, C., Turner, E., Foote, M., & Roth McDuffie, A. (2019). Engaging Children’s Multiple Mathematical Knowledge Bases with Mathematics Modeling Tasks in Elementary Classrooms. Proceedings from the International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71), Braga, Portugal.
• Anhalt, C. O., & Cortez, R. (2019, August). Mathematical Modeling Thinking: Laying the Foundation for Mathematical Modeling Competency. In 15th International Conference in Mathematics Education for the Future Project (ICMEFP).
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  Anhalt, C. & Cortez, R. (2019). Mathematical Modeling Thinking: Laying the Foundation for Mathematical Modeling Competency. Procedings from the 15th International Conference in Mathematics Education for the Future Project (ICMEFP), Maynuth University, Kildare, Ireland.
• Anhalt, C. O., Aguirre, J., & Suh, J. (2019, July). Mathematical Modeling: Raising Awareness and Exploring a Community-based Water Crisis through a Critical, Social Justice and Environmental Lens. In International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71).
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  Anhalt, C., Aguirre, J. & Suh, J. (2019). Mathematical Modeling: Raising Awareness and Exploring a Community-based Water Crisis through a Critical, Social Justice and Environmental Lens. Proceedings from the International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71), Braga, Portugal.
• Guzman, L., Anhalt, C. O., & Sheldon, J. (2019, July). Complex Competencies in Mathematics Teacher Education: Prospective Teachers Unpacking Mathematics and Mathematics Teacher Identities. In International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71).
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  Guzman, L., Anhalt, C. & Sheldon, J. (2019). Complex Competencies in Mathematics Teacher Education: Prospective Teachers Unpacking Mathematics and Mathematics Teacher Identities. Proceedings from the International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71), Braga, Portugal.
• Suh, J., & Anhalt, C. O. (2019, July). Defining Core Practices in Early Mathematical Modeling. In International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71).
  More info

  Suh, J. & Anhalt, C. (2019). Defining Core Practices in Early Mathematical Modeling. Proceedings from the International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71), Braga, Portugal.
• Anhalt, C. O. (2018, November). Exploring the Nature of Mathematical Modeling in the Early Grades. In North American Chapter of the International Group for the Psychology of Mathematics Education, 1478-1486.
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  Suh, J., Matson, K., Carlson, M.A., Levy, R, Wickstrom, M., Roth McDuffie, A., Jamieson, S., Turner, E., Seshaiyer, P. & Anhalt, C. (2018). Exploring the Nature of Mathematical Modeling in the Early Grades, pp. 1478-1486. In Hodges, T.E., Roy, G. J., & Tyminski, A. M. (Eds.). Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Greenville, SC: University of South Carolina & Clemson University.This working group will engage PMENA members to better understanding the nature of mathematical modeling in the early grades while considering the student perspective and recognizing the importance of teachers knowing their students and the contexts that are meaningful to their students. We will investigate how K-6 teachers demonstrate the interdisciplinary nature of mathematical modeling, the diversity of mathematical approaches taken by student modelers, and the multiple pathways the teacher can use to elicit students’ mathematical thinking. We will explore how mathematical modeling bridges equity and social community in teaching and learning mathematics for all students. Exemplar tasks that emphasized local contexts and tapped into students’ funds of knowledge and student artifacts will be shared to illustrate the child’s perspective and the developmental progression. These topics will facilitate group discussions exploring the learning progression for mathematical modeling thinking and habits of mind that can develop for emergent mathematical modelers from an early grade. We will map out productive learning pathways for mathematical modeling and task design for K-6 mathematics education and beyond.. Finally, based on the interests of the participants, we will devote work time to finding synergistic collaborative topics to pursue for future research and practice.
• Anhalt, C. O., & Turner, E. E. (2017, Summer). A Didactic Approach in Mathematical Modeling: Raising Critical Consciousness within Social and Culturally Relevant Contexts. In Commission for the Study and Improvement of Mathematics Teaching (CIEAEM) International Conference.
• Anhalt, C. O. (2015, January). Mathematical Modeling: Secondary Teacher Preparation in the United States. In Commission for the Study and Improvement of Mathematics Teaching (CIEAEM) International Conference, 24.
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  Anhalt, C. (2015). Mathematical Modeling: Secondary Teacher Preparation in the United States. Proceedings of the Commission for the Study and Improvement of Mathematics Teaching (CIEAEM) International Conference. Aldon, G., Di Paola, B., Fazio, C. (Eds.). Mathematics and reality, Proceedings of CIEAEM 66, Quaderni di Ricerca in Didattica Mathematics (QRDM), 24(1), p.388, ISSN 1592-4424, Editor in-Chief: Claudio FAZIO, University of Palermo, Italy. http://math.unipa.it/~grim/quaderno24_suppl_1.htm
• Araujo, Z., Roberts, S., Anhalt, C. O., Civil, M., Fernandes, A., Moschkovich, J., Wiley, C., & Zahner, W. (2015, November). Mathematics Education and English Learners. In Psychology of Mathematics Education – (PME) 37th Annual Meeting of the North American Chapter of the International Group, 37, 1384-1393.
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  Mathematics Education and English Learners, A Working Group in Psychology of Mathematics Education – (PME) 37th Annual Meeting of the North American Chapter of the International Group., pp. 1384-1393. Authors: Araujo, Z., Roberts, S., Anhalt, C., Civil, M., Fernandes, A., Moschkovich, J., Willey, C., Zahner, W. (2015).
• Anhalt, C. O. (2014, July). Mathematical Modeling: Secondary Teacher Preparation in the United States.. In Commission for the Study and Improvement of Mathematics Teaching (CIEAEM) International Conference, 24, 388.
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  Anhalt, C. (2015). Mathematical Modeling: Secondary Teacher Preparation in the United States. Proceedings of the Commission for the Study and Improvement of Mathematics Teaching (CIEAEM) International Conference. Aldon, G., Di Paola, B., Fazio, C. (Eds.). Mathematics and reality, Proceedings of CIEAEM 66, Quaderni di Ricerca in Didattica Mathematics (QRDM), 24(1), p.388, ISSN 1592-4424, Editor in-Chief: Claudio FAZIO, University of Palermo, Italy. http://math.unipa.it/~grim/quaderno24_suppl_1.htm
• Anhalt, C. O., Fernandes, A., & Civil, M. (2008, Summer). U.S. Latino Students’ Thinking and Communication on National Assessment Educational Progress (NEAP) Measurement Items. In International Congress of Mathematics Education (ICME).
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  Anhalt, C., Fernandes, A., & Civil, M. (2008). U.S. Latino Students’ Thinking and Communication on National Assessment Educational Progress (NEAP) Measurement Items, Proceedings from the Eleventh International Congress of Mathematics Education (ICME), TSG 33: Mathematics Education in a Multilingual and Multicultural Environment, Monterrey, MX, July.
• Anhalt, C. O., Civil, M., & Fernandes, A. (2007, October). Exploring Latino Students' Understanding of Measurement on NAEP Items. In Psychology of Mathematics Education North-American Chapter (PME-NA) Annual Conference.

Presentations

• Anhalt, C. O. (2022, July). Research in Mathematical Modeling for Secondary Teacher Education. Society of the Industrial and Applied Mathematics (SIAM)Education Conference. Pittsburgh, PA: Society of the Industrial and Applied Mathematics.
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  Research in prospective teachers’ development of mathematical modeling knowledge for teaching is gaining momentum. We found that project-based mathematical modeling experiences provide opportunities for prospective secondary teachers to develop foundational knowledge in modeling and a vision for teaching and learning mathematical modeling. We designed modeling problems for the MODULE(S2) Project with a variety of social contexts that allow prospective teachers to examine critical social issues to consider in their future teaching. We describe two modeling projects: (1) the use of sandbags as emergency barriers for damage-causing flooding, and (2) the use of historic maps to examine the shrinking land of the Sioux Reservation. The first problem focuses on the arrangement of sandbags as standard protocol by safety guidelines, and the latter explores different methods for finding the area of land in connection to the injustice deeply rooted in the treatment of indigenous people. Both problems call for explicit attention to pedagogical knowledge in structuring discussions around the contextualization of the mathematical results. Our work informs teacher preparation programs for inclusion of mathematical modeling with authentic social contexts that embrace meaningful curriculum.
• Anhalt, C. O., Cortez, R., Kohler, B., & Tidwell, W. (2022, August). Interrogation of Social Justice Contexts in Mathematical Modeling: The Use of Simulations of Practice in the Mathematical Preparation of Teachers. 16th International Conference of the Mathematics Education for the Future Project. King’s College, Cambridge University, United Kingdom.
• Lischka, A., Casey, S., Anhalt, C. O., & Lai, Y. (2022, February). Using Representations of Teaching Practice in Content Courses: Opportunities for Developing Mathematical Knowledge for Teaching. Association of Mathematics Teacher Educators (AMTE) Annual Conference. Las Vegas, NV: AMTE.
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  Mathematics educators and mathematicians will explore mathematically-intensive representations of practice that help develop secondary teachers’ content and pedagogical knowledge. Participants will examine the foundations of such tasks, consider secondary teachers’ responses, and discuss characteristics of effective feedback to PSMTs.
• Anhalt, C. O. (2021, May). Hot Topic in K-12 Mathematics Education: Mathematics of Social Justice, Diversity, Equity and Inclusion Panel. Loyola Marymount University Master of Arts in Mathematics Teaching Program. Loyola Marymount University: Master of Arts in Mathematics Teaching Program.
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  Anhalt, C. Hot Topic in K-12 Mathematics Education: Mathematics of Social Justice, Diversity, Equity and Inclusion Panel, Loyola Marymount University Master of Arts in Mathematics Teaching. Invited by Prof. Christina Eubanks-Turner, May 3, 2021
• Anhalt, C. O., & Cortez, R. (2021, January). Examining MKT in Mathematical Modeling through PSTs’ Participation in Simulations of Practice. Joint Math Meetings (JMM). Virtual: AMS, MAA.
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  Anhalt, C., & Cortez, R., Examining MKT in Mathematical Modeling through PSTs’ Participation in Simulations of Practice. Invited Special Session of the AMS of the Joint Mathematics Meetings, Mathematics Courses Designed to Develop Mathematical Knowledge for Teaching (MKT) High School, JMM Virtual Conference, January 6-8, 2021.
• Tidwell, W., Anhalt, C. O., Cortez, R., & Kohler, B. (2021, November). Development of Prospective Elementary Teachers’ Mathematical Modeling Competencies and Conceptions. Herenga Delta Conference, 13th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics. Auckland, New Zealand.
• Aguirre, J., Turner, E. E., & Anhalt, C. O. (2020, February). Mathematical Modeling in K-12 Mathematics Teacher Preparation,. Association of Mathematics Teacher Educators (AMTE) Annual Conference. Phoenix, AZ: AMTE.
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  Aguirre, J., Turner, E., & Anhalt, C. Mathematical Modeling in K-12 Mathematics Teacher Preparation, Association of Mathematics Teacher Educators (AMTE), February 2020, Pheonix, AZ.
• Anhalt, C. O. (2020, March). Envisioning an Inclusive Pedagogy: Building Collaborative Learning Communities in Mathematics. Mathematics for ∀LL Conference, Tulane University. New Orleans, LA: Tulane University.
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  Anhalt, C. Keynote: Envisioning an Inclusive Pedagogy: Building Collaborative Learning Communities in Mathematics, Mathematics for ∀LL Conference, Tulane University, March 6-7, 2020. (https://sites.google.com/view/mathforallnola/past-editions?authuser=0)
• Anhalt, C. O., Aguirre, J. M., & Turner, E. E. (2020, February). Mathematical Modeling with Cultural and Community Contexts, Panel: Advocacy and Emerging Issues Breakfast. Association of Mathematics Teacher Educators. Phoenix, AZ: AMTE.
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  Anhalt, C., Aguirre, J., Turner, E. Mathematical Modeling with Cultural and Community Contexts, Panel: Advocacy and Emerging Issues Breakfast, AMTE Annual National Conference, Phoenix, AZ, February 7, 2020.
• Anhalt, C. O., Cortez, R., & Kohler, B. (2020, June). Mathematical Modeling Modules: Curriculum Material for Secondary Teacher Education. Mathematics Teacher Education Partnership (MTEP) Annual Conference. Virtual: Association of Public Land-grant Universities.
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  Anhalt, C., Cortez, R., Kohler, B. Mathematical Modeling Modules: Curriculum Material for Secondary Teacher Education, Mathematics Teacher Education Partnership (MTEP) annual conference, June 28-30, 2020, virtual: https://www.aplu.org/projects-and-initiatives/stem-education/mathematics-teacher-education-partnership/mtep-conferences-meetings.
• Strayer, J., Lai, Y., & Anhalt, C. O. (2020, January). Purposeful Use of Simulations of Teaching Practice to Uncover Mathematical Knowledge for Teaching,. Joint Mathematics Meetings. Denver, CO: American Mathematics Association and Mathematics Association of America.
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  Srayer, J., Lai, Y., Anhalt, C. Purposeful Use of Simulations of Teaching Practice to Uncover Mathematical Knowledge for Teaching, Joint Mathematics Meeting, Denver, CO, January 2020.
• Aguirre, J. M., Anhalt, C. O., Turner, E., Foote, M., & Roth McDuffie, A. (2019, July). Engaging Children’s Multiple Mathematical Knowledge Bases with Mathematics Modeling Tasks in Elementary Classrooms. International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71). Braga, Portugal.
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  Aguirre, J., Anhalt, C., Turner, E., Foote, M., & Roth McDuffie, A. Engaging Children’s Multiple Mathematical Knowledge Bases with Mathematics Modeling Tasks in Elementary Classrooms. International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71), Braga, Portugal, July 22-26, 2019.
• Anhalt, C. O., & Beck, E. (2019, July). Noyce Scholars and Fellows as Change Agents in STEM Teaching: Research Report from the 2019 Western Regional Noyce Conference-AZ.. Noyce Summit. Washington, DC: National Science Foundation.
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  Anhalt, C. & Beck, E. Noyce Scholars and Fellows as Change Agents in STEM Teaching: Research Report from the 2019 Western Regional Noyce Conference-AZ. NSF Noyce Summit, Washington DC, July 10-12, 2019.
• Anhalt, C. O., & Cortez, R. (2019, August). Mathematical Modeling Thinking: Laying the Foundation for Mathematical Modeling Competency. 15th International Conference in Mathematics Education for the Future Project (ICMEFP). Maynuth University, Kildare, Ireland.
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  Anhalt, C. & Cortez, R. Mathematical Modeling Thinking: Laying the Foundation for Mathematical Modeling Competency. 15th International Conference in Mathematics Education for the Future Project (ICMEFP), Maynuth University, Kildare, Ireland, August 4-9, 2019.
• Anhalt, C. O., Aguirre, J., & Suh, J. (2019, July). Mathematical Modeling: Raising Awareness and Exploring a Community-based Water Crisis through a Critical, Social Justice and Environmental Lens.. International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71). Braga, Portugal.
  More info

  Anhalt, C., Aguirre, J. & Suh, J., Mathematical Modeling: Raising Awareness and Exploring a Community-based Water Crisis through a Critical, Social Justice and Environmental Lens. International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71), Braga, Portugal, July 22-26, 2019.
• Anhalt, C. O., Guzman, L., & Sheldon, J. (2019, July). Complex Competencies in Mathematics Teacher Education: Prospective Teachers Unpacking Mathematics and Mathematics Teacher Identities.. International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71). Braga, Portugal.
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  Guzman, L., Anhalt, C. & Sheldon, J., Complex Competencies in Mathematics Teacher Education: Prospective Teachers Unpacking Mathematics and Mathematics Teacher Identities. International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71), Braga, Portugal, July 22-26, 2019.
• Guzman, L., Anhalt, C. O., & Sheldon, J. (2019, February). Interrogating Identity Narratives within Academic, Social, and Cultural Contexts for Mathematics Teaching. Association of Mathematics Teacher Educators (AMTE). Orlando, FL.
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  Guzman L., Anhalt, C. & Sheldon, J., Interrogating Identity Narratives within Academic, Social, and Cultural Contexts for Mathematics Teaching, Association of Mathematics Teacher Educators (AMTE), February 2019, Orlando, FL.
• Lischka, A., Lai, Y., Strayer, J., & Anhalt, C. O. (2019, February). Developing Prospective Secondary Teachers’ MKT through Approximations of Practice. Association of Mathematics Teacher Educators (AMTE). Orlando, FL.
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  Alyson Lischka, Yvonne Lai, Jeremy Strayer, Cynthia Anhalt, Developing Prospective Secondary Teachers’ MKT through Approximations of Practice, Association of Mathematics Teacher Educators (AMTE), February 2019, Orlando, FL.
• Suh, J., & Anhalt, C. O. (2019, July). Defining Core Practices in Early Mathematical Modeling. International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71). Braga, Portugal.
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  Suh, J. & Anhalt, C., Defining Core Practices in Early Mathematical Modeling. International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 71), Braga, Portugal, July 22-26, 2019.
• Turner, E. E., Aguirre, J. M., Foote, M., Roth McDuffie, A., & Anhalt, C. O. (2019, February). Mathematical modeling in cultural and community contexts with elementary teachers and students grades 3-5,. Association of Mathematics Teacher Educators (AMTE). Orlando, FL.
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  Turner, E., Aguirre, J., Foote, M., Roth McDuffie, A. & Anhalt, C. Mathematical modeling in cultural and community contexts with elementary teachers and students grades 3-5, Association of Mathematics Teacher Educators (AMTE), February 2019, Orlando, FL.
• Aguirre, J. M., Anhalt, C. O., Turner, E. A., Simic-Muller, K., & Cortez, R. (2018, February). Mathematical Modeling and Social Justice: A Powerful Combination for Teacher Learning and Preparation. Association of Mathematics Teacher Educators (AMTE). Houston, TX.
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  Aguirre, J., Anhalt, C., Turner, E., Simic-Muller, K., Cortez, R. Mathematical Modeling and Social Justice: A Powerful Combination for Teacher Learning and Preparation. Association of Mathematics Teacher Educators (AMTE), February 2018, Houston, TX.This session addresses the challenge to prepare equity-based teachers of mathematics. Utilizing mathematical modeling tasks connected to environmental justice and fairness, presenters share ways to deepen teachers’ understanding of mathematics and social justice in content courses, methods, and professional development.
• Anhalt, C. O. (2018, July). Mathematical Modeling in Secondary Teacher Preparation, Mini-Symposium. Society of Industrial and Applied Mathematics (SIAM) Education Conference. Poertland, OR: Society of Industrial and Applied Mathematics (SIAM).
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  Anhalt, C., Mathematical Modeling in Secondary Teacher Preparation, Mini-Symposium, Mathematical Modeling: Practice and Education. Ricardo Cortez, Symposium Chair, Tulane University, Society of Industrial and Applied Mathematics (SIAM) Education Conference, Portland, OR, July 8-11, 2018.
• Anhalt, C. O. (2018, June). t Really is ALL about ALL students learning quality mathematics: Advocating for Equity and Social Justice. TODOS: Mathematics for ALL. Scottsdale, AZ: TODOS: Mathematics for ALL Organization.
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  Anhalt, C. It Really is ALL about ALL students learning quality mathematics: Advocating for Equity and Social Justice, Ignite Session, TODOS: Mathematics For ALL National Conference, June 21-23, 2018.
• Anhalt, C. O., & Cortez, R. (2018, February). Mathematical Modeling, “Modeling Thinking,” and the Mathematical Horizon of Elementary School Teachers. Association of Mathematics Teacher Educators. Houston, TX.
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  Anhalt, C. & Cortez, R. Mathematical Modeling, “Modeling Thinking,” and the Mathematical Horizon of Elementary School Teachers, Association of Mathematics Teacher Educators, Houston, TX, February 8-19, 2019.Model with mathematics is a Standard for Mathematical Practice in the Common Core. Modeling tasks are open-ended problems derived from everyday situations that use mathematics in order to understand, explain or predict something. In modeling, students make assumptions and decisions to simplify the situation, they describe it mathematically, and interpret the mathematical solutions in the context of the situation. They reflect on the appropriateness of the results and improve the model, if it has not served its purpose (CCSSI, 2010). This model improvement points out the cyclical nature of the modeling process. Echoing this mathematical practice, the SPTM call for grade 6-8 teachers to “understand how to engage middle level learners in meaningful and interdisciplinary contexts, including the use of mathematical modeling.” Research indicates that developing competencies take time (Author), making it critical to develop aspects of the modeling process early on. Our proposal addresses the question, how can elementary school teachers be supported to implement tasks that focus on developing students’ competencies appropriate for their grade level as part of a coherent curriculum in mathematical modeling?
• Anhalt, C. O., & Cortez, R. (2018, January). A Report on Prospective Teachers’ Development of Content Knowledge in Mathematical Modeling and the Use of Reflections to Promote the Emergence of Mathematical Knowledge for Teaching. Joint Mathematics Meetings. San Diego, CA: American Mathematical Society (AMS) and Mathematical Association of America (MAA).
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  Anhalt, C. & Cortez, R. A Report on Prospective Teachers’ Development of Content Knowledge in Mathematical Modeling and the Use of Reflections to Promote the Emergence of Mathematical Knowledge for Teaching, Joint Mathematics Meetings, San Diego, CA, January 9-11, 2018.Recent infusion of mathematical modeling in k-12 has generated research and teacher preparation activity to understand the modeling process as content and to develop mathematical knowledge for teaching (MKT) modeling. For mathematics majors in teacher preparation programs, this new activity is aligned with CUPM (2015) cognitive and content modeling recommendations. Given that most prospective teachers (PTs) are not familiar with mathematical modeling, there is an urgent need to design ways for them to simultaneously develop modeling content knowledge and MKT. This presentation focuses on PTs’ development of specific modeling competencies that indicate both the possession of content knowledge and the practice of “modeling thinking” as a cognitive goal for PTs to develop MKT. We report on the implementation of a mathematical modeling module in secondary teacher preparation courses that emphasizes multiple solution paths to open-ended problems and assumption making to develop modeling competencies combined with reflections on teaching. We will present results from studies with PTs using theoretical frameworks for MKT (Ball, Thames, and Phelps 2008, Journal of Teacher Education, 59(5), 389-407) and competencies (Maa\ss\ 2006, ZDM, 38(2), 113-142).
• Anhalt, C. O., Turner, E. E., Aguirre, J., Foote, M., Amy, R. M., & Civil, M. (2018, June). The Price of Guacamole: Designing Rigorous and Relevant Mathematical Modeling Tasks that Build on the Strengths of Community and Cultural Contexts. TODOS: Mathematics for ALL. Scottsdale, AZ: TODOS: Mathematics for ALL Organization.
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  Anhalt, C., Turner, E., Aguirre, J., Foote, M., Roth McDuffie, Amy, Civil. M. The Price of Guacamole: Designing Rigorous and Relevant Mathematical Modeling Tasks that Build on the Strengths of Community and Cultural Contexts. TODOS: Mathematics for ALL Conference, Scottsdale, AZ June 21-23, 2018.
• Strayer, J., Lai, Y., Alyson, L., & Anhalt, C. O. (2018, June). An Emerging Framework for Understanding the Development of Mathematical Knowledge for Teaching. Mathematics Teacher Education Partnership Annual Conference. Denver, CO: Association of Public Land-grant Universities (APLU).
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  Strayer, J., Lai, Y., Lischka, A. & Anhalt, C. An Emerging Framework for Understanding the Development of Mathematical Knowledge for Teaching, Mathematics Teacher Education Partnership Annual Conference, Association of Public Land-grant Universities (APLU), Denver, CO, June 24-28, 2018.
• Suh, J., Matson, K., Carlson, M. A., Levy, R., Wickstrom, M., Roth McDuffie, A., Jamieson, S., Turner, E. E., Seshaiyer, P., & Anhalt, C. O. (2018, November). Exploring the Nature of Mathematical Modeling in the Early Grades, Working Group. North American Chapter of the International Group of the Psychology of Mathematics Education. Greenville, SC.
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  Suh, J., Matson, K., Carlson, M.A., Levy, R, Wickstrom, M., Roth McDuffie, A., Jamieson, S., Turner, E., Seshaiyer, P. & Anhalt, C. Exploring the Nature of Mathematical Modeling in the Early Grades, Working Group, North American Chapter of the International Group of the Psychology of Mathematics Education, Greenville, SC, November 15-17, 2018.
• Anhalt, C. O. (2017, July). A Didactic Approach in Mathematical Modeling: Raising Critical Consciousness within Social and Culturally Relevant Contexts. Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 69) International Conference. Freie Universitat Berlin, Berlin, Germany..
• Anhalt, C. O. (2017, July). Discussant, Working Group: Mathematisation as a didactic principle: Mathematizing and modelling of everday contexts. Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 69) International Conference. Freie Universitat Berlin, Berlin, Germany..
• Anhalt, C. O., & Cortez, R. (2017, April). Developing Mathematical Modeling Competency: Theory and Reality. National Council of Teachers of Mathematics (NCTM) Annual Research Conference,. San Antonio, TX: National Council of Teachers of Mathematics.
• Anhalt, C. O., & Cortez, R. (2017, January). Mathematical Modeling in the Middle Grades (M3): A Professional Development Project for Grades 5-8 Teachers in Rural School Districts near the Southern US Border. Joint Mathematical Meetings (JMM). Atlanta, GA: Mathematical Association of America.
• Anhalt, C. O., & Fernandez, M. (2017, June). To Be or Not To Be: A Study of Prospective Teachers’ Underlying Reasons to Pursue the Teaching Profession Across Two Geographic Areas.. Mathematics Teacher Educuation Partnership. New Orleans, LA: Association of Public Land-grant Universities.
• Anhalt, C. O. (2016, September/October). Leveraging Students' Cultural Competencies Through Mathematical Modeling. Society for Industrial and Applied Mathematics (SIAM) Conference on Applied Education. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
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  Anhalt, C. Leveraging Students' Cultural Competencies Through Mathematical Modeling, Increasing Diversity and Inclusion in Mathematics Symposium, Rosalie Bélanger-Rioux, Symposium Chair, Harvard University, Society for Industrial and Applied Mathematics (SIAM) Conference on Applied Mathematics Education, September 30-October 2, 2016, Philadelphia, PA.
• Anhalt, C. O., & Belanger-Rioux, R. (2016, September/October). Diversity Training for Mathematics Faculty. Society for Industrial and Applied Mathematics (SIAM) Conference in Applied Education. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
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  Bélanger-Rioux, R. & Anhalt, C. Diversity Training for Mathematics Faculty. Increasing Diversity and Inclusion in Mathematics Symposium, Rosalie Bélanger-Rioux, Symposium Chair, Harvard University, Society for Industrial and Applied Mathematics (SIAM) Conference on Applied Mathematics Education, September 30-October 2, 2016, Philadelphia, PA.
• Anhalt, C. O., & Cortez, R. (2016, January). Design and Implementation of an Undergraduate Mathematical Modeling Course with no College Prerequisites. Joint Mathematical Meetings (JMM). Seattle, WA: Joint Mathematical Meetings (JMM).
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  Cortez, R. & Anhalt, C., Design and Implementation of an Undergraduate Mathematical Modeling Course with no College Prerequisites. Joint Mathematical Meetings (JMM) January 2016, Seattle, WA. MAA Session on Mathematical Modeling in the Undergraduate Classroom, Organizers: Jason Douma, University of Souix Falls and Rachel Levy, Harvey Mudd College. http://jointmathematicsmeetings.org/meetings/national/jmm2016/2181_program_saturday.html
• Anhalt, C. O., & Cortez, R. (2016, January). Designing a Progression for Mathematical Modeling: From Early Elementary to High School Grades. Association of Mathematics Teacher Educators (AMTE). Irvine, CA: Association of Mathematics Teacher Educators (AMTE).
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  Anhalt, C. & Cortez, R. Designing a Progression for Mathematical Modeling: From Early Elementary to High School Grades. Association of Mathematics Teacher Educators (AMTE) Annual Conference, Irvine, CA, January 2016. http://amte.net/sites/default/files/20thamteconfprogram.pdf
• Anhalt, C. O., & Ricardo, C. (2016, January). Rethinking the Undergraduate Curriculum for Secondary Mathematics Teacher Preparation: Using Mathematical Modeling Modules to Address Common Core Standards. Joint Mathematical Meetings (JMM). Seattle, WA: Joint Mathematical Meetings (JMM).
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  Anhalt, C. & Cortez, R., Rethinking the Undergraduate Curriculum for Secondary Mathematics Teacher Preparation: Using Mathematical Modeling Modules to Address Common Core Standards. Joint Mathematical Meetings (JMM) January 2016, Seattle, WA. MAA Session on Common Core State Standards (CCSS) for Mathematics Practices and Content: The Role of Math Departments in Preparing Math Education Candidates for New Assessments. Organizers: William Martin, North Dakota State University, Karen Morgan, New Jersey City University, Gulden Karakok, University of Northern Colorado, James A. Mendoza Epperson, University of Texas-Arlington. http://jointmathematicsmeetings.org/meetings/national/jmm2016/2181_program_thursday.html#2181:MCPMARC1
• Been, A. L., Anhalt, C. O., & Turner, E. E. (2016, Jan 2016). Mathematical Modeling in the Middle Grades. MEAD: Mathematics Educator Appreciation Day. Tucson, AZ: Center for Recruitment and Retention, University of Arizona.
• Anhalt, C. O. (2015, September). Equity and Mathematics Education. MATH 196A. UA, Mathematics Department, CRR: Center for Recruitment and Retention.
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  Anhalt, C., Equity and Mathematics Education, Math 196A Workshop for mathematics tutors, Center for Recruitment and Retention, September 2015.
• Anhalt, C. O., & Liston, J. (2015, July). The Tangram Chinese Puzzle in Context: Using Language as a Resource to Develop Geometric Reasoning in a Collaborative Environment. Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 67) International Conference. Aosta, Italia: Università della valle d'Aosta (University of Aosta, Italy).
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  Anhalt, C. & Liston, J., The Tangram Chinese Puzzle in Context: Using Language as a Resource to Develop Geometric Reasoning in a Collaborative Environment. Workshop at the Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 67) International Conference, Aosta, Italy, July 20-24, 2015.
• Anhalt, C. O., Shafer, M., Buchanan, D., & Collingwood, C. (2015, January). Mentoring the Next Generation of Teachers. Mathematics Educators Appreciation Day (MEAD) Annual Conference. Tucson, AZ: Center for Recruitment and Retention, Mathematics Department, Univeristy of Arizona.
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  Anhalt, C. & Shafer, M. Mentoring the Next Generation of Teachers, Mathematics Educators Appreciation Day (MEAD) Annual Conference, Co-presenters: David Buchanan (UA Math Dept. SMEP graduate), Charles Collingwood (Catalina High School), January 2015.
• Ramirez, N., Civil, M., Anhalt, C. O., & McDonald, B. (2015, January). Keeping Equity at the Forefront. Mathematics Educators Appreciation Day (MEAD) Annual Conference. Tucson, AZ: Center for Recruitment and Retention, Mathematics Department, Univeristy of Arizona.
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  Ramirez, N., Civil, M, Anhalt, C. & McDonald B., Keeping Equity at the Forefront, Mathematics Educators Appreciation Day (MEAD) Annual Conference, January 2015.
• Anhalt, C. O. (2014, July). Mathematical modeling: Secondary teacher preparation in the United States. Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 66) International Conference. Lyon, France.
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  Anhalt, C. Mathematical modeling: Secondary teacher preparation in the United States. Commission for the Study and Improvement of Mathematics Teaching (CIEAEM 66) International Conference, Forum of Ideas Session, Lyon, France, July 2014.
• Anhalt, C. O. (2014, June). Scaffolding in Mathematical Modeling for ELLs. TODOS 2014 National Conference “Beyond Awareness: Equity, Access and Achievement for All”. Chandler, AZ, USA: TODOS: Mathematics for ALL Organization.
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  Anhalt, C., Scaffolding in Mathematical Modeling for ELLs, Symposium speaker, Wiley, C. (Symposium Chair), Civil, M., Turner, E., Moschkovich, J., Thompson, A., Fernandez, A., Kahn, L., Lopez Leiva, C., Chval, K., Pinnow, R., Zahner, W., Kitchen, R, Celedon-Pattichis, S., Musanti, S., "Exploring Practices that Support the Common Core State Standards in Mathematics with English Language Learners." TODOS 2014 National Conference “Beyond Awareness: Equity, Access and Achievement for All” June 26-28, 2014, Chandler, AZ
• Anhalt, C. O. (2014, March). The MTE-Partnership: Rethinking secondary mathematics teacher education, Recruitment and Retention Research Action Cluster. Critical Issues in Mathematics Education Workshop 2014: The Role of Mathematics Departments in the Mathematical Preparation of Teacher. Berkeley, CA, USA: Mathematical Sciences Research Institute (MSRI).
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  Anhalt, C., Panel Speaker: The MTE-Partnership: Rethinking secondary mathematics teacher education, Recruitment and Retention Research Action Cluster. Panel: W. Gary Martin, Chair, Auburn University, Jim Lewis, University of Nebraska, and Mike Mayes, University of Virginia. Mathematical Sciences Research Institute (MSRI) Critical Issues in Mathematics Education Workshop 2014: The Role of Mathematics Departments in the Mathematical Preparation of Teacher. UC Berkeley, March 2014.
• Anhalt, C. O., & Cortez, R. (2014, February). Mathematical Modeling: Secondary Teacher Preparation in the Era of Common Core. Association of Mathematics Teacher Education (AMTE) Annual Conference. Irvine, CA, USA.
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  Anhalt, C. & Cortez, R., Mathematical Modeling: Secondary Teacher Preparation in the Era of Common Core, Association of Mathematics Teacher Education (AMTE) Annual Conference, Irvine, CA, February 2014.
• Anhalt, C. O., Aguirre, J., Crespo, S., & Gutierrez, R. (2014, October). Empowering Prospective Teachers to Take Ownership: Mathematical Modeling as Leverage for Defining Mathematical Pathways. Society for the Advancement of Hispanics/Chicanos and Native Americans in the Sciences (SACNAS) National Conference. Los Angeles, CA, USA: National Science Foundation Grant.
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  Anhalt, C., Empowering Prospective Teachers to Take Ownership: Mathematical Modeling as Leverage for Defining Mathematical Pathways, Society for the Advancement of Hispanics/Chicanos and Native Americans in the Sciences (SACNAS) National Conference. Scientific Symposium sponsored by a grant from the National Science Foundatin (NSF): Advancing the Next Generation in STEM: Rethinking K-12 Mathematics Teacher Education in the Era of High Stakes Education. Speakers: Julia Aguirre, Chair, University of Washington, Tacoma, Cynthia O. Anhalt (University of Arizona), Sandra Crespo, (Michigan State University), Rochelle Gutierrez (University of Illinois at Urbana Champaign), Los Angeles, CA, October 2014.
• Anhalt, C. O., Baker, D., Livio-Velez, P., Murray, D., Takagi, J., & Collingwood, C. (2014, January). Mentoring the Next Generation of Teachers. Mathematics Educators Appreciation Day (MEAD) Conference. Tucson, AZ, USA: Department of Mathematics.
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  Anhalt, C. (Chair), Teacher Panel: Baker, D., Collingwood, C., Livio-Velez, P., Murray, D., & Takagi, J. Mentoring the Next Generation of Teachers, Mathematics Educators Appreciation Day (MEAD) Conference, January 25, 2014
• Anhalt, C. O., Eubanks-Turner, C., Cortez, R., Civil, M., & Mosqueda, E. (2014, October). Current Research Trends in Mathematics Education: Issues That Matter. Society for the Advancement of Hispanics/Chicanos and Native Americans in the Sciences (SACNAS) National Conference. Los Angeles, CA, USA: Mathematics Association of America (MAA).
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  Anhalt, C. , Chair, Scientific Symposium sponsored by the Mathematics Association of America (MAA), Current Research Trends in Mathematics Education: Issues That Matter. Society for the Advancement of Hispanics/Chicanos and Native Americans in the Sciences (SACNAS) National Conference. Speakers: Christina Eubanks-Turner (Loyola Marymount University), Ricardo Cortez (Tulane University), Marta Civil (University of Arizona), Eduardo Mosqueda (University of California, Santa Cruz). Los Angeles, CA, October 2014.

Poster Presentations

• Alyson, L., Ross, A., Lai, Y., Kohler, B., Aubrey, J., Strayer, J., Casey, S., Anhalt, C. O., & Gobstein, H. (2018, January). MODULES: Mathematics of Doing, Understanding, Learning and Educating for Secondary Schools.. Joint Mathematics Meeting. San Diego, CA: American Mathematical Society (AMS) and Mathematical Association of American (MAA).
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  Lischka, A., Ross, A., Lai, Y., Kohler, B., Aubrey, J., Strayer, J., Casey, S., Anhalt, C., Gobstein, H., MODULES: Mathematics of Doing, Understanding, Learning and Educating for Secondary Schools. MAA Poster Session: Projects Supported by the NSF Division of Undergraduate Education. Joint Mathematical Meetings (JMM) January 2018, San Diego, CA.
• Anhalt, C. O., & Murrell, M. (2018, July). Noyce Seminars: At the Heart of Mathematics Teacher Preparation. Noyce Summit. Washington, DC: National Science Foundation (NSF) and American Association for the Advancement of Science (AAAS).
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  Anhalt, C. & Murrell, M. Noyce Seminars: At the Heart of Mathematics Teacher Preparation. National Science Foundation (NSF) & American Association for the Advancement of Science (AAAS) Noyce Summit, Washington, DC, July 16-18, 2018.
• Anhalt, C. O., & Stimans, J. (2017, July). AZ Noyce Scholars Preparing to Teach Mathematics to Culturally Diverse Students. NSF Robert Noyce Summit. Washington, DC: National Science Foundation.

Other Teaching Materials

• Lyschka, A., Anhalt, C. O., Strayer, J., Lai, Y., Casey, S., & Ross, A. (2022. MODULES: Materials to Support the Implementation of the Standards for the Preparation of Teachers of Mathematics. Association of Mathematics Teacher Educators AMTE.net.
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  Online materials developed by the authors of the NSF funded MODULES2 curriculum materials for the mathematical preparation of secondary teachers in algebra, geometry, mathematical modeling, and statistics.

Others

• Anhalt, C. O. (2015, November). Mathematical Modeling with Southern AZ Teachers. Mathematics Newsletter. http://online.fliphtml5.com/xxyc/kcbq/#p=1
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  Description of "Mathematics Modeling in the Middle Grades (M^3) Project - page 12 of Newsletter. Project Funded by AZ Board of Regents, Improving Teacher Quality (ITQ) for 2015-16 Academic Year.
• Anhalt, C. O., Cortez, R., & Zeeman, M. L. (2014, February). “MAA-Sponsored Sessions at the Society for the Advancement of Latinos, Chicanos, and Native Americans in Science”. Mathematical Association of America (MAA). http://digitaleditions.walsworthprintgroup.com/publication/?i=212119
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  Anhalt, C., Cortez, R., & Zeeman, M.L. “MAA-Sponsored Sessions at the Society for the Advancement of Latinos, Chicanos, and Native Americans in Science” Mathematical Association of America (MAA) FOCUS Newsletter, June/July 2014. http://digitaleditions.walsworthprintgroup.com/publication/?i=212119
• Cortez, R., & Anhalt, C. O. (2014, February). “Readers Write” – “More on Modeling Eliciting Activities”. Letter to the Editor.
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  Cortez, R. & Anhalt, C. (2014). “Readers Write” – “More on Modeling Eliciting Activities” Vol. 19, No. 6, February 2014). A correction response to “Model Eliciting Activities: A Home Run” by Marta T. Magiera (February 2013 issue, pp. 348-55), Mathematics Teaching in the Middle School (MTMS), Vol. 19, No. 6, pp. 324-26.