*Editor-in-Chief:*

**Mark Saul**is the Senior Scientist at the Julia Robinson Mathematics Festival (JRMF). The JRMF runs non-competitive after-school events in which students engage cooperatively in solving non-standard mathematical problems and activities. The festivals have reached thousands of students in 25 states and 6 foreign countries.

Saul worked as Director of Competitions for the Mathematical Association of America, directed the Center for Mathematical Talent at the Courant Institute of Mathematical Sciences at New York University, served as a program officer for the National Science Foundation, and was a senior scholar for the John Templeton Foundation. He received the Presidential Awards for Excellence in Mathematics and Science Teaching in 1984.

Saul went to public schools in the Bronx, then got his BA from Columbia University and his Ph.D. from NYU. He spent 35 years in and around New York, teaching mathematics in classrooms from grades 3 through 12. While teaching, Saul directed the Research Science Institute at MIT for twelve years. Internationally, he co-directed the AAAS Olympiad program, which brought US students from minority backgrounds to the Pan-African Mathematics Olympiad and similar olympiads in Latin America. He initiated a student exchange program between Russian and American students, as well as an "Intel/Westinghouse" style competition for students of mathematics in China. He served as President of the American Regions Mathematics League, mathematics field editor of

*Quantum*(the English-language version of the Russian journal

*Kvant*), a board member of the National Council of Teachers of Mathematics, and a member of the Mathematical Sciences Education Board.

Saul's publications include numerous articles and 12 books. Among them is an elementary text on trigonometry, co-authored with I.M. Gelfand, and a translation and 'reader's companion' for Jacques Hadamard's

*Elementary Geometry*. His most recent volume, written with Titu Andreescu for the American Mathematical Society, is about algebraic inequalities, leading students from very ordinary classroom fare to Olympiad-level problems in incremental steps.

*Contributing Editors:*

**Carolyn Abbott**did her undergraduate work at Tufts where she received a B.A. in mathematics and Asian Studies in 2004. After spending a year at Jagiellonian University in Kraków, Poland, studying Polish language and literature, she returned to the US and completed a M.A.T in Secondary Math Education at Cornell. From there, she moved to New York City and taught middle and high school math for 5 years before going back to graduate school. She received her Ph.D. from the University of Wisconsin-Madison in 2017. She was a Morrey Visiting Assistant Professor and then a NSF Postdoctoral Fellow at UC Berkeley. She is currently an NSF Postdoctoral Fellow at Columbia University, and starting in Fall 2021, she will be an Assistant Professor at Brandeis University.

Abbott’s research is in geometric group theory and low-dimensional topology. She focuses on group actions by isometries on hyperbolic metric spaces, especially acylindrical actions. Her broad goal is to use the group action to translate geometric and topological properties of the hyperbolic spaces into algebraic properties of the group. The kinds of groups she thinks about include hyperbolic and relatively hyperbolic groups, mapping class groups, Out(F

_{n}), CAT(0) groups, three manifold groups, hierarchically hyperbolic groups, and many more.

**Ben Blum-Smith**received a B.A. in anthropology from Yale University in 2000, an M.A.T. in mathematics teaching from Tufts University in 2001, and a Ph.D. in mathematics from NYU in 2017, with a thesis in representation and invariant theory of finite groups. He worked as a middle and high school teacher in public schools in Cambridge, MA and New York City, and then as a mathematics professional development specialist for high schools and as a faculty member of Bard College’s teacher training program, before beginning his training as a research mathematician in 2011. He is currently a part-time faculty member of Eugene Lang College’s Department of Natural Sciences and Mathematics, and has also taught in the Bard Prison Initiative.

His research interests lie in invariant theory, algebraic combinatorics, their applications to data science, and connections between mathematics and democracy. He was a 2018 TED Resident, developing a TED talk about math’s relationship with democracy, and is a founding organizer of the Math and Democracy Seminar at the NYU Center for Data Science. He remains involved in teacher professional development through Math for America, an organization devoted to the career-long professional growth of teachers. He is also engaged in mathematical outreach. He has led math circles with students and teachers at the School of Mathematics, the New York Math Circle, the Westchester Area Math Circle, the LREI Summer Institute, the Center for Mathematical Talent at NYU, and the MathLeague International Mathematics Tournament, and is regularly a faculty member and faculty mentor at the Bridge to Enter Advanced Mathematics, an organization focused on creating a realistic pathway for underserved students to enter the mathematical sciences.

**Al Cuoco**is a Distinguished Scholar in mathematics at the Education Development Center, Waltham, MA. He taught high school mathematics to a wide range of students in the Woburn, Massachusetts public schools from 1969 until 1993. He then moved to Education Development Center, where he works in curriculum and professional development. Al is lead author for

*The CME Project,*a four-year high school curriculum, and he works with Paul Goldenberg and June Mark on

*Beauty and Joy of Computing*, a computer science curriculum that originated at Berkeley. For the past three decades, Al and Glenn Stevens have worked together on Boston University's

*PROMYS for Teachers*, a professional development program for teachers based on an immersion experience in mathematics.

A student of Ralph Greenberg, Al holds a Ph.D. from Brandeis, with a thesis and research in Iwasawa theory. Recent books include

*Mathematical Connections: a Companion for Teachers and Others*,

*Learning Modern Algebra*(with Joseph Rotman), and

*Applications of Algebra and Geometry to the Work of Teaching*(with Bowen Kerins, Ben Sinwell, Darryl Yong, and Glenn Stevens), all published by MAA/AMS. But his favorite publication is a 1991 paper in the

*American Mathematical Monthly*, described by his wife as an attempt to "explain a number system that no one understands with a picture that no one can see."

**E. Paul Goldenberg**is a Distinguished Scholar in mathematics at the Education Development Center, Waltham, MA. He has spent over 40 years in curriculum development at both elementary and secondary levels, teaching, research, and professional development, using both his knowledge of K–12 mathematics, and of the cognitive bases of mathematics learning. He has taught from Grade 2 through high school mathematics and computer science, as well as graduate school mathematics and psychology for education. Before EDC, he worked at the MIT Logo Laboratory with Seymour Papert and at Bolt Beranek and Newman with Wallace Feurzeig. He brings particular knowledge and expertise to curriculum development, his major focus at EDC.

Goldenberg has served as PI on a wide range of projects. He, Al Cuoco, and June Mark have championed the use of mathematical habits of mind—now aggregated within the Common Core State Standards for Mathematical Practice—as organizers of curriculum since their initial paper written in the early 1990s. One such curriculum is

*Transition to Algebra*, the product of an NSF-funded project he co-led with Mark. He is also PI, along with Mark and Cuoco, of

*BJC4NYC*—an NSF MSP, with UC Berkeley and the New York City DoE and other partners to broaden participation in CS in the NYC public high schools. He consulted on the development of standards for the American Diploma Project in mathematics, resources for Common Core State Standards, and worked closely with the Rwanda Education Board developing new mathematics standards for grades 1–6.

Recent primary authorships include two books:

*Making Sense of Algebra: Developing Students' Mathematical Habits of Mind*coauthored with June Mark and others (2015, Heinemann), and

*Developing Essential Understanding of Geometry and Measurement for PreK–Grade2*, coauthored with Douglas Clements (2014, NCTM).

**Yvonne Lai**received her S.B. in Mathematics from MIT and Ph.D. from UC Davis, specializing in geometric group theory and hyperbolic geometry. Following a post-doctoral position at the University of Michigan in mathematics, she took a second post-doctoral position at the University of Michigan School of Education where she conducted research in the area of mathematical knowledge for teaching, in the group led by Deborah Ball and Hyman Bass. Lai is now an associate professor in the Department of Mathematics at the University of Nebraska-Lincoln.

Lai's research is in mathematical knowledge for teaching at the secondary level, and on teaching proof practices at the undergraduate level. She has also examined teaching and mathematical knowledge for teaching at the elementary level. Her aim is to improve teaching at all levels, and to promote community among mathematics faculty invested in teacher education and development. She is founding chair of the MAA's Special Interest Group on Mathematical Knowledge for Teaching (SIGMAA-MKT), chair of the MAA Committee on the Mathematical Education of Teachers (COMET), and a member of the writing team for the NCTM publication

*Catalyzing Change*.

**Jonathan Montaño**was born in Barranquilla, Colombia. He finished his undergraduate studies in mathematics at Universidad Nacional de Colombia, Bogotá in 2008. He joined Purdue University in the fall of 2009 as one of the recipients of the Ross Fellowship. While pursuing his graduate studies he was a member of the Mathematical Sciences Research Institute (MSRI) in the fall of 2012. Montaño was awarded the Bilsland Dissertation Fellowship from the College of Science at Purdue, where he earned his Ph.D. in Mathematics in 2015 under the direction of Bernd Ulrich. Upon graduation, Montaño joined the University of Kansas for a three-year postdoctoral appointment in the fall of 2015. During the summer of 2018, he was granted an extended research visit at the Oberwolfach Research Institute for Mathematics (MFO) as a recipient of one of their Leibniz Fellowships. Currently, he is an Assistant Professor at New Mexico State University. In the summer of 2020 he was granted a three-year research award from the National Science Foundation. Montaño is committed to promoting mathematics among underrepresented minority students through organizing conferences and seminars, as well as other outreach opportunities.

Montaño’s research is in commutative algebra. He is particularly interested in asymptotic information that can be obtained from analyzing invariants of powers of ideals in Noetherian rings. Recently, he has worked on multiplicities of ideals and modules, integral closures, symbolic powers of ideals, arithmetic properties of blowup algebras, and local cohomology of powers of ideals.

**Sarah Sword**is a Principal Research Scientist at Education Development Center. She is Principal Investigator for

*Center for Inquiry and Equity in Mathematics*(ciemathematics.com), which focuses on the question, “who gets to ask question in mathematics?” She is co-Principal Investigator on the

*Studying Successful Doctoral Students in Mathematics from Underrepresented Groups*(https://minoritymath.org/core/).

As Principal Investigator for the

*Center for Scholarship of School Mathematics*, she created a model for fellowships for university faculty who wished to deepen their practice of mathematics. As Principal Investigator for

*Assessing Secondary Teachers’ Algebraic Habits of Mind*, a collaborative project with St. Olaf College and Boston University, she co-created a suite of assessment tools for measuring teachers’ use of habits of mind for themselves and their practice. As co-director of research for

*Designing for Equity by Thinking in and about Mathematics,*she has studied how professional development can shift secondary teachers’ thinking about mathematics and equity. Dr. Sword has worked on numerous professional development and school curricula, including

*CME Project*, a four year high school curriculum organized around mathematical habits of mind. Her PhD is in Commutative Algebra from Michigan State University, and she did a post-doctoral fellowship in Curriculum and Instruction at the University of Maryland. She is co-author of the book

*Mathematical Learning and Understanding in Education*, in the Routledge

*Insights in Education*series.

Sarah lives in Northfield, Minnesota, with her husband Ryota Matsuura, who is in the mathematics department at St. Olaf College. They have two daughters, ages eight and eleven, and a very sweet dog.

*Previous Members of the Editorial Board:*

**Benjamin Braun**(founder of the On Teaching and Learning Blog and Editor-in-Chief from 2014 to June 2018), University of Kentucky.

**Priscilla Bremser**(contributing editor, 2014-2018), Middlebury College.

**Art Duval**(contributing editor, 2014-2019), University of Texas at El Paso.

**Jess Ellis**(contributing editor from 2016-2017), Colorado State University.

**Dr. Luis David García Puente**(contributing editor from 2016-2017), Sam Houston State University.

**Steven Klee**(contributing editor from xx-2020), Seattle University.

**Elise Lockwood**(contributing editor from 2014-2016), Oregon State University.

**Amanda Serenevy**(contributing editor from xx - 2020), Riverbend Community Math Center.

**Diana White**(contributing editor from 2015-2018), University of Colorado Denver.