• Home
  • Benjamin Dickman
Benjamin Dickman

Benjamin Dickman
The Hewitt School · Mathematics

Doctor of Philosophy

About

19
Publications
13,380
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
50
Citations
Introduction
Benjamin Dickman, Ph.D, majored in Mathematics at Amherst College, and received his doctorate in Mathematics Education from Columbia University. He was a 2008-09 Fulbright Fellow in Mathematics in China and a 2022 Fulbright DAST recipient in the Philippines. After postdocking in Mathematics Education at Boston University, Benjamin began his current position as a math educator at The Hewitt School in New York, NY. His interests include mathematical creativity, problem posing, and problem solving.
Additional affiliations
August 2016 - October 2021
The Hewitt School
Position
  • Math Teacher & Math Coach
Description
  • Grades 7-12 courses taught: Algebra I (part 1); Algebra I (part 2); Algebra II; Calculus; Problem Solving & Problem Posing [+ non-math: Independent studies in Mandarin Chinese]
September 2014 - July 2016
Boston University
Position
  • Instructor
Description
  • Graduate Courses Taught: SED ME 503: Number Systems; SED ME 504: Algebra, Geometry, & Statistics; SED ME 560: Mathematics for Teaching: Algebra; SED ME 563: Problem Solving in Mathematics.
July 2013 - August 2013
Teachers College
Position
  • Instructor
Description
  • Instructor for doctoral students in Mathematics Education during a study tour to Shanghai, China. Course title: Teaching Mathematics in Diverse Cultures.
Education
September 2010 - May 2014
Columbia University
Field of study
  • Mathematics Education
September 2004 - May 2008
Amherst College
Field of study
  • Mathematics

Publications

Publications (19)
Thesis
Full-text available
Mathematical problem posing and creativity are important areas within mathematics education, and have been connected by mathematicians, mathematics educators, and creativity theorists. However, the relationship between the two remains unclear, which is complicated by the absence of a formal definition of creativity. For this study, the Consensual A...
Article
Full-text available
In creating rich mathematical tasks, one technique is to require routine propositions be proved in multiple ways. We provide an example using a statement about divisibility, and include seven proofs along with commentaries about their presentation. Moreover, we investigate how our proposition can be generalized and connected to higher-level mathema...
Article
Full-text available
Explore three original problems, the thinking behind their formulation, how they can be solved, and related extensions.
Article
Full-text available
Let f in Q[z] be a polynomial of degree d at least two. The associated canonical height \hat{h}_f is a certain real-valued function on Q that returns zero precisely at preperiodic rational points of f. Morton and Silverman conjectured in 1994 that the number of such points is bounded above by a constant depending only on d. A related conjecture cla...
Article
Full-text available
In the first part of this paper, we provide an example of a project designed to foster mathematical creativity among students at an independent, all-girls school in the Northeastern United States. The mathematical motivator for the project is a polyomino proof by induction first formulated by Solomon Golomb. We explain how the project has been impl...
Preprint
Full-text available
Although many well-intentioned organizations and institutions emphasize the importance of antiracism and social justice in mathematics education, there remains a lack of practitioner-oriented curricular materials exhibiting how these long-overdue shifts can and do manifest in classrooms. This article describes how modifying a project on absolute va...
Article
Full-text available
We present in this paper a pair of approaches to support mathematics educators and learners in formulating original tasks. In particular, we facilitate the posing of rich mathematical problems by using two novel methods that were created by a mathematics department at a K-12 school in the United States, and further developed alongside our students...
Research
Full-text available
Noticing Humans refers to the importance of students being aware that they are seen by others – including, but not limited to, their math teachers – and that we, as teachers, would do well to interrogate how our external perspectives match or don’t match students’ internal perspectives. Noticing Wonders refers to a specific in-class activity relat...
Chapter
Full-text available
As digital spaces evolve, mathematics educators must develop an awareness of the ways in which these environments can facilitate discussion and foster creativity. Question and Answer (Q&A) sites such as Mathematics Educators Stack Exchange (MESE) provide a platform through which those interested in the teaching and learning of mathematics can harne...
Article
Full-text available
In this paper, the role of mathematical pathologies as a means of fostering creativity in the classroom is discussed. In particular, it delves into what constitutes a mathematical pathology, examines historical mathematical pathologies as well as pathologies in contemporary classrooms, and indicates how the Lakatosian heuristic can be used to formu...
Article
Full-text available
Guessing is typically incorporated into mathematical problem solving by drawing from intuition while seeking a solution. We advocate for a form of guessing in which the answer is already known, and our goal is to engage in Pólya's “Looking Back” stage by using the known solution to develop mathematical intuition.
Research
Full-text available
Sunken Treasure (pp. 99-106); Viral Marketing (pp. 167-174); Picking a Painting (pp. 225-232). Three lesson plans on mathematical modeling from the COMAP Mathematical Modeling Handbook.
Article
Full-text available
In mathematical modeling, the topic of apportionment provides powerful tools for the design of games. In particular, letter frequency based modeling can be used to compute appropriate letter distributions for a variety of word games. This paper will provide possible letter distributions for two different games: Scrabble and Boggle.
Article
Full-text available
Mathematical problem posing is an important skill for teachers of mathematics, and relates readily to mathematical creativity. This article gives a bit of background information on mathematical problem posing, lists further references to connect problem posing and creativity, and then provides 20 problems based on the multiplication table to be use...
Conference Paper
Full-text available
Festschrift for Dr. Henry Otto Pollak. Contributors: Benjamin Dickman & Andrew Sanfratello; Henry Pollak & Sol Garfunkel; Alan H. Schoenfeld; Rita Borromeo Ferri; Hugh Burkhardt; Werner Blum.
Article
Full-text available
The Evolving Systems approach to case studies due initially to Piaget-contemporary Howard Gruber, and complemented by subsequent work on sociocultural factors developed by Mihaly Csikszentmihalyi and others, provides an inroad for examining creative achievements in a variety of domains. This paper provides a proof of concept for how one might begin...
Article
Full-text available
George Polya's seminal work "How to Solve it" describes general methods for approaching and solving mathematical problems. The book begins with Polya's four principles for solving a problem: understand the problem, make a plan, carry out the plan, and look back. Much of the remainder of the book is devoted to an encyclopedic listing of different he...
Thesis
Full-text available
This thesis concerns the number of zeros of a multivariable polynomial $f$ over a finite field. More specifically, the zeta-function of $f$ is defined in terms of a certain power series with coefficients determined by the number of zeros of $f$ over various finite fields. Our main result is Dwork's Theorem, stating that the zeta-function of $f$ is...

Network

Cited By