HoM Toolbox, or Historiography and Methodology for Mathematicians: Introduction – Why Articulate a Philosophy of the History of Mathematics?

Author(s):

Amy Ackerberg-Hastings (MAA Convergence)

As students or instructors gain experience with researching and writing the history of mathematics, it can be useful to take some time to reflect on the issues raised on the previous pages of this article and articulate how they see themselves as historians of mathematics. I was instructed to complete such an exercise near the end of my first semester in a graduate history of technology and science program, and I subsequently used such an assignment in the courses I taught on historical methods and historical writing.

The general guidelines for the assignment (excluding specific formatting requirements) are reprinted below, but it is not necessary to replicate its depth or time commitment to reap the benefits of the concepts discussed in this article. Instructors of history of mathematics courses that include readings by professional historians may want to use the components of the assignment as student guidelines for evaluating the arguments in the readings. In courses with a research project, instructors could ask students to read this article and discuss the assignment questions as preparation for undertaking their projects. Undergraduates or faculty contemplating taking up the history of mathematics as a career path may better understand the discipline and themselves by preparing an essay independently or to share with a mentor. Because the objective is for individuals to define and elucidate their own philosophy of historical practice, there are many acceptable ways to approach and structure responses to the assignment.

Sample Assignment: Essay-Length Philosophy of the History of Mathematics

The Big Idea: Demonstrate how your understanding of historical practice and its theoretical foundations has evolved throughout this course by presenting a fully-developed philosophy of history of mathematics.

Format: Prepare a formal essay that sets out the conceptual framework you expect to employ as a participant in the professional academic discipline of history of mathematics, particularly while analyzing and synthesizing primary sources. In the course of your essay, comment on:

The distinction between "history" and "the past."
Why you study the history of mathematics (i.e., your conception of the purpose of history).
The role and reliability of evidence in history.
Why and how change occurs in history.
The relationship between objectivity and bias in historical interpretation.

Your response should be 1350–1650 words in length, plus footnotes and bibliography. It should be written in essay form, with an introduction paragraph containing your thesis statement, a body of approximately 5–6 paragraphs, a conclusion paragraph, footnotes, and bibliography. Make your essay as mechanically perfect as you can manage: excellent spelling and grammar, no run-on sentences, no subject/verb disagreements, correct use of punctuation. Use active voice and past tense verbs. Cite any and all sources that you use.

Relevant Learning Outcomes: Explain what history is and why it matters that humans record it; Identify historical paradigms and distinguish how they affect interpretation and practice; Explain the strengths and limitations of various types, formats, and conditions of historical evidence; Employ the moral and ethical standards of the historical profession; Cultivate an identity as a historian.

Sample Scoring Rubric (based on 100 points):

Points	Criteria
	Analysis (15%)
14–15 (Excellent)	Author directly addresses the questions of the assignment. Essay contains a clear argument-—i.e., lets the reader know exactly what the author is trying to communicate.
12–13 (Good)	Author competently addresses the questions of the assignment. An argument is present, but the reader must reconstruct it from the text.
10–11 (Needs Improvement)	Author attempts to address the questions of the assignment. Author attempts, but fails, to make an argument (e.g., starts with a rhetorical question or anecdote that is never put into context).
0–9 (Unacceptable)	Essay does not address the questions of the assignment. No attempt is made to articulate an argument.
	Content/Evidence (20%)
18–20 (Excellent)	Provides compelling and accurate supporting evidence that convinces reader to accept main argument. The importance/relevance of all pieces of evidence is clearly stated. There are no gaps in reasoning—i.e., the reader does not need to assume anything or do additional research to accept main argument.
16–17 (Good)	Provides necessary supporting evidence to convince reader of most aspects of the main argument but not all. The importance/ relevance of some evidence presented may not be totally clear. Reader must make a few mental leaps or do some additional research to fully accept all aspects of main argument.
13–15 (Needs Improvement)	Insufficient evidence is provided to support author’s argument, or evidence is incomplete, factually incorrect, or oversimplified.
0–12 (Unacceptable)	Either no evidence is provided, or there are numerous factual mistakes, omissions or oversimplifications.
	Professional Development & Reflection (15%)
14–15 (Excellent)	The essay includes original, thoughtful reasons why the author wants to study the history of mathematics. These reasons also indicate the author's sophistication in thought and expression has deepened throughout the semester. The author presents a professional demeanor and shows interest and enthusiasm for the historical profession.
12–13 (Good)	The essay includes thoughtful reasons why the author wants to study the history of mathematics but may lack originality. There are indications of growth in the author's sophistication in thought and expression, but at least one conceptual breakthrough is yet to be achieved. The author shows interest and enthusiasm for the historical profession and is developing a professional demeanor.
10–11 (Needs Improvement)	The essay is perfunctory in indicating the reasons why the author wants to study the history of mathematics. The author shows interest and enthusiasm for the historical profession. The complexities of historical practice are acknowledged but not resolved.
0–9 (Unacceptable)	The complexities of historical practice are misconstrued or ignored. The author's interest in the history of mathematics is not apparent.
	Organization (10%)
9–10 (Excellent)	Thesis statement for entire essay is contained within first paragraph of paper, and all paragraphs have obvious topic sentences. Transitions between paragraphs make it very easy to follow the argument. Underlying logic of claims is apparent and sound. The reader understands the author's thinking throughout the paper.
8 (Good)	Thesis statement for entire essay is contained within first paragraph of paper, and all paragraphs contain topic sentences. Transitions between paragraphs are generally clear. Underlying logic of claims is sound, but reader may have to stop once to discern the author's thinking.
6–7 (Needs Improvement)	Thesis and topic sentences do not stand out to the reader. Paragraphs change topic abruptly. Underlying logic is difficult to follow. Reader has to read essay twice to understand it.
0–5 (Unacceptable)	There is no hierarchy among the sentences of the paper. It is impossible to follow the argument because the underlying logic is random or contradictory. There seem to be many arguments, and it is completely unclear which is the main one.
	Clarity and Style (15%)
14–15 (Excellent)	Ideas expressed in active voice and clear, fluent sentences. All words are chosen for their precise meanings. All new or unusual terms are well-defined. Key concepts and theories are accurately and completely explained. No rhetorical questions or slang.
12–13 (Good)	Ideas usually expressed in active voice and clear sentences. Most words are chosen for their precise meanings. Most new or unusual terms are well-defined. Key concepts and theories are explained. No rhetorical questions or slang.
10–11 (Needs Improvement)	A few sentences are not clearly written. Passive voice is prevalent. Words are not chosen for their precise meanings. New or unusual terms are not well-defined. Key concepts and theories are not explained. Paper has several rhetorical questions or uses of slang.
0–9 (Unacceptable)	Prevalent problems with clarity. Essay uses words that do not fit the context at all. Phrasings are awkward and incoherent. Style reflects the author's stream-of-consciousness or conversational tone.
	Mechanics (15%)
14–15 (Excellent)	Sentence structure, grammar, and expression are excellent; absolutely no run-on sentences or subject/verb disagreements. Correct use of punctuation. Minimal to no spelling errors.
12–13 (Good)	Sentence structure, grammar, and expression are strong despite occasional lapses. Punctuation is often used correctly. Some (minor) spelling errors; may have one run-on sentence, sentence fragment, or subject/verb disagreement.
10–11 (Needs Improvement)	Some problems in sentence structure, grammar, and expression, as well as errors in punctuation and spelling. The mistakes do not intrude on the reader's ability to understand the essay. May have several run-on sentences or fragments.
0–9 (Unacceptable)	Prevalent problems in sentence structure, grammar, and expression that interrupt the reader's concentration. Frequent (in nearly every sentence) major errors in punctuation and spelling. May have many run-on sentences, fragments, and subject/verb disagreements.
	Citations & Formatting (10%)
9–10 (Excellent)	Specifed citation style (e.g., Chicago, MLA, APA) used consistently in footnotes and in bibliography; direct quotations, paraphrases, and summaries are all cited; paper meets any specified formatting requirements (e.g., for title, student name, font size, spacing, margins, page numbers, etc.); paper within the required length range.
8 (Good)	Specifed citation style (e.g., Chicago, MLA, APA) attempted in footnotes and in bibliography with a few minor inconsistencies between citations; direct quotations are all cited but author may have failed to cite 1 or 2 paraphrases or summaries; a few errors in any specified formatting requirements (title, student name, font size, spacing, margins, page numbers, etc.); paper within 10% of the required length range.
6–7 (Needs Improvement)	Specified citation style (e.g., Chicago, MLA, APA) attempted in footnotes and in bibliography with some substantial inconsistencies between citations; citations provided only for direct quotations; several errors in any specified formatting requirements (title, student name, font size, spacing, margins, page numbers, etc.); paper within 20% of the required length range.
0–5 (Unacceptable)	Frequent errors in specified citation style (e.g., Chicago, MLA, APA) that impede the reader's ability to identify and locate the sources used; multiple failures to follow any specified formatting guidelines; paper within 30% of the required length range.

Amy Ackerberg-Hastings (MAA Convergence), "HoM Toolbox, or Historiography and Methodology for Mathematicians: Introduction – Why Articulate a Philosophy of the History of Mathematics?," Convergence (December 2022)

Convergence

Tags:

History of Mathematics