Group Members: Maria, Hong Dang, Raman.
Project Description: Students will research the life of a famous mathematician, and will post the highlights of his life and work in a life-size mock-up 2D or 3D model, to mark the ghostly presence of the mathematicians.
Project Description: Students will research the life of a famous mathematician, and will post the highlights of his life and work in a life-size mock-up 2D or 3D model, to mark the ghostly presence of the mathematicians.
Project Objective: To incorporate a human and historical element in math classes
Intended Grade Level: 11
NCTM Standard/Principles Addressed: Connection: Math is an integrated field of study. Students must see the mathematical connections in the rich interplay among mathematical topics, in contexts that relate math to other subjects, and in their own interests & experiences Learning: Students must actively build on new knowledge from experience & previous knowledge
Project Development Stages:
Stage 1: Going through the project from a student’s perspective
1. Selected Emmy Noether, from list of Asian and women mathematicians
2. Extensively researched in the internet, visiting at least 20 sites.
3. Prepared an executive summary of life and work.
4. Analyzed contributions to Math and Physics.
5. Constructed 2D life-size mock-up.
6. Posted highlights of life and work on mock-up figure.
7. Placed the mock-up in a corner of the classroom.
Stage 2: Looking at the project with teacher eyes
Having gone through the full project, the weaknesses, strengths, and points for improvement are:
Task | Strengths/Points for Improvements | Weaknesses/Points for Improvement |
A. Research on biography of mathematician in the internet | Easy access to internet with comprehensive database on mathematician To improve: 1.Use related links to provide an even wider net of information for a more holistic understanding and appreciation of mathematician 2. Use related links see to how mathematician’s work impacted on other mathematicians, and the development of specific branches of math | 1. Too much easy information available may lure students to read only a few sources 2. Authenticity & integrity of information may not be verifiable 3. Over-reliance on the internet to the exclusion of other excellent media sources like books, scholarly articles To improve: 1.Document at least 10 sources 2.Check the reliability of source 3.Include other media sources like books, scholarly articles |
B. Organizing research findings, and select highlights | 1. Need to read entire biography to distill the most important points of mathematician To improve: 1. Find unifying themes in the mathematician’s life and use these to thread the summary | 1. Copy and paste portions from different sources, Superficial editing of words, & pass as own summary To improve: 1. Write key names, places and phrases in index cards Arrange cards in chronological order. |
C. Mock-up model of mathematician with life’s highlights strategically displayed in body | 1 Resurrected ghost hovering in class, palpable, permanent, real member of class 2 Teacher can refer to mock-up during relevant points a math class discussion 3 Student are reminded of key details of mathematician every time they enter the math classroom | 1. In time, the novelty will wear off and nobody will pay attention to the mock-up, unless the teacher explicitly refers to it. To improve: 1 Relate as many intellectuals and events to Mathematician to continually “reinvent” image. |
C. D. Oral presentation of mathematician’s life | 1 Mathematician come alive for the class 2 Focus on high points of biography To improve: 1 Dramatize crucial or unusual highlights in biography | 1 Reading from notes, little audience contact 2 Too much lecture-type talk, little audience participation To improve: 1. Note cards used for presentation |
Stage 3: Devising a New Project
From a static and outdated mock-up to a vibrant and evolving one, reflecting the dynamic, interconnected nature of math and mathematicians through time.
Purpose:
1. Bring the human and historical element in math classrooms
2. To spark / create interest in pursuing higher mathematics
3. To appreciate that math is a dynamic, evolving subject build upon the ideas of mathematicians through the centuries
Time frame: One grading period (one week for the mock-up, and highlights every two weeks).
New project
1. Research on biography to include links and other media sources.
2. Find unifying themes and select highlights of life and works
3. Oral presentation to include mini-play/skit of significant events
4. Periodically add new information to existing posted highlights.
5. Write a journal entry on the positive impact of the project on student.
The revised project will basically go through the same steps as in Stage 2 but incorporating the suggested improvements.
Posted highlights on the Model:
Accolades | Gender/Race | Educational institution |
In a letter to the New York Times, Albert Einstein wrote: “…Noether was the most significant creative mathematical genius thus far produced since the higher education of women began.” | Jewish woman scholar in Nazi Germany; Went to finishing school instead of college preparatory school | University of Gottingen, founded by King George II of Great Britain, world-renown center of math research, associated with 45 Nobel laureates |
“Greatest woman mathematician in recorded history,” “mathematical originality absolute beyond comparison,” “changed the face of algebra” | Academic Senate: coeducation would overthrow all academic order. One of 2 women out of 1000 students, forced to audit class for 2 years. | Nazi – remotion of all Jewish scholars, positions revoked |
Moon crater, asteroid named after her Association of Women in Mathematics Noether’s Lecture | Women: 16% of undergraduate and 11% of doctorate degrees in engineering; less than 22% of doctorate degrees in math and physical sciences. Women < than 1/3 of all full- and part-time faculty in US colleges/univ 1992, and only 18% of all full professors. | Academic Ranking of World Universities: Harvard (1), U.Cambridge(5), U .Toronto (27), UBC(36), U.Gottingen(93), |
Professional Qualification | International Congress of Mathematicians | Teacher |
After PhD, lectured 14 yrs w/o pay nor official position | Visiting Prof: U.Moscow, U.Frankfurt | Nurturing, scholarly family |
Faculty member: What will our soldiers think when they return to the university & find that they are required to learn at the feet of a woman? Hilbert: I do not see that the sex of a candidate is an argument against her admission as a privadozent, After all, we are a university, not a bath house.” US/Can: PhD >tenure review>Tenured Prof Europe: PhD>habilitation>Tenured Prof | 1932 Plenary address – 1st woman 35 years after 1st congress in 1897 Karen Uhlenbech – 1990, 58 years after Noether’s address - 1990 | Noether’s Boys: No lesson plan, spontaneous discussion in cutting-edge problems in math. Lecture notes of students basis for several important textbooks; |
2004: major political debate to abolish habilitation: Jr Prof>Tenured Prof2004: : 2006: Hab restricted to top PhD grads | 2010 ICM in India 26 ICMs-19 Europe, 2/2 US/Can, 3 Asia |
Outstanding contributions in Math and Physics. |
Three Epochs of Noether's scholarly work. First Epoch (1908-1919) · dealt primarily with differential and algebraic invariants. · produced her seminal work for physics , the two Noether’s theorems. Second Epoch (1920-1926) · crafted new theories of mathematical definitions of Ideals in Rings. · Renowned for developing ascending chain conditions, · Commutative rings ,ideals, and modules, · Elimination theory · Invariant theory of finite groups · contributions to topology. Third Epoch (1927-1935) · Hyper-complex Numbers, and Representation Theory of Groups · Non-commutative algebra, linear transformations and commutative number field |
Assessment Rubric:
1. Posted highlights - 5
2. Oral presentation - 5
3. Iconic figure - 3
4. Individual participation - 3
5. Journal entry - 4
Total: 20
Susan's assessment of your project presentation:
ReplyDeleteGhostly presence of mathematicians (b)
Raman., Hung Dang, Maria L.
Beautiful life-size drawing of Emmy Noether (by Hung Dang’s wife, who is an artist!) Lovely powerpoint presentation as well.
Thanks for finding a female mathematician.
Note that the life-sized mathematician does not have to be professionally drawn though – there are lots of good ways to do this without a strong art background! (see the student versions of this project from our cupboard…)
Very good analysis of strengths and weaknesses of the project! Your work is very thoughtful and well-considered.
I like the improvements you propose.
The revised project is very good. I like the idea of doing mini-plays of significant events, and the idea of making links to the historical period. I love the idea of using unifying themes that relate to the present too, and the idea of adding new information to keep the iconic figure “alive”! Excellent idea too to write a journal reflection on the project.
You’ve illustrated the idea of unifying themes very well for the case of Emmy Noether -- it makes sense once it is exemplified.
You spent longer talking about the specific story of Emmy Noether than I had foreseen, but you did so with such passion , and in a way that offered examples for how to do the project – so I didn’t mind.
Good assessment rubric.
Excellent.
Susan's comments on your write-up: Terrific work! I am particularly impressed by your very thoughtful assessment of the strengths and weaknesses of the original project and your excellent suggestions for improvements. It is always difficult to get away from kids just copying and pasting information (whether electronically or physically), and then just reading it aloud. It's also difficult to prevent kids from using just one or two supposedly authoritative sources in an uncritical way. It was like that back in the days of printed encyclopedias, and the internet has made it even easier just to copy, paste, and read.
ReplyDeleteI like your many ideas for getting away from that and revitalizing the knowledge, bringing it in contact with contemporary issues. The worked example with Emmy Noether was impressive! Well done! I want to try the project again using your suggestions.
Just one caveat: asking kids to use 10 sources (and to read scholarly articles) may be taking things just a bit too far. I would suggest that 5 sources would be quite adequate, as long as they're not copies of each other. You might find one or two suggested reliable sources where everyone should start -- for example, this excellent site from the University of St. Andrews, Scotland: http://www-history.mcs.st-and.ac.uk/BiogIndex.html.
Excellent work!