Math Project Assignment.

 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 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

My Reflections: Creativity, Flexibility, Adaptivity, and Strategy Use in Mathematics

    The article has discussed very crucial aspects of strategy use in mathematics teaching and learning - creativity, flexibility, and adaptivity. When I was going through the Ferit,s example, I was thinking that it happens with most of us while using  strategies,and wandering why this is so. Although the previous knowledge is crucial for the understanding of the new concepts, but it acquires so much space in our mind and don't let anything new to grab some space there.  Most of us try to follow one direction and find it very hard to look  for some other ways, that is, finding  it hard to adapt to the new conditions, and getting the better ways.

      I strongly admit that the conceptual understanding is the base for the adaptivity, which is not given the due preference in the traditional teaching methods that are based on instrumental understanding,instead of relational understanding. The strategies are therefore developed once the problems are understood properly. I want to share my personal experience. I taught my 5 years old son (who already knew counting 1-100) to add 4and 1, 5and 1 on his fingers, but when I gave him the third question to add 9and1, he answered me without counting on fingers and reflected that I was just asking for one number ahead. This is what Threlfall viewed about use of strategies in arithmetic that strategies are developed, not selected and applied.

      The analysis of the six contributions on the strategy use discussed in the article,is very insightful, and I feel that in order to make our students use the strategies, flexibly, creatively and adaptively, we are needed to change our instructional strategies in teaching mathematics. We must reconsider the role of teacher and the curriculum developers, so as to achieve the objectives of mathematics teaching and learning.

Practicum Memories

Practicum is the most exciting part of an education course as it sets the stage for the students to preform their roles as teachers.This experience is especially memorable for me as it is my first teaching experience in a new system of education. On the first day, I  was so nervous, and just adding to this nervousness, when I reached the school I got to know that the school had no information  regarding  my arrival. I was so confused, but soon they figured out everything, and I was able to meet one of my sponsor teachers. Even my F.A. gave a surprise visit  to observe my first lesson  at very short notice,  which was in grade 12 Calculus, although I started with nervousness, but was able end up positively.

        I want to share a touching experience during my short practicum.On my 3rd day of practicum, I was in my grade 10 class for principles Mathematics, to do a review on sine and cosine ratios.There was a blind male student in the class, who just love to do Mathematics. After the class he approached me, and said that he liked today's lesson, and got the idea properly.Even his two teacher aids appreciated the lesson, and were happy that they are able to get the idea of using trig. ratios, and convey the lesson properly to him. The student expressed his views regarding the deep relationship between Mathematics and music. His views regarding his passion for the music, and love for Mathematics inspired me a lot to think more passionately about the students of his kind.