You can select any topic from below
Option 1, False Proofs: There are many falseproofs. For example, the following article is an MIT student project:•Xing Yuan, Mathematical Fallacy Proofs http://dspace.mit.edu/bitstream/handle/1721.1/100853/18-304-spring-2006/contents/projects/fallacy_yuan.pdf
You also see two other examples in our lecture, Proof Techniques (1), Introduction. For this project, you need to search the Internet for more new false proofs. Do not use the examples from our lectures and Yuan’s paper. For each false proofyou use, please explain what lead to the false proof, and how the false proof helps students learn and understandand/orenhance your teaching
Option 2, Analysis and Classification of Student mistakesand difficulties: Students often have difficulties and make mistakes in arithmetic,algebra, trigonometry, and calculus. Why? What kind of mistakesand difficulties do theymakeor have? How can you help? You may read the following articles from the following link:https://www.semanticscholar.org/paper/Classifying-students-mistakes-in-Calculus-Hirst/436f1e13390e367c9647d493a5b462561d63b003
- Keith Hirst.Classifying Students’ Mistakes in Calculus
- Nourooz Hashemia,*, Mohd Salleh Abua , Hamidreza Kashefia , Khadijeh Rahimib Undergraduate students’ difficulties in conceptual understanding of derivation.
If you have taught or tutored before, you may collect the mistakes that your students made, then classify and analyze them. You may also develop a plan how you would apply your findings in your classroom.
Direction to be followed
1.Excluding the title and reference pages, your paper musthave at least 10 pages with double line space. Each missing page will result in a deduction of 15 points in addition to the deductions based on the following rubrics
2.(5 points) Professional appearance and format of your paper: The margins are not more than 1” from each side; the font size should not be larger than 12; and the fontcan be Calibri, or Times New Roman. The paper must be numbered. The sizes of tables and picturesneed to be reasonable. Your paper should be organized in the following format:a.Project title, names of authors, emails and affiliations (optional)b.Project summary, abstract, and/or objectivesc.Project Body (you may use sections, bullets tables, pictures)d.Acknowledgement (if applicable)e.References:If you obtained any information from the Internet, include the URL. Youneeduse the MLA (Modern Language Association) citation style, or the Chicago citation style, or the style of a reputable mathematical journal, for example, the Journal of Mathematical Analysis and Applications (http://www.elsevier.com/wps/find/journaldescription.cws_home/622886?generatepdf=true)
3 .(5 points) Summary or abstract of your project. You may include objectivestatements. a.Project title, namesof authors, emails,affiliations, abstract should be included in the title page
- (15 points) Difficulty and complexity: There are four options for your project (see the next page). For Project Option 1 and 2, the difficulty refersto the level of school mathematics from the lowest, arithmetic,to the highest, calculus II. For Project Option 3, your project needs to be at least at the level you taught, teach, or will teach. The appropriatelength of the project is also a consideration of difficulty, thoughthe minimum length is 10 pages with double space. An unnecessarily lengthy paper will not be considered more difficult. Difficulty may mean complexity. Use and inclusion of definitions, theorems and proofs will reflect difficulty and complexity. The more difficult the mathematics is, the more points you may earn.
- (15points) Originality or creativity: The first meaning of originality is that your paper must be your own work. Plagiarism is prohibited, and hence will resultin 0 for the entireproject. Anymaterials taken from the Internet, publications and other people’s work must be well cited. The second meaning of originality is that your work has not been seen on the Internet and in publications. Originality may also mean creativity. The more original work your project has, the more points you may earn.
- (60 points) Readability and Communication: clear and correct calculation, derivation, proofs, applications and explanation; sufficient and appropriate examples; real world examples, particularly related to your students, school and community (this also contributesto originality); smooth connection and transition among concepts, definitions,theorems, examples, and explanations; use of pictures, diagrams, and tables; easiness for understanding; appropriate citation; completeness of the project; fun to read.
7.Correctness: mathematically your project must be correct. Errors and mistakes in mathematics will be subject to deduction of points you earn. Errors and mistakes inother areas (English, Education, Science…) may or may not cause a deduction, depending on the nature and significance of the errors andmistakes.
8.The instructor retains the final interpretation of the grading rubrics