MDM4U: Mathematics of Data Management Culminating Project

Transcription

1 : Mathematics of Data Management The is a research assignment on statistics in which students will collect data, analyze the data and present a report on their findings. This is a very large project, and students must work on it for several months. While some class time will be allotted for the project throughout the semester, students will be spending the vast majority of their time working on it outside of class time. Components of the Project Collection of data on a topic of your choice Analysis of the data and related research Final Report Presentation of results Your Presentation should consist of the following components: o Introduction to topic and explanation of the issues and relevant research o Presentation of the data o Your analysis of the data combined with related findings from other research o Conclusion, limitations of your conclusion and avenues of further study Evaluation All categories will be evaluated during this project. There are three components to the evaluation: Research, Final Report and Presentation. Topic Students may choose their own topics, but they should be intrinsically interesting. No two students may have the same topic. The teacher has the right to turn down a student s choice of topic. Deadlines Throughout the semester, students will meet with the teacher to update him/her on the progress of the research. Progress Reports will be evaluated and will contribute to one s final Culminating Project mark. To Be Handed In Due Date Submit a topic Thursday, March 24 Progress Update #: Project Proposal Friday, April Progress Update #2: Presentation of Data Thursday, April 4 Progress Update #3: Data Analysis Tuesday, May 3 Progress Update #4: Presentation Plan Wednesday, May 25 Final Presentation May 30-June 3 **Note: Presentation schedule will be determined closer to the due date Final Report of Investigation Wednesday, June 8

2 Process ) Determine your topic First, develop a question or series of questions choose a topic that interests you and that you feel you will be able to collect data on. Once you choose your question or series of questions, you should come up with a hypothesis for what you think the answer to each question will be. Make sure you back up your hypothesis with reasoning relevant to the social context of your particular question 2) Progress Update #: Project Proposal (5% of mark) Clearly state your thesis question. If it helps, use the format: Is there a relationship between. Clearly state your hypothesis (i.e. what you predict the answer to your question will be) Cite the sources you have already found for your project. Your sources may be online or in printed form. You should include sources where you have found raw data for your project (i.e. Statistics Canada, Nationmaster, etc.) AND sources for related research (i.e. studies performed by someone else that relate to your research question/hypothesis). Use a recognized format to cite sources properly (i.e. APA, MLA, etc. Easybib.com is a helpful website to cite sources properly). Useful Internet Data Resources Websites that contain data on various attributes of the Canadian population: E-Stat Statistics Canada Websites that compare various attribute measurements between countries. NationMaster.com Central Intelligence Agency The World Factbook Sample Projects: 3) Progress Update #2: Presentation of Data (5% of mark) Collect data from a valid secondary source (i.e. educational books, magazines, or websites such as Statistics Canada). Primary data (i.e collected through your own, unbiased survey) may be included if you choose, but only to supplement your secondary sources. Aim for pieces of raw data (discuss with your teacher based on what your study is on) All of the data should be raw (i.e. just numbers). This means no charts, graphs, summary statistics or conclusions from another source. Organize your data using meaningful tables. 2

3 4) Progress Update #3: Data Analysis (5% of mark) Organize your data using a variety of graphs. Graphs and tables should be formatted so that they are easy to read and understand (i.e. label the axes, title the graph, remove any unnecessary legends, etc.) Look for trends in your data and confirm these trends using statistics. Your analysis should include one-variable statistics (studied in Chapter 2) AND two-variable statistics (studied in Chapter 3). (Include standard deviation, variance, line of best fit (linear regression), correlation coefficient or coefficient of determination, etc,) You should do your calculations using technology (i.e. Excel), so there is no need to show all of your calculation steps. You should, however, ensure that you are applying the correct kind of statistical analysis to your data (linear or exponential, etc.). 5) Progress Update #4: Summary of Findings and Presentation Plan (0% of mark) Study the results from your analysis and develop a conclusion with a logical argument. Your conclusion should be based on the statistics you calculated. Develop a written outline for your presentation. You should include a description of each graph you intend to show and what you will say about it, and a breakdown of which group member will discuss each topic. 6) Final Presentation (25% of mark) Create a Powerpoint presentation summarizing your research and findings. The presentation should outline your research question, data, statistical analysis and conclusions. Your presentation is expected to be 0-5 minutes long. 7) Final Report (50% of mark) Write a final report taking into account all your research, analysis and any feedback based on your presentation. See FINAL REPORT section for more information. REMEMBER!! This is a STATISTICS project your focus at every point should be on the NUMBER, GRAPHS and YOUR CALCULATIONS!!! 3

4 Progress Update #: PROJECT PROPOSAL Due Date: Name: Objective - Submit a proposal (approximately ½ - page) describing your thesis question and hypothesis, and citing sources found to date. Evaluation: This update assignment is worth a portion of your overall mark. It will be evaluated for Communication. The evaluation rubric is shown below. Submit this rubric with your Progress Update #. (5% of project mark) Weight: Level (50-59%) Level 2 (60 69%) Level 3 (70-79%) Level 4 (80 00%) Topic (COM) Data (COM) -The hypothesis is explained briefly. -The topic will not lend itself to many different forms of analysis. -No thought has been given to problems that may occur in the future. -No evidence of data searches apparent in proposal -The hypothesis is explained in some detail. -The topic will not lend itself to different forms of quantitative analysis. -Very little thought has been given to problems that may occur in the future. -It is apparent that some relevant raw data has been found. -Two or three sources have been found and referenced appropriately -The hypothesis is explained thoroughly, showing how a major topic has been reduced to a manageable problem. -The idea lends itself to a variety of quantitative statistical analysis. -Possible problems have been discussed with some solutions being presented. -Shows that relevant and reliable raw data is available on the topic. - Four or five sources have been found and referenced appropriately -The hypothesis is explained thoroughly, showing how a major topic has been reduced to a manageable problem. -The idea lends itself to a variety of quantitative statistical analysis. -Possible problems have been presented and the approaches presented to solve them. -The topic is broad enough to be extended if necessary -Demonstrates that extensive, relevant and reliable raw data is available on the topic -Six or more sources have been found and referenced appropriately Flexibility (COM) -No alternative topic/ hypothesis has been considered. -No thought has been given to the possibility that the original thesis may not work. -One or two alternate hypotheses are discussed, as well as one or two data sets the student would like to find. -Student includes other hypotheses related to the data they collected that would allow them to broaden their topic. -Shows where additional data may be found -Student indicates many other hypotheses related to the data they collected that would allow them to broaden their topic. -Indicates in depth what other data sets they would need to extend current hypothesis. 4

5 Progress Update #2: PRESENTATION OF DATA Due Date: Name: Objective Submit a paper copy of the data you have collected so far. The data should be organized into meaningful tables and charts. Evaluation: This update assignment is worth a portion of your overall mark. It will be evaluated for Knowledge. The evaluation rubric is shown below. Submit this rubric with your Progress Update #2. (5% of project mark) Weight: Level (50-59%) Level 2 (60 69%) Level 3 (70-79%) Level 4 (80 00%) Type and Quantity of Data (KU) Presentation of Data in Tables (Comm) -Data will lend itself to an extensive enough topic -No evidence of tidying data is apparent. Data has just been pasted into spreadsheet with no effort to re-arrange or improve the quality of its presentation -Data will lend itself to perform a simple analysis (either one or two variable) -Data has been somewhat tidied. There is evidence that work has been done to make the data set easier to follow and use in analysis -There is enough relevant raw data to perform substantial statistical analysis. -Some evidence is given showing that further data sets have been researched. -Data has been fully tidied. The data set has been manipulated so that it will be very straight forward to use in analysis. -There is enough relevant raw data to perform substantial statistical analysis. -Several data sources have been found that add to the quality of the original data. -Data has been fully tidied, using colour or other formatting to organize clearly. All formatting problems have been addressed so that data can be used in analysis. 5

6 Progress Update #3: DATA ANALYSIS Due Date: Name: Objective Organize your data into a variety of graphs. Look for trends and calculate one and two variable statistics, as appropriate to the data. Submit a copy of your data analysis (i.e. your statistical calculations). Evaluation: This update assignment is worth a portion of your overall mark. It will be evaluated for Application. The evaluation rubric is shown below. Submit this rubric with your Progress Update #3. (5% of project mark) Weight: Level (50-59%) Level 2 (60 69%) Level 3 (70-79%) Level 4 (80 00%) Presentation of Data in Graphs (Comm) Data analysis is complete (APP) Data analysis is appropriate to support or disprove hypothesis (APP) -Data is organized, but method is sometimes inappropriate to data being used -Graphs are untidy and hard to read/understand -Limited one or two variable analysis performed -Draws conclusions and justifies them with limited evidence produced from their data set (i.e. uses a scatter plot and R 2 values to support claims for a correlation) -Data is organized in a somewhat appropriate matter -Graphs are somewhat untidy, missing labels or contain extra information -Uses a wide range of both one and two variable analysis appropriately Justifies their calculations by showing some mathematical insight into the situation being investigated -Data is organized in an appropriate matter. More than one type of organization is evident -Graphs are fully tidied, with appropriate labeling and titles. Some distracting elements are present -Has been exhaustive in exploring all analysis tools covered in the course. -Enough quantitative analysis has been performed to support or disprove hypothesis -Data is organized in an extremely appropriate matter. Extensive use of different types of organization is evident -Graphs are fully tidied, with appropriate labeling and titles and distracting information is eliminated -Not only has student been exhaustive in exploring all analysis tools covered in the course, they have researched new approaches beyond the scope of the course and applied them correctly. -The analysis performed is exhaustive and more than sufficient to support or disprove hypothesis. 6

7 Progress Update #4: SUMMARY OF FINDINGS AND PRESENTATION PLAN Due Date: Name: Preamble: Lack of planning an organizational structure is a major reason for poor oral presentations. The more carefully you prepare, plan and organize your presentation, the better it will be. Take time to create a clear, understandable, tight and efficient outline for your presentation. Use brainstorming, tree diagrams, mind maps and any other planning strategy to help organize your thoughts. Objective Submit paragraph(s) describing your overall findings and a description of related research that supports or challenges your findings (at least page). These descriptions will form your conclusions. In addition, submit your presentation plan. Your presentation plan should include paragraph(s) that answers each question below in as much detail as possible. Your response should be at least page long.. Your presentation should contain an introduction, a body, and a conclusion. a) What will be the main focus of your presentation? b) What are some of the points/ideas you will illustrate/discuss in each of the three parts of the presentation listed above? 2. Describe in detail the types of visuals you will be using. This may include graphs, charts, overheads, graphing calculator use, computer programs (be specific), handouts, posters, tree diagrams and videos. 3. Describe what special equipment you will need (overhead projector, video projector, whiteboard, or TV/VCR) Evaluation: This update assignment is worth a portion of your overall mark. It will be evaluated for Thinking. The evaluation rubric is shown below. Submit this rubric with your Progress Update #4. (0% of project mark) Weight: 2 Level Level 2 Level 3 Level 4 Description of overall findings (T) Description of related research (T) Presentation is outlined in detail (T) (50-59%) Few overall findings have been identified and/or are not described. Few findings from related research have been identified and/or relationship to overall findings are not discussed. Presentation is outlined roughly, no supporting documents or description of methods are mentioned (60 69%) Some overall findings have been identified and described briefly. Some related research has been identified and its relationship to overall findings has been discussed briefly. Presentation is somewhat outlined, with supporting documents (i.e. graphs, tables, charts) (70-79%) Considerable overall findings have been identified and described in detail. Considerable related research has been identified and its relationship to overall findings has been discussed in detail. Presentation is outlined in detail, with supporting documents (i.e. graphs, tables, charts) and description of methods (i. e. who will present what, etc.) (80 00%) Significant overall findings have been identified and described thoroughly. Significant related research has been identified and its relationship to overall findings has been discussed thoroughly, including future applications/ investigations. Presentation is outlined thoroughly, with supporting documents (i.e. graphs, tables, charts) included and a thorough description of methods (i. e. who will present what, etc.) 7

8 FINAL PRESENTATION Due Date: Name(s): Objective Present your research question and findings to the class. Include ALL of the required elements. You should be prepared to answer questions on your topic. Required Elements for your Presentation: Statement of your research question/area of investigation Highlights from the relevant research Presentation of data (i.e. in tables, charts and/or graphs) Summary and discussion of analysis Interpretations and Conclusions Evaluation: The final presentation is worth a significant portion of your overall mark. The evaluation rubric is shown below. Submit this rubric on your presentation day. (25% of project mark) Weight: 5 Category Level Level 2 Level 3 Level 4 Use of Mathematical Terminology: (Co) - Correct use of terminology learned in course terminology occasionally terminology some of the time terminology most of the time Organization of Presentation: (Co) - Presentation is clear and logical Presentation Skills: (Co) - Clear voice and eye contact with audience Slide Design: (Co) -Text is clearly stated -There is not too much writing on the slide Visual Aides: (Co) -Graphs are easy to read/interpret Communication: (Co) - Ideas are clearly stated and Audience Questions: (T) - Able to respond to appropriate content related questions from the audience Presentation has limited flow. Student reads presentation from notes. Five or six slides are not well limited effectiveness Ideas are stated and connections are occasionally Student has difficulty creating a response to questions. Presentation is at times clear and logical Student is occasionally hard to understand and extended time periods pass without eye contact. Three or four slides are not very well some effectiveness Ideas are stated and usually Student s response to questions goes into limited depth. Participation in other students presentations: (T) - Engaged in other students presentations, asks appropriate questions during presentations they are evaluating - Student is present for all presentations Presentation is mostly clear and logical Student is occasionally hard to understand or extended time periods pass without eye contact. One or two slides are not very well considerable effectiveness Ideas are mostly clearly stated and Student s response goes into considerable depth. Does ask appropriate questions. terminology all of the time Presentation is clear and logical Student has clear voice, makes eye contact with audience, and does not use notes All slides are very well. well presentation Ideas are clearly stated and Able to respond to questions from the audience Asks very good, insightful questions 8

9 FINAL PRESENTATION PEER ASSESSMENT Student Presenter: Assessment for Learning by: Category Level Level 2 Level 3 Level 4 Use of Mathematical Terminology: - Correct use of terminology learned in course terminology occasionally terminology some of the time terminology most of the time Organization of Presentation: - Presentation is clear and logical Presentation Skills: - Clear voice and eye contact with audience Slide Design: -Text is clearly stated -There is not too much writing on the slide Visual Aides: -Graphs are easy to read/interpret Communication: - Ideas are clearly stated and Presentation has limited flow. Student reads presentation from notes. Five or six slides are not well limited effectiveness Ideas are stated and occasionally Notes on presentation/ questions to ask: Presentation is at times clear and logical Student is occasionally hard to understand and extended time periods pass without eye contact. Three or four slides are not very well used to enhance some effectiveness Ideas are stated and usually Presentation is mostly clear and logical Student is occasionally hard to understand or extended time periods pass without eye contact. One or two slides are not very well considerable effectiveness Ideas are mostly clearly stated and terminology all of the time Presentation is clear and logical Student has clear voice, makes eye contact with audience, and does not use notes All slides are very well. well used to enhance presentation Ideas are clearly stated and Did you find that presenters answers to your questions helpful? Explain. 9

10 FINAL REPORT Due Date: Name: You must submit a written report that is written like a journal article. It must include the following sections: (50% of project mark) Abstract ( words): [Weight: ] - Summarizes whole paper in one paragraph - Indicates thesis, purpose, hypothesis, sources of data, and the conclusion that was reached Introduction ( words): [Weight: ] - Purpose is clearly indicated and reason for the choice of topic is clearly explained (based on personal interest and application for others) Thesis/Problem/Hypothesis Statement ( words): [Weight: ] - Specific question that will be addressed in the project - Variables to be explored are included and defined clearly - Expected or suggested outcome to the proposed relationship based on preliminary research Observations: [Weight: ] - Description of target population, and description of the sample used, and sampling methods (if you didn t use all of the possible population, explain why and how you chose the sample that you did. Discuss any related bias.) Analysis: [Weight: 2] - Summary of research that you collected from your primary source include all charts of primary data in appendix at the end of your report - Summary of research and conclusions that may have been done previously on this topic (secondary sources) - Include a minimum of 3 charts, graphs or diagrams (which are accurately described consider bar graphs, Frequency Polygons, 2-Variable graph with equation for curve or line of best fit line drawn on graph, boxand-whisker plot, etc.), as best appropriate for your data Discussion: [Weight: 2] - Discussion of how the research supported or did not support the hypothesis - Discussion of whether results are valid and how are or are not supported by research. - An analytical discussion of how your research could have been improved and suggestions for future study. Conclusion ( words): [Weight: ] - A complete description of the conclusions derived from the analysis of the data obtained in this project. References and Appendices: [Weight: ] - All resources, in print and/or electronic, properly referenced using MLA or APA. (Be sure to include web addresses if using easybib.com). - Data tables from secondary sources Final Report Evaluation Weight Level Level 2 Level 3 Level 4 Abstract: Summarizes entire paper (Indicates thesis, purpose, hypothesis, sources of data, and the conclusion reached.) (C) Introduction: States the purpose of the paper and includes an in-depth discussion of why the topic is of interest to them and applicable to others. (C) Thesis/Hypothesis: (K/A) Statement of the: -question that is being addressed, -variables being studied (define these clearly) -expected outcome based on preliminary research Provides an adequate summary of the paper but is not easy to read. Purpose is stated but it is not very clear. All three are included. One needed to be revised and another two could have been improved. Provides an adequate summary of the paper that could have been improved in one or two places Purpose is stated but description of why the topic was of particular interest to the student is vague. All three are included, one needed to be revised or two could have been improved Provides a clear summary of the paper and is easy to read. Purpose is clearly stated and explains why the topic is of importance to the student well. All three are clearly stated, one statement could have been improved. Provides an excellent summary of the paper and is very easy to read and comprehend. Purpose is clearly stated and the reasoning for the topic choice is clearly explained and engages the reader s interest. All three are clearly stated with no errors. 0

11 2 2 Observations: (K/A) Descriptions of: -Target Population -Sampling Methods -Sample -Eliminates/minimizes bias Analysis: (K/A) Secondary Sources Analysis: (K/A) Organization of Primary Data -Primary data must be in an appendix at the end Analysis: (K/A) Graphs/Charts/Diagrams -At least 3 graphs/diagrams are properly labeled and unbiased -Data is in graph in analysis or discussion sections. -Data is presented using appropriate method (type of graph or table) Discussion of Hypothesis: - Discussion of how the research supported or did not support the hypothesis. -If no correlation was found, reference related research and extraneous variables that might explain. (T) Discussion of whether they think their results are valid and how are or are not supported by research. (T) Suggestions for Future Studies and Improvement (T) Conclusion -Complete summary of the analysis and conclusions drawn (C) References (MLA or APA format) and Appendices (C) Level Level 2 Level 3 Level 4 Descriptions are very Target population is good but a little bias appropriate for survey was present that could topic and is accurately have been eliminated. represented by the The bias was discussed sampling methods, which though are chosen to minimize potential bias. Descriptions are clear but a significant amount of bias from sampling methods is not discussed and could have been eliminated. Includes information from two secondary sources but the descriptions are very difficult to understand or have not been put into their own words (must be referenced still) Results are organized, but little logic in method of organization is evident. All of the criteria are included, but two or more could have been improved. Conclusions are without adequate support from the data or the explanations are not clear. Analytical look at the analysis and discussion demonstrated some thought but no supporting research. Student suggests future steps that are not logical to furthering the study or misses a very logical next step, and includes no discussion of possible improvement of research. Conclusions are stated and an explanation of how they were is included but was not logical or easy to read. References are not properly sourced and tables of data used for analysis are included but not properly referenced OR tables are missing Summarizes the research of two secondary sources related to the thesis but more clarity is required in summary Results are clearly organized but it would have been easier to analyze if it had been done differently All of the criteria are included, but one of the items should have been improved. Conclusions are drawn without clear explanation. Analytical look at the analysis and discussion demonstrated considerable though but no supporting research. Student suggests future steps that are logical to furthering the study but misses a logical next step, and includes little discussion of possible improvement of research. Conclusions are stated and an explanation of how they were is included. Some clarification was required though. References are not properly sourced OR tables of data used for analysis are included but not properly referenced Accurately summarizes the research of two secondary sources related to the thesis Results are clearly organized so that the data can be analyzed and conclusion. All of the criteria are properly presented. Explanation of why data did or did not support the hypothesis is clear. Analytical look at the analysis and discussion demonstrated considerable thought and refers to other research. Student suggests future steps that are logical to furthering the study, and includes clear discussion of possible improvement of research. Conclusions are clearly stated and an explanation of how they were is included. References are properly sourced and tables of data used for analysis are included and properly referenced Target population is excellently chosen and described. Description of the sampling methods clearly show that student attempted to eliminate as much of the bias as possible. Accurately summarizes the research of more than two secondary sources related to the thesis. Organization of the results is excellent. It is clear and easy to see how it related to questions being addressed. All of the criteria are done thoroughly and more than three very applicable graphs/diagrams are included. Explanation of how the data did or did not support the hypothesis is excellent Analytical look at the analysis and discussion demonstrated a high degree of thought and refers to other sources. Student suggests future steps that are logical and applicable for furthering the study, and includes a very clear, informative discussion of how future research could be improved. Conclusions are clearly stated and a very clear explanation of how they were is included All references are properly organized and properly sourced, Tables are very nicely and properly referenced Comments (continued on back):