President Clinton just celebrated his 50th birthday, while candidate Bob Dole is currently 74 years old. It seems possible that age could be a major factor in the upcoming presidential election. What is the typical age, at inauguration, of the 41 men who have been elected President of the United States in the past? Based on this information, which current candidate seems most likely to be elected? We all know that age is not the only important characteristic of a presidential candidate. Examine some other characteristics of past presidents and determine which current candidate has the best probability of becoming president based on your analysis. Based on this information, what are the chances that a member of our team could be elected President of the United States? In what future election year would it be most likely to occur?
As this is an election year, this seemed like a good data analysis task that would tie in with the social studies unit we were studying, as well as provide a context for surveying classmates and using reference materials. This was the first problem-solving task of the year, done during the first week of school. Half of the students had been with me last year and were able to partner up with the new students in the preteaching of measures of central tendency (mean, mode and median). These students offered assistance in reviewing the fine points of conducting research and surveys. This is a good opportunity for students to decide on comparison factors, select characteristics that hold interest to them, and find sources of information that fit their needs. They have the opportunity to explore various measures of central tendency and to select the most appropriate for their data and the point they are trying to make. It also gives students a chance to consider their distant future and consider their chances of being elected president. Students have to conduct research to find the ages of all past presidents at inauguration and determine the typical age. They have to select some other characteristic of these men and determine the chances of the current candidates to be elected this year based on their sharing of this attribute. Students then need to survey their classmates to see which of them share this trait, to determine their current ages and to determine in which election year they will be closest to the "most electable" age, based on data they analyzed in part one of the task. I gave this task to kids on Friday and asked them to gather materials and information over the weekend. They worked on it for two class periods (two hours) and then were able to complete their write ups at home. I collected them on Friday the following week. This task fit in perfectly with our team study of the upcoming elections. Many classes study past presidents or the office of president, as part of a course in American history or government, and this task could be a useful tie at that time as well. I gave the students a weekend to gather resources before actually beginning to solve the task. An almanac will have a list of presidents and their ages at election. Many students had various books on presidents, as did the school library. Many students had access to the Internet, which has a host of resources available. For students in my class who have special academic needs, I gave them a version of the task asking only for the typical age of the Presidents of the United States. I also gave them a copy of the list of past presidents from the almanac. This proved to be a sufficient challenge to them at this point of the year.
- World Almanacs®
- Reference books on U.S. history
- Calculators
- Graph paper
The mean age of the past presidents at inauguration was 55 years of age. The modes are 51, 54, 55 and 57. Clinton will be 50 and Dole 74, so Clinton is closer to both the mean and mode age. The students in this class will be closest to age 55 in the election of 2036 or 2040 depending on the sample of students taken. The student has to make a case for correctness according to the characteristic chosen as the other factor for determining electability.
There were no students who completely misunderstood this task. Many did not have work to support their answers or expressed their solutions in vague or nonmathematical terms. Some students failed to respond to all parts of the question. The Novices did not use much mathematical language and had no representations. The benchmark Novice states s/he found the "typical age to be between 50 and 60." This is too vague. The fact that eight presidents came from Virginia is not useful information.
The Apprentices fell into two categories. They either did not deal with all aspects of comparing Dole and Clinton's chances or did not deal correctly with determining the year when their classmates would most likely be elected. Some of them used older reference books and did not include presidents elected after the publication of that reference. Many did not show calculations, did not use much math language, or did not have suitable representations.
Practitioners generally used more than one measure of central tendency and compared them. They all found some method of determining the chances of a classmate being elected - some, like the benchmark shown here, calculated the odds based on the current U.S. population, which is probably not very valid, but does point out that it is a true long shot! This student mentions that the odds are better for lawyers. Many students looked at the career choices of the past presidents and discovered that many were lawyers. Most of the Practitioners used some form of math representation and had some math language beyond the language of computation.
There were very few Experts in the group. Probably owing to the fact that this was the first week of school and students had not been given any Exemplars tasks yet this year. The benchmark chosen here was about the best of the lot. This student restates the problem clearly and selects more than one characteristic for comparison. The student selected more than one measure of central tendency and compared the results favorably. While the student does not take the time to carefully calculate the odds of a classmate being elected, s/he states that s/he knows how to do so and realizes that the chances are very small. This student realizes that neither of the characteristics that s/he chose to compare are very significant indicators of the current candidates' success in the upcoming election. This piece would be of better quality if the student had included the spreadsheet formula used to generate the solutions on the second page of his/her solution. There is strong math language throughout the solution and the math representation is accurate and appropriate.
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