Ideas for Integrating quantitative reasoning activities and reflection

    1. ONE WAY TO CREATE ACTIVITIES for a FRINQ class is by coming up with the outcomes you want to address and then creating an activity to address them.

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    2. WHAT USUALLY HAPPENS. In our experiences, the best assignment starts with an idea or a problem. One person gets excited by the possibilities and several others chime in as to what would and would not be feasible or interesting. At some point the question of "What are the students supposed to learn from this?" comes up, creating another whole round of discussion and construction.
So how do you incorporate QUANTITATIVE REASONING in this mechanism? By keeping focus of your goals for student learning. Ask yourselves when you are in the creative process:
  "Given this 'idea' that we are creating, where do the students need to understand and deal with numbers?" Example I: A common subject in FRINQ seems to be Immigration, and one text that has been used frequently is The Huddled Masses, The Immigrant in American Society, 1880-1921 b Alan M. Kraut, Harlan Davidson, Inc. (1982).On p59, Kraut states,
  "In 1907, a peak immigration year, there were 195,540 detentions as compared to a total of 1,004,756 admissions. Of those stopped, 121,737 were temporarily detained, 64,510 were held for specific inquiry, and 9,203 were hospitalized. Board-of-Inquiry exclusions comprised approximately 15 percent of the total cases heard."


The obvious question is, What percentage of the immigrants were not let into the country.? Most people would immediately say 15%. It is worthwhile to have a conversation with the students about what the actual number of exclusions there were. By the way, we can estimate the maximum number of exclusions (15% of 121,737 would be my guess), but the paragraph is not clear.  It is definitely NOT 15% of the total number of admissions.

Example II:
In an article about the high school dropout rate (The Oregonian, April 17, 2000), we read:
"Schools saw a modest decline in the one-year dropout rate for 1998-99 from the previous year, from 6.9 percent to 6.6 percent.  Over four years, the state projects the dropout rate is 21.7 percent…"
If the one-year dropout rate is about 6.6 percent, how can the four-year rate be only 21.7 percent?

To help you think about this, consider the following analogous situation:
The department store has a clearance rack where the prices have been marked down 30%.  For the early bird sale, all prices are discounted another 20%.  What is the total discount?
Answer:  A $100 item is marked down to $_____ on the clearance rack; 20% of $____ is $____, for a final price of $____, giving a total discount of ______%.*

Once you have worked out the analogy, try to answer the question about the dropout rate.

*Completed answer:  A $100 item is marked down to $70 on the clearance rack; 20% of $70 is $14, for a final price of $56, giving a total discount of 44%.
Similarly, if you start with 100,000 students, a 6.6% drop leaves you with 93,400 students; another 6.6% drop leaves you with 87,236 students.  The third year drop of 6.6% leaves you with 81,478 students and then the fourth year drop of 6.6% leaves you with 76,100 students, which is 76.1% of the original 100,000, i.e. a four-year dropout rate of 23.9%.  The state’s projection must have assumed that the one-year rate would continue to decline.
 

Example III:
On Friday, May 4, 2001, The Oregonian published information about the number of people stopped by police, categorized by race.  Of the people stopped by police in Portland, 67.1% were white and 16.2% were African American.  In Portland, there are almost 11 times as many whites as African Americans.
How would you adjust these percentages to reflect the population ratio?
One conclusion in the article was that an African American was 2.6 times more likely to be stopped by the police than a white person.  How was this conclusion reached?
What other information would give you a clearer understanding of the situation?

Possible answers:
You have 67.1 "white stops" for every 16.2 "African American stops"; divide the number of "white stops" by 11 to adjust for the population ratio; the adjusted comparison is 6.1 "white stops" for every 16.2 "African American stops" or 2.6 times as many "African American stops" as "white stops."  It might be helpful to know how many miles each racial group tends to drive within Portland and average age of cars driven (taillight stops?).