Calculus in the popular press
1. Complete these sentences according to the
information in the article.
The ___________ (value, first derivative, second derivative)
of retail sales is ________________(positive, negative).
The __________ (value, first derivative, second derivative)
of car sales is ____________(positive, negative).
The _____________ (value, first derivative, second
of the economy is
___________________(positive, negative).
derivative)
The _____________ (value, first derivative, second
of JP Morgan's estimate of the risk of
a mini-depression is ____________(positive, negative).
derivative)
2. The first paragraph of the article contains a
description of "the second derivative ... turning
positive." Explain why you do or do not think
the description is accurate.
3. The second paragraph of the article claims
to contain a few bits of data to back up the
assertion mentioned in 2. Each of the next
four sentences of the second paragraph
evaluates an economic indicator. Only two of
these sentences actually give data that show
the second derivative of an economic indicator
is positive. Which two indicators: retail sales,
car sales, the economy, or the risk of a minidepression as estimated by JP Morgan Chase?
4. What is the difference between the phrase,
"the second derivative is turning positive" and
an alternative phrase, "the second derivative is
positive"?
5. What effects do you think imprecise
language about mathematics in the popular
press will have on students studying calculus?
6. What effects might imprecise language have
on non-technical consumers of news?
7. What effects might imprecise language have
on mathematically savvy economists and
policy makers who read this news?
Calculus in the Popular Press, Instructor Notes (Sommer Gentry):
This activity should be presented after the students have had significant practice using
first derivative and second derivative information to describe graphs of functions. This is
an in-class activity with an at-home reflective writeup. Give students about six to eight
minutes to read the article and possibly start answering the questions. Mindful that we
shouldn't let students work silently for too long at a stretch, lead a short discussion of
math in the media. Take an informal survey of who reads print news, reads online news,
or watches TV news. Have they ever considered that one purpose of math class is to
enable them to critically evaluate what they're being told by news agencies?
Form discussion teams of three, with leftovers as pairs rather than foursomes. Each
student first works alone. In writing, each answers questions 1-3 and 4 if there's time.
Then they exchange papers around the table and read silently before discussion starts.
The students should discuss their answers, first finding a consensus among the students,
then finding evidence to support that. As students advocate for their answers, encourage
them to argue their points by drawing graphs that depict data from the article.
Only after a little while, you can tell them that there are multiple correct sentences for
some of the prompts in question 4. For instance, retail sales rose, so one could say the
first derivative of retail sales is positive, or one could also say that the second derivative
of retail sales is positive, since this was the first increase in retail sales since June.
The article does not contain enough information for us to say that ANY of the indicators
has a second derivative that is turning positive (previously the second derivative was
negative and now the second derivative is positive). The two sentences that contain
enough information to say the second derivative is positive are the ones about retail sales
and the economy. The economy is actually shrinking (first derivative is negative) but at a
slower rate than before (first derivative used to be more negative and is now less
negative, so first derivative is growing, so second derivative is positive).
The questions form a progression along Bloom's Taxonomy. The questions also
deliberately move from more specific, direct questions to longer reflection questions.
Questions 1. Bloom's Revised Taxonomy Level 3, Applying.
Questions 2. Bloom's Revised Taxonomy Level 3, Applying.
Questions 3. Bloom's Revised Taxonomy Level 3, Analyzing.
Questions 4. Bloom's Revised Taxonomy Level 4, Analyzing
Questions 5, 6, and7. Bloom's Revised Taxonomy Level 5, Evaluating. Making
judgements and critiquing.
For homework, students should write three short paragraphs responding to 5, 6, and 7. If
there is time at the end of the period, they can discuss these questions with their groups. I
would call on a few students randomly to read their paragraphs aloud before they turn
them in on the second day, and hope that generates a bit more class discussion.