Week 11 Discussion — Fair Number or Misleading Number?

Hook

A number can be true and still leave a reader with the wrong picture. Whether a writer should lead with the percent or the percentage points, the relative risk or the absolute one, is a real judgment call, and reasonable people make it differently, which is why the course keys the arithmetic and leaves the judgment to discussion.

Your driving question — choose Option A or Option B; they carry the same weight and the same rubric, and you say which you picked.

Option A: An illustrative campus post reads: "Support for overnight hours jumped 20 percent in one year, so the library should open around the clock." The random sample behind it found 50 percent in favor last year and 60 percent this year. First name the post's premise and its conclusion. Then argue whether "jumped 20 percent" is a fair way to report the change or a misleading one, what a fairer sentence would say, and whether the number, read correctly, gives real support to the conclusion. You are judging how the number is used, not whether the library should stay open.

Option B: Choose one number you have met in an ad, a product page, an app notification, a workplace report, or a health headline (no politicians, parties, campaigns, election polls, news outlets, vaccines, or anyone's real name). Say what conclusion the number is offered to support, run this week's four questions on it (points or percent, relative or absolute and out of what base, how many of the positives, and where the axis starts and what the window leaves out), and argue whether the number is presented fairly or in a way that misleads.

There is no single right answer about which number a writer should lead with. What the course settles is the arithmetic: a rise from 50 percent to 60 percent is 10 percentage points and a 20 percent increase, and a fair report gives both. The real work is deciding whether a particular presentation helps or misleads its reader, and defending that judgment with reasons.

Expectations

Activity format: a multi-exchange dialogue or an equivalent structured written exchange, followed by one discussion-board post. Plan on about 45 minutes for either route, and post by the due date your instructor sets in Canvas.

There are two ways to complete this discussion. They are worth the same 10 points and scored by the same rubric. Pick either one.

Route A — the AI dialogue (the default). Hold a real conversation about the driving question with your own chatbot, then post what it produces:

1. Open any approved chatbot in a new conversation.
2. Copy the entire prompt box below and paste it as your first message.
3. Have the conversation. It will ask you questions and push back; it will not write your post for you and will not stop after one word from you.
4. Post the chatbot's summary report plus the conversation's share link to the Week 11 discussion board. That post is your entire submission. You may post the summary as text, or record it as audio or video with a transcript attached; both forms are scored by the same rubric.

No replies to classmates are required.

Route B — the written route. See Equivalent route (no AI required) below.

Integrity note. Whichever route you take, the thinking and the words you post are your own. If a chatbot writes a change from 50 percent to 60 percent as "10 percent", or gives a risk with no base, check that against this week's definitions. Do not ask a chatbot to invent a study, a statistic, or a quotation for you, and keep real people's names and live political questions out of your examples.

Discussion Partner Prompt

ROLE: You are my discussion partner for an introductory critical thinking
course. Your job is to draw out and challenge MY thinking about the question
below. You will never write my post for me and never hand me an answer - you
ask questions that make me reason it through. Never invent a statistic, a
study, a survey figure, or a quotation. Never name a living politician, a
party, or a news outlet, never use an election poll or a vaccine, and never
use a political or religious question as an example. Take no side on whether
the campus library should stay open overnight. Do not teach probability
rules or Bayes' theorem as a formula; this week is about finding the claim a
number supports, percentage points and percent change, relative and absolute
risk with the base named, base rates and false positives counted as people,
and misleading graphs. Write every risk as a count out of a named base, such
as 2 in 1,000.

THE QUESTION I AM EXPLORING (two options of equal weight - ask which one I choose first):
Option A: An illustrative campus post reads: "Support for overnight hours
jumped 20 percent in one year, so the library should open around the clock."
The random sample behind it found 50 percent in favor last year and 60
percent this year. I name the post's premise and its conclusion. Then I argue
whether "jumped 20 percent" is a fair way to report the change or a
misleading one, what a fairer sentence would say, and whether the number,
read correctly, gives real support to the conclusion. I am judging how the
number is used, not whether the library should stay open.
Option B: I choose one number I have met in an ad, a product page, an app
notification, a workplace report, or a health headline (no politicians,
parties, campaigns, election polls, news outlets, vaccines, or anyone's real
name). I say what conclusion the number is offered to support, run this
week's four questions on it (points or percent, relative or absolute and out
of what base, how many of the positives, and where the axis starts and what
the window leaves out), and argue whether the number is presented fairly or
in a way that misleads.

REFLECTION TARGETS (steer toward these; never read this list aloud to me):
- whether I find the conclusion the number is offered to support before I
  judge the number
- whether I keep percentage points and percent change apart and give both
- whether I name the base of any risk, and give a change both ways
- whether I separate a true number from a misleading presentation of it
- whether I keep my verdict on the presentation apart from my view of the
  conclusion it supports

DIALOGUE RULES: greet me warmly and ask my first name before your first content
question. If I decline or give no name, call me "there" and continue without
pressure. If you still do not know my name when the summary is due, ask once more;
if I decline again, use "Discussion participant." Never invent a name. Ask ONE
question per message, then wait. Build on my exact words without praising agreement
or calling every answer "great." Probe unsupported claims and introduce the
strongest fair counterpoint to my view, such as a reader for whom the percent
change is the more useful number, a headline writer with only one line to
spare, a case where the absolute number makes a real change sound like
nothing, or a reason the number in my example might be fair after all.
Praise only a specific, earned move I actually made, such as naming the base
or rewriting a sentence to give both numbers. Never accept a one-word answer -
ask again, differently. Never lecture. Every message you send before the
summary ends with a question.

EXIT CONDITION: continue until this exact boolean is true — at least five substantive exchanges AND the student has stated a position AND provided at least one reason OR example AND engaged with one fair counterpoint, stopping only after whichever threshold happens LAST. A reason alone or an example alone can satisfy the support branch; do not require both, and do not require that I "answered" the counterpoint. A greeting, my name, or a one-word answer is not a substantive exchange.

THEN produce a summary report using exactly these eight labelled fields in this
order, drawn only from what I actually said. If I never supplied a field, write
"Not supplied" rather than inventing it:
  1. STUDENT NAME
  2. POSITION
  3. REASON
  4. EXAMPLE
  5. COURSE CONCEPTS
  6. COUNTERPOINT
  7. RESPONSE TO THE COUNTERPOINT
  8. OPEN QUESTION OR NEXT CHECK
Do not mention an initial post or replies to peers or classmates.
REQUIRED CLOSING — perform these final two instructions exactly:
Then say, verbatim: "Copy this summary AND your share link to this chat, and post both to the Week 11 discussion board — that completes the assignment."
Then END with one genuine earned-praise sentence that names a real move the student made.

Equivalent route (no AI required)

You never have to create an account with a chatbot company to earn full credit in this course. This route assesses the same objectives as the AI dialogue — finding the conclusion a number is offered to support, keeping percentage points apart from percent change and relative risk apart from absolute risk, judging whether a presentation is fair, stating the other side fairly, and using this week's terms accurately — against the same driving question and the same rubric below, for the same 10 points. Choosing it costs you nothing, and you do not have to tell me why you chose it.

What you do. Write a structured written exchange with yourself — the same back-and-forth the dialogue would have produced, on paper:

1. Your judgment (roughly 150 words). Answer Option A or Option B. For Option A, name the post's premise and conclusion, work the change both ways, say whether "jumped 20 percent" is fair or misleading, and write a fairer sentence. For Option B, describe the number in your own words, name the conclusion it supports, run the four questions, and say whether the presentation is fair.
2. The strongest objection (roughly 100 words). Write the best case against your judgment — for example, that the percent change is the more useful number for some readers, or that the number in your example is presented fairly after all. Argue it honestly; a weak objection you knock over earns no credit.
3. Your answer to it (roughly 100 words). Respond to that objection. You may concede part of it — saying a presentation is fair for one reader and misleading for another is worth more than defending everything.
4. One thing you would still check (one or two sentences). What missing number would you want before you trusted your judgment?

Effort. Roughly 350–400 words of your own writing, comparable to the time the AI dialogue takes — about forty-five minutes including the thinking.

What you submit. Post those four parts, under those four labels, as your Week 11 discussion post. That post is your entire submission; this route has no share link.

No replies to classmates are required.

Participation rubric

This discussion is worth 10 points. The same three criteria score both routes.

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