Template Leading Mathematical Discussions Performance-Based.docx

Template: Leading Mathematical Discussions
Performance-Based Assessment #3
Due November 6 at 11:59 PM
Use the template below for Performance-based Assessment # 3
Lesson Plan for the Number Talk
Number Talk Problem
How will you set up the activity?
Describe what you will say/do to introduce the number talk.
Since you will be working with a
small group of students, friends, classmates or family you’ll
need to give an in-depth
explanation of what to expect and what silent signals to use
(e.g., thumb on chest, agree
sign). See this video for inspiration and adjust according to
your audience. Delete this and
replace it with your plan.
Anticipated Student Strategies
List as many solution strategies as possible
Plan for Talk Moves
Look at the talk moves handout provided in Module 9 and
consider how you will use them.

Which ones do you want to focus on using? Your goal is to use
three or more different moves
a total of five times.
Wrap Up Questions
https://www.youtube.com/watch?v=X18cQkKMlhs
https://fiudit-
my.sharepoint.com/:w:/g/personal/bking_fiu_edu/ESdTxTbBjRJ
MqA0KjhZF_https:/fiudit-
MqA0KjhZF_V8Bygvy1ocQGKi3lTURI-
PKwg?e=HuuHcdV8Bygvy1ocQGKi3lTURI-PKwg?e=HuuHcd
Record Talk Moves
What questions might you ask after several students have shared
their methods?
Talk Moves
Find examples of different talk moves you used during the
discussion. Discuss each talk
move up to the fifth one used in the discussion.
1) List the time stamp in your video for the talk move,
2) Explain which talk move you used (use the handout to
identify the type of move) and
state the question you asked,
3) Explain the student’s response, and
4) Explain whether the talk move was effective? If you think it
was effective, explain why.
If you don’t think it was effective, explain what you hoped
would have happened.

Time in
Video
Talk Move (Name and what you said) Student Response
Effectiveness
Time in
Video
Effectiveness
Time in
Video
Effectiveness
Time in
Video
Effectiveness
Time in
Video

Self-Reflection
• Use the following questions to guide your reflection.
o How did the number talk go? Give a brief overview of what
happened.
o Evaluate your use of talk moves.
o What were your strengths? What do you need to work on
more?
Write your reflection here.
Self-Assessment
● Review your work and assess yourself on indicators A-C
below.
● Change the color of the cell or text to show which level (1, 2,
or 3) corresponds with the
quality of your work.
● Write an explanation for why you selected the rating you did.
Make connections
between the rubric and your work.
Effectiveness
Course Objective # 3: I can facilitate meaningful mathematical
discourse.
1 2 3
A: Type of
Talk Moves
I can use one or no
talk moves during a

discussion.
I can use two different
talk moves during a
discussion.
I can use three different
talk moves during a
discussion.
Explanation:
B: Number
of Talk
Moves
I can integrate less
than two talk moves
appropriately into a
discussion.
I can integrate three or
four talk moves
discussion.
I can integrate five talk
moves appropriately
into a discussion.
Explanation:

C:
Explaining
Talk Moves
I can rarely explain the
effectiveness of the
talk moves I use.
I can sometimes
explain the
talk moves I use.
I can explain the
effectiveness of the talk
moves I use.
Explanation:
Reality TV, Fake News, and Politics
This interview from Vox is a worthwhile exploration of fake
news Links to an external
site.from its birth in Putin's Russia in the 1990s and 2000s to its
use in the US and
Europe. It's one possible answer to the question, "Why all the
obvious lies?" The
interview is with a Russian-born former reality TV show
producer, Peter Pomerantsev.

Here are some key quotes from the interview:
"So propagandists are negotiating a new terrain where big ideas
don’t matter anymore.
Old social identities have collapsed, all the old professions and
social roles that were in
the Soviet Union have collapsed. There’s no idea of the future
anymore. Instead of trying
to argue in a rational way, politicians become these great
performance artists, trying to
be outrageous, reveling in the fact that they don’t care about the
facts. And this is all
very new...
"It’s not about proving something, it’s about casting doubt. This
has always been a
function of propaganda, like the tobacco companies trying to
make people doubt
whether their product causes cancer. But overall most political
ideologies have not
been about casting doubt — they’ve claimed to be telling the
truth about the way the
world is or should be.
"But this new propaganda is different. Putin isn’t selling a
wonderful communist future.
He’s saying we live in a dark world, the truth is unknowable,
the truth is always
subjective, you never know what it is, and you, the little guy,
will never be able to make
sense of it all — so you need to follow a strong leader.
"This is the way it works now, only it’s spread from Russia
across the world...

"Content is not where the battle is anymore. It’s about
manipulated campaigns and the
lack of transparency of the internet. I think we live in a new
form of censorship where
we don’t understand how the information environment around
us is shaped. We don’t
know why an algorithm shows us one piece of content and not
another. We don’t know
which bits of our data are used to target us and why. We don’t
know if what we’re
seeing is organic or part of a coordinated campaign. All of this
is in the dark..."
Trump, Russia, and fake news: How bullshit conquered the
world - Vox
https://www.vox.com/world/2019/10/24/20908223/trump-russia-
fake-news-propaganda-peter-pomerantsev
Are We Stuck in Place?
At this point you would be justified in saying, "You're
depressing me."
Nonetheless, there is good news in Historical Institutional
Theory akin to the Buddha's
key insight that life is always changing so you can never cling
to anything in your life
whether the experience is happy or sad. On the one hand it
sucks, on the other hand

when things are bad you can also count on circumstances to
change so you aren't
always stuck in bad times.
What overcomes path dependency?
Losers. They actually (sort of) rule. On this point Historical
Institutional Theory says
organizations rely on rules and always make decisions.
Decisions always create
winners and losers. So far, this isn't rocket science.
Decisions always provoke the unhappy campers and they hold
the key. Because losers
aren’t happy, they push for changing the rules. Since there are
always rules and
decisions, and thus losers, policy is never set in stone, but in
state of permanent flux.
Take a moment to give some thought to the current political
climate. What points of
conflict do we have now? Where are folks pushing for change?
Those 3 journal entries are a minimum of 250 words for each
idea
reflection per idea reflection. You can go longer on text or
video if needed.
If you are doing text it would run about 2000 words for the
three weeks of
reflections and about 2750 words in the final journal which will
cover four

weeks.
The format is your choice depending on your comfort level with
technology
and what you feel best fits your topic and creative inspiration. It
could be a
written Word doc. It could be a video. You could include your
own creative
work such as photographs, memes, graphics, artwork, poems,
songs,
graphs, diagrams, and tables. You can also use PowerPoint (link
from
Google Drive in your assignment post), Prezi, or an audio file.
Include links
to what is being discussed in your reflections when its from
something
other than our course. If you are using video and it is a file
smaller than 500
mb you can upload it directly to Canvas.
This can be a painless and enjoyable learning process if you do
it regularly.
If an idea grabs you as you are reading the Canvas site or the
Our Own
Worst Enemy book, do a short write-up. If you wait until a day
before it’s
due, or worse, the day of, it will be unpleasant.
Credible sources are a must
As you analyze the different ideas, your evaluation of the pluses
and
minuses of each idea is up to you. You will not be graded or
judged
on your beliefs and values. This course is about reflecting on

critical
political questions and issues and learning how to think, not
what to
think. You are required to include citations and supporting
evidence
for all your views. See the next page for definitions of credible
sources. Use it as a checklist. If it meets all the criteria use the
source. If it doesn't meet all criteria don't use it. You are
responsible
for vetting your sources before using them in this course!
https://ucdenver.instructure.com/courses/488814/pages/how-to-
get-a-better-grade-on-an-assignment
https://ucdenver.instructure.com/courses/488814/pages/how-to-
get-a-better-grade-on-an-assignment
How to Get a Better Grade on an
Assignment
To improve your grade on assignments use the following list of
things to do
and things to avoid. Use it as a checklist as you edit your
assignment. The
more checks the better your grade will be.
Above all remember as you analyze different perspectives, your
evaluation of the relative strengths and weaknesses of any
political
position is up to you. You will not be graded or judged on your
beliefs

and values. This course is about teaching you HOW to think,
not
WHAT to think. I do not care if you are Republican, Democrat,
Right or
Left or none of the above. What is important is to make the best
possible argument you can for your position. The tips on this
page
will help you do just that. It begins with the six most common
mistakes that I've seen in assignments.
A) The Big Six:
1: Thoroughly read through the assignment prompt and make
sure
you have done all required parts of the assignment. Don't throw
away
grade points unnecessarily. If you have any questions, or if
something is
unclear to you, reach out. I am here to help.
2: Define your terms. For example, writing "President Biden is
making the
US a socialist and maybe even a Communist country." (I heard
this from a
friend on Facebook so it is a real life example). Possible
responses: How
are defining you "socialism?" It's thrown around like a political
football as a
loaded word. But what defines it? What does it look like? How
do you know
when you see it? Thomas Dye, a conservative political scientist,
defines
socialism simply as central government control of the market.
He goes on
to say many of his fellow conservatives define any
governmental economic

regulation as socialism, but that is inaccurate as a capitalist
system with
some government regulation isn't socialism. Is a government run
utility
company or garbage service socialism? What is the difference
between
state central socialism, democratic socialism and social
democracies?
Know terms before throwing them around.
3: Examples help clarify meaning and definitions. Continuing
our
example above socialism above. For one example, Bernie
Sanders
identifies as a socialist, but isn't a socialist. He is social
democrat. Why?
For example, he would leave free market capitalism in place,
but have
more social programs. Social welfare programs with a capitalist
economy
aren't socialism. Social assistance programs historically were
created to
counter the appeal of socialism to workers. We'll have more on
this later in
the course.
4: Avoid generalizations. To use a simple example: All dogs
have curly
hair. Generalizations are the easiest statements to disprove.
Find one
exception and poof, it melts. By the way, did you know all the
superheroes
in the Marvel cinematic universe are ethical and serve only to

help people?
5: Cite evidence. We all have opinions. Its fine to swap
opinions over a
cup of coffee. A school assignment is different because it
requires
evidence. Evidence raises an opinion to the level of reasoned
argument. In
the socialism discussion above above I don't just assert Bernie
Sanders
isn't a socialist, and let it go as an obvious truth. I give reasons,
examples
and evidence. My sources are on the page linked. Which leads
us to the
next point.
6: Use credible sources. You are responsible for vetting your
sources
before turning in your assignment. My PSCI department
colleague
Sasha Breger Bush has excellent and concise advice on
determining what
a credible source is in her book Global Politics: A Toolkit for
Learners (pp
80-81) co-written with Kay M. O'Dell. Hint, a Q-drop is
unlikely to be
credible. Her checklist is as follows:
-Identify the author. If author is not identifiable, do not use the
source/information (author can be a credible organization,
government, or
other source, such as the WTO as an author);
-Identify the author’s credentials and ensure they are experts in
the subject.
Credentials need not be academic but could also include

relevant life or
work experience, or time spent researching the subject matter.
Don’t use
source/information without good reason to trust the author’s
credentials;
-Identify source information. Does the author reveal where they
get their
information, such that their findings could be replicated? If not,
don’t use
the source or the information provided;
-Identify possible interests or affiliations. Is the source
affiliated with a
company, interest group, political party, or political persona? If
so, factor
https://ucdenver.instructure.com/courses/488814/pages/sanders-
and-warren-compared-to-socialisms?module_item_id=3645705
https://ucdenver.instructure.com/courses/488814/pages/sanders-
and-warren-compared-to-socialisms?module_item_id=3645705
this into analysis of the author’s/publisher’s bias in conveying
information in
the text.
B) Other sure fire ways to weaken your arguments (i.e. more
logical
fallacies to avoid). This advice from the Perdue University
writing lab is
worth reviewing.
Fallacies are common errors in reasoning that will undermine
the logic of
your argument. Fallacies can be either illegitimate arguments or

irrelevant
points, and are often identified because they lack evidence that
supports
their claim. Avoid these common fallacies in your own
arguments and
watch for them in the arguments of others.
Slippery Slope: This is a conclusion based on the premise that if
A
happens, then eventually through a series of small steps,
through B, C,...,
X, Y, Z will happen, too, basically equating A and Z. So, if we
don't want Z
to occur, A must not be allowed to occur either. Example:
If we ban Hummers because they are bad for the environment
eventually
the government will ban all cars, so we should not ban
Hummers.
In this example, the author is equating banning Hummers with
banning all
cars, which is not the same thing.
Hasty Generalization: This is a conclusion based on insufficient
or biased
evidence. In other words, you are rushing to a conclusion before
you have
all the relevant facts. Example:
Even though it's only the first day, I can tell this is going to be
a boring
course.
In this example, the author is basing his evaluation of the entire
course on

only the first day, which is notoriously boring and full of
housekeeping tasks
for most courses. To make a fair and reasonable evaluation the
author
must attend not one but several classes, and possibly even
examine the
textbook, talk to the professor, or talk to others who have
previously
finished the course in order to have sufficient evidence to base a
conclusion on.
Post hoc ergo propter hoc: This is a conclusion that assumes
that if 'A'
occurred after 'B' then 'B' must have caused 'A.' Example:
I drank bottled water and now I am sick, so the water must have
made me
sick.
In this example, the author assumes that if one event
chronologically
follows another the first event must have caused the second. But
the illness
could have been caused by the burrito the night before, a flu
bug that had
been working on the body for days, or a chemical spill across
campus.
There is no reason, without more evidence, to assume the water
caused
the person to be sick.
Genetic Fallacy: This conclusion is based on an argument that
the origins
of a person, idea, institute, or theory determine its character,

nature, or
worth. Example:
The Volkswagen Beetle is an evil car because it was originally
designed by
Hitler's army.
In this example the author is equating the character of a car
with the
character of the people who built the car. However, the two are
not
inherently related.
Begging the Claim: The conclusion that the writer should prove
is
validated within the claim. Example:
Filthy and polluting coal should be banned.
Arguing that coal pollutes the earth and thus should be banned
would be
logical. But the very conclusion that should be proved, that coal
causes
enough pollution to warrant banning its use, is already assumed
in the
claim by referring to it as "filthy and polluting."
Circular Argument: This restates the argument rather than
actually
proving it. Example:
George Bush is a good communicator because he speaks
effectively.
In this example, the conclusion that Bush is a "good
communicator" and the

evidence used to prove it "he speaks effectively" are basically
the same
idea. Specific evidence such as using everyday language,
breaking down
complex problems, or illustrating his points with humorous
stories would be
needed to prove either half of the sentence.
Either/or: This is a conclusion that oversimplifies the argument
by reducing
it to only two sides or choices. Example:
We can either stop using cars or destroy the earth.
In this example, the two choices are presented as the only
options, yet the
author ignores a range of choices in between such as developing
cleaner
technology, car-sharing systems for necessities and
emergencies, or better
community planning to discourage daily driving.
Ad hominem: This is an attack on the character of a person
rather than his
or her opinions or arguments. Example:
Green Peace's strategies aren't effective because they are all
dirty, lazy
hippies.
In this example, the author doesn't even name particular
strategies Green
Peace has suggested, much less evaluate those strategies on
their merits.

Instead, the author attacks the characters of the individuals in
the group.
Ad populum/Bandwagon Appeal: This is an appeal that presents
what
most people, or a group of people think, in order to persuade
one to think
the same way. Getting on the bandwagon is one such instance of
an ad
populum appeal.
Example:
If you were a true American you would support the rights of
people to
choose whatever vehicle they want.
In this example, the author equates being a "true American," a
concept that
people want to be associated with, particularly in a time of war,
with
allowing people to buy any vehicle they want even though there
is no
inherent connection between the two.
Red Herring: This is a diversionary tactic that avoids the key
issues, often
by avoiding opposing arguments rather than addressing them.
Example:
The level of mercury in seafood may be unsafe, but what will
fishers do to
support their families?
In this example, the author switches the discussion away from
the safety of

the food and talks instead about an economic issue, the
livelihood of those
catching fish. While one issue may affect the other it does not
mean we
should ignore possible safety issues because of possible
economic
consequences to a few individuals.
Straw Man: This move oversimplifies an opponent's viewpoint
and then
attacks that hollow argument.
People who don't support the proposed state minimum wage
increase hate
the poor.
In this example, the author attributes the worst possible motive
to an
opponent's position. In reality, however, the opposition
probably has more
complex and sympathetic arguments to support their point. By
not
addressing those arguments, the author is not treating the
opposition with
respect or refuting their position.
Moral Equivalence: This fallacy compares minor misdeeds with
major
atrocities, suggesting that both are equally immoral.
That parking attendant who gave me a ticket is as bad as Hitler.
In this example, the author is comparing the relatively harmless
actions of a

person doing their job with the horrific actions of Hitler. This
comparison is
unfair and inaccurate.
Instructions: Leading Mathematical Discussions
Performance-Based Assessment #3
Due November 6 at 11:59 PM
Goal
The purpose of this assessment is for you to demonstrate your
ability to facilitate mathematical
discourse. You will lead a group of ‘students’ in a problem-
solving session and incorporate talk
moves to engage a range of students in discussion. You will use
evidence from this
assessment to show your understanding of Course Objective # 3.
Description
For this assessment, you will conduct a number talk. [I highly
recommend practicing the
number talk once or twice before doing the official lesson.]
You will compile a small group of
classmates friends and/or family either in person or on zoom.
Lead a number talk, use
talk moves to facilitate discussion, and reflect on the process.
Part One: Preparing for the Number Talk
• Select a problem to use during the number talk from the list
below.

o 256 + 84
o 103 – 65
o 142 x 6
o 168 / 21
• If working with children, you may need to select a problem
with smaller numbers. Feel
free to do so if necessary.
• Complete the lesson plan for the talk (template provided
below).
• Practice leading the number talk before you do the official
project, if possible.
• Select a small group of friends or family members or
classmates to participate in
the number talk (it would be best to have at least 3 people +
you).
• Find a way to record your number talk.
• Print out the talk moves handout to have available during the
number talk.
o Remember your focus is going to be on using as many talk
moves as
possible to facilitate an effective discussion of the problem.
• Lead the Number Talk!
discourse.

Part One: Lesson Plan for the Number Talk
Number Talk Problem
How will you set up the activity?
Describe what you will say/do to introduce the number talk.
Since you will be working with a
small group of students, friends or family you’ll need to give an
in depth explanation of what to
expect and what silent signals to use (e.g., thumb on chest,
agree sign). See this video for
inspiration and adjust according to your audience. Delete these
directions and replace it with
your plan.
Anticipated Student Strategies
List as many solution strategies as possible (refer to some of the
methods learned in class)
Plan for Talk Moves
Look at the talk moves handout provided in Module 9 and
consider how you will use them.
Which ones do you want to focus on using? Your goal is to use
three or more different moves
and to use talk moves at least five times.
Wrap Up Questions
What questions might you ask after several students have shared
their methods?

https://www.youtube.com/watch?v=X18cQkKMlhs
https://fiudit-
MqA0KjhZF_https:/fiudit-
MqA0KjhZF_V8Bygvy1ocQGKi3lTURI-
PKwg?e=HuuHcdV8Bygvy1ocQGKi3lTURI-PKwg?e=HuuHcd
Part Two: The Number Talk
• Assemble a small group of classmates, friends, or family to
participate in the number
talk.
• Video record the number talk.
• Explain to students how a number talk works.
• Give the problem.
• After students have time to search for multiple methods for
solving the problem begin
leading the discussion.
• Be sure you have a way to visually record the students’
methods.
• As students share their methods, be sure to use talk moves to
support the
conversation.
• Keep the talk moves handout in front of you to help you
remember to use the
moves.
Part Three: Reflect on the Number Talk and Record Talk Moves
• Watch the video recording of the number talk.
• Reflect on the process.
• Identify times you used talk moves. Which ones did you use?

Were they effective?
• Use the chart below (and found in the template) to record your
use of talk moves
during the number talks.
Talk Moves
was effective, explain why.
If you don’t think it was effective, explain what you hoped
would have happened.
Time in
Video
Effectiveness
Time in
Video
Effectiveness

Part Four: Self-Reflection
• Answer the following questions on the Template
o How did the number talk go? Give a brief overview of what
happened.
o Evaluate your use of talk moves.
o What were your strengths? What do you need to work on
more?
Part Five: Self-Assessment
● Review your work and assess yourself on indicators A-C
below.
● Change the color of the cell or text to show which level (1, 2,
or 3) corresponds with the
quality of your work.
● Write an explanation for why you selected the rating you did.
Make connections
between the learning scale and your work.
Time in
Video
Effectiveness
Time in
Video

Effectiveness
Time in
Video
Effectiveness
discourse.
1 2 3
A: Type of
Talk Moves
I can use one or no
talk moves during a
discussion.
types of talk moves
during a discussion.
types of talk moves
during a discussion.
Explanation:
Below is an example of an answer for the Talk Move table and
for the self-

assessment.
Record Talk Moves
B: Number
of Talk
Moves
I can integrate less
than two talk moves
discussion.
I can integrate three or
four talk moves
discussion.
I can integrate five talk
moves appropriately
into a discussion. (Use
the three talk moves at
least five different times
during your discussion).
Explanation:
C:
Explaining
Talk Moves
I can rarely explain the

talk moves I use.
I can sometimes
explain the
talk moves I use.
I can explain the
effectiveness of the talk
moves I use.
Explanation:
Talk Moves
was effective, explain
why. If you don’t think it was effective, explain what you
hoped would have happened.
Time in
Video
1:05

Talk Move
Elaborating – “Expanding student
thinking, asking for details.”
Question: “What did you mean by you
cut eighteen in half and then doubled
it?”
Response
After I asked the question the student
responded, “I meant to say that I cut
eighteen in half and then multiplied
nine by six and got 54. Then I doubled
54 to get 108.”
Effectiveness
I believe this talk move was effective. I think the student knew
what he was doing, but his
language was imprecise making it hard for other students to
understand what he did. I wanted
to make sure everyone was clear on the method he used.
A: Type of
Talk Moves
I can use one or no
talk moves during a
discussion.
talk moves during a
discussion.

talk moves during a
discussion.
Explanation: I used three different talk moves. First, I used
Elaboration to ask the
student for more details. Next, I used Explaining another
student’s thinking to
make sure students were understanding the explanations given
and so students who
did not hear could listen to it a second time. Finally, I used
Evaluating someone else’s
work when I asked if the students agreed or disagreed with the
solution method
presented so students can also measure accuracy on the methods
presented by
agreeing or disagreeing.

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