argumentation tuesday, october 7, 2014 “argument is the soul of an education” “argument, in...
Post on 25-Dec-2015
218 Views
Preview:
TRANSCRIPT
ArgumentationTuesday, October 7, 2014
“Argument is the soul of an education”
“Argument, in short, is the essence of thought.”
Schmoker & Graff (2011)
Our focus todayDeveloping language and criteria
for discussing argumentation and arguments◦In ways that clarify our thinking◦In ways that help us provide
feedback (and feedforward) to students
Guiding QuestionsWhat are characteristics of **written**
(communicated) mathematical arguments?
What counts as quality?What can we do to promote high
quality arguments? To use argumentation to promote conceptual understanding? ◦What are we already doing?◦What can we tweak?◦What else can we do?
One model: A pedagogy of mathematical reasoning
New question(s)
Generate ideas
Elicit and Publicize ideas
Press on and develop ideas collaboratively
Solidify and/or refine new meanings
A Mathematical ArgumentIt is…
◦A sequence of statements and reasons given with the aim of demonstrating that a claim is true or false
◦“an argument is a collective series of statements to establish a definite proposition” (Monte Python)
It is not… ◦ (Solely) an explanation of what you did (steps)◦A recounting of your problem solving process◦Explaining why you personally think it’s true for
reasons that are not necessarily mathematical (e.g., popular consensus; external authority, etc. It’s true because Adrianne said it, and she’s always, always right.)
Argumentation in ELA
Persuasion• Claim Based on Opinion
• Claim not always substantiated
• Pathos – appeals to emotions, desires, needs
• Ethos – appeals to writer’s/speaker’s trustworthiness or character
• May not consider opposing view
Argumentation• Claim (Position, Hypothesis, Thesis,
Opinion)• Claim substantiated with relevant &
sufficient evidence• Logos – appeals to logical reasoning &
evidence (e.g. facts, examples, historical & legal precedents, extended definitions)
• Ethos – appeals to writer’s/speaker’s credibility – established through knowledge & merits of evidence & reasoning
• Considers opposing view accurately and uses evidence and reason to refute it
Slip or Trip?
With your tablemates, review the picture and text. Determine whether you think that Queenie Valentine is telling the truth or lying. Identify the evidence that supports your decision. Be ready to defend how your evidence supports your decision.
From Hillocks, G. (2011). Teaching Argument Writing, Grades 6-12: Supporting Claims with Relevant Evidence and Clear Reasoning. Portsmouth, NH: Heinemann.
Evidence (concrete, observable information;testimony; objects and their condition or appearance)
Rule or Warrant Claim(slipped or tripped?)
Glass in left hand 1) When people walk downstairs, they hold onto a railing, and that should have been his left hand for downstairs. 2) When people fall, they try to stop themselves, so he would have dropped his glass, or dropped it when he hit the ground
Queenie is lying
His body position is legs up and facing up
When people fall coming downstairs, they don’t generally land face up
Queenie is lying
She’s only 5’ 6” and he’s 5’ 10”
Generally, when someone is significantly shorter, it’s hard to kill them
Queenie is not lying
Argumentation in ELA
backing
warrant
evidence claim
rebuttal
qualificationToulmin’s Argumentation Schemata
Features/Components ELA MATHTypes Arguments of Fact, Judgment &
PolicyComponents Claim, evidence, warrant,
qualifications, rebuttals
Evidence Concrete, observable information; Testimonies & Quotes; Textual passages; Quantitative data
Warrants & Backing Rules, laws, agreed upon common sense, scientific findings, and (particularly in arguments of judgment) extended definitions
Purposes Convince audience of the rightness of claims using logical reasoning and relevant evidence
Features/Components ELA MATHTypes Arguments of Fact, Judgment &
PolicyComponents Claim, evidence, warrant,
qualifications, rebuttals Claim, evidence, warrant(qualifications, rebuttals = refutations)
Evidence Concrete, observable information; Testimonies & Quotes; Textual passages; Quantitative data
Graph, table, diagrams (representations);
Warrants & Backing Rules, laws, agreed upon common sense, scientific findings, and (particularly in arguments of judgment) extended definitions
Definition; properties;
Purposes Convince audience of the rightness of claims using logical reasoning and relevant evidence
Convince audience of the truth of claims using logical reasoning and relevant evidence
Features/Components ELA MATHTypes Arguments of Fact, Judgment &
PolicyDeductive; proof by exhaustion; induction; proof by contradiction
Components Claim, evidence, warrant, qualifications, rebuttals,
Claim, evidence, warrant
Evidence Concrete, observable information; Testimonies & Quotes; Textual passages; Quantitative data
Representations (graphs, number lines, etc.); calculations; generic examples; details of the objects under inquiry; givens of the problem
Warrants & Backing Rules, laws, agreed upon common sense, scientific findings, and (particularly in arguments of judgment) extended definitions
theorems, properties, definitions, previously established ideas; using models (e.g. area model)
Purposes Convince audience of the rightness of claims using logical reasoning and relevant evidence
Convince audience of the truth of claims using logical reasoning and relevant evidence
A NUMBER TRICK!
Think of a number between 0 and 10 (inclusive)….
Opportunity to use our language of claims, warrants and evidence to analyze student work
Example of a task targeting the develop-ment of a core conceptual understanding
Your task… What is the claim?Identify the argument
◦ What’s the evidence the student offers?◦ What’s the warrant(s) that links the evidence to
the claim?Critique the argument
◦ Is the approach (chain of reasoning) mathematically sound?
◦ Are there logical gaps? Must the reader fill in connections or pieces of evidence?
Conceptual understanding◦ What can you infer about the student’s
(developing) understanding of the distributive property?
Let’s look at some student work
STUDENT A
Warrant: (one interpretation) I think it works for numbers 1-10 because if you try itfor each number you get the same answer
Evidence: none given –alludes to fact that someone may have tested each case
Claim: Yes
Let’s look at some student work
STUDENT A
Warrant:Not all types of numbers work
Evidence:none
Claim:No
Conceptual understanding?
Let’s look at some student work
STUDENT B
Claim:Yes
Warrant: if you multiply a number before adding it vs just adding a number, the second number has to be more [for the end result to be the same]Evidence: appeals to shared common understanding of a products [of positive integers]Conceptual understanding?
Your turn… What is the claim?Identify the argument
◦ What’s the evidence the student offers?◦ What’s the warrant(s) that links the evidence to
the claim?Critique the argument
◦ Is the approach (chain of reasoning) mathematically sound?
◦ Are there logical gaps? Must the reader fill in connections or pieces of evidence?
Conceptual understanding◦ What can you infer about the student’s
(developing) understanding of the distributive property?
Please do C – H first
I & J “knew” the distributive property
Stars
Stars: comments that highlight aspects of the response that are part
of a competent performance
Stairs: comments that indicate “next steps” that would help
improve the quality of the work
and Stairs
One way to frame itClaim: the claim is stated clearlyArgument (warrants & evidence)• presents a chain of reasoning that links
evidence to build to the claim• uses previously established ideas and
facts, including definitions, and/or ideas that are established as true within the argument
• uses representations (words, symbols, graphs, tables, pictures, etc.) that help convey ideas; the representations used are those the class knows or is able to understand
• addresses all cases covered by the claim Other: Contains no errors in calculations that detract from the argument
Stars & Stairs!
Select 2 student work samplesIdentify what the student is doing
well with respect to argumentation. Write a comment that conveys to the student what s/he is doing well.
Identify an area of improvement for the student with respect to argumentation. Write a learning promoting comment that conveys to the student how s/he might grow.
Goal – make progress on these questionsHow does argumentation help us
promote conceptual understanding of important ideas (e.g., the distributive property)? How does argumentation reveal students’ understanding of important ideas (here, the distributive property)?
How does our work getting better at identifying the claim, evidence and warrant help us give feedback and feedforward to students’ arguments?
Argumentation – solidifying
• What currently counts in your classroom for a valid argument? What qualities or criteria are important to you?
• How are these criteria communicated to students?
• What kinds of proficiencies did you find at the beginning of the year? Where will growth be?
WORKING LUNCH!
Reminders: * Share your summer preferences• If you’re having trouble with the wikispace,
find Steve, Maddie or SharonPLEASE RETURN AT 12:20
• What currently counts in your classroom for a valid argument? What qualities or criteria are important to you?
• How are these criteria communicated to students? • What kinds of proficiencies did you find at the
beginning of the year? Where will growth be?
top related