welcome to…

“Setting the Tone: Establishing a Culture of Engagement”

2012 Georgia Math Conference

open-access versions:

Nov. 2011 Journal of Statistics Education paper

Jan. 2012 causeweb.org webinar(partial support from NSF DUE-0618861 “Cultivating Authentic Discourse for the 2020 Engineer”,

PI: L. Everett; included developing inquiry-based models based on “counterintuitive concepts”)

Larry Lesser, Professor at The University of Texas at El Paso

initial impetus

• Assigned to teach a statistics class in spring 2009 with 3-hour meeting each week

• What do I do for the first day (i.e., week!)?

Discussing syllabus and calling roll not enough, but students have had no chance to do HW or reading!

Day 1 Matters Lesser & Kephart (2011)

• Brouillette & Turner (1992): “Students will never be more receptive…”

• Dorn (1987): high correlation of student evals on Day 1 or 2 with those at end of the term

• Wilson & Wilson (2007) randomly assigned students to + or - first day experience: the former reported higher motivation for most of the course, and ended with higher grades (p < 0.05)

Day 1 Likes & Dislikes Lesser & Kephart (2011) has much more Day 1 lit review

• Faculty like: set positive atmosphere, communicate objectives, introduce oneself, preview content

• Students like: practical information, grading standards, work required

• Students don’t like: covering new material, HW assigned, using full class time

can set the tone for PROCESS…

• Address anxiety & misconceptions• Build classroom community/norms of engagement• Model process for active learning• Let them (and me) see that they have prior

knowledge/intuition to build on• Standard #1 for Mathematical Practice (CCSSM):

make sense of problems & persevere in solving them• Examine assumptions, which supports

reasoning and sense-making (NCTM)

instructional cycle* Lesser & Kephart (2011)

Good problem presentedInitial Individual Reflection reduces anxiety, prepares students to share in

groups, especially ELLs (Fischer & Perez, 2008; Gibbons, 1998)

Small Group (3-4 students each) discussion makes it more likely students will share in whole class; creates contexts for meaning (Rosebery, Warren & Conant, 1992); active learning called for by ASA (2010)

Whole Class Discussion (with instructor as facilitator and co-learner)

optional: further individual reflection* variation on “think-pair-share” (Lyman, 1981) or “1-2-4-whole group” (Minich, 2010) structures

plan to allow about 5 minutes per stage, but be prepared to modify as needed

a good problem...• Has context relevant to student backgrounds

• Has minimal (math) prerequisites

• Is efficient to pose• Is efficient to compute (e.g., simple numbers; Lesser, 2011)

• Will be revisited/deepened later in course

• Is open to multiple approaches, representations, interpretations

• Stimulates habits of mind/questioning

• Shows statistics as “numbers with a context”

• May reveal a misconception

Methodology of case study

• DESIGN: case study; discourse analysis of lesson

• DATA: transcribed video of all Day 1 group and class discussions

• RIGOR: transcripts checked and analyzed by multiple researchers

• DELIMITATION: not designed to make claims about student learning, but rather to identify features of inquiry-based class

enough theory/background/literature:

Let’s explore some problems!

“Student Test Performance” Who did better, Amy or Bob?

fall fall spring spring

TESTS Amy Bob Amy Bob

passed 3 1 2 3

taken 8 3 3 5

Who did better, Amy or Bob?

fall fall spring spring full year full year

TESTS Amy Bob Amy Bob Amy Bob

passed 3 1 2 3 5 4

taken 8 3 3 5 11 8

3/8 > 1/3 ; 2/3 > 3/5 ; but 5/11 < 4/8

Whole-class debrief• Clarify what “doing better” means:

Amy had higher test passing % each term, but Bob did for the year;

for number of tests passed, Bob won in spring, but Amy won for fall and overall year

• Explore when comparisons can reverse upon aggregation (Lesser, 2001), but delay explicit label “Simpson’s Paradox” because that can inhibit student exploration (Harper & Edwards, 2011)

• Make decisions carefully of when/how to group

Let’s try another problem….

that’s been in the news a lot

(e.g., recent front page of

El Paso Times)

“Average Class Size” Exploration (Lesser, 2009, 2010a)

185 students are divided among 7 rooms as: 20, 20, 20, 25, 30, 35, and 35.

What would you say is the ‘average class size’?

we can use a simpler substitute dataset:

20 students divided among 4 rooms as:

3, 3, 4, and 10

what’s Average Class Size?

Room 1: 3 kids

Room 2: 3 kids

Room 3: 4 kids

Room 4: 10 kids

Give answers your students would likely give.

Go ahead, call one out!

what’s Average Class Size?

Room 1: 3 kids

Room 2: 3 kids

Room 3: 4 kids

Room 4: 10 kids

answers I usually get:

5 (mean), 3.5 (median), 3 (mode), and sometimes 6.5 (midrange)

Average per what?

basis mean median mode

Class 5 3.5 3

Student ? ? ?

Above answers were on per-class basis: {3,3,4,10}. Now, have students use a “per-student basis” with: {3,3,3, 3,3,3, 4,4,4,4, 10,10,10,10,10,10,10,10,10,10}Al,Bob,Carl,Dee,Ed,Flo; Gil,Hal,Ivy,Jo; Kay,Lia,Mo,Ned,Olga,Pat,Qing,Ray,Sue,Ted

Average class size per…..?

basis mean median mode

Class 5 3.5 3

Student 134/20 = 6.7 (10+4)/2 = 7 10

{3,3,4,10} for per-class basis

{3,3,3, 3,3,3, 4,4,4,4, 10,10,10,10,10,10,10,10,10,10}for per-student basis

whole-class debrief

• Ambiguity of the word “average”: need to specify not only which average, but also basis unit over which you are averaging!

• Which basis results in a larger number?

• Which basis is more useful for consumers?

• How to count auditing students, online courses, lab/recitation sections, etc.?

• Connection to “student-teacher ratio”?

• Students often made assumptions explicit: “My assumption was that each test has the same weight” (Kara) [‘who did better?’]

• Professor was facilitator/co-learner, eliciting multiple responses and finding something to validate in each

• Technique: Professor asked class: “How do you all think Kara came up with 3?” [‘avg. class size’]

some observations from transcripts(see Lesser & Kephart 2011 for detail)

in Sept. 2012 MTMS…

Nadia Kennedy’s “What Are You Assuming?” poses these problems:

A frog finds itself at the bottom of a 30-foot well. Each hour, it climbs 3 feet and slips back 2 feet. How many hours would it take the frog to get out?

A clock strikes 6 times in 5 seconds.

How long would it take to strike 12 times?

in Sept. 2012 MTMS…

A frog finds itself at the bottom of a 30-foot well. Each hour, it climbs 3 feet and [then] slips back 2 feet. How many hours would it take the frog to [first] get out?

A clock strikes 6 times in 5 seconds.

How long would it take to strike 12 times? [Assumes time begins with or after stroke #1?]

from letter I just sent to MTMS

Such problems help prepare middle school students to cultivate and exercise reasoning habits (e.g., “Reflecting on a solution – revisiting initial assumptions; reconciling different approaches”) that NCTM calls for in Focus in High School Mathematics: Reasoning and Sense Making.

Jokes/riddles make assumptions!

• How many months have 28 days?

• I have two coins whose values add up to 55¢. One is not a nickel.

What are the coins?

Jokes/riddles make assumptions!

• How many months have

[exactly or at least] 28 days?

• I have two coins whose values add up to 55 cents. One is not a nickel. What are the coins?

joke from protagonist in Mark Haddon’s 2003 novel The Curious Incident of the Dog in the Night-Time (p. 142)

There are 3 men on a train….And they have just crossed the border into Scotland…and they see a brown cow standing in a field from the window…. And the economist says, 'Look, the cows in Scotland are brown.' And the logician says, 'No. There are cows in Scotland of which at least one is brown.' And the mathematician says, 'No. There is at least one cow in Scotland, of which one side appears to be brown.'

Logic Puzzle: How could this be?

A man’s son is in a terrible accident.

The man rushes the boy to a hospital

where his son is whisked away into the OR.

The surgeon sees the boy and exclaims,

“Oh no! This is my son!”

Find the ages of H’s kidsadapted from Shilling-Traina (2012)

P: How old are your 3 kids?

H: The product of their ages is 36.

P: Hmmm….I can’t figure out their ages.

H: Right. Well, the sum of their ages is the same as the number of your address.

P: Hmmm….. I still need another clue.

H: Of course. The oldest has blonde hair.

P: Aha! Now I know their ages.

Time for Discussion

You’re invited to:

• Ask questions• Share your insights & experiences• Propose a new good opening problem

Thanks for attending this talk!

May you set a good tone with your next class!

Professor Lesser easy-to-Google open-access versions:

Nov. 2011 Journal of Statistics Education paper or Jan. 2012 causeweb.org webinar (half-hour)

Which of these 5 countries did best at the 2008 Summer Olympics? (Isaacson, 2011)

Nation Gold Silver Bronze

 China  51 21 28

 USA 36 38 36

 Zimbabwe  1 3 0

 Bahamas 0 1 1

 Australia  14 15 17

How to adapt for:• Shorter periods

• Larger classes

• Other days of the course

• Other courses

Scaling to shorter periodsLesser & Kephart (2011)

• Shorten periods in the instructional cycle Individual, Small Group, Whole Class, Further Individual

• Move individual post-reflection to out of class

• Use problems even more streamlined, such as:

On a high-stakes test where minimum passing score is a 7, which teacher’s class did better?

Mr. Jones’ 5 students’ scores were: 2,3,7,7,7.

Ms. Gomez’ 5 students’ scores were 4,5,6,6,8.

Scaling to larger classes Lesser & Kephart (2011)

• Have more groups (but keep each group size the same: 3 or 4 per group)

• You may not have time for every group to report out, but you can have only groups report out that had different results or approaches than the first group reporting

Other days of the course

• When introducing a new concept/unit

• Day after test or holiday break (when students did not do HW/reading since last class meeting)

• Anytime you sense that they need a reminder about the importance of identifying and questioning assumptions

Setting the tone on the last day(Hulsizer & Woolf, n.d.)

• Have students write letters of accomplishment & advice to future students

• Assess increase in learning & reasoning• Present certificates of accomplishment• Parting e-mail of appreciation to the class• Tyrrell (2003) gave out individual bags of chips

and had students brainstorm how to apply all tools they had learned to their supply of chips

How I started Day 1 for my intro stat(literacy) class, spring 2012

• Showed many stories in that day’s front page section and had them discuss how they thought statistics was used in them

[ bar graph for GOP primary poll, graph of child obesity rates by state, fingerprints database upgrade, redistricting maps(using Census data), projections for Alzheimer’s, wait times on El Paso bridges ]

• Top 10 facts about me• Survey to learn about them• “Opening Intention” reading (Lesser, 2010)• Collection of anonymous data for repeated

future use

a “liberating structure”“We call [this] a ‘structure’ because it is a constraint imposed on the participants. We call such a structure ‘liberating’ because it also unleashes people to engage, in pairs and quartets, in conversations and exchanges that would not happen going directly into the whole group discussion.

People in pairs automatically talk to each other; this immediately creates engagement of all participants….Quartets deepen the pairs’ exchanges in mostly safe spaces. These additional conversations will frequently lead to significantly different outcomes.

LS do not create a ‘free-for-all’ environment; rather the facilitator maintains a well-defined but minimal structure, and freedom flourishes within its confines.” -- Lipmanowicz & McCandless (2010, p. 9)

Henri Lipmanowicz & Keith McCandless “Liberating Structures: Innovating by Including and Unleashing Everyone” March 2010 E&Y Performance, 2(4), 6-19)