A Wealth of
Activities
From the Statway and New
Mathways Projects
Colleen Hosking
Gustavo Cepparo
Mary Parker
Austin Community College
www.austincc.edu/mparker/talks/uscots13/
To download activities
See the slides at the end of this presentation
for information about how to contact us
and
how to download the handouts for today’s
presentation and ALL the activities.
Overview of
the Course
Prerequisites and Expectations
 Basic
Math
 The course length is 2 semesters
Students are told in advance that they will
be expected to work in groups, and that
they will need to complete both semesters
to earn credit for the college-level course.
Some of the design principles
The next slide is from the Carnegie
Foundation for the Advancement of
Teaching. We include it here as a “teaser”
for you to look at the websites.
 Productive
Struggle
 Explicit connections to statistical concepts
 Deliberate Practice
Learning Opportunities
Stigler, Givvin UCLA
Statistics and
Mathematics
Proficiency:
Flexible and
stable
knowledge
of concepts,
procedures,
strategies;
and
productive
disposition
Instruction / Learning Opportunities
Primary Drivers
Struggle with
important
mathematics
/
statistics
Explicit
connections
to
mathematic
al/
statistical
concepts
Deliberate
practice
applying
concepts/
procedures
to solving
problems
Secondary Drivers: How do these teachers use these
Instructional resources to create learning opportunities
for these students
Students engage productively with learning
opportunities:
•Believe they are capable of learning math,
gradually over time
•See math as something that makes sense, that
one can “figure out”
•Willing to invest persistent effort
Teachers effectively implement curriculum with
students to create learning opportunities:
•Belief that these students are capable of
learning math and statistics
•See math as something that makes sense, that
one can “figure out”
•Skills and knowledge to implement instructional
system: engage students in problems; make
concepts explicit in ways students can
understand; provide emotional support
Instructional resources that afford creation of
learning opportunities:
•Relevant to students interests
•Statistics (as distinct from math, to allay anxiety)
•Focus on understanding/thinking with concepts
•Clear learning goals (concepts & skills) aligned
with formative and summative assessments
•Lesson structure: struggle, then instruction
•Conceptual flows to structure6instruction
Activity
From the student
perspective
Activity: Scatterplots and
Correlation
Investigating Consumer Reports
Cereal Ratings
Rating Cereal: 0 to 100
0 = unhealthy
100 = very nutritious
Rating Cereal: 0 to 100
0 = unhealthy
100 = very nutritious
Student Handout PG 1
Rating Cereal: 0 to 100
•On what are you basing your
decision? How would we decide what
rating to give this cereal?
•Consumer Reports does this kind of
work and provides it to consumers
•CR rated 77 cereals, but their rating
formula is not available to the public.
Student Handout PG 2
• What does each dot represent in this distribution?
• For this distribution, what seems to be an
average rating?
• How would you describe the variability in ratings?
• How would you describe the shape of this
distribution?
Your Mission: Crack their code!
At the end of this lesson you will be designing a
children’s cereal. You want your cereal to receive
above average Consumer Report ratings but also taste
good. Of course, we all know that what tastes good
may not be the most nutritious. So this will be a
balancing act.
CLUES: We have the nutritional information from
ingredients we think might influence the ratings for
these 77 cereals and have created scatterplots.
Student Handout PG 2
Student Handout PG 3
Two new cereals are being rated by Consumer
Reports. Cereal A has 10.5 grams of sugar in a
serving and Cereal B has 2.5 grams of sugar.
(1)Based on the data shown, predict the
Consumer Reports rating for the two cereals.
(2)For which cereal do you think your prediction
is probably more accurate (more likely to be
closer to the actual Consumer Report rating)?
Why?
Student Handout PG 4
Reading and Interpreting
Scatterplots
(3) Captain Crunch has the lowest Consumer
Reports rating of the 77 cereals in the data
set. How much fat is in a serving of Captain
Crunch?
(4) In this set of 77 cereals, Product 19 has the
most sodium in a serving. What is the rating
for Product 19?
(5) All-Bran Extra Fiber is the cereal with the
highest rating. How much sugar, fat, and
sodium are in a serving of All-Bran Extra Fiber?
Student Handout PG 5
Seeing Patterns and
Relationships in Scatterplots
(6) There are four cereals that have 3 grams of fat in
a serving. Estimate the ratings for these four cereals.
What might explain the variability in the ratings?
(7) Imagine changing the recipe for a cereal that has
0 grams of fat in a serving and a rating of 60.
Increase the amount of fat to 3 grams in a serving.
Do you think the rating will probably increase,
decrease, or remain the same? Or do you think that
it is impossible to use the scatterplot to predict the
impact of this change on the rating? How does the
pattern in the data support your decision?
Student Handout PG 6
Seeing Patterns and
Relationships in Scatterplots
(8) Think about how the amount of fiber in a cereal
might relate to the Consumer Reports rating. Here
are three scatterplots with make-believe data from
10 made-up cereals. Which scatterplot do you think
displays a pattern similar to what you may see in the
actual data? Why?
Student Handout PG 6
Seeing Patterns and
Relationships in Scatterplots
(9) Suppose that carbohydrates are not used in the
Consumer Reports rating formula. Sketch a
scatterplot with make-believe data from 10 makebelieve cereals to illustrate what the data might look
like in this situation.
Get to it, cereal detectives!
Now it’s your turn to design your cereal. List how
much of each of the four ingredients your cereal will
contain (fat, sugar, protein, sodium) and why you
chose each amount. Estimate the rating of your
cereal.
Activity
From the teacher’s
perspective
How students react
 Eager:
They are interested in the context
and discussions are lively. Everyone has
strong opinions about cereal!
 Surprised:
Not all ingredients are as
influential as they might have originally
thought. They see data can be surprising.
 Group
dynamic: Some students who are
unsure about concepts (ex. how to read
a scatterplot) can ask their group in a low
pressure situation. It’s not as big a deal to
be corrected in your group than to be
corrected by the instructor. In a lecture
format they may never even feel
comfortable enough to ask. Here they are
not left behind.
 Making
connections: One student
pointed out that in predicting ranges of
ratings you could picture a vertical
boxplot.
Instructor version of lesson
 Rich
task
 Scaffolding
 Wrap-up
 Objectives
Caution: The version here, 1.0, is a first
version and there are some errors in answers
Organize
around
concepts
Examples:
Module 2 and on. Distributions. “What are
unusual values?” “What are usual values?”
(hypothesis testing and confidence
intervals)
Module 2. Compare groups. (comparing
two means)
Module 1: Collecting data. (hypothesis
testing)
Group Activity
1.
2.
3.
What do you do now in an elementary
statistics course that has some discussion
of concepts well before you are
“covering them?
What topics are hard for students and so
it might be good to do this?
For each topic you identified, brainstorm
ideas about how to do this.
Group Report
Each group report as many of these as you
wish.
 Statistics


“hard” topic.
Suggested activity / discussion / brief
lecture to address that earlier in the course.
Nothing suggested – still looking for one.
What are the
activities?
Resources
 Table
of Contents (blue pages in handout)
 List of Activities (green page in handout)
Both of these are version 1.0, upon which
both Statway and the New Math Pathways
is based.
 Information
page in handout)
from Carnegie Foundation (tan
Impact on
other courses
we teach
Early introduction of concepts
Regular stat course - in the chapter on
normal calculations, scale back the
complexity of the homework and talk
more about “unusual” and “usual” scores.
 Regular stat course – early discussion of
making decisions so that they are familiar
with the main ideas of hypothesis testing.

Writing activities
 Always
write an instructor edition of the
activity.
 Always consider scaffolding.
 Try to get other faculty members working
on activities for developmental math to
think in this way – that really sets us up for
improving our activities.
-- Mary
Style of activities
 Incorporated
these activities in place of
more mundane activities in my stats
course
 The structure of the course with
collaborative learning and struggling with
a rich problem is so impressive I have
started using this in my regular math
courses
--Colleen
Thank you!
Thanks for attending today.
If you have any further questions about this or
how to find the materials, please contact us.
Mary Parker mparker@austincc.edu
Colleen Hosking cneroda@austincc.edu
Gustavo Cepparo gcepparo@austincc.edu
www.austincc.edu/mparker/talks/uscots13/
Downloading activities
The activities themselves, Version 1.0, are on
the website of the Charles A Dana Center.
Read the copyright information to see how
you can use and adapt them.
Find links to the activities and other useful
information from the website for this talk:
http://www.austincc.edu/mparker/talks/uscots13/