1. MATH LITERACY FOR COLLEGE STUDENTS:
CONNECTING MYMATHLAB, REDESIGN, & QUANTWAY
Kathleen Almy & Heather Foes
ICTCM 2012

2. Explore
It is the story that matters, not just
the ending.
- Paul Lockhart

3. Background
 Problems
 Solutions
 Lesson exploration
 Initiatives

4. Problems with Developmental Math
Nationally
 Lengthy sequence with low pass rates
 Repeat of high school content
 Skill-heavy initiatives repackage but do not change
content
Locally
 Successful traditional program but one size fit all
 Intermediate algebra was not an appropriate
prerequisite for all college level courses

5. Solutions
 Look forward to courses students will take
 Update content, balance instruction, diversify assessment
 Use technology when it is most appropriate
 Differentiate pathways with new prerequisite courses

6. A New Course, A Simple Goal
In one semester, Mathematical Literacy for
College Students gives a student at the beginning
algebra level the mathematical maturity to be
successful in statistics, liberal arts math, or
intermediate algebra.

7. Initiatives
2009 AMATYC New Life initiative begins.
2010 New Life leads to Statway and
Quantway (formerly Mathway),
funded by Carnegie.
Carnegie AMATYC
2011 19 Carnegie grant schools pilot Quantway New Life
Statway.
2011 Rock Valley College pilots MLCS.
MLCS
2012 8 Carnegie grant schools pilot MLCS.

8. FAQs
What is the difference between Statway and
Quantway?

9. Take a look
Explore a lesson

17. Discover
Somewhere, something incredible is
waiting to be known.
- Carl Sagan

18. Content
 Philosophy
 Areas of focus
 Role of intermediate algebra

19. A New Perspective
We do not act as though these students have
never seen algebra because most have for years.
New approach:
 Emphasis on understanding over manipulation alone
 Application, connections, retention
 Evaluation of appropriate methods per the situation
 Focus on needs of outcome courses, work, life
 Incorporate needs of other disciplines
 biology, nursing, chemistry, business

20. Area 1: Numeracy
Start with numbers and Example:
understand them. Program cells in Excel to
Generalize when it makes evaluate a formula.
sense to.
Stay concrete; stay tangible.
Goal: Understand that
numbers are quantities.
Emphasize units.

21. Area 2: Algebraic Reasoning
Avoid problems without Example:
context whenever possible. Build a cost model for a Kindle
and Nook to compare against
Use numeric methods until the cost of a hardcover book.
students want and value the When is each worth it? Use
algebraic method. graphs, equations, and tables.
Strive for meaningful situations N=179 + 12.99B
and variables.
K=79 + 12.99B
Goal: Judge when algebra H=35B
makes sense and how to use it.

22. Area 3: Proportional Reasoning
We work with fractions, Example:
Interpret a nutrition label. Use
rates, and proportions in recommended values for a 2000
multiple places in many calorie diet to determine values for
a 3000 calorie diet.
ways.
Goal: Write rates with
units; scale, interpret,
and use them.

23. Area 4: Functions
We work on numeracy, Example:
algebraic reasoning, and Build a model. Plot points by hand
proportions all the while or Excel. Determine shape and
developing function analyze.
understanding.
 Constant vs. variable Hours to pay for gallon of gas
7
 Independent vs. dependent
6
variable
5
 Input values that make sense 4
3
Goal: Move between tables, 2
1
graphs, and equations fluidly. 0
0 10 20 30 40

24. Additional Embedded Areas
Geometry Statistics
Measurement, units, shapes, simil Centers, variation, correlation, pro
arity bability
Example: Example:
If we overfill a medical measuring Understand variation, build the
cup/spoon by 1 mm, which would standard deviation formula, use it
produce a greater overdose error? to find s.d. for a data set, interpret
Estimate volume in cc’s and find it in context.
actual and percentage change.
( x mean)2
s
n 1

25. Additional Embedded Areas
Student Success
 Approach to content increases motivation and develops metacognition
 First week lays foundation for first unit
 First unit lays foundation for course
 Lessons address student success while addressing math topics
 Specific strategies for studying and test taking are taught
Mathematical Success
 Role of accuracy, precision, and error are explored
 Polya’s problem solving method is used regularly
 Multiple approaches to problems build understanding
 Verbal, numeric, algebraic, graphic

26. Addressing Intermediate Algebra
Modeling with non-linear functions
(quadratic, exponential, rational, radical)
 Numerical, graphical, and conceptual understanding is emphasized
Emphasis on scatterplots, correlation, and regression
De-emphasize worst case algebraic problems in favor of
time on other topics
*Symbolic manipulation can be addressed in a traditional IA
course for STEM-bound students or future bridge course

27. FAQs
What about factoring?
Does this course “dumb down” developmental
math standards for entry into college level
courses?
Are you pushing students away from STEM majors?

28. Development & Instruction
 Research
 Content approach
 Quantway goals
 Technology

29. Using Research
 Researched schools, programs, and countries
who are effectively teaching mathematics (not
just algebra)
 Read and incorporated information on how the
brain learns

30. Traditional Approach: Linear
 Theory, then
applications if time
Proportions
 Each strand done
Functions
separately to
Numbers
Algebra
completion
 Algebra is primary focus
 Skill based
 Examples of every
possible variation of skill
(problem recognition)

31. New Approach: Integrated & Layered
 Applications to
motivate, then theory as
needed
Proportional
Reasoning
Reasoning
Numeracy
Functions
Algebraic
 Strands addressed each
unit in an integrated
fashion going deeper
each time
 Equal time on each
strand
 Concepts-based
 Fewer skills, more
connections Undercurrent of geometry, statistics,
student success, mathematical success

32. Technology for the 21st Century
 Mental arithmetic is encouraged
whenever possible.
 Calculators are used when they are
needed.
 Excel is used for analyzing patterns
and making graphs.

33. Quantway Goals for Instruction
Students actively work on rich
Engagement problems, both closed and open-
ended. Instruction is balanced.
Connections Students make sense of topics in the
given setting and others.
Students are allowed to struggle, but
Productive persistence assistance is provided when necessary.
Students complete homework
Deliberate practice assignments which forge connections
and deepen conceptual understanding.

34. Strike a Balance: Accessible Challenges
Engagement Frustration
Need enough
structure to
give students Contextual Theoretical
comfort but
not so much Online HW/Tech Paper HW/By hand
that it is
monotonous
Group Work Lecture
Open-ended Single solution

35. FAQs
Is there any direct instruction?
What reaction do you get from students? Do they
buy-in?
Will students be able to transition back to a
traditional course?

36. Assessment
 Homework
 Unit assessments

37. Homework
Structure: Specific and intentional
 MyMathLab for skill mastery
 Paper conceptual homework to connect & apply
 Fewer problems – do them all
Approach: Flipping the classroom
 Use online system for skill development
 Problem solve in the classroom

38. Unit Assessments
Regular assessments
 Online quiz and paper assessment twice in unit
 Project completed throughout unit
 Open-ended problem
 Tests Maintain
 MML-type skills accountability
 Concepts (fill-in-blank)
 Applications
 Project-related questions

39. FAQs
Can developmental students complete
open-ended problems?

40. Take a look
Explore an open-ended project

47. Connect
Success is a science; if you have the
conditions, you get the result.
- Oscar Wilde

48. Making MLCS a Reality
 Lessons from RVC redesign & pilot
 Implementation ideas
 Tips for getting started

49. Using experience to redesign with MLCS
Incorporated lessons learned in our redesign
 Advising
 Pace A comprehensive
approach
 Materials
 Continual assessment
 Training sessions and materials

50. Lessons from the pilot
Students want to mimic. They resist at first.
They have to be taught how to study and succeed in
this type of course, which is like a college level class.
Mastery learning in online systems ≠ learning.
Context can go a long way in improving connections and understanding.
Reflection is necessary to make sense of a lesson in the larger scheme.
We cannot help them all, but we can accelerate the process for many.

51. Implementation Ideas
Replace Beginning Algebra
STEM
Intermediate College
Algebra Level Math
Prealgebra MLCS
Non-STEM
College
Level Math
(Statistics, Libe
ral Arts Math)

52. Implementation Ideas
Use MLCS lessons in an emporium for once-
weekly problem solving sessions
Beginning Intermediate College
Prealgebra
Algebra Algebra Level Math
0 Previews content for some, connects for others
0 Everyone is engaged
0 More than just skills

53. Implementation Ideas
Augment traditional sequence with MLCS
as a non-STEM alternative preparation
for statistics/liberal arts math.
STEM
Beginning Intermediate College
Algebra Algebra Level Math
Prealgebra
Non-STEM
MLCS College
Level Math
(Statistics, Libe
ral Arts Math)
Students who change their major can take
intermediate algebra as a bridge to STEM courses.

54. RVC Course Sequence

55. Getting Started with MLCS
 Choose materials
 Create a collaboratory for pilot
 Sit in on other MLCS classes is possible
 Meet with other MLCS instructors regularly
 Test with common instruments
 Train new faculty
 Developing training workshops
 Materials provide great faculty support

56. FAQs
What is your placement tool?
How many credit hours is the course?
Can we omit topics that you may need?

57. Reflect
The farther backward you can
look, the farther forward you can
see.
-Winston Churchill

58. Lesson and Unit Protocol
 MOTIVATE: Explore an interesting
situation or hook
 DEVELOP: Learn more about a
topic through activities, mini-
lecture, hands-on activities, etc.
 CONNECT: Associate concepts
back and forward
 REFLECT: Wrap-up topic
Self-similarity approach
 PRACTICE: online for skills, paper
for concepts & applications

59. Questions?

60. For More Information
Kathleen Almy
 kathleenalmy@gmail.com
 http://almydoesmath.blogspot.com
 Blog contains info from pilot including video
 Contains info on our school’s redesign
Heather Foes
 heather.foes@gmail.com