1. MATHEMATICAL LITERACY
FOR COLLEGE STUDENTS:
ONE YEAR LATER
Kathleen Almy
IMACC 2012

2. Background
 Problems
 Solutions
 Initiatives

3. Problems with Developmental Math
Nationally
 Lengthy sequence, low pass rates
 High school 2.0
 Skill-heavy initiatives
Locally
 Successful traditional program but one size fit all
 Intermediate algebra issues

4. Solutions
 Look forward
 Update content
 Balance instruction
 Diversify assessment
 Use technology strategically
 Differentiate pathways

5. 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.

6. 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.

7. Take a look
Explore a lesson

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

16. A New Perspective:
Recognizing a History of Algebra
 Emphasis on understanding over manipulation alone
 Focus on application, connections, retention
 Focus on needs of outcome courses, work, life
 Incorporate needs of other disciplines

17. Area 1: Numeracy
Understand numbers and Example:
their uses concretely, then Program cells in Excel to
evaluate a formula.
generalize.
Goal: Understand that
numbers are quantities
with units.

18. Area 2: Algebraic Reasoning
Avoid problems devoid of Example:
context. When is an e-reader worth
it?
N=179 + 12.99B
Strive for meaningful K=79 + 12.99B
variables and situations.
H=35B
Goal: Judge when algebra
makes sense and how to
use it.

19. Area 3: Proportional Reasoning
Make sense of fractions, Example:
Interpret a nutrition label.
rates, and proportions in
multiple ways.
Goal: Use units to write
rates. Scale when
possible.

20. Area 4: Functions
Develop an understanding of Example:
relationships between Build and analyze a model.
quantities and variables.
 Constant vs. variable Hours to pay for gallon of gas
7
 Independent vs. dependent 6
variable 5
 Input values that make 4
sense 3
2
1
Goal: Move between tables, 0
0 10 20 30 40
graphs, and equations fluidly.

21. Additional Embedded Areas
Geometry Statistics
Measurement, units, shapes, simil Centers, variation, correlation, pro
arity bability
Example: Example:
If we overfill a medical measuring How can we measure variability
cup/spoon by 1 mm, which would within a data set?
produce a greater overdose error?
( x mean)2
s
n 1

22. Additional Embedded Areas
Student Success
 Approach
 Motivation and metacognition
 First week and first unit
 Integrate math with student success
Mathematical Success
 Role of accuracy, precision, and error
 Polya’s method
 Multiple approaches build understanding
 Verbal, numeric, algebraic, graphic

23. Addressing Intermediate Algebra
Modeling with non-linear functions
 quadratic, exponential, rational, radical
 numerical, graphical, and conceptual approach
Emphasis on scatterplots, correlation, and regression
Symbolic manipulation addressed if needed in later course

24. 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?

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

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

27. 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)

28. 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

29. Lesson and Unit Protocol
MOTIVATE
DEVELOP
CONNECT
REFLECT
Self-similarity approach
PRACTICE

30. 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.

31. Quantway Goals for Instruction
Engagement Active work on rich problems
Application of concepts in new
Connections contexts
Productive persistence Struggling is permitted but assistance is
given when needed
Specific practice forges connections
Deliberate practice and deepens conceptual understanding

32. Strike a Balance
Between Structure and Monotony
Accessibility Challenges

33. FAQs
What reaction do you get from students? Do they
buy-in?
Will students be able to transition back to a
traditional course?
What do assessments look like?

34. Take a look
Explore an open-ended project

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

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

43. Lessons from the pilot
Students want to mimic.
Teach students how to study since the course
has college level expectations.
Mastery learning in online systems ≠ learning.
Context improves connections and understanding.
We cannot help them all, but we can accelerate the process for
many.

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

45. 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

46. 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.

47. RVC Course Sequence

48. 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

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

50. Questions?

51. 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