Opening the Algebra Gate

Opening'the'Algebra'Gate:'A'Pre2Statistics'Path'to'Transfer'Level'Math'
CMC3'South'Conference'Spring'2013'
10:30211:30'Saturday'February'23'
Sunset'Room'
'
Hal$Huntsman,[email protected]$
Myra$Snell,[email protected]$
California$Acceleration$Project$$$cap.3csn.org$
'
'
Agenda:''
$
• Introduction$
$
• Why$offer$a$statistics$pathway?$
$
• What$is$the$impact$on$student$achievement?$$
Early$data$from$CCSF$and$LMC$
Video$from$Myra’s$class$$
$
• Overview$of$the$packet$
What$does$the$course$cover?$$
Is$the$course$rigorous?$$
Does$this$course$jeopardize$articulation$of$Statistics?$
$
• Q&A$
$
$
Table'of'Contents''
Overview$of$the$California$Acceleration$Project$……………………….$ 1Q3$
Rationale:$The$Problem$…………………………………………………………..$ 4Q5$
Results$from$LMC$and$CCSF$…………………………………………………….$ 6Q8$
Learning$Goals$and$Content$Summary$……………………………………..$ 9$
Instructional$Cycle$………………………………………………………………….$ 10$
Sample$Class$Activities$to$Illustrate$the$Cycle$…………………………..$ 11Q17$
Sample$Assessments$and$Student$Work$…………………………………..$ 18Q26$
FAQs$………………………………………………………………………………………$ 27Q29$
Articulation$Issues$………………………………………………………………….$ 30Q32$
What$do$instructors$have$to$say?$…………………………………………….$ 33$
AMATYC$position$statement$……………………………………………………$ 34$
$
$
$
OVERVIEW'
'
What'is'the'California'Acceleration'Project?'
!
The!California!Acceleration!Project!is!a!community!college!initiative!developed!to!address!
the!unacceptably!high!rates!of!attrition!among!students!classified!as!under;prepared!for!
college.!CAP!provides!professional!development!for!math!and!English!faculty!in!the!
redesign!of!developmental!pathways!in!those!disciplines!to!provide!students!with!broader!
access!to!and!success!in!college;level!courses.!Redesign!is!guided!by!3!principles.!
!
CAP$Principles$for$Curricular$Redesign$
1. Increasing!completion!of!college;level!English!and!math!requires!shorter!
developmental!pathways!and!broader!access!to!college;level!courses.!
2. Community!colleges!must!reduce!our!reliance!on!high;stakes!placement!tests.!
3. Streamlined!developmental!curricula!should!include:!
• Backwards!design!from!college;level!courses!
• Just;in;time!remediation!!
• Intentional!support!for!students’!affective!needs!
In!2011;2012!and!2012;2013!CAP!supported!over!100!faculty!from!30!California!
community!colleges!in!the!development!and!implementation!of!more!than!300!sections!of!
new!accelerated!courses.!!
!
In!mathematics,!CAP!has!worked!with!16!colleges!to!develop!localized!versions!of!a!
shortened!statistics!pathway!for!under;prepared!students!who!are!in!majors!that!are!not!
math!intensive.!This!pathway!consists!of!a!current!UC;CSU!articulated!Statistics!course!plus!
a!new!pre;statistics!developmental!math!course,!where!the!latter!replaces!some!or!all!of!
the!traditional!sequence!of!arithmetic,!pre;algebra!and!algebra!courses!for!these!students.!
Algebra!content!is!replaced!with!content!that!is!better!aligned!with!the!skills!and!concepts!
required!in!statistics.!(Most!Intermediate!Algebra!topics!are!irrelevant!to!B4!Statistics!
courses!and!other!courses!in!fields!that!are!not!math!intensive.)!In!addition,!the!pre;
statistics!courses!have!an!explicit!focus!on!quantitative!literacy!skills!required!for!the!
baccalaureate!and!an!informed!citizenry,!which!is!more!difficult!with!traditional!algebra!
content.!!
!
!
What'is'the'rationale'for'redesigning'remediation'for'students'in'majors'that'are'not'
math'intensive?''
!
We!are!seeking!a!solution!to!the!well;documented!problem!of!attrition!in!the!remedial!
math!pipeline!in!community!colleges.!In$short,$the$more$levels$of$remedial$courses$a$student$
must$go$through,$the$less$likely$the$student$will$ever$complete$a$college$math$course.$The!
intermediate!algebra!prerequisite!requirement!for!transferable!courses!drives!the!
existence!of!a!multi;level!remedial!algebra!sequence!in!the!community!college.!!
!
!
!
1
National'Data:!256,672!first;time!degree;seeking!students!from!57!community!colleges!
participating!in!the!Achieving!the!Dream!initiative!
Students’!initial!enrollment!in!remedial!math!
%!of!students!who!
sequence!
successfully!complete!a!
college;level!math!course!
1!level!below!college!(Intermediate!Algebra)!
27%!
2!levels!below!college!(Elementary!Algebra)!
20%!
3!or!more!levels!below!college!(Pre;
10%!
algebra/Arithmetic)!
Source:!Referral,!Enrollment,!and!Completion!in!Developmental!Education!Sequences!in!Community!Colleges!
(CCRC!Working!Paper!No.!15).!By:!Thomas!Bailey,!Dong!Wook!&!Sung;Woo!Cho.!December!2008.!New!York:!
Community!College!Research!Center,!Teachers!College,!Columbia!University.!
!
California'Data:!143,587!students!from!all!CA!community!colleges!enrolled!in!remedial!
math!in!Fall!2009!(tracked!through!Spring!2012)!
Students’!initial!enrollment!in!remedial!math!
%!of!students!who!
sequence!
successfully!complete!a!
college;level!math!course!
1!level!below!college!(Intermediate!Algebra)!
35%!(15,531!of!45,047)!
2!levels!below!college!(Elementary!Algebra)!
15%!(7,341!of!47,741)!
3!or!more!levels!below!college!(Pre;
6%!(2,930!of!50,802)!
algebra/Arithmetic)!
Source:!Basic!Skills!Cohort!Tracker,!Data!Mart!CCCCO!
http://datamart.cccco.edu/Outcomes/BasicSkills_Cohort_Tracker.aspx.!Data!includes!repeaters.!
!
Statewide$data$also$demonstrate$that$attrition$in$the$remedial$math$pipeline$has$a$
disproportionate$impact$on$students$of$color.$$
$
For!example,!in!California,!black!and!Latino!students!are!much!more!likely!to!be!placed!3;4!
levels!below!college!math.!According!to!a!2010!EdSource!study!“Course!taking!patterns,!
policies,!and!practices!in!developmental!education!in!California!Community!Colleges”!by!
Perry,!Bahr,!Rosin,!and!Woodward,!61%!of!Black!students!and!53%!of!Latino!students!
placed!3;4!levels!below!college!math!in!California!community!colleges,!compared!to!34%!of!
White!students.!
How'is'the'CAP'initiative'related'to'Statway?''
!
CAP!is!not!formally!affiliated!with!Statway.!Our!work!is!synergistic!with!the!Statway!
initiative!in!that!it!focuses!on!alternative!pathways!through!statistics!for!under;prepared!
students!with!majors!that!are!not!math!intensive.!But!our!approach!is!different!from!
Statway.!The!colleges!participating!in!CAP!have!not!made!changes!to!the!rigor!or!outcomes!
of!their!transfer;level!statistics!course!that!is!articulated!with!CSU!–!students!enrolling!in!
alternative!pathways!take!the!same,!rigorous!college;level!course!as!they!would!in!the!
traditional!path.!All!that!has!changed!are!the!non;transferable!developmental!courses,!
which!have!been!redesigned!for!better!alignment!with!the!skills!and!concepts!required!in!
statistics!and!with!an!explicit!focus!on!quantitative!reasoning!that!is!not!possible!with!
traditional!algebra!content.!
!
2
How'are'CAP'colleges'navigating'the'intermediate'algebra'requirement'for'CSU'
articulation'of'their'Statistics'courses?''
'
Currently,!CAP!colleges!have avoided the articulation issue by using existing local mechanisms
that allow students to challenge prerequisites if they have the knowledge or ability to succeed in
the course (see California Ed. Code § 55003, section p, item 4) or by using the pre-statistics
course as a multiple measure for placement as mandated by section 55003(k). Thus,!most!
colleges!have!not!made!changes!to!the!stated!pre;requisite!of!intermediate!algebra!on!their!
statistics!course!outlines!of!record.!This!has!allowed!us!to!begin!to!gather!data!on!student!
performance!and!persistence.!!
!
!
Proof'of'Concept:'Early'results''
'
In!the!early!data!from!four!community!colleges,!we!see!completion!of!transferable!math!at!
2$to$4$times!the!rates!of!students!in!the!traditional!developmental!pipeline.!We!have!a!
contract!with!the!Research!and!Planning!Group!of!California!to!track!student!achievement!
through!Statistics!with!comparable!comparison!groups!for!a!larger!group!of!colleges.'
!
Early!data!also!suggests!that!pre;statistics!courses!provide!better!preparation!for!Statistics.!
For!example,!of!those!enrolled!in!Statistics!at!1st!census!in!a!northern!California!
community!college,!71%!of!38!pre;Stats!completers!versus!59%!of!153!Intermediate!
Algebra!completers!were!successful.!Pre;Stats!completers!were!enrolled!in!statistics!taught!
in!three!different!community!college!departments.!In!all!departments,!the!pre;Stats!
completers!out;performed!the!Intermediate!Algebra!completers.1!At!another!community!
college,!73%!of!101!pre;Stats!completers!versus!74%!of!1041!were!successful!(C!or!better).!
Pre;stats!completers!had significantly lower drop rates than students taking Statistics with no
remediation (14% vs. 20%, p < 0.057).2
!
!
!
!
!
!
The!California!Acceleration!Project!is!funded!by!the!California!Community!
Colleges!Chancellor’s!Office,!through!3CSN!with!additional!support!from!the!
Walter!S.!Johnson!Foundation,!Learning!Works,!and!the!“Scaling!Innovation”!
project!of!the!Community!College!Research!Center,!funded!by!the!William!and!
Flora!Hewlett!Foundation.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1!This data provided by Office of Institutional Research at the college from 2 sections of pre-stats taught by two
instructors. One section was in a program for students of color who are first generation college students. The other
section was open enrollment, predominately students of color with a broad age range. !
2!This data provided by a CC District Research Office from the first 4 sections of pre-stats taught by two instructors.
Pre-stat sections at the college are open to voluntary enrollment; roughly half of each section was comprised of
students also enrolled in programs targeting Latino and black first generation college students. !
3
Why have our colleges developed alternative math pathways for underprepared students?
We are seeking a solution to the well-documented problem of attrition in the remedial
math pipeline in community colleges. In short, the more levels of remedial courses a
student must go through, the less likely the student will ever complete a college math
course.
National Data: 256,672 first-time degree-seeking students from 57 community colleges
participating in the Achieving the Dream initiative
Students’ initial enrollment in remedial math sequence
% of students who
successfully complete a
college-level math course
1 level below college (Intermediate Algebra)
27%
2 levels below college (Elementary Algebra)
20%
3 or more levels below college (Pre-algebra/Arithmetic) 10%
Source: Referral, Enrollment, and Completion in Developmental Education Sequences in Community
Colleges (CCRC Working Paper No. 15). By: Thomas Bailey, Dong Wook & Sung-Woo Cho. December
2008. New York: Community College Research Center, Teachers College, Columbia University.
California Data: 143,587 students from all CA community colleges enrolled in remedial
math in Fall 2009 (tracked through Spring 2012)
Students’ initial enrollment in remedial math sequence
% of students who
successfully complete a
college-level math course
1 level below college (Intermediate Algebra)
35% (15,531 of 45,047)
2 levels below college (Elementary Algebra)
15% (7,341 of 47,741)
3 or more levels below college (Pre-algebra/Arithmetic) 6% (2,930 of 50,802)
Source: Basic Skills Cohort Tracker, Data Mart CCCCO
http://datamart.cccco.edu/Outcomes/BasicSkills_Cohort_Tracker.aspx. Data includes repeaters.
Statewide data also demonstrate that attrition in the remedial math pipeline has a
disproportionate impact on students of color.
For example, in California, black and Latino students are much more likely to be placed
3-4 levels below college math. According to a 2010 EdSource study “Course taking
patterns, policies, and practices in developmental education in California Community
Colleges” by Perry, Bahr, Rosin, and Woodward, 61% of Black students and 53% of
Latino students placed 3-4 levels below college math in California community colleges,
compared to 34% of White students.
High rates of attrition are inevitable given the length of the remedial pipeline.
For students enrolled in Elementary Algebra, the pipeline to and through a transferable
math course has 5 exit points and we lose significant numbers of students at each point.
This is illustrated with the Fall 2009 statewide community college Elementary Algebra
cohort (tracked through Spring 2012).
4
63% (30,289 of 47,741) pass Elementary Algebra
Of those who pass, 74% (22,406 of 30,289) enroll in Intermediate Algebra*
Of those who enroll, 70% (15,658 of 22,406) pass Intermediate Algebra**
Of those who pass, 64% (9,955 of 15,658) enroll in a college-level math course*
Of those who enroll, 74% (7,341 of 9,955) pass the college-level course**
* Enrollment counts are taken at 1st census.
** Passing is a C or better.
As a result, approximately 15% of the cohort passed a college-level math course in 3
years:
(0.63)(0.74)(0.71)(0.64)(0.74) = 0.15, which is 7,341 of 47,741
Can we increase the college course completion rate to an acceptable level by improving
course success rates and course-to-course persistence rates? Unfortunately, the answer is
no. For example, if success and persistence rates were an unprecedented 85%, the
completion rate would only be 44%, 0.85^5, which is a huge improvement but an
unacceptable general outcome.
Our conclusion: If the goal is to increase the college math completion rate for underprepared students, we must shorten the remedial course pipeline AND still prepare
students adequately for the rigors of the college math course that is appropriate for their
major.
5
Early Results from Two Statistics Pathway Pilots
Note: the California Acceleration Project has a contract with the Research and Planning Group of
CA to evaluate the impact of pre-statistics courses on student completion of college Statistics
against appropriate comparison groups.
Los Medanos College Path2Stats
The Statistics pathway at LMC is comprised of Math 27, an intensive 6-unit non-transferable
math course with no pre-requisite, followed by Math 34, a UC-CSU articulated introductory
Statistics course.
Significantly higher completion rates of college-level math regardless of placement level
As of spring 2012, 58% of the 151 Path2Stats students have completed transferable math,
compared to 19% of developmental students overall. This improvement in transferable math
completion rates is seen in all math placement groups. In a study of the 119 students in the 1st
three cohorts (4 sections), Path2Stats students completed transferable math at 2.2 to 4.3 times the
rates of students with comparable math placement who took the traditional algebra sequence.
Student placement
in traditional math
sequence
Transfer-level
Intermediate
Algebra
Elementary
Algebra
Pre-algebra or
Arithmetic
Unknown
Placement
Overall
Completion Rate
LMC
Path2Stats*:
% of Math 27
students passing
Statistics (in 1
year – no repeats)
100% (3 of 3)
82% (18 of 22)
LMC Traditional
Path*: % passing any
college math course
(in 3 years)– includes
repeaters
CA**: % passing any
college math course (in 3
years) – Fa 2009 cohort (all
CCC students enrolled at 1st
census) tracked through Sp
2012 – includes repeaters
37% (121 of 325)
35% (15,531 of 45,047)
78% (25 of 32)
18% (57 of 315)
15% (7,341 of 47,741)
38% (21 of 55)
10% (64 of 619)
6% (2,930 of 50,802)
19% (242 of 1259)
18% (25,805 of 143,590)
57% (4 of 7)
60% (71 of 119)
* Source: CCCCD Office of Institutional Research
** Source: Basic Skills Cohort Tracker, Data Mart CCCCO.
Comparable performance in Statistics as measured by course success rates
Student performance in
Statistics (Math 34)
Pass (A, B, C, or P)
Fail (D or F)
Withdraw (W)
From Path2Stats
(Math 27)
73% (74 of 101)
13% (13 of 101)
14% (14 of 101)
From Intermediate
Algebra (Math 30)
74% (772 of 1041)
10% (100 of 1041)
16% (169 of 1041)
Source: CCCCD Office of Institutional Research, includes repeaters
No remediation at
LMC
69% (1054 of 1523)
11% (162 of 1523)
20% (310 of 1523)
6
Achievement of learning outcomes as measured by departmental final exam assessment
In college Statistics, the first Path2Stats cohort outperformed the Honors section on the
departmental final exam. In the most recent assessment of learning outcomes in college
Statistics, 100% of Path2Stats students were rated proficient or better on 2 of 3 learning
outcomes; 82% were proficient on the 3rd. On items from the Comprehensive Assessment of
Outcomes for a first course in Statistics (CAOS), Path2Stats students’ overall performance was
within 3% of the national average.
Who enrolls in Path2Stats? Can these results be explained by differences in student populations
(Path2Stats vs traditional algebra enrollment)?
Though these sections were open to voluntary enrollment, roughly half of each section was
comprised of students also enrolled in Puente or ACE. Puente students are Latino first generation
college students. ACE is targeted at high-risk under-represented student groups. So these cohorts
of Path2Stats were predominantly students of color with other factors typically associated with
high-risk populations.
Further results from ACE (a program for high-risk students):
As reported by an external evaluator of the ACE program, 35 ACE students were enrolled in
Path2Stats in Fall 2010 and Spring 2011. 51% (18 of 35) passed Statistics in the subsequent
semester, while 0-5.9% of the comparison groups passed any transferable math course in the
same time frame.
CCSF
The Statistics pathway at CCSF is comprised an intensive 5-unit non-transferable math course
with a pre-algebra pre-requisite, followed by a variety of UC-CSU articulated introductory
Statistics courses. The intro Stats courses are taught in three different departments. The pre-Stats
course was offered for the first time in Fall 2011, so these results describe the first cohort (2
sections).
A nearly two-fold improvement in transferable math completion rates
33% of students in pre-Stats course at 1st census successfully completed Statistics the next
semester (27 of 81), compared to completion of any transferable math by students in the
traditional pipeline who took Elementary or Intermediate Algebra: 17-19%.
Better outcomes in Statistics:
Of those enrolled in Statistics at 1st census in SP 2012, 71% of pre-Stats completers (27 of 38)
versus 59% of Intermediate Algebra completers (91 of 153) were successful. Pre-Stats
completers were enrolled in statistics taught in three different departments at CCSF. In all
departments, the pre-Stats completers out-performed the Intermediate Algebra completers.
Who enrolls in CCSF’s pre-stats course? Can these results be explained by differences in student
populations (pre-stats vs. traditional algebra enrollment)?
One of the two sections was part of a Metro Health Program. This section was almost
exclusively students of color in their first semester of college. The other section was open
enrollment and resembled a typical developmental math course at CCSF – predominantly
students of color, though with a much broader age range than the Metro section.
7
Details
!!
Passing!Course!(Fall!2011)!
Passing'Math'80'(Spring'2012)'
Passing!Psych!5!(Spring!2012)!
Passing!Econ!5!(Spring!2012)!
Spring'2012'Passing'a'
statistics'course'(total)'
Preparation!for!
Statistics!
67%!
(54/81)!
66%'
(19/29)'
88%!
(7/8)!
100%!
(1/1)!
71%'
(27/38)'
Elementary!
Algebra!
55%!
(626/1145)!
N/A'
39%!
(7/19)!
0%!
(0/2)!
33%'
(7/21)'
Intermediate!
Algebra!
53%!
(548/1042)!
50%'
(44/88)'
71%!
(32/45)!
75%!
(15/20)!
59%'
(91/153)'
8
Path2Stats(Learning(Goals(for(CCSF(and(LMC(
!
Students!will!be!able!to:!
!
1. Formulate!questions!that!can!be!addressed!with!data,!then!organize,!display!
and!analyze!relevant!data!to!address!these!questions!and!communicate!
results;!
!
2. Apply!the!basic!principles!of!study!design!to!develop!and!analyze!the!validity!
of!simple!experiments!and!sampling!plans!related!to!a!given!situation!and!
goal;!
!
3. Demonstrate!numerical!and!algebraic!reasoning!skills!to!support!statistical!
analysis;!
!
4. Construct,!use!and!interpret!mathematical!models,!specifically!linear!and!
exponential!functions,!to!represent!relationships!in!quantitative!data;!!
!
5. Use!effective!learning!strategies!for!success!in!college.!!
!
!
Path2Stat(Content(
!
Order!of!operations!!
Unit!analysis!!
Measurement,!including!logarithmic!scales!
Geometric!analysis!of!algebraic!structures!to!describe!properties!of!a!
statistical!measure!
• Absolute!vs.!relative!difference!to!compare!quantities!!
• Graphical!representations!of!data:!bar!charts,!ribbon!charts,!dotplots,!
histograms,!boxplots,!scatterplots!!
• Symbolic,!graphical!and!numerical!analysis!of!proportional,!linear,!and!
exponential!relationships!
• Correlation!and!regression!!
• Correlation!vs.!causation!
• Data!distributions:!shape,!measures!of!central!tendency!and!variability,!
outliers!(mean!and!average!deviation!from!the!mean!or!standard!deviation;!
median!and!quartiles)!
• TwoPway!tables,!marginal!and!conditional!percents!!
• Empirical!probability!!
• Principles!of!good!survey!and!experiment!design!
!
!
Note:!Content!in!prePstats!courses!varies!across!the!state.!In!particular,!the!amount!
of!algebra!and!probability!differs!by!college.!!
•
•
•
•
9
Path2Stats
Path2Stats
Instructional
Cycle
Introduction to
Unit
Purpose
•
•
•
•
Contextualize
to “real life”
Build preknowledge of
context
Connect to and
build on
personal
reasoning
Motivate
Preliminary
investigation of a data
set relevant to the Unit
questions
• Activate math preknowledge
• Connect to and build
on personal reasoning
• Move away from
“show me” and
toward “what makes
sense to me”
• Take risks
• Practice listening and
responding
• Gain respect for and
learn from peers
Structured development of Application of
statistical tools
statistical tools to data
analysis relevant to
Unit questions
• Build pre• Apply concepts to
knowledge/schema to
Unit Problem or an
prepare for direction
open-ended task
instruction
• Build statistical
• Learn from direct
literacy
instruction on key
• Take risks
concepts
• Practice listening and
• Directed practice on
responding
skills with application to • Gain respect for and
new contexts
learn from peers
Culminating Task:
Paper, exam, or
presentation
Group work, mini-lectures
Some redo
opportunities
Pedagogy
Small group and
class discussion
Group work, poster
presentations, group
reflection and revision
Assessment/
Feedback
Homework:
Newspaper
articles, websites
to analyze
statistical evidence
used to support an
argument;
just-in-time
remediation
Feedback: future
discussion (class
or groups)
Homework:
As for Intro to Unit, also
revision of group’s
presentation,
Feedback: Peer and
instructor feedback or
class discussion of
student work samples
Individual work on
Tinkerplots, speeddating, individual
reflection and revision,
class discussion
Peer and instructor feedback Homework: individual
during group work;
revision of argument and
homework problems for
data analysis.
direct practice with core
Feedback: Individualized
concepts (feedback from
peer and instructor
instructor, feedback routine feedback on drafts of
by peer, group, or self),
arguments or class
multiple-choice quizzes
discussion of student
with solutions and
work samples
explanations
•
•
•
Apply concepts
to Unit Problem
or an open-ended
task
Make an
argument backed
by data analysis
Build persistence
and pride in work
Feedback: Self and
peer feedback prior
to due date. Optional
feedback from
instructor prior to
due date.
Rubric evaluation.
10
Example of Intro to a Unit and Preliminary Investigation of the Data
Introduction to the Breakfast Cereal Unit
In your group, discuss the following questions. Make notes of key points raised in your
group’s discussion.
1. Should we be concerned about advertisers targeting children in breakfast cereal
advertisements? Why or why not?
2. What impact, if any, do you think this advertising has on children’s health? Be
specific.
3. How do you define “unhealthy” cereals?
4. Do you think this is a world health issue or one confined to the United States?
Explain.
Breakfast Cereal Data Analysis Activity
For this initial activity your group will be working on a data set containing information
about 24 breakfast cereals.
Questions to be investigated:
1. Are the cereals marketed to children less healthy than the cereals marketed to adults?
2. Do cereals marketed to children appear to be deliberately located on grocery store
shelves to attract children’s attention?
Explore the Data:
Explore the data by making graphs and doing calculations that make sense to you. Try as
many different ideas as you can think of. Different approaches will probably highlight
different features in the data.
With the questions in mind, record the parts of your exploration that provided the most
useful insights.
Summarize and draw a conclusion:
Write your conclusions. Make sure you answer the questions. Your poster should
illustrate how your analysis of the data supports your answers and conclusions.
11
Breakfast Cereal Data
Name: Name of cereal
Manufacturer: Manufacturer of cereal
Target: Target audience for cereal (adult, child)
Shelf: Display shelf at the grocery store
Calories: Calories per serving
Carbs: Grams of complex carbohydrates in one serving
Fat: Grams of fat in one serving
Fiber: Grams of dietary fiber in one serving
Potassium: Milligrams of potassium in one serving
Protein: Grams of protein in one serving
Sodium: Milligrams of sodium in one serving
Sugars: Grams of sugars in one serving
Vitamins: Vitamins and minerals - 0, 25, or 100% of daily need in
one serving
CRRating: Consumer Report rating
Cups: Number of cups in one serving
Weight: Weight in ounces of one serving
12
Example of Structured Development of Statistical Tools
Measuring Spread
Goal: Develop methods for measuring the variability (the spread) in data.
1. Use the dotplots at the right.
a. Each of these distributions has a mean of 10, but each
distribution has a different amount of spread. Based on
looks, order the distributions from least amount of
variability to most amount of variability.
Order
_______________________
Least spread ……….. Most spread
Collection 1
A
B
C
It may help to fill in the table of data values.
8
9
10
11
12
Values1
Circle Icon
b. Devise a way to measure the variability in a
distribution.
Data set A
Data set B
Data set C
Here are the specs:
• Use the data in your measurement.
• Your measurement gives a single number
that represents the spread in the data.
• Your measurement ranks the distributions appropriately (smallest
measurement corresponds to distribution with least spread, etc.)
Explain or show how your measurement works:
13
2. Here we have a new set of 3 distributions. As before, each of these distributions has a
mean of 10 but a different amount of spread.
Collection 1
a. Based on looks, order the distributions from least amount
of variability to most amount of variability.
Order
D
______________________
Least spread ……….. Most spread
E
It may help to fill in the table of data values.
F
b. Use your measurement of spread to measure the
variability in each of these distributions. Does your
measurement work? Why or why not?
8
9
10
11
12
Values2
Circle Icon
Data set D
Data set E
Data set F
c. If necessary, devise a new measurement using the same specifications as above.
Explain or show how your measurement works:
14
3. Here we have a new set of 3 distributions. As before, each of these distributions has a
mean of 10 but a different amount of spread.
a. Based on looks, order the distributions from least amount of
variability to most amount of variability.
Order
Collection 2
G
______________________
Least spread ……….. Most spread
H
It may help to fill in the table of data values.
b. Use your measurement of spread to measure the variability in
each of these distributions. Does your measurement work?
Why or why not?
I
9
9.5
10
10.5
11
Values3
Circle Icon
Data set G
Data set H
Data set I
c. If necessary, devise a new measurement using the same specifications as above.
Explain or show how your measurement works:
15
Math 45X
Comparing Groups Categorical
Example of Application of Statistical Tools
Handout #7
(1) Last fall Myra gave her Math 80 students a quiz containing a question from a national statistics exam.
29 students took the quiz. She compared their performance on this question to the performance of the
1470 students included in the national sample. 24 of her students got the item right compared to 1001 of
the national sample. Did the Math 80 students do as well as the national sample?
(2) This data comes from a study of the factors that impact birth weight. Here the variable Visit indicates
whether a woman visited a physician during the first trimester of her pregnancy. The variable Low_Wt
indicates whether a baby was born weighing less than 2500 grams. Does visiting a doctor during the
early stages of pregnancy seem to be associated with a lower incidence of low weight births for these
women?
16
Math 45X
Comparing Groups Categorical
Handout #7
(3) A study in Sweden looked at impact of playing soccer on the incidence of arthritis of the hip or knee.
They gathered information on former elite soccer players, people who played soccer but not at the elite
level, and those who never played soccer. Does this study suggest that playing soccer makes someone
more likely to have arthritis of the hip or knee?
Arthritis
No arthritis
Column Total
Elite
10
61
71
Non-elite
9
206
215
Did not play
24
548
572
Row total
43
815
858
(4) This data was collected from 8 Arizona high schools. In this study are students with parents who smoke
more likely to be smokers?
Student smokes Student does not smoke
Both parents smoke
400
1380
One parent smokes
416
1823
Neither parent smokes
188
1168
What did you learn from this activity?
17
Assessment Samples – CAP colleges’ pre-statistics courses
Assessment Sample #1: LMC Quiz 1 Data Analysis – Pre-Statistics course
Background: This is part of the first quiz given in week 3 of an 18-week semester.
Students take this quiz in a computer lab and use Tinkerplots to make the graphs that are
part of their analysis. The quiz also contains a multiple-choice segment.
Quiz prompt:
Medical researchers conducted a study of the factors potentially associated with low birth
weight. Low birth weight is a concern because premature or very small babies are at
greater risk for a variety of health problems. They collected data from 189 women who
gave birth at a hospital in Massachusetts in 1992.
(1) Choose a variable that you think may be associated with low birth weight. Explain
why you think this variable may be associated with low weight births.
(2) Pose a question to investigate that involves the variable you chose and the variable
low birth weight.
3) Create a graph to explore the relationship between the variable you chose and the
variable “low birth weight”. Determine percentages that will provide a convincing
comparison to answer your question.
Description of Data Set:
Students use computer software (Tinkerplots) to analyze a spreadsheet of data collected
from 189 pregnant women. Data includes the following attributes:
• Age (18 or younger, over 18),
• Low birth weight (birth weight less than 2500 grams: yes, no)
• Smoking status during pregnancy (yes, no)
• Labor (History of premature labor: yes, no)
• Physician visit during first trimester (yes, no)
• Mother’s weight at last menstrual cycle (100 pounds or less, greater than 100
pounds)
18
Student Work Sample #1 (Note: Students submit work in Tinkerplots, which does
not have a Spell Check feature.)
1) The variable that I believe is greatly
associated with low bith wieght is smoking.
I believe that this is the variable that is most
likely to greatly affect low birth wieght because
smoking durring pregnancy is known to cause
low birth wieght along with other serious
medical conditions.
2)This data was collected from 189 women who
gave birth at a hospital in Massachusetts in 1992
as part of a study on the factors associated with
low birth weight . Does the data suggest that
women who smoke are at greater risk of having a
low birth weight baby as opposed to women who
don't smoke? Explain.
low_birth_weightplus.txt
29
30
86
44
yes
no
no
yes
Smoker
Circle Icon
3)Yes, the data shows the percentage of women who smoke vs the percentage of women
who don't smoke. Out of these two categories 25% (29 of 115) of the women who don't
smoke had a low birth wieght baby as opposed to 41% (30 of 74) of the women who do
smoke had a low bith weight baby. You are 1.6 times more likely to have a low birth
weight baby if you smoke than if you don't smoke.
Student Work Sample #2
A variable that I think that may be associated with low birth wieght is wheter or not the
she mother vistedthe doctor. I think this a good variable because women who don't go to
the docotr have no idea on what happening with their baby and so they wont know if they
need to eat more or less.
low_birth_weightplus.txt
QUESTION:
DOES NOT VISITING THE THE DOCTOR
AFFECT YOUR BABY'S WIEGHT?
SO all in all you are 1.5 times more likely to have
low birth weight baby by not visiting the doctor.
23
64
66
yes
Total women who went to the Doctor during their
pregnancy was 89. And the total women who
didn't go was 100.
23/89=26%
36/100=36%
36%/26%=1.5
36
no
no
yes
Visit
Circle Icon
19
Assessment Sample #2: CCSF Quiz – Pre-Statistics course
Background: This is part of a quiz given during the 5th week of an 18-week semester at
CCSF. Students take this quiz in a computer lab and use Tinkerplots to make the graphs
that are part of their analysis.
Quiz prompt:
Do males pay a higher insurance premium than females?
Do more experienced drivers pay a lower insurance premium than less experienced
drivers?
Create a graph(s) to answer the question you chose and refer to the graph in your answer.
Make sure to discuss the either ADM or IQR (as appropriate) in your answer.
Description of the Data Set:
A spreadsheet with 50 individuals and 3 variables:
• Experience categories (fewer than 6 years, 6 or more years driving experience)
• Gender (female, male)
• Annual premium (amount of car insurance paid annually in 2005)
Sample of student work:
Do males pay a higher insurance premium than females?
Yes, the data indicates that men pay higher insurance premiums per year than women.
Men have a higher median premium of $3264 per year compared to the median for
women, which is only $2400 per year. The IQR indicates that the lowest paying 25% of
men paid approximately between $2200 and $2900, whereas the lowest paying 25% of
women paid approximately between $1700 and $2200.
72% of the men pay between $3000 and $4500 per year, compared to only 25% of
women who pay within the same range. 28% of men pay between $2000 and $3000 per
year, while 57% of the women paid within the same range. While the lowest premium
for men was $2000, 19% of women paid premiums between only $1500 and $2000 per
year.
20
Assessment Sample #3: CCSF Project Report – Pre-Statistics course
Background: This is the first of two projects assigned in the pre-statistics course at
CCSF.
Project prompt:
Write a report that answers the following two questions:
Are the cereals marketed to children less healthy than the cereals marketed to
adults? Do cereals marketed to children appear to be deliberately located on grocery
store shelves to attract children’s attention?
Your report should be between 500 and 750 words. Your report should include at least
three graphs, one of which analyzes categorical information only. In your discussion of
whether child cereals are less healthy, you should analyze 2-3 ingredients.
Description of the Data Set:
Students analyze a spreadsheet with information about 77 breakfast cereals. Attributes
include the following:
•
•
•
•
•
•
•
Name of manufacturer (Quaker Oats, Kelloggs, etc.)
Target (adults or children)
Shelf (Location on grocery store shelf: bottom, middle, top)
Nutritional data (grams per serving unless stated otherwise): Calories,
Carbohydrates, Fat, Fiber, Potassium (milligrams per serving), Protein, Sodium
(mg per serving), Sugar, Vitamins ( % of RDA per serving)
Consumer Report Rating
Volume per Serving (cups per serving)
Weight per Serving (ounces per serving)
Sample of student work:
Breakfast of Champions? A Cereal Analysis
Cereals marketed to children are placed on grocery store shelves to attract
children’s attention. The middle shelf on the grocery store aisle would correspond to a
child’s gaze regardless if they were in the cart or walking down the grocery aisle.
21
Therefore, to attract a child’s attention, the middle shelf would be the most effective
merchandising location. In this data set, the results are striking (Figure 1).
Cereals.txt
Options
36%
64%
0%
21%
10%
69%
Target
child
adult
bottom
middle
Shelf
top
Circle Icon
Figure 1
64% of child cereals are merchandised on the middle shelf compared to only 10%
of adult cereals. Child cereals are 6.4 times more likely—almost 6 ½ times more likely-to be merchandised on the middle shelf. It is worth noting that 3 of the 5 “adult” cereals
on the middle shelf—Raisin Bran, Frosted Mini-Wheats, and Nut & Honey Crunch-would appeal to both child and adult palates. In stark contrast, the top shelf contains 0%
of the child cereals, while 69% of the adult cereals are merchandised on the top shelf,
which would be above a child’s eye level.
Cereals marketed to children have deliberate shelf placement and marketing
strategies. Are cereals marketed to children less healthy than those marketed to adults?
To answer this question, the data will be analyzed to compare sugar content, calories per
serving, and sodium content, since these are often attributes that contribute to obesity in
both children and adults. I would submit that child cereals and adult cereals are both
22
relatively similar with the only exception being the sugar content which would be higher
in child cereals and lower in adult cereals.
Consumers International, a global advocacy working to educate consumers
regarding marketing of unhealthy food to children, reports, “While breakfast cereals have
the potential to be a source of beneficial whole grains, there is increasing concern that the
high levels of sugar in some products take them out of the realm of cereal foods and into
the realm of cookies, candy, and desserts” (Lobstein). When Consumer Reports rated
cereals they found alarmingly high rates of sugar in children’s cereals: “There is at least
as much sugar in a serving of Kellog’s Honey Smacks and 10 other rated cereals as there
is in a glazed doughnut from Dunkin’ Donuts” (Consumer Reports). The data confirms
cereals with a target market of children have much more sugar per serving than adult
cereals (Figure 2).
Cereals.txt
Options
Target, ordered by Sugars
Box Plot of Sugars
4%
12%
4%
4%
12%
20%
32%
12%
14%
25%
10%
20%
12%
11
10%
6%
4%
child
adult
0
2
4
6
6
8
Sugars
10
12
14
16
Fuse Rectangular
Figure 2
The median sugar content for child cereals is 11 grams per serving, compared to
the median for adult cereals which is only 6 grams. It is worth noting that the child cereal
23
data is skewed to the left by a few lower sugar options—primarily Cheerios which has
only 1g of sugar per serving. The box plot indicates that 75% of child cereals have 815grams of sugar per serving, compared to adult cereals where only 25% have 8-14g of
sugar per serving. In contrast, 75% of adult cereals have 0-8g of sugar per serving, while
only 25% of child cereals have 0-8g of sugar per serving. 44% of child cereals have 1215g of sugar, compared to only 10% of adult cereals have 12-15g of sugar per serving.
Consumers International suggests that the sugar content of child cereals is also
related to the calories per serving: “For children especially, highly sweetened cereals can
add significantly to the daily calorie intake” (Lobstein). However, in this data set, child
and adult cereals don’t seem to differ that much when it comes to calories per serving
(Figure 3).
Cereals.txt
Options
0%
0%
4%
84%
12%
0%
0%
0%
6%
4%
13%
110
48%
17%
10%
2%
0%
Target, ordered by Calories
child
adult
40
60
80
100
105
120
140
160
180
200
Calories
Fuse Rectangular
Figure 3
24
The median calories per serving for child cereals is 110 compared to adult cereals
which have a median of 105 calories per serving. Furthermore, 100% of child cereals are
between 80-139 calories per serving compared to 79% of adult cereals in the same range.
Child cereals have a smaller spread with the calories per serving falling between 90-120
calories. The adults have a much wider spread, with the calories per serving ranging
between 50-160 calories.
Similar data patterns also exist in sodium content (Figure 4).
Cereals.txt
Options
4%
8%
4%
20%
20%
24%
8%
12%
19%
2%
4%
19%
180
17%
25%
8%
6%
Target, ordered by Sodium
child
adult
0
40
80
120
160
170
200
240
280
320
Sodium
Fuse Rectangular
Figure 4
The median milligrams of sodium per serving for child cereals is 180 mg
compared to the median for adult cereals which is 170mg. The data is also similarly
centered, with 84% of child cereals containing between 120-240mg per serving, and 61%
of adult cereals falling within that range. However, 19% of adult cereals contain 0-40mg
of sodium compared to only 4% of child cereals (and 8 adult cereals contain 0mg of
sodium per serving).
25
In conclusion, the data proves that cereals marketed to children are deliberately
placed on the middle shelf to correspond with a child’s eye level. However, when it
comes to nutritional value as measured by sugar, calories, and sodium content per
serving, the results indicate that child and adult cereals are very similar with the
exception being sugar content, which reflects that child cereals are heavily sweetened to
appeal to a child’s palate.
Works Cited
Consumer Reports. “Better Cereal Choices for Kids?” ConsumerReports.org, 2008.
Web. 18 March 2012. < http://www.consumerreports.org/health/healthyliving/diet-nutrition/healthy-foods/breakfast-cereals/overview/breakfast-cerealsov.htm>
Lobstein, Tim. “Cereal Offences: A Wake Up Call on the Marketing of Unhealthy Food
To Children.” Consumersinternational.org, 2008. Web. 18 March 2012.
< http://www.consumersinternational.org/media/540304/cereal_offences.pdf>
26
Frequently Asked Questions about Pre-Statistics Courses
Note: This document reflects information provided by the math faculty teams from the
16 community colleges that participated in the California Acceleration Project in the
academic years 2011-2012, 2012-2013.
How many colleges are offering a pre-statistics course?
- In the academic years 2011-2012 and 2012-2013, sixteen community colleges in
California had math teams who participated in the California Acceleration Project (CAP).
These colleges are offering between 2 and 28 sections of pre-statistics courses a year.
(In StatwayTM, a separate initiative lead by the Carnegie Foundation for the
Advancement of Teaching, there are 9 California community colleges and 5 CSUs
offering a statistics pathway.)
Will CSU and UC accept college-level statistics courses with pre-statistics as a
prerequisite?
Most colleges working with CAP have not made changes to the stated pre-requisite of
intermediate algebra on the course outline of record for their statistics courses. During
the pilot phase, these colleges have avoided the articulation issue by using existing
local mechanisms that allow students to challenge prerequisites if they have the
knowledge or ability to succeed in the course (see California Ed. Code § 55003, section
p, item 4) or by using the pre-statistics course as a multiple measure for placement as
mandated by section 55003(k). The CSU Chancellor’s Office and UCOP are aware of
this use of prerequisite challenges. This has allowed CAP to begin to gather data on
student performance and persistence.
Please see the separate “Articulation Issues” handout for more details.
How much algebra is in pre-statistics courses?
- Specific content varies from college to college, but all 16 colleges have “designed
backwards” from their statistics courses in order to prepare students for statistics. Some
colleges include more algebra than others. Typically, topics such as factoring
polynomials, simplifying and performing arithmetic with polynomials and rational
expressions, properties of logarithms and solving quadratic and exponential equations
are left out of pre-statistics courses.
What are the prerequisites for pre-statistics courses?
- Most pre-statistics colleges in the state require arithmetic or pre-algebra before
students take a pre-statistics course; a few colleges have no prerequisite.
Do pre-statistics students learn mathematical skills, literacy, and reasoning for
use in the modern world – or, as one department chair put it, “Do pre-statistics
students know that ½ = 50%?”
27
Yes. Instructors report that pre-statistics students understand and use mathematical
and quantitative reasoning – including fundamental knowledge about fractions,
decimals, percentages, linear (and in some cases non-linear) functions, and basic
statistical ideas – at a higher level than the typical algebra student. This has been
supported by student work collected across colleges on assignments designed to
promote quantitative literacy.
How many units and hours per week do students meet?
Varies by college with a range of 4-6 units, 4-8 hours/week.
Does pre-statistics require a computer lab?
14 of the 16 colleges offering a pre-statistics course meet 2-4 hours/week in a computer
lab. Some colleges are using software from Key Curriculum Press called Tinkerplots.
Others are using programs such as MiniTab, Statcato, and free online learning
materials provided by the Open Learning Initiative.
What does a typical day in a pre-statistics class look like?
Faculty report that their pre-statistics courses are “hands-on” Students spend the
majority of time working on challenging problems in groups, including in a computer lab
setting. Some class time is also devoted to individual data exploration with software.
Faculty also report that student investigations are interspersed with mini-lectures, the
facilitated sharing of student work or a group presentations.
What textbooks do pre-statistics courses use?
Some colleges use some version of a 200-page packet of activities developed at Los
Medanos College and a printable index for TinkerPlots. This dramatically reduces
student cost to only a few dollars. Other colleges use part of a statistics textbook along
with supplemental algebra materials or free open source software from the Open
Learning Initiative (Modules 1-6 of the Concepts of Statistics course.) Several colleges
have written activity packets to accompany the Concepts of Statistics course. A few
colleges are also piloting a pre-lease version of Mathematical Literacy for College
Students, a Pearson textbook by Kathy Almy and Heather Foes.
How can you teach arithmetic students and algebra students in the same class?
Pre-statistics courses focus predominantly on descriptive statistics concepts, of which
very few students are familiar. So there is a level playing field initially in the class. More
algebra intensive topics come later in the courses after the class has coalesced into a
productive learning environment, so students are able to support each other when
reviewing algebra topics. Throughout the courses, remediation is “just-in-time.”
How do you grade?
Instructors use homework, quizzes, projects and exams. In preparation for the critical
thinking and writing required in statistics, most assignments require writing, both short
response and longer essays in which students support a decision with analysis of data.
These are graded using rubrics. Most statistics classes require a research paper and/or
28
project presentations. Most pre-statistics instructors include one or both in their grading
schema.
Are students from pre-statistics courses successful in college-level statistics?
Yes. Students from pre-statistics courses complete college-level statistics courses at an
equal or higher rate compared to students who take college-level statistics after
completing traditional algebra sequences. At CCSF the first cohort of pre-stats
completers out-performed intermediate algebra completers in statistics courses offered
in 3 different departments.
How is the college-level statistics course affected when students coming from
traditional algebra preparation mix with students from pre-statistics?
All the colleges currently teaching a pre-statistics course have left their college-level
statistics course outline unchanged. In most pilots, students from the pre-statistics
course are not taking statistics with the pre-stats instructor. In colleges that offered the
pre-stats paired with statistics in a learning community, the instructors report raising the
level of the college-level course because of the more specific preparation pre-statistics
students received.
Do pre-statistics courses satisfy A.A. degree requirements?
Each community college is making this decision locally. Most colleges are not pushing
the issue, but rather allowing the completion of college-level statistics to satisfy the A.A.
degree requirements.
How do you learn how to teach this course?
Over the past 2 years, the California Acceleration Project has run a series of
professional development retreats with follow-up coaching. The pre-statistics courses
are locally-developed according to CAP’s design principles, but instructors are part of a
network that supports them in their piloting of the their course. CAP is funded by 3CSN,
Walter S. Johnson, the Career Ladders Project, and the Community College Research
Center.
29
Statistics'Pathways,'Articulation'Issues'and'Current'Policy'Work'
'
We#know#of#at#least#21#community#colleges#in#California#(nearly#20%#of#CA#CCs)#that#
have#implemented#localized#versions#of#a#shortened#Statistics#pathway#for#underB
prepared#students#who#are#in#nonBmath#intensive#majors.#For#most#colleges#(those#
not#involved#in#Statway),#this#pathway#consists#of#a#current#UCBCSU#articulated#
Statistics#course#plus#a#new#preBstatistics#developmental#math#course,#where#the#
latter#replaces#some#or#all#of#the#traditional#sequence#of#arithmetic,#preBalgebra#and#
algebra#courses#for#these#students.##
#
One#obstacle#to#this#innovation#and#other#alternative#math#pathway#work#is#the#
current#IGETC#Standard#for#Subject#Area#2A#[1012#IGETC#Standards,#p.16]#which#
states,##
#
The$Mathematical$Concepts$and$Quantitative$Reasoning$requirement$shall$be$fulfilled$by$
completion$of$a$one<term$course$in$mathematics$or$statistics$above$the$level$of$
intermediate$algebra,$with$a$stated$course$prerequisite$of$intermediate$algebra.$
#
The#CSU#Executive#Order#1065#has#a#similar#statement#about#intermediate#algebra:##
#
Courses$in$subarea$B4$shall$have$an$explicit$intermediate$algebra$prerequisite,$and$
students$shall$develop$skills$and$understanding$beyond$the$level$of$intermediate$
algebra.$Students$will$not$just$practice$computational$skills,$but$will$be$able$to$
explain$and$apply$basic$mathematical$concepts$and$will$be$able$to$solve$problems$
through$quantitative$reasoning.$
#
The#Policy#on#Course#Transferability/Transferable#Course#Agreement#(TCA)#
Guidelines#from#UCOP#[TCA#Guideline,#p.9]#is#less#rigid#in#its#statement#on#this#issue,#
allowing#“a#prerequisite#of#intermediate#algebra#or#its#equivalent”:##
#
Statistics/Probability$[TCA$Guidelines,$p.$9]$
At$minimum,$statistics$courses$must$have$a$prerequisite$of$intermediate$algebra$or$its$
equivalent…$
#
And#the#Transfer#Policy#described#in#the#Regulations#of#the#Academic#Senate,#
University#of#California,#is#mute#on#the#issue#of#prerequisites#for#transferable#college#
courses#in#Mathematical#Concepts#and#Quantitative#Reasoning#[Regulations#476#and#
478].#
#
How$have$colleges$navigated$these$policy$obstacles$in$order$to$offer$statistics$
pathways$without$endangering$articulation$of$their$statistics$courses?$$
#
Some#colleges#have#simply#utilized#existing#local#mechanisms#for#determining#
equivalency.#Currently,#it#is#common#practice#for#each#community#college#to#
establish#equivalency#to#intermediate#algebra#by#using#placement#tests#and#locally#
established#cut#scores,#by#deciding#whether#to#recognize#high#school#course#work,#
30
by#considering#multiple#measures,#and#by#developing#remedial#courses.#The#preB
stats#courses#were#reviewed#by#local#mathematics#faculty#and#curriculum#
committees#and#determined#to#be#equivalent#to#intermediate#algebra,#not#in#content#
but#according#to#locally#developed#criteria,#such#as#the#depth,#scope,#and#rigor#of#the#
learning#outcomes.#At#most#of#these#colleges,#the#preBrequisite#for#Statistics#remains#
intermediate#algebra,#but#the#Office#of#Admissions#and#Records#recognizes#that#
successful#completion#of#the#preBstats#course#as#“equivalent”#to#intermediate#
algebra#for#the#purpose#of#enrolling#in#Statistics.#At#all#of#these#colleges,#mechanisms#
are#in#place#to#make#sure#that#preBstats#completers#are#not#able#to#enroll#in#
transferable#math#courses#other#than#Statistics.#
#
Some#colleges#have#made#use#of#existing#local#mechanisms#for#challenging#preB
requisites.#The#California#Ed.#Code#makes#specific#provisions#for#students#to#be#able#
to#challenge#prerequisites#if#they#have#the#knowledge#or#ability#to#succeed#in#the#
course.##
#
§#55003.#Policies#for#Prerequisites,#Corequisites#and#Advisories#on#Recommended#
Preparation.##
(p)#Any#prerequisite#or#corequisite#may#be#challenged#by#a#student#on#one#or#more#of#
the#grounds#listed#below.#The#student#shall#bear#the#initial#burden#of#showing#that#
grounds#exist#for#the#challenge.#Challenges#shall#be#resolved#in#a#timely#manner#and,#if#
the#challenge#is#upheld,#the#student#shall#be#permitted#to#enroll#in#the#course#or#
program#in#question.#Grounds#for#challenge#are:#
…#
(4)#the#student#has#the#knowledge#or#ability#to#succeed#in#the#course#or#program#despite#
not#meeting#the#prerequisite#or#corequisite;#...#
Most#of#these#colleges#have#developed#streamlined#preBrequisite#challenge#
mechanisms#to#facilitate#the#process#by#which#preBstat#completers#qualify#for#
statistics.##
Other#colleges#have#used#successful#completion#of#a#preBstat#course#as#one#of#the#
multiple#measures#to#determine#placement#into#statistics.#This#practice#builds#on#
Title#5#mandates#for#the#use#of#multiple#measures#in#placement#that#are#described#in#
Section#55003(k)##
Section#55003(k)#Requirement#for#Multiple#Measures#in#Assessment#as#a#Prerequisite#
(k)#The#determination#of#whether#a#student#meets#a#prerequisite#shall#be#based#on#
successful#completion#of#an#appropriate#course#or#on#an#assessment#using#multiple#
measures,#as#required#by#section#55521(a)(3).#…#
#
#
31
My$department$or$college$has$a$content:based$definition$of$equivalency$or$is$not$
willing$to$use$multiple$measures$or$pre:requisite$challenge$processes$to$support$a$
statistics$pathway.$Is$it$possible$that$UC$and$CSU$will$change$the$pre:requisite$policy$
for$Statistics$and$other$quantitative$reasoning$courses$that$require$minimal$algebra$
skills?$$
$
A#change#in#policy#may#not#occur#in#the#immediate#future,#but#there#are#several#
important#developments#around$implementation#of#existing#policy#that#could#create#
a#space#for#colleges#to#experiment#with#a#statistics#pathway#without#endangering#
articulation#of#their#statistics#course.##
#
The#most#recent#agenda#(September#2012)#for#the#Intersegmental#Committee#of#
Academic#Senates#included#a#discussion#of#“possible#ICAS#Position#Paper#on#
prerequisites#(including#Algebra)#for#transferable#quantitative#courses#including#
Statistics.”##ICAS#oversees#policy#that#affects#IGETC#agreements.#ICAS#has#not#posted#
minutes#from#the#meeting,#but#a#letter#in#support#of#statistics#pathways,#signed#by#
faculty#from#10#community#college#districts,#was#sent#to#the#5#community#college#
representatives#on#ICAS#with#the#following#requests#for#action:##
#
• refrain from developing a content list definition of ‘equivalent to intermediate
algebra’ in order to maintain space for innovation in developing effective
alternative remedial math pathways;
• include the perspectives of community college math faculty developing
alternative math pathways;
• request a 3- to 5-year study of the impact alternative math pathways (including
Statistics pathways) on student outcomes and transfer-preparedness in which
participating community colleges are not in danger of losing articulation of their
quantitative courses (including general introductory Statistics);
• support a minor revision to the IGETC Standard for Subject Area 2A to include
the phrase “or equivalent.” We ask that implementation of this revised standard
respect the integrity of the local community college curriculum approval process
by acknowledging that the community college has purview in determining
“equivalency” to non-transferable developmental math courses.
#
An#upcoming#meeting#of#the#CSU#GE#Advisory#Committee#will#include#a#discussion#of#
statistics#pathways#with#consideration#of#a#variety#of#options#for#supporting#pilots#
without#endangering#CSU#GE#Breadth#articulation#of#statistics.#Early#discussions#
with#the#CSU#Chancellor’s#Office#suggest#that#options#may#include#a#variance#from#
existing#policy#for#colleges#currently#running#pilots#with#guidelines#for#study#of#
outcomes,#the#inclusion#of#“or#equivalent”#into#B4#requirements#with#community#
colleges#having#purview#in#determining#equivalency,#or#an#open#recognition#of#the#
preBrequisite#challenge#mechanisms#to#give#students#an#alternative#to#algebra.#
#
For#more#information#on#these#issues,#contact#Myra#Snell#at#
[email protected].#
32
#
What%do%instructors%teaching%a%pre1stats%course%have%to%say?%
Excerpts%from%a%recent%CAP%workshop%
!
What%I%learned%about%students:%%
!
“Students!are!smarter!than!what!we!give!them!credit!for.”!
!
“Students!will!rise!to!the!occasion!if!they!know!the!class!will!shoot!them!through!the!pipeline!more!
quickly:!they!will!take!on!an!increased!workload!and!they!will!tackle!concepts!difficult!for!them.”!
!
“Math!brings!out!a!lot!of!emotions!(mostly!negative)!from!students.!Those!emotions!often!interfere!
with!their!cognitive!skills!preventing!them!from!being!fully!engaged.!However,!once!they!have!
positive!feelings!about!math!and!are!challenged,!they!will!work!hard!to!meet!the!challenge.”!
!
“Many!students!are!afraid!of!failure,!and!students!I!had!thought!of,!previously,!as!irresponsible!are!
actually!avoiding!another!failure!by!not!showing!up!or!turning!things!in.”!!
!
“Students!are!interested!in!learning!the!‘understanding,’!not!just!the!‘how.’!I!get!lots!of!‘what!if’!
questions,!more!than!before.”!
!
“Students’!life!experiences!often!far!outweigh!their!math!skills.!Therefore,!they!often!have!much!
more!to!contribute!to!a!‘thinking’!curriculum!as!opposed!to!a!‘skillIbased’!curriculum.”!
!
What%I%learned%about%myself%as%a%teacher:%
!
“I!learned!that!I!love!working!with!colleagues!to!share!ideas!and!that!I’m!willing!to!work!much!longer!
because!of!the!energy!I!gain!from!learning!from!those!colleagues.”!
!
“I!love!teaching!this!class.!It!resonates!with!everything!I!want!out!of!teaching.”!
!
“I’m!still!a!student.”!
!
“What!I!learned!about!myself!as!a!teacher!is!that!the!less!teaching!I!do,!the!better.!!Students!seem!to!
gain!more!with!studentIcentered!classes.”!
!
“When!I!get!stuck!I!go!back!to!my!‘old!ways’!without!knowing!I’m!doing!it.”!
!
“I!unconsciously!and!unknowingly!‘teach’!in!ways!that!sometimes!exacerbate!rather!than!ameliorate!
‘affective!issues.’”!
!
What%I%am%worried%about%moving%forward%with%acceleration:%%
%
“Moving!forward!with!acceleration,!I’m!worried!about!the!speed!of!change!at!my!college.!I!feel!very!
passionate!about!this!program!and!this!way!of!teaching,!and!I!want!to!see!this!class!available!to!more!
students.!But!I’m!also!really!unable!to!do!much!to!make!change!happen.”!
!
“I!am!worried!that!students!will!continue!to!fall!behind!as!a!result!of!the!traditional!path.”!
!
What%excites%me%about%moving%forward%with%acceleration:%%
%
“I’m!excited!for!the!opportunity!for!students!to!succeed!that!might!not!have!otherwise.”!
!
“I!never!ever!want!to!introduce!a!topic!by!saying!‘I’m!sorry,!but!we!have!to!cover!this.!I!know!you!will!
never!use!it!again!once!you!leave!college,’!I!don’t!have!to,!when!I!teach!preIstatistics.”!!!
“I’m!excited!to!bring!the!course!to!campus!for!the!first!time!and!I’m!hopeful!it!will!become!a!common!
pathway!within!the!department!and!school.”!
!
“I’m!excited!to!help!the!future!teachers!of!accelerated!classes.!I!am!convinced!the!way!I!teach!is!
33
evolving!due!to!involvement!with!CAP.”!
AMATYC’s(Developmental(Math(Committee’s(Draft(Position(Statement(on(the(
Appropriate(Use(of(Intermediate(Algebra(as(a(Prerequisite(Course!!
(DRAFT)(
Whereas(!
•
The!prerequisites!of!a!mathematics!course!should!be!those!appropriate!to!
providing!a!foundation!for!student!success!in!that!course;!!
•
The!course!description!and!learning!outcomes!of!a!mathematics!course!
determine!the!prerequisite!level!of!mathematical!literacy,!skills,!and!knowledge!
necessary!for!successful!completion!of!the!course;!!
•
The!content!in!intermediate!algebra!courses!is!generally!required!to!master!the!
content!of!algebra<based!STEM!courses;!and,!!
•
The!content!in!intermediate!algebra!courses!is!not!required!to!master!the!
content!for!most!non<STEM!college<level!mathematics!courses.!!
Therefore,(it(is(the(position(of(AMATYC(that:(!
•
Intermediate!algebra!is!generally!an!appropriate!prerequisite!for!mathematics!
courses!in!a!STEM!path!leading!to!calculus;!and,!!
•
Survey!courses,!mathematical!modeling!courses,!mathematical!literacy!courses,!
statistics!courses!and!other!courses!not!leading!to!calculus!are!better!served!by!
more!appropriate!prerequisites!than!intermediate!algebra.!!
The!DRAFT!of!the!Intermediate!Algebra!Position!Statement!was!approved!by!the!
Developmental!Math!Committee!(DMC)!at!the!2012!AMATYC!conference.!The!position!
statement!will!be!sent!to!the!AMATYC!Board!for!preliminary!approval!and!then!an!Input!
Hearing!will!be!held!at!the!Anaheim!Conference!2013.!A!final!hearing!and!a!call!for!
Board!approval!will!be!held!at!the!Nashville!conference!2014!and!then!the!statement!is!
sent!to!the!Delegate!Assembly!for!final!approval!in!2014.!
https://sites.google.com/site/amatycdmc/position<statements!
!
34