EQUITY AND ACCESS TO HIGH-QUALITY
INSTRUCTION IN MIDDLE SCHOOL
MATHEMATICS
(A SGER PROJECT)
KARA JACKSON
VANDERBILT UNIVERSITY
NSF DR-K12 PI CONFERENCE, NOVEMBER
2009
GOAL OF THE TALK
• Report findings regarding related aspects of
institutional settings that support equitable
opportunities to learn in middle-grades
mathematics classrooms
– Category systems
– Shared vision of high-quality mathematics
instruction
– Teachers’ access to expertise
– Accountability relations between Principal and
Teachers
CONJECTURED INSTITUTIONAL SUPPORTS FOR
TEACHERS’ DEVELOPMENT OF EQUITABLE FORMS OF
AMBITIOUS INSTRUCTIONAL PRACTICES
• Access to rigorous mathematics
curriculum
– (e.g., Schoenfeld, 2002)
• Provision of high-quality professional
development focused on equity-specific
instructional practices in mathematics
CONJECTURED INSTITUTIONAL SUPPORTS FOR
TEACHERS’ DEVELOPMENT OF EQUITABLE FORMS OF
AMBITIOUS INSTRUCTIONAL PRACTICES
• Un-tracked instructional program
– (e.g., Boaler, 1997; Gamoran, Nystrand, Berends,
& LePore, 1997; Oakes, 1985)
• Positive category systems for describing
students in relation to views of mathematics
– (e.g., Horn, 2007; Jackson, 2009; Martin, 2000;
Moschkovich, 2007)
WHAT DO WE MEAN BY CATEGORIES?
• Distinguish types of phenomena, objects, and people
• Categories render some aspects as visible and some as
invisible (Bowker & Star, 1999)
• Formal (e.g., NCLB categories, academic tracks) and informal
(e.g., “smart”); circulate locally and more widely
• Always an empirical question as to what people mean by the
categories they use
• “Frames problems of practice” (Horn, 2007)
WHAT DO WE MEAN BY CATEGORY SYSTEMS?
• Shared by majority of participants in a
community
• Emergent phenomena
• Category systems are
naturalized/normalized over time
(Bowker & Star, 1999; Foucault,
1995/1977)
WHAT DO WE MEAN BY “POSITIVE”
CATEGORY SYSTEMS?
• Teachers did not tend to describe students as
having innate or fixed abilities or characteristics
• When teachers described groups of students, they
tended to describe the instructional actions they
took to support the groups of students
• Mathematics teachers tended to frame student
motivation as a relation between the individual
student and classroom instruction
ANALYSIS
• Cross-case analysis of 2 schools in the
same district (A) that have “positive”
category systems and sophisticated
visions of HQMI
– One school (A4) had notably better
opportunities to learn and student valueadded achievement results for subpopulations than the other school (A5)
FOCUS OF ANALYSIS
• Explain why a positive category system
was “productive” in A4 and not in A5
through an analysis of 3 related aspects
of the institutional setting
• Quality of professional development
• Teachers’ access to expertise
• Accountability relations between instructional
leaders and teachers
PRE- CASE SELECTION
• Coded Round 1 District A interview data for the
following:
– Categories participants used to describe groups of students
and the characteristics they ascribed to those categories
– Pedagogical actions teachers described taking to meet the
perceived needs of different groups
– Instructional leaders’ instructional expectations, particularly
for differentiation
– Extent to which participants took responsibility for student
learning
– Supports specific to issues of equity (e.g., ELLs)
– Stances toward curriculum and mathematics
CRITERIA FOR CASE SELECTION
• Schools in District A with more than 1
participating teacher (n = 8)
• Majority of teachers in a school expressed
positive categories the majority of the time
• Majority of teachers had sophisticated visions
of high-quality mathematics instruction
SELECTED A4 & A5
SIMILARITIES BETWEEN A4 & A5
• Positive category system
• Teachers’ visions of high-quality mathematics
instruction
• PreK-8 Schools, large % of economically
disadvantaged students
• Size of schools, 3 middle-grades math teachers
• Did not track in 6th or 7th grade
• Offered one advanced course in 8th grade
(Algebra)
• Used Connected Mathematics Program
DIFFERENCES
A4
A5
PREDOMINANTLY LATINO POPULATION
PREDOMINANTLY AFRICAN AMERICAN
POPULATION
46% of STUDENTS ARE ELLs,
SINGLE LANGUAGE
30% of STUDENTS ARE ELLs,
MULTIPLE LANGUAGES
EVERY STUDENT TAKES 1 MATH CLASS
EVERY STUDENT TAKES 2 MATH CLASSES
PRINICPAL’S VISION OF HQMI IS CONTENTFREE
PRINCIPALS’ VISION OF HQMI IS
SOPHISTICATED
RECONSTITUTED IN 2007
DIFFERENCES:
OPPORTUNITIES TO LEARN
Task Potential
Mean
1 or 2 (-)
3 or 4 (+)
Median
A4
(n = 3)
A5
*Deleted one
teacher b/c no
discussions
(n=2)
Task Implementation
Mean
1 or 2 (-)
3 or 4 (+)
Median
+
3.5
+
3
+
3.5
+
3
Discussion
Mean
1 or 2 (-)
3 or 4 (+)
Median
+
3
2
ANALYSIS OF ADDITIONAL ASPECTS OF THE
INSTITUTIONAL SETTING
Quality of Professional Teachers’ Access to
Development Specific Expertise Specific to
to Equity
Equity
Accountability Relations
between Ts and P
A4
Ongoing support of the No time to meet
ELL Dept.
Ts and P turn to one of
2 Ts in Designing Group the teachers (Mr. C),
Work
whose vision is most
sophisticated
Culturally Responsive
training (one-off)
Principal communicated
instructional expectations
particular to supporting all
students’ learning
A5
Highly-mobile
population (one-off)
Principal did not
communicate instructional
expectations particular to
supporting all students’
learning
2 Math Consultants, but
not focused on
supporting teacher
learning
One isolated T
COMMUNICATION OF INSTRUCTIONAL
EXPECTATIONS AT A4
Well basically it starts with the lesson plan of expecting that I’m going to look at
my student’s test data, get to know my students well just within the classroom of
being able to have more individual idea about what’s going on with each student
and plan a good lesson that takes into account where each students is at and
what they need. There’s the expectation that as I’m planning that lesson that I’m
thinking about what activities am I going to do, how is that going to motivate the
students, how is it going to teach the standards are the expected to be taught.
How am I going to [get] students actively involved in that lesson? It’s basically
looking at all those good quality teaching things and thinking about how is that
going to play out within that lesson and then within the classroom the
expectation is that while I’m delivering that lesson that I am differentiating from
my students. That I have some way of being able to figure out at the end of the
lesson did they get it? What do I need to do tomorrow? What happened that I
didn’t expect and what am I going to do to able to deal with that? You know did it
go better than I thought and I need to move on? Did it not go so well and I need
to bring something else in and present it a different way? He’s expecting me to be
reflective about that.
COMMUNICATION OF INSTRUCTIONAL
EXPECTATIONS AT A5
T: He expects us to run a classroom and to operate in the
building. He’s very clear on that and that, that has, that has
been great.
I: And what does he say?
T: It’s just making sure that … as far as clear expectations, the
kids …should expect to know what…work is to be completed,
how it’s to be completed, when it’s to be completed by….[H]e
expects us to deliver lessons as far as inquiring, questioning
and those kind of things, …behavior management, you know,
are we going to run morning meetings, is that part of our
management plan, are we gonna use infractions and referrals
and, so those expectations have been set up, but he, we,
there hasn’t really been conversations about what he
expects…teaching just math.
IMPLICATIONS
• Importance of principal communicating clear
instructional expectations regarding how to
support all students’ learning (but is that
enough?)
• Nature of the instructional expectations that
the principal needs to communicate is related
to the nature of teachers’ expertise (and
access to expertise)
SUMMARY
• Category systems and sophisticated visions of
HQMI might be necessary but are not
sufficient for increasing opportunities to learn
(and hence, student achievement) for lowperforming groups of students.
– I.e., high expectations/beliefs that all students can
learn + sophisticated visions of HQMI are not
enough
SGER TEAM
Vanderbilt University
 Kara Jackson, PI
 Paul Cobb, Co-PI
 Richard Milner & Robert Jiménez, Senior Researchers
 Glenn Colby, Annie Garrison, Lynsey Gibbons, Jonee
Wilson, Graduate Assistants
Collaborators from Other Universities
 Melissa Boston (Duquesne University)
 Lindsay Clare Matsumura (University of Pittsburgh)
STUDENTS AS INNATELY ONE WAY OR ANOTHER
Because I figure, you know the good, the kids
who want to learn are going to learn and the
smart kids will always be smart. It’s the
bottom dwellers that you want to see how
they handle the instruction of that particular
teacher.
SUPPORTING STRUGGLING STUDENTS
[W]henever I can, like I’ll take some of the kids that are
not at grade level and I’ll pre-teach them something
that when they get into those groups they have
something that the other kids don’t know. So it raises
their status. Like I had a whole group of kids that were
like, like if they were doing 3 times 1 ½ or something,
they were multiplying the numerator and the
denominator by 3. And so, taking those kids and
teaching them how you can write whole number as a
fraction but putting something real simple and then
they went back and they felt great cause they shared
that with their whole group.
MOTIVATION AS A RELATIONSHIP
All of my students are motivated at different
times. I think all of them want to
learn…they’re motivated by different things.
Every single one of those kids at some point
has shown me that they want to learn and has
put effort at some point in that class. So I
have to believe that all of them want to learn
within that classroom.