EQUITY AND ACCESS TO HIGH-QUALITY INSTRUCTION IN MIDDLE SCHOOL

MATHEMATICS(A SGER PROJECT)

KARA JACKSONVANDERBILT 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 value-added achievement results for sub-populations 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 A5PREDOMINANTLY 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 CONTENT-FREE

PRINCIPALS’ VISION OF HQMI IS SOPHISTICATED

RECONSTITUTED IN 2007

DIFFERENCES:OPPORTUNITIES TO LEARN

Task Potential

Mean1 or 2 (-)3 or 4 (+)Median

Task Implementation

Mean1 or 2 (-)3 or 4 (+)Median

Discussion

Mean1 or 2 (-)3 or 4 (+)Median

A4(n = 3)

+3.5

+3.5

+3

A5*Deleted one teacher b/c no discussions (n=2)

+3

+3

-2

ANALYSIS OF ADDITIONAL ASPECTS OF THE INSTITUTIONAL SETTING

Quality of Professional Development Specific to Equity

Teachers’ Access to Expertise Specific to Equity

Accountability Relations between Ts and P

A4 Ongoing support of the ELL Dept.

2 Ts in Designing Group Work

Culturally Responsive training (one-off)

No time to meet

Ts and P turn to one of the teachers (Mr. C), whose vision is most sophisticated

Principal communicated instructional expectations particular to supporting all students’ learning

A5 Highly-mobile population (one-off)

2 Math Consultants, but not focused on supporting teacher learning

One isolated T

Principal did not communicate instructional expectations particular to supporting all students’ learning

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 low-performing groups of students.– I.e., high expectations/beliefs that all students can

learn + sophisticated visions of HQMI are not enough

SGER TEAMVanderbilt UniversityKara Jackson, PIPaul Cobb, Co-PIRichard Milner & Robert Jiménez, Senior ResearchersGlenn Colby, Annie Garrison, Lynsey Gibbons, Jonee

Wilson, Graduate Assistants

Collaborators from Other UniversitiesMelissa 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.