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**Deborah Ball, Hyman Bass, MerrieBlunk, Katie Brach,**

Teacher Quality, Quality Teaching, and Student Outcomes: Measuring the Relationships Heather C. Hill Deborah Ball, Hyman Bass, MerrieBlunk, Katie Brach, CharalambosCharalambous, Carolyn Dean, Séan Delaney, Imani Masters Goffney, Jennifer Lewis, Geoffrey Phelps, Laurie Sleep, Mark Thames, Deborah Zopf

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**Measuring teachers and teaching**

Traditionally done at entry to profession (e.g., PRAXIS) and later ‘informally’ by principals Increasing push to measure teachers and teaching for specific purposes: Paying bonuses to high-performing teachers Letting go of under-performing (pre-tenure) teachers Identifying specific teachers for professional development Identifying instructional leaders, coaches, etc. Not going to give the long history of measuring teachers here, but….wanted to give a sense for history, what’s out there, and what’s coming down the pike. In Boston, 97% of teachers received highest rating.

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**Methods for identification**

Value-added scores Average of teachers’ students’ performance this year differenced from same group of students’ performance last year In a super-fancy statistical model Typically used for pay-for-performance schemes Problems Self-report / teacher-initiated Typically used for leadership positions, professional dev. However, poor correlation with mathematical knowledge R= 0.25

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**Identification: Alternative Methods**

Teacher characteristics NCLB’s definition of “highly qualified” More direct measures Educational production function literature Direct measures of instruction CLASS (UVA)—general pedagogy Danielson, Saphier, TFA—ditto But what about mathematics-specific practices?

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Purpose of talk To discuss two related efforts at measuring mathematics teachers and mathematics instruction To highlight the potential uses of these instruments Research Policy?

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Begin With Practice Clips from two lessons on the same content – subtracting integers What do you notice about the instruction in each mathematics classroom? How would you develop a rubric for capturing differences in the instruction? What kind of knowledge would a teacher need to deliver this instruction? How would you measure that knowledge? Middle school, southwestern district in US Want to show you these instruments because it’ll mimic our own process of developing this instrument

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**Bianca Teaching material for the first time (Connected Mathematics)**

Began day by solving 5-7 with chips Red chips are a negative unit; blue chips are positive Now moved to 5 – (-7) Set up problem, asked students to used chips Given student work time

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**Question What seems mathematically salient about this instruction?**

What mathematical knowledge is needed to support this instruction?

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**Mercedes Early in teaching career**

Also working on integer subtraction with chips from CMP Mercedes started this lesson previous day, returns to it again

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**Find the missing part for this chip problem**

Find the missing part for this chip problem. What would be a number sentence for this problem? Start With Rule End With Add 5 Subtract 3

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**Questions What seems salient about this instruction?**

What mathematical knowledge is needed to support this instruction?

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**What is the same about the instruction?**

Both teachers can correctly solve the problems with chips Both teachers have well-controlled classrooms Both teachers ask students to think about problem and try to solve it for themselves

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What is different? Mathematical knowledge Instruction

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Observing practice… Led to the genesis of “mathematical knowledge for teaching” Led to “mathematical quality of instruction”

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**Mathematical Knowledge for Teaching**

Source: Ball, Thames & Phelps, JTE 2008

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MKT Items created an item bank of for K-8 mathematics in specific areas (see (Thanks NSF) About 300 items Items mainly capture subject matter knowledge side of the egg Provide items to field to measure professional growth of teachers NOT for hiring, merit pay, etc.

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MKT Findings Cognitive validation, face validity, content validity Have successfully shown growth as a result of prof’l development Connections to student achievement - SII Questionnaire consisting of 30 items (scale reliability .88) Model: Student Terra Nova gains predicted by: Student descriptors (family SES, absence rate) Teacher characteristics (math methods/content, content knowledge) Teacher MKT significant Small effect (< 1/10 standard deviation): weeks of instruction But student SES is also about the same size effect on achievement (Hill, Rowan, and Ball, AERJ, 2005) What’s connection to mathematical quality of instruction??

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**History of Mathematical Quality of Instruction (MQI)**

Originally designed to validate our mathematical knowledge for teaching (MKT) assessments Initial focus: How is teachers’ mathematical knowledge visible in classroom instruction? Transitioning to: What constitutes quality in mathematics instruction? Disciplinary focus Two-year initial development cycle ( ) Two versions since then

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**MQI: Sample Domains and Codes**

Richness of the mathematics e.g., Presence of multiple (linked) representations, explanation, justification, multiple solution methods Mathematical errors or imprecisions e.g., Computational, misstatement of mathematical ideas, lack of clarity Responding to students e.g., Able to understand unusual student-generated solution methods; noting and building upon students’ mathematical contributions Cognitive level of student work Mode of instruction

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**Initial study: Elementary validation**

Questions: Do higher MKT scores correspond with higher-quality mathematics in instruction? NOT about “reform” vs. “traditional” instruction Instead, interested in the mathematics that appears

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**Method 10 K-6 teachers took our MKT survey**

Videotaped 9 lessons per teacher 3 lessons each in May, October, May Associated post-lesson interviews, clinical interviews, general interviews

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**Elementary validation study**

Coded tapes blind to teacher MKT score Coded at each code Every 5 minutes Two coders per tape Also generated an “overall” code for each lesson – low, medium, high knowledge use in teaching Also ranked teachers prior to uncovering MKT scores

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**Projected Versus Actual Rankings of Teachers**

Projected ranking of teachers: Actual ranking of teachers (using MKT scores): Correlation of .79 (p < .01) Hill, H.C. et al., (2008) Cognition and Instruction

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**Correlations of Video Code Constructs to Teacher Survey Scores**

Construct (Scale) Correlation to MKT scores Responds to students 0.65* Errors total -0.83* Richness of mathematics 0.53 One of the next steps was to correlate the video code scale scores (what Heather earlier referred to as constructs) to teachers’ multiple choice measure scores. Here I’ve listed some of the scales you’ve heard mentioned along with their correlations to the measure scores. Although only one scale listed here is significantly related to the measure scores, all of these correlations are pretty big on the grand scale of educational measurement. All our other scales are of similar magnitude and are described further in my paper. Again, these correlations suggest that the survey measures and the video codes are both assessing mathematical knowledge for teaching. *significant at the .05 level

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**Validation Study II: Middle School**

Recruited 4 schools by value-added scores High (2), Medium, Low Recruited every math teacher in the school All but two participated for a total of 24 Data collection Student scores (“value-added”) Teacher MKT/survey Interviews Six classroom observations Four required to generalize MQI; used 6 to be sure

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**Validation study II: Coding**

Revised instrument contained many of same constructs Rich mathematics Errors Responding to students Lesson-based guess at MKT for each lesson (averaged) Overall MQI for each lesson (averaged to teacher) G-study reliability: 0.90

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**Validation Study II: Value-added scores**

All district middle school teachers (n=222) used model with random teacher effects, no school effects Thus teachers are normed vis-à-vis performance of the average student in the district Scores analogous to ranks Ran additional models; similar results* Our study teachers’ value-added scores extracted from this larger dataset

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**Results MKT MQI Lesson-based MKT Value-added score* 1.0 0.53** 0.72****

0.41* 0.85** 0.45* 0.66** Value added score Significant at p<.05 Significant at p<.01 Source: Hill, H.C., Umland, K. &Kapitula, L. (in progress) Validating Value-Added Scores: A Comparison with Characteristics of Instruction. Harvard GSE: Authors.

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**Additional Value-Added Notes**

Value-added and average of: Connecting classroom work to math: 0.23 Student cognitive demand: 0.20 Errors and mathematical imprecision: -0.70** Richness: 0.37* **As you add covariates to the model, most associations decrease Probably result of nesting of teachers within schools Our results show a very large amount of “error” in value-added scores

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**Lesson-based MKT vs. VAM score**

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**Proposed Uses of Instrument**

Research Determine which factors associate with student outcomes Correlate with other instruments (PRAXIS, Danielson) Instrument included as part of the National Center for Teacher Effectiveness, Math Solutions DRK-12 and Gates value-added studies (3) Practice?? Pre-tenure reviews, rewards Putting best teachers in front of most at-risk kids Self or peer observation, professional development

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**Problems Instrument still under construction and not finalized**

G-study with master coders indicates we could agree more among ourselves Training only done twice, with excellent/needs work results Even with strong correlations, significant amount of “error” Standards required for any non-research use are high KEY: Not yet a teacher evaluation tool

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**Next Constructing grade 4-5 student assessment to go with MKT items**

Keep an eye on use and its complications Questions?

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