supp.apa.orgsupp.apa.org/.../supplemental/a0035073/DEV_Robinson_… · Web view... Third Grade....

Math gender gaps and teacher ratings

Supplemental Online MaterialsList of Figures and Tables

TablesTable 1. Means and SDs, overall and by genderTable 2. CorrelationsTable 3. IV instrument validity informationTable 4. Study 2A resultsTable 5. Study 2B results

FiguresFigure 1. Study 1 Math Teacher Ratings FigureFigure 2. Study 1 Reading Teacher Ratings FigureFigure 3. Conceptual Design Analyses in Study 2Figure 4. Four Fixed Effects Mediation Figures (with the Non-matched Samples)Figure 5. Four Fixed Effects Mediation Figures (with the Matched Samples)

Supplemental TablesTable S1. ECLS-K teacher questionnaire for mathematics proficiency scales – KindergartenTable S2. ECLS-K teacher questionnaire for mathematics proficiency scales – First GradeTable S3. ECLS-K teacher questionnaire for mathematics proficiency scales – Third GradeTable S4. ECLS-K teacher questionnaire for mathematics proficiency scales – Fifth GradeTable S5. Study 1 Regressions – Spring KTable S6. Study 1 Regressions – First GradeTable S7. Study 1 Regressions – Third GradeTable S8. Study 1 Regressions – Fifth GradeTable S9. Study 2A Regressions – K-1 No Fixed EffectsTable S10. Study 2A Regressions – K-1 Fixed EffectsTable S11. Study 2A Regressions – 1-3 No Fixed EffectsTable S12. Study 2A Regressions – 1-3 Fixed EffectsTable S13. Study 2B Regressions – K-1 No Fixed EffectsTable S14. Study 2B Regressions – K-1 Fixed EffectsTable S15. Study 2B Regressions – 1-3 No Fixed EffectsTable S16. Study 2B Regressions – 1-3 Fixed EffectsTable S17. Balance Before and After Propensity-Score Matching K-1 Study 2A RegressionsTable S18. Balance Before and After Propensity-Score Matching 1-3 Study 2A RegressionsTable S19. Balance Before and After Propensity-Score Matching K-1 Study 2B RegressionsTable S20. Balance Before and After Propensity-Score Matching 1-3 Study 2B RegressionsTable S21. Study 2A Regressions – K-1 Propensity Score MatchingTable S22. Study 2A Regressions – 1-3 Propensity Score MatchingTable S23. Study 2B Regressions – K-1 Propensity Score MatchingTable S24. Study 2B Regressions – 1-3 Propensity Score Matching

Supplemental FiguresFigure S1. Four Fixed Effects Mediation Figures (with the Non-matched Samples)Figure S1. Four No Fixed Effects Mediation Figures (with the Non-matched Samples)

1


Instructions to teachers for completing mathematics proficiency scales (on Tables S1-S4).

Please rate this child’s skills, knowledge, and behaviors in mathematics based on your experience with the child identified on the cover of this questionnaire. This is NOT a test and should not be administered directly to the child. Each question includes examples that are meant to help you think of the range of situations in which the child may demonstrate similar skills and behaviors. The examples do not exhaust all the ways that a child may demonstrate what he/she knows or can do. The examples do, however, indicate the level of proficiency a child should have reached in order to receive the highest rating. Some of these examples describe a very high level of performance (beyond typical standards) in order to be able to evaluate achievement levels of even the high performing students.

The following five-point scale is used for each of the questions. It reflects the degree to which a child has acquired and demonstrates the targeted skills, knowledge, and behaviors.

1 = Not yet Child has not yet demonstrated skill, knowledge, or behavior.

2 = Beginning Child is just beginning to demonstrate skill, knowledge, or behavior but does so very inconsistently.

3 = In progress Child demonstrates skill, knowledge, or behavior with some regularity but varies in level of competence.

4 = Intermediate Child demonstrates skill, knowledge, or behavior with increasing regularity and average competence but is not completely proficient.

5 = Proficient Child demonstrates skill, knowledge, or behavior competently and consistently.

N/A

= Not Applicable

Skill, knowledge, or behavior has not been introduced in classroom setting.

Rate only the child’s current achievement. Please use the full range of ratings. If the skill, knowledge, or behavior has been introduced in the classroom, please rate the child using the numbers 1-5. Circle “NA” only if the skill, knowledge, or behavior has not been introduced in your classroom setting.

2


Table S1Kindergarten teacher questionnaire items

THIS CHILD . . . CIRCLE ONE FOR EACH ITEM

Not YetBeginnin

gIn

ProgressIntermediat

eProficien

t

Not Applicabl

e 1. Sorts, classifies, and compares

mathematics materials by various rules and attributes—for example creating a rule for sorting keys, such as “keys with numbers” in one pile and “keys without numbers” in another pile, or sorting shapes by several attributes such as “large plastic shapes” and “small wooden shapes.” 1 2 3 4 5 N/A

2. Orders a group of objects—for example, by ordering rods or sticks by length, or arranging paints from lightest to darkest, or musical instruments from softest to loudest. 1 2 3 4 5 N/A

3. Shows an understanding of the relationship between quantities—for example, knowing that a group of ten small stones is the same quantity as a group of ten larger blocks. 1 2 3 4 5 N/A

4. Solves problems involving numbers using concrete objects—for example “Vera has six blocks, George has three, how many blocks are there in all?” or “How many do I need to give George so he will have the same number of blocks as Vera?” 1 2 3 4 5 N/A

5. Demonstrates an understanding of graphing activities—for example, by looking at a picture graph on favorite ice-cream flavors and knowing which flavor is the most popular and which one is the least. 1 2 3 4 5 N/A

6. Uses instruments accurately for measuring—for example, by using a balance scale to compare the weight of two objects, or using tablespoons and teaspoons during a cooking project, or using a measuring tape to measure the length of different objects. 1 2 3 4 5 N/A

7. Uses a variety of strategies to solve mathematics problems—for example, using manipulative materials, looking for a pattern, or acting out a problem. 1 2 3 4 5 N/A

3


Table S2First-grade teacher questionnaire items


Not YetBeginnin

gIn

Progress Intermediate ProficientNot

Applicable 1. Demonstrates an understanding of

place value—for example, by explaining that fourteen is ten plus four, or using two stacks of ten and five single cubes to represent the number 25. 1 2 3 4 5 N/A

2. Models, reads, writes, and compares whole numbers—for example, recognizing that 30 is the same quantity if it is 30 rabbits or 30 tallies or 15 + 15 red dots, or describing that the number 25 is smaller than 41. 1 2 3 4 5 N/A

3. Counts change with two different types of coins—for example, two quarters and a nickel, or three dimes and two pennies. 1 2 3 4 5 N/A

4. Surveys, collects, and organizes data into simple graphs—for example, making tally marks to represent the number of children who want to play jump rope at recess, or making a picture, bar, line, or circle graph to show the different kinds of fruit children bring to school and the quantity of each type. 1 2 3 4 5 N/A

5. Makes reasonable estimates of quantities—for example, looking at a group of objects and deciding if it is more than 10, about 50, or less than 100. 1 2 3 4 5 N/A

6. Measures to the nearest whole number using common instruments—for example, rulers, or tape measures, or thermometers, or scales. 1 2 3 4 5 N/A

7. Uses a variety of strategies to solve mathematics problems—for example, using manipulative materials, using trial and error, making an organized list or table, drawing a diagram, looking for a pattern, acting out a problem, or talking with others. 1 2 3 4 5 N/A

4


Table S3Third-grade teacher questionnaire items


Not YetBeginnin

gIn


Applicable1. Creates and extends patterns – for

example, extends an alternating pattern involving addition and subtraction (+3, -1, +3, -1, +3… or +5, -3, +5, -3,…) or creates a complex visual pattern (aabc). 1 2 3 4 5 N/A

2. Uses a variety of strategies to solve math problems – for example, adds 100 and then subtracts 4 when doing the mental math problem 467+96, or writes the algorithms or equations needed to solve a word problem, or orders steps sequentially in a multistep problem. 1 2 3 4 5 N/A

3. Recognizes properties of shapes and relationships among shapes – for example, recognizes that rectangles are composed of two right triangles, or demonstrates congruence by copying the exact size and shape of a pentagon onto a geoboard. 1 2 3 4 5 N/A

4. Uses measuring tools accurately – for example, measures with rulers to the quarter-inch, or measures liquids to the nearest milliliter. 1 2 3 4 5 N/A

5. Shows understanding of place value with whole numbers – for example, correctly orders the numbers 19,321, 14,999, 9,900, and 20,101 from least to greatest, or correctly regroups when adding and subtracting. 1 2 3 4 5 N/A

6. Makes reasonable estimates of quantities and checks answers – for example, estimates the cost of a list of 8 different items and compares to actual cost, or estimates the perimeter of a bulletin board and then checks with a yardstick. 1 2 3 4 5 N/A

7. Surveys, collects, and organizes data into simple graphs – for example, charts temperature changes over time, or makes a bar or line graph comparing the population in different cities of their state, or interprets a pictograph in which each symbol represents 5 people. 1 2 3 4 5 N/A

8. Models, reads, writes, and compares fractions – for example, shows that 1/2 of the candy bar is 1/4 + 1/4, or shows that 1/4 of a set of 12 is 3. 1 2 3 4 5 N/A

9. Divides a 3 digit number by a 1 digit number – for example, 348÷4 or 228÷6. 1 2 3 4 5 N/A

5


Table S4Fifth-grade teacher questionnaire items


Not YetBeginnin

gIn


Applicable 1. Subtracts numbers that require

regrouping, for example, 1300 – 579, or 2302 – 947, or 2603 – 1594. 1 2 3 4 5 N/A

2. Reduces fractions to lowest denominator, for example, reduces 27/63 to 3/7, or 41/6 to 6 5/6. 1 2 3 4 5 N/A

3. Demonstrates money management skills, for example, computes savings on a 20% off sale, balances a classroom savings account, or determines profit earned on candy bar sales. 1 2 3 4 5 N/A

4. Recognizes properties of shapes such as area, perimeter, and volume, for example, accurately estimates the capacity and volume of a tub or sink, or computes the area of an irregular polygon. 1 2 3 4 5 N/A

5. Uses measuring tools accurately, for example, measures with rulers to the 1/8 inch or metric sticks to the nearest millimeter, or uses tiles to measure area and cubes to measure volume. 1 2 3 4 5 N/A

6. Shows understanding of place value, for example, compares decimals to the thousandths place (1.04 > 1.009). 1 2 3 4 5 N/A

7. Makes reasonable estimates of quantities and checks answers, for example, estimates the product in a problem such as $19.95 x .75 by mentally multiplying 20 x .8 = 16. 1 2 3 4 5 N/A

8. Uses strategies to multiply and divide, for example, estimates a product or quotient and then uses the calculator to check the estimate, or divides by 4 to determine 25% of 32. 1 2 3 4 5 N/A

9. Divides multi-digit problems with remainders in the quotient, for example, computes 536 ÷ 30, or 6,135 ÷ 7. 1 2 3 4 5 N/A

10. Demonstrates algebraic thinking, for example, solves for an unknown in an equation such as 16 x A = 48; or expresses a function as a general rule that enables them to determine any term in the sequence. 1 2 3 4 5 N/A

6


Table S5Study 1: Spring Kindergarten Regression Results

Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7Female 0.12*** 0.14*** 0.12*** 0.10*** -0.02 -0.02 -0.01

(0.02) (0.02) (0.01) (0.01) (0.01) (0.01) (0.01)Race = Black or African American, Non-Hispanic -0.24*** -0.07* -0.06 -0.05 -0.04 -0.02

(0.05) (0.04) (0.04) (0.03) (0.03) (0.03)Race = Hispanic (Race specified) -0.20*** -0.05 -0.05 -0.07* -0.05 -0.04

(0.04) (0.04) (0.04) (0.03) (0.03) (0.03)Race = Hispanic (Race not specified) -0.32*** -0.10* -0.10* -0.13*** -0.11** -0.09**

(0.06) (0.04) (0.04) (0.04) (0.04) (0.03)Race = Asian 0.08 0.08 0.07 -0.01 0.00 0.00

(0.06) (0.05) (0.05) (0.04) (0.04) (0.04)Race = Native Hawaiian, Other Pacific Islander -0.04 -0.02 -0.01 -0.11 -0.13* -0.12

(0.12) (0.08) (0.08) (0.06) (0.06) (0.06)Race = American Indian or Alaska Native -0.28* -0.07 -0.08 -0.10 -0.07 -0.06

(0.11) (0.09) (0.09) (0.07) (0.07) (0.07)Race = More than one race, Non-Hispanic -0.13* -0.02 -0.02 -0.03 -0.03 -0.01

(0.06) (0.05) (0.05) (0.04) (0.04) (0.04)

SES composite 0.28**

* 0.09**

* 0.09**

* 0.06**

* 0.03** 0.03*(0.02) (0.01) (0.01) (0.01) (0.01) (0.01)

Age at Spring K 0.08 0.08 0.07 0.04 0.03 0.01(0.05) (0.05) (0.04) (0.04) (0.04) (0.04)

Age at Fall K -0.05 -0.07 -0.07 -0.05 -0.03 -0.01(0.05) (0.05) (0.04) (0.04) (0.04) (0.04)

Fall K Math Test Score 0.58**

* 0.58**

* 0.36**

* 0.29**

* 0.17**

*(0.01) (0.01) (0.01) (0.01) (0.01)

7


Spring K Externalizing Behaviors -0.07*** 0.15*** 0.13*** 0.12***(0.02) (0.02) (0.02) (0.02)

Fall K Externalizing Behaviors 0.00 0.11*** 0.07*** 0.07***(0.02) (0.02) (0.02) (0.02)

Spring K Approaches to Learning 0.54*** 0.52*** 0.48***(0.02) (0.02) (0.02)

Fall K Approaches to Learning 0.17*** 0.03 0.02(0.02) (0.02) (0.02)

Fall K Teacher Rating of Math 0.27*** 0.25***(0.02) (0.02)

Spring K Math Test Score 0.18***(0.01)

Constant -0.06*** -2.78*** -0.73* -0.58 -2.70*** -1.86*** -1.61***(0.01) (0.39) (0.33) (0.32) (0.30) (0.29) (0.27)

R-squared 0.42 0.48 0.70 0.70 0.77 0.79 0.80N 9223 9223 9223 9223 9223 9223 9223

Note: * p<0.05, ** p<0.01, *** p<0.001

8


Table S6. Spring First Grade Study 1 Regressions

Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7Female 0.00 0.02 0.01 -0.03 -0.13*** -0.13*** -0.10***

(0.03) (0.03) (0.02) (0.02) (0.02) (0.02) (0.02)Race = Black or African American, Non-Hispanic -0.41*** -0.16** -0.12* -0.10* -0.09* -0.07

(0.08) (0.05) (0.05) (0.05) (0.04) (0.04)Race = Hispanic (Race specified) -0.09 0.05 0.04 0.03 0.04 0.04

(0.06) (0.04) (0.04) (0.04) (0.04) (0.04)Race = Hispanic (Race not specified) -0.30*** -0.02 -0.02 -0.04 -0.04 -0.03

(0.08) (0.06) (0.06) (0.05) (0.05) (0.05)Race = Asian 0.21** 0.14** 0.11* 0.06 0.06 0.08

(0.07) (0.05) (0.05) (0.05) (0.05) (0.05)Race = Native Hawaiian, Other Pacific Islander 0.19 0.06 0.06 -0.03 -0.03 0.00

(0.18) (0.13) (0.13) (0.11) (0.11) (0.10)Race = American Indian or Alaska Native 0.11 0.23* 0.22 0.25* 0.24* 0.26*

(0.14) (0.11) (0.11) (0.10) (0.10) (0.10)Race = More than one race, Non-Hispanic -0.06 0.05 0.06 0.01 0.02 0.04

(0.09) (0.06) (0.06) (0.05) (0.05) (0.05)SES composite 0.29*** 0.07*** 0.07*** 0.04* 0.03 0.03

(0.03) (0.02) (0.02) (0.02) (0.02) (0.02)Age at First Grade -0.06 -0.05 -0.03 -0.01 -0.01 -0.05

(0.13) (0.13) (0.11) (0.09) (0.09) (0.09)Age at Spring K 0.14 0.04 0.02 0.00 0.00 0.04

(0.10) (0.10) (0.09) (0.08) (0.08) (0.08)Age at Fall K -0.06 -0.01 0.00 -0.01 0.00 0.00

(0.08) (0.07) (0.07) (0.06) (0.06) (0.06)Spring K Math Test Score 0.41*** 0.39*** 0.27*** 0.25*** 0.16***

(0.02) (0.02) (0.02) (0.02) (0.02)Fall K Math Test Score 0.27*** 0.27*** 0.19*** 0.16*** 0.12***

9


(0.02) (0.02) (0.02) (0.02) (0.02)First Grade Externalizing Behaviors -0.13*** 0.09*** 0.08** 0.07**

(0.02) (0.02) (0.02) (0.02)Spring K Externalizing Behaviors -0.06 0.02 0.01 0.00

(0.03) (0.03) (0.03) (0.03)Fall K Externalizing Behaviors 0.03 0.06* 0.05 0.05

(0.03) (0.03) (0.03) (0.03)First Grade Approaches to Learning 0.52*** 0.51*** 0.47***

(0.03) (0.02) (0.02)Spring K Approaches to Learning 0.09*** 0.03 0.03

(0.03) (0.03) (0.03)Fall K Approaches to Learning 0.02 -0.02 -0.02

(0.02) (0.02) (0.02)Spring K Teacher Rating of Math 0.12*** 0.11***

(0.02) (0.02)Fall K Teacher Rating of Math 0.03 0.02

(0.02) (0.02)First Grade Math Test Score 0.19***

(0.02)Constant 0.00 -0.78 1.48 1.59 -0.92 -0.51 -0.04

(0.01) (1.88) (1.90) (1.68) (1.29) (1.27) (1.29)

R-squared 0.38 0.43 0.69 0.70 0.77 0.77 0.78N 6658 6658 6658 6658 6658 6658 6658

Note: * p<0.05, ** p<0.01, *** p<0.001

10


Table S7. Spring Third Grade Study 1 Regressions

Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7Female -0.08* -0.07 -0.03 -0.08** -0.18*** -0.17*** -0.11***

(0.04) (0.04) (0.03) (0.03) (0.03) (0.03) (0.03)Race = Black or African American, Non-Hispanic -0.26** -0.05 0.00 -0.02 -0.01 0.03

(0.08) (0.06) (0.06) (0.06) (0.06) (0.06)Race = Hispanic (Race specified) -0.01 0.10 0.10 0.05 0.04 0.04

(0.09) (0.07) (0.07) (0.06) (0.06) (0.06)Race = Hispanic (Race not specified) -0.23* 0.04 0.04 0.02 0.00 -0.01

(0.10) (0.07) (0.07) (0.06) (0.06) (0.06)Race = Asian 0.26** 0.21* 0.18* 0.06 0.07 0.08

(0.09) (0.09) (0.09) (0.08) (0.08) (0.08)Race = Native Hawaiian, Other Pacific Islander 0.16 0.29 0.29 -0.02 0.01 0.01

(0.21) (0.16) (0.16) (0.14) (0.14) (0.14)Race = American Indian or Alaska Native -0.22 0.00 -0.02 -0.02 -0.04 -0.01

(0.17) (0.11) (0.12) (0.12) (0.11) (0.10)Race = More than one race, Non-Hispanic 0.05 0.17 0.16 0.10 0.09 0.12

(0.16) (0.13) (0.13) (0.12) (0.12) (0.13)SES composite 0.31*** 0.11*** 0.10*** 0.08*** 0.08*** 0.06**

(0.03) (0.03) (0.03) (0.02) (0.02) (0.02)Age at Third Grade 0.23 0.18 0.15 0.13 0.13 0.11

(0.13) (0.11) (0.10) (0.09) (0.09) (0.08)Age at First Grade -0.04 -0.09 -0.07 -0.06 -0.06 -0.06

(0.10) (0.08) (0.08) (0.08) (0.08) (0.07)Age at Spring K 0.11 0.10 0.08 0.04 0.04 0.05

(0.11) (0.09) (0.09) (0.08) (0.08) (0.07)Age at Fall K -0.29** -0.21* -0.19* -0.12 -0.11 -0.12

(0.11) (0.10) (0.09) (0.08) (0.08) (0.08)First Grade Math Test Score 0.26*** 0.25*** 0.19*** 0.17*** 0.08***

(0.02) (0.02) (0.02) (0.02) (0.02)

11


Spring K Math Test Score 0.16*** 0.15*** 0.11*** 0.08** 0.03(0.03) (0.03) (0.03) (0.03) (0.03)

Fall K Math Test Score 0.21*** 0.21*** 0.15*** 0.13*** 0.10***(0.03) (0.03) (0.02) (0.02) (0.02)

Third Grade Externalizing Behaviors -0.19*** 0.09** 0.08* 0.10**(0.03) (0.03) (0.03) (0.03)

First Grade Externalizing Behaviors 0.00 0.06 0.05 0.02(0.03) (0.03) (0.03) (0.03)

Spring K Externalizing Behaviors 0.00 0.05 0.05 0.05(0.04) (0.04) (0.04) (0.04)

Fall K Externalizing Behaviors 0.00 -0.02 -0.04 -0.05(0.03) (0.03) (0.03) (0.03)

Third Grade Approaches to Learning 0.53*** 0.51*** 0.47***(0.03) (0.03) (0.03)

First Grade Approaches to Learning 0.07* 0.03 0.03(0.03) (0.03) (0.03)

Spring K Approaches to Learning 0.06 0.01 0.01(0.03) (0.04) (0.03)

Fall K Approaches to Learning -0.04 -0.06 -0.05(0.03) (0.04) (0.03)

First Grade Teacher Rating of Math 0.09*** 0.07***(0.02) (0.02)

Spring K Teacher Rating of Math 0.06* 0.07**(0.02) (0.02)

Fall K Teacher Rating of Math 0.00 -0.01(0.02) (0.02)

First Grade Math Test Score 0.24***(0.02)

Constant 0.04* -10.22* -5.21 -3.99 -5.49 -4.87 -4.68(0.02) (4.83) (4.10) (4.05) (3.45) (3.45) (3.34)

12


R-squared 0.42 0.46 0.67 0.68 0.74 0.74 0.76N 3919 3919 3919 3919 3919 3919 3919

Note: * p<0.05, ** p<0.01, *** p<0.001

13


Table S8. Fifth Grade Study 1 Regressions

Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7Female -0.18* -0.16* -0.06 -0.15** -0.26*** -0.25*** -0.18**

(0.07) (0.07) (0.06) (0.06) (0.05) (0.06) (0.06)Race = Black or African American, Non-Hispanic -0.21 0.13 0.12 0.10 0.09 0.12

(0.21) (0.16) (0.16) (0.18) (0.18) (0.18)Race = Hispanic (Race specified) 0.01 0.00 0.01 0.02 -0.01 0.01

(0.17) (0.13) (0.12) (0.11) (0.11) (0.10)Race = Hispanic (Race not specified) -0.03 -0.07 -0.07 -0.08 -0.09 -0.13

(0.28) (0.24) (0.24) (0.22) (0.23) (0.23)Race = Asian 0.43** 0.27 0.27 0.20 0.17 0.18

(0.15) (0.15) (0.15) (0.15) (0.15) (0.14)Race = Native Hawaiian, Other Pacific Islander 0.79 0.66* 0.70* 0.33 0.30 0.41

(0.45) (0.30) (0.32) (0.31) (0.33) (0.34)Race = American Indian or Alaska Native -0.14 -0.42 -0.33 -0.17 -0.17 -0.13

(0.40) (0.32) (0.29) (0.24) (0.27) (0.23)Race = More than one race, Non-Hispanic -0.19 -0.04 -0.02 0.02 0.02 -0.03

(0.24) (0.18) (0.18) (0.16) (0.16) (0.17)SES composite 0.26*** 0.15** 0.13* 0.11* 0.10* 0.10

(0.07) (0.06) (0.05) (0.05) (0.05) (0.05)Age at Fifth Grade 0.21 0.13 0.08 0.02 0.04 -0.05

(0.18) (0.18) (0.17) (0.19) (0.19) (0.18)Age at Third Grade -0.50* -0.25 -0.22 -0.14 -0.13 -0.12

(0.25) (0.21) (0.20) (0.20) (0.20) (0.22)Age at First Grade 0.08 0.07 0.05 -0.01 -0.04 0.06

(0.24) (0.19) (0.18) (0.16) (0.16) (0.16)Age at Spring K 0.24 0.01 0.00 0.01 -0.01 -0.04

(0.19) (0.19) (0.17) (0.15) (0.15) (0.16)Age at Fall K -0.01 0.03 0.09 0.10 0.13 0.16

14


(0.17) (0.15) (0.15) (0.13) (0.13) (0.13)Third Grade Math Test Score 0.31*** 0.30*** 0.24*** 0.20*** 0.07

(0.06) (0.05) (0.05) (0.05) (0.06)First Grade Math Test Score 0.14* 0.13* 0.11* 0.10* 0.07

(0.05) (0.05) (0.05) (0.04) (0.04)Spring K Math Test Score 0.02 0.02 0.00 -0.02 -0.04

(0.06) (0.05) (0.05) (0.05) (0.05)Fall K Math Test Score 0.11* 0.11* 0.09* 0.08 0.06

(0.05) (0.05) (0.05) (0.05) (0.05)Fifth Grade Externalizing Behaviors -0.13 0.15 0.14 0.15

(0.07) (0.08) (0.08) (0.08)Third Grade Externalizing Behaviors -0.13 -0.06 -0.07 -0.09

(0.08) (0.08) (0.08) (0.08)First Grade Externalizing Behaviors -0.02 0.03 0.03 0.04

(0.09) (0.09) (0.09) (0.09)Spring K Externalizing Behaviors -0.04 -0.07 -0.06 -0.04

(0.08) (0.08) (0.08) (0.07)Fall K Externalizing Behaviors -0.07 0.01 0.00 -0.03

(0.08) (0.08) (0.08) (0.08)Fifth Grade Approaches to Learning 0.52*** 0.50*** 0.46***

(0.07) (0.07) (0.07)Third Grade Approaches to Learning 0.00 -0.04 -0.04

(0.06) (0.06) (0.06)First Grade Approaches to Learning 0.06 0.03 0.04

(0.06) (0.07) (0.07)Spring K Approaches to Learning 0.01 0.04 0.04

(0.07) (0.07) (0.07)Fall K Approaches to Learning 0.05 0.04 0.03

(0.06) (0.07) (0.06)Third Grade Teacher Rating of Math 0.10* 0.07

(0.04) (0.04)

15


First Grade Teacher Rating of Math 0.08 0.07(0.04) (0.04)

Spring K Teacher Rating of Math -0.06 -0.05(0.05) (0.05)

Fall K Teacher Rating of Math 0.02 0.02(0.05) (0.05)

First Grade Math Test Score 0.26***(0.06)

Constant 0.09* 3.90 0.60 3.82 2.71 1.71 5.90(0.04) (12.65) (11.32) (10.79) (10.88) (11.11) (10.72)

R-squared 0.47 0.51 0.67 0.69 0.74 0.74 0.75N 1099 1099 1099 1099 1099 1099 1099

Note: * p<0.05, ** p<0.01, *** p<0.001

16


Table S9.Spring K -First Grade Study 2A Regressions – No Fixed Effects

Raw difference

Conditional difference

among boys and girls,

before accounting for teacher ratings


among boys and girls, after accounting for

current teacher ratings


among boys and girls, after accounting for prior teacher

ratings

Conditional difference among boys and girls, after accounting for

predicted current teacher ratings

WLS WLS WLS WLS IV -Stage 1 IV - Stage 2[1] [2] [3] [4] [5]

Female -0.07*** -0.13*** -0.11*** -0.13*** -0.14*** -0.08***(0.02) (0.02) (0.02) (0.02) (0.02) (0.02)

Spring K Math Test Score 0.78*** 0.52*** 0.48*** 0.51*** 0.23*** 0.42***(0.01) (0.02) (0.02) (0.02) (0.02) (0.03)

Age at First Grade 0.09*** 0.09*** 0.09*** 0.09*** 0.04* 0.08***(0.01) (0.01) (0.01) (0.01) (0.02) (0.01)

Age at Spring K -0.10*** -0.07*** -0.07*** -0.07*** 0.02 -0.08***(0.01) (0.02) (0.01) (0.02) (0.02) (0.02)


Age at Fall K -0.03* -0.02 -0.03* -0.07*** 0.00(0.01) (0.01) (0.01) (0.02) (0.02)

First Grade Externalizing Behaviors 0.01 -0.01 0.00 0.09*** -0.03(0.02) (0.02) (0.02) (0.02) (0.02)

First Grade Approaches to Learning 0.15*** 0.06*** 0.14*** 0.61*** -0.09(0.02) (0.02) (0.02) (0.02) (0.06)

Spring K Externalizing Behaviors 0.04 0.04 0.03 0.00 0.03(0.02) (0.02) (0.02) (0.03) (0.02)

Spring K Approaches to Learning 0.07*** 0.06** 0.04 0.03 0.03(0.02) (0.02) (0.02) (0.02) (0.02)

Fall K Externalizing Behaviors -0.01 -0.03 -0.02 0.07** -0.05

17


(0.02) (0.02) (0.02) (0.03) (0.02)Fall K Approaches to Learning 0.03 0.03 0.02 -0.01 0.03

(0.02) (0.02) (0.02) (0.02) (0.02)Race = Black or African American, Non-Hispanic -0.24*** -0.24*** -0.24*** 0.00 -0.24***

(0.03) (0.03) (0.03) (0.03) (0.03)Race = Hispanic (Race specified) 0.00 -0.02 0.00 0.11** -0.04

(0.04) (0.04) (0.04) (0.04) (0.04)Race = Hispanic (Race not specified) 0.01 -0.01 0.01 0.12** -0.04

(0.03) (0.03) (0.03) (0.04) (0.04)Race = Asian -0.13* -0.12 -0.12* -0.05 -0.10

(0.06) (0.06) (0.06) (0.04) (0.06)Race = Native Hawaiian, Other Pacific Islander -0.21** -0.18* -0.21** -0.21* -0.12

(0.08) (0.08) (0.08) (0.09) (0.08)Race = American Indian or Alaska Native -0.10 -0.10 -0.09 0.05 -0.11

(0.07) (0.07) (0.07) (0.07) (0.07)Race = More than one race, Non-Hispanic -0.11* -0.12* -0.11* 0.07 -0.13*

(0.05) (0.05) (0.05) (0.07) (0.05)SES composite 0.04** 0.03** 0.03** 0.03 0.02

(0.01) (0.01) (0.01) (0.01) (0.01)First Grade (Current) Teacher Rating 0.14***

(0.01)Spring K Teacher Rating (Instrument) 0.05*** 0.13***

(0.01) (0.02)Fall K Teacher Rating (Instrument) -0.01

(0.01)Predicted First Grade (Current) Teacher Rating 0.39***

(0.09)Constant -0.80*** -1.44*** -1.10*** -1.28*** -2.10 -0.47

(0.24) (0.28) (0.27) (0.28) (0.33) (0.36)

18


R-squared 0.60 0.64 0.64 0.64 0.52 0.61N 6658 6658 6658 6658 6658 6658

Note: * p<0.05, ** p<0.01, *** p<0.001

19


Table S10.Spring K - First Grade Study 2A Regressions – With Fixed Effects

Raw difference

Conditional difference among

boys and girls, before accounting

for teacher ratings


boys and girls, after accounting for current teacher

ratings


boys and girls, after accounting for prior teacher

ratings



WLS-FE WLS-FE WLS-FE WLS-FEIV-FE –Stage 1

IV-FE –Stage 2

[1] [2] [3] [4] [5]Female -0.07*** -0.15*** -0.12*** -0.15*** -0.13*** -0.08***

(0.02) (0.02) (0.02) (0.02) (0.02) (0.02)Spring K Math Test Score 0.74*** 0.48*** 0.41*** 0.47*** .25*** 0.33***

(0.01) (0.02) (0.02) (0.02) (0.02) (0.04)Age at First Grade 0.21*** 0.22*** 0.22*** 0.22*** -0.01 0.22***

(0.05) (0.06) (0.06) (0.06) (0.07) (0.06)Age at Spring K -0.21*** -0.21*** -0.22*** -0.22*** 0.00 -0.21***

(0.05) (0.06) (0.06) (0.06) (0.06) (0.06)Fall K Math Test Score 0.21*** 0.16*** 0.20*** 0.16*** 0.11***

(0.02) (0.02) (0.02) (0.02) (0.03)Age at Fall K -0.01 -0.01 -0.01 0.00 -0.01

(0.06) (0.05) (0.05) (0.05) (0.05)First Grade Externalizing Behaviors 0.04 0.01 0.03 0.07*** -0.02

(0.02) (0.02) (0.02) (0.02) (0.02)First Grade Approaches to Learning 0.22*** 0.09*** 0.21*** 0.51*** -0.07

(0.02) (0.03) (0.02) (0.02) (0.06)Spring K Externalizing Behaviors 0.03 0.02 0.02 0.01 0.02

(0.03) (0.03) (0.03) (0.02) (0.02)Spring K Approaches to Learning 0.05* 0.03 0.02 0.03 0.00

(0.03) (0.03) (0.03) (0.02) (0.03)Fall K Externalizing Behaviors -0.01 -0.03 -0.02 0.05* -0.04

20


(0.03) (0.03) (0.03) (0.02) (0.03)Fall K Approaches to Learning 0.03 0.02 0.02 -0.02 0.02

(0.03) (0.02) (0.03) (0.02) (0.02)Race = Black or African American, Non-Hispanic -0.11* -0.09 -0.11* -0.09* -0.06

(0.04) (0.04) (0.04) (0.04) (0.04)Race = Hispanic (Race specified) -0.04 -0.05 -0.04 0.04 -0.06

(0.04) (0.04) (0.04) (0.03) (0.04)Race = Hispanic (Race not specified) -0.04 -0.03 -0.04 -0.04 -0.02

(0.05) (0.05) (0.05) (0.04) (0.04)Race = Asian -0.11 -0.12 -0.11 0.06 -0.14

(0.09) (0.09) (0.09) (0.04) (0.07)Race = Native Hawaiian, Other Pacific Islander -0.16 -0.15 -0.16 -0.03 -0.14

(0.09) (0.09) (0.09) (0.09) (0.08)Race = American Indian or Alaska Native -0.09 -0.15 -0.09 0.24* -0.23*

(0.11) (0.11) (0.11) (0.10) (0.11)Race = More than one race, Non-Hispanic -0.10 -0.10 -0.09 0.02 -0.10

(0.07) (0.07) (0.07) (0.05) (0.06)SES composite 0.00 -0.01 0.00 0.03* -0.02


(0.02)Spring K Teacher Rating (Instrument) 0.06*** 0.12***

(0.02) (0.02)Fall K Teacher Rating (Instrument) 0.03*


(0.12)

21


Constant -2.13*** -2.82** -2.59*** -2.67***(0.66) (0.91) (0.97) (0.91)

R-squared 0.67 0.70 0.71 0.70 0.63 0.47N 6658 6658 6658 6658 6658 6658

* p<0.05, ** p<0.01, *** p<0.001

22


Table S11.First-Third Grade Study 2A Regressions – No Fixed Effects

Raw difference



for teacher ratings


boys and girls, after accounting

for current teacher ratings


among boys and girls, after

accounting for prior teacher

ratings


boys and girls, after accounting for


WLS WLS WLS WLSIV –

Stage 1IV –

Stage 2[1] [2] [3] [4] [5]

Female -0.16*** -0.24*** -0.21*** -0.23*** -0.20*** -0.06(0.03) (0.03) (0.02) (0.02) (0.03) (0.04)

First Grade Math Test Score 0.76*** 0.44*** 0.41*** 0.43*** 0.17*** 0.34***(0.01) (0.02) (0.02) (0.02) (0.02) (0.04)

Age at Third Grade 0.05* 0.03 0.04* 0.04* -0.02 0.06*(0.02) (0.02) (0.02) (0.02) (0.02) (0.02)

Age at First Grade -0.06** -0.05* -0.06** -0.06** 0.06* -0.11***(0.02) (0.02) (0.02) (0.02) (0.03) (0.03)

Spring K Standardized Math Test Score 0.19*** 0.17*** 0.17*** 0.08** 0.11**(0.02) (0.02) (0.02) (0.03) (0.03)

Fall K Standardized Math Test Score 0.13*** 0.11*** 0.11*** 0.08*** 0.04(0.02) (0.02) (0.02) (0.03) (0.03)

Age at Spring K -0.01 -0.01 -0.01 -0.01 -0.01(0.02) (0.02) (0.02) (0.03) (0.03)

Age at Fall K 0.00 0.01 0.01 -0.05* 0.05*(0.02) (0.02) (0.02) (0.02) (0.03)

Third Grade Externalizing Behaviors -0.04 -0.06* -0.04 0.12*** -0.15***(0.03) (0.03) (0.03) (0.04) (0.04)

Third Grade Approaches to Learning 0.17*** 0.08** 0.17*** 0.57*** -0.32***(0.02) (0.02) (0.02) (0.03) (0.09)

23


First Grade Externalizing Behaviors 0.11*** 0.10*** 0.10*** 0.07* 0.04(0.03) (0.03) (0.03) (0.03) (0.04)

First Grade Approaches to Learning 0.06* 0.04 0.00 0.03 -0.02(0.02) (0.02) (0.03) (0.03) (0.03)

Spring K Externalizing Behaviors -0.02 -0.04 -0.03 0.06 -0.08(0.03) (0.03) (0.03) (0.04) (0.04)

Spring K Approaches to Learning 0.09** 0.07** 0.07** 0.06 0.01(0.03) (0.03) (0.03) (0.04) (0.04)

Fall K Externalizing Behaviors 0.07* 0.07* 0.05 -0.05 0.10**(0.03) (0.03) (0.03) (0.03) (0.04)

Fall K Approaches to Learning -0.04 -0.04 -0.05 0.03 -0.03(0.03) (0.03) (0.03) (0.03) (0.04)

Race = Black or African American, Non-Hispanic -0.20*** -0.24*** -0.20*** 0.24*** -0.41***

(0.04) (0.04) (0.04) (0.06) (0.07)Race = Hispanic (Race specified) 0.12 0.09 0.10 0.15** -0.02

(0.07) (0.06) (0.07) (0.06) (0.07)Race = Hispanic (Race not specified) 0.03 -0.02 0.01 0.31*** -0.25**

(0.05) (0.05) (0.05) (0.07) (0.09)Race = Asian 0.00 -0.01 0.01 0.05 -0.03

(0.05) (0.05) (0.05) (0.09) (0.08)Race = Native Hawaiian, Other Pacific Islander -0.03 -0.01 0.00 -0.09 0.08

(0.08) (0.08) (0.08) (0.12) (0.10)Race = American Indian or Alaska Native -0.16 -0.11 -0.17 -0.27* 0.06


(0.08) (0.09) (0.08) (0.12) (0.14)SES composite 0.09*** 0.08*** 0.09*** 0.06 0.03

(0.02) (0.02) (0.02) (0.04) (0.04)Third Grade (Current) Teacher Rating 0.16***

24


(0.01)First Grade Teacher Rating of Math 0.11*** 0.14***

(0.02) (0.02)Spring K Teacher Rating of Math 0.01

(0.02)Fall K Teacher Rating of Math 0.02

(0.02)Predicted Third Grade (Current) Teacher Rating 0.85***

(0.15)Constant -0.02 -0.03 0.22 0.14 -1.04 1.03

(0.54) (0.75) (0.73) (0.74) (0.84) (0.88)

R-squared 0.59 0.67 0.69 0.68 0.42 0.41N 3919 3919 3919 3919 3919 3919

Note: * p<0.05, ** p<0.01, *** p<0.001

25


Table S13.First-Third Grade Study 2A Regressions – With Fixed Effects

Raw difference



for teacher ratings


boys and girls, after accounting

for current teacher ratings



ratings

Conditional difference among boys and girls, after accounting for predicted current

teacher ratings


IV-FE –Stage 2

[1] [2] [3] [4] [5]Female -0.16*** -0.24*** -0.19*** -0.22*** -0.17*** -0.04

(0.03) (0.03) (0.03) (0.03) (0.02) (0.05)First Grade Math Test Score 0.72*** 0.41*** 0.36*** 0.39*** 0.17*** 0.20***

(0.02) (0.02) (0.03) (0.02) (0.02) (0.05)Age at Third Grade 0.07 0.06 0.03 0.06 0.13 -0.08

(0.08) (0.08) (0.08) (0.08) (0.07) (0.10)Age at First Grade -0.08 -0.03 -0.01 -0.03 -0.07 0.03

(0.08) (0.08) (0.07) (0.07) (0.07) (0.08)Spring K Standardized Math Test Score 0.24*** 0.21*** 0.22*** 0.08*** 0.13***

(0.03) (0.02) (0.03) (0.02) (0.04)Fall K Standardized Math Test Score 0.13*** 0.09*** 0.11*** 0.13*** -0.03

(0.03) (0.02) (0.02) (0.02) (0.04)Age at Spring K -0.08 -0.08 -0.07 0.04 -0.12

(0.08) (0.08) (0.08) (0.07) (0.08)Age at Fall K 0.03 0.06 0.04 -0.11 0.17

(0.07) (0.07) (0.07) (0.07) (0.09)Third Grade Externalizing Behaviors -0.05 -0.07* -0.06 0.08** -0.15***

(0.04) (0.04) (0.04) (0.03) (0.04)Third Grade Approaches to Learning 0.21*** 0.07* 0.19*** 0.51*** -0.38**

(0.03) (0.03) (0.03) (0.03) (0.13)First Grade Externalizing Behaviors 0.11*** 0.10** 0.10** 0.05 0.05

26


(0.03) (0.03) (0.03) (0.03) (0.03)First Grade Approaches to Learning 0.04 0.03 0.00 0.03 -0.04

(0.03) (0.03) (0.03) (0.03) (0.04)Spring K Externalizing Behaviors 0.00 -0.02 0.00 0.05 -0.06

(0.04) (0.04) (0.04) (0.03) (0.04)Spring K Approaches to Learning 0.02 0.00 0.01 0.03 0.01

(0.03) (0.03) (0.03) (0.03) (0.04)Fall K Externalizing Behaviors 0.05 0.05 0.04 -0.04 0.09*

(0.04) (0.04) (0.04) (0.03) (0.04)Fall K Approaches to Learning -0.03 -0.02 -0.04 -0.05 0.03

(0.04) (0.03) (0.04) (0.03) (0.04)Race = Black or African American, Non-Hispanic -0.20** -0.19** -0.19** -0.01 -0.18*

(0.07) (0.07) (0.07) (0.05) (0.07)Race = Hispanic (Race specified) 0.00 -0.01 -0.01 0.04 -0.06

(0.05) (0.05) (0.05) (0.05) (0.07)Race = Hispanic (Race not specified) 0.07 0.07 0.06 0.00 0.06

(0.07) (0.07) (0.07) (0.05) (0.08)Race = Asian -0.02 -0.04 -0.02 0.07 -0.10

(0.08) (0.08) (0.08) (0.07) (0.09)Race = Native Hawaiian, Other Pacific Islander -0.01 -0.01 0.02 0.01 0.00

(0.14) (0.14) (0.13) (0.12) (0.18)Race = American Indian or Alaska Native -0.06 -0.05 -0.09 -0.04 -0.06


(0.08) (0.09) (0.08) (0.10) (0.13)SES composite 0.09*** 0.07** 0.09*** 0.08*** 0.00

(0.02) (0.02) (0.02) (0.02) (0.03)Spring K Teacher Rating of Math -0.01 0.06*** -0.09**

(0.02) (0.02) (0.03)

27


Third Grade (Current) Teacher Rating 0.25***(0.02)

First Grade Teacher Rating of Math 0.11*** 0.05(0.02) 0.04

Fall K Teacher Rating of Math -0.06(0.05)

Interaction between First Grade and Spring K Teacher Rating -0.01


(0.24)

Constant -1.37 -1.40 -0.01 -0.81(2.02) (2.93) (2.81) (2.91)

R-squared 0.67 0.74 0.76 0.75 0.57 0.24N 3919 3919 3919 3919 3919 3919

Note: * p<0.05, ** p<0.01, *** p<0.001

28


Table S13.Spring K- First Grade Study 2B Regressions – No Fixed Effects

Raw difference


boys and girls, before accounting for teacher ratings



accounting for current teacher

ratings



ratings


teacher ratings


Stage 1IV –

Stage 2[1] [2] [3] [4] [5]

Female -0.07*** -0.13*** -0.11*** -0.13*** -0.16*** -0.07***(0.01) (0.01) (0.01) (0.01) (0.02) (0.02)

Spring K Math Test Score 0.78*** 0.51*** 0.48*** 0.50*** 0.23*** 0.42***(0.01) (0.01) (0.01) (0.01) (0.02) (0.02)

Age at First Grade 0.10*** 0.10*** 0.10*** 0.11*** 0.05*** 0.09***(0.01) (0.01) (0.01) (0.01) (0.01) (0.01)

Age at Spring K -0.11*** -0.07*** -0.07*** -0.08*** -0.01 -0.07***(0.01) (0.01) (0.01) (0.01) (0.01) (0.01)


Age at Fall K -0.04*** -0.04** -0.04*** -0.05*** -0.02(0.01) (0.01) (0.01) (0.01) (0.01)

First Grade Externalizing Behaviors 0.02 0.00 0.02 0.11*** -0.03(0.01) (0.01) (0.01) (0.02) (0.02)

First Grade Approaches to Learning 0.16*** 0.08*** 0.16*** 0.61*** -0.06(0.01) (0.02) (0.01) (0.02) (0.05)

Spring K Approaches to Learning 0.07*** 0.05*** 0.04** 0.06** 0.03*(0.01) (0.01) (0.01) (0.02) (0.02)

Race = Black or African American, Non-Hispanic -0.21*** -0.21*** -0.21*** 0.01 -0.22***

(0.02) (0.02) (0.02) (0.03) (0.02)

29


Race = Hispanic (Race specified) -0.02 -0.03 -0.01 0.08** -0.04(0.03) (0.03) (0.03) (0.03) (0.03)

Race = Hispanic (Race not specified) -0.02 -0.04 -0.02 0.13*** -0.07*(0.03) (0.03) (0.03) (0.03) (0.03)

Race = Asian -0.14** -0.13** -0.13** -0.05 -0.11*(0.05) (0.05) (0.05) (0.04) (0.05)

Race = Native Hawaiian, Other Pacific Islander -0.23*** -0.20*** -0.23*** -0.24*** -0.14*

(0.06) (0.05) (0.06) (0.07) (0.06)Race = American Indian or Alaska Native -0.15* -0.17** -0.14* 0.13* -0.19**

(0.06) (0.06) (0.06) (0.06) (0.06)Race = More than one race, Non-Hispanic -0.09* -0.09* -0.09* 0.00 -0.09*

(0.04) (0.04) (0.04) (0.05) (0.04)SES composite 0.03** 0.03** 0.03** 0.02 0.02*


(0.01)Spring K Teacher Rating of Math (Instrument) 0.05*** 0.12***

(0.01) (0.01)Spring K Externalizing Behaviors (Instrument) 0.07***


(0.08)Constant -0.71*** -1.46*** -1.12*** -1.34*** 2.27*** -0.57***

(0.20) (0.23) (0.23) (0.23) (0.28) (0.30)

R-squared 0.60 0.64 0.65 0.64 0.51 0.62N 9363 9363 9363 9363 9363 9363

Note: * p<0.05, ** p<0.01, *** p<0.001

30


Table S14.Spring K- First Grade Study 2B Regressions – With Fixed Effects

Raw difference






ratings



accounting for prior teacher

ratings


teacher ratings


IV-FE –Stage 2

[1] [2] [3] [4] [5]Female -0.07*** -0.15*** -0.12*** -0.15*** -0.15*** -0.08***

(0.02) (0.02) (0.02) (0.02) (0.01) (0.02)Spring K Math Test Score 0.74*** 0.48*** 0.41*** 0.47*** 0.25*** 0.35***

(0.01) (0.02) (0.02) (0.02) (0.01) (0.03)Age at First Grade 0.16** 0.15* 0.15* 0.15** -0.02 0.16**

(0.05) (0.06) (0.06) (0.06) (0.05) (0.05)Age at Spring K -0.17*** -0.16** -0.16** -0.16** 0.00 -0.16**

(0.05) (0.06) (0.06) (0.06) (0.05) (0.05)Fall K Math Test Score 0.22*** 0.17*** 0.21*** 0.16*** 0.13***

(0.02) (0.02) (0.02) (0.01) (0.02)Age at Fall K 0.00 0.00 0.00 0.01 -0.01

(0.05) (0.04) (0.05) (0.04) (0.04)First Grade Externalizing Behaviors 0.05** 0.01 0.04* 0.11*** -0.02

(0.02) (0.02) (0.02) (0.02) (0.02)First Grade Approaches to Learning 0.23*** 0.10*** 0.23*** 0.53*** -0.03

(0.02) (0.02) (0.02) (0.02) (0.06)Spring K Approaches to Learning 0.06*** 0.04* 0.03 0.05** 0.02

(0.02) (0.02) (0.02) 0.02 (0.02)Race = Black or African American, Non-Hispanic -0.08* -0.06 -0.08* -0.10** -0.04

(0.04) (0.04) (0.04) (0.03) (0.03)

31


Race = Hispanic (Race specified) -0.04 -0.05 -0.04 0.03 -0.05(0.04) (0.04) (0.04) (0.03) (0.03)

Race = Hispanic (Race not specified) -0.05 -0.05 -0.05 -0.02 -0.04(0.04) (0.04) (0.04) (0.03) (0.04)

Race = Asian -0.12 -0.13* -0.12 0.05 -0.14**(0.06) (0.06) (0.06) (0.04) (0.05)

Race = Native Hawaiian, Other Pacific Islander -0.15* -0.15* -0.15 0.00 -0.15*

(0.08) (0.07) (0.08) (0.07) (0.07)Race = American Indian or Alaska Native -0.1 -0.15 -0.11 0.18* -0.20*

(0.10) (0.10) (0.10) (0.08) (0.10)Race = More than one race, Non-Hispanic -0.11 -0.09 -0.10 -0.06 -0.07

(0.06) (0.05) (0.06) (0.04) (0.05)SES composite 0.01 0.00 0.01 0.03** -0.01


(0.02)Spring K Teacher Rating of Math (Instrument) 0.06*** 0.11***

(0.01) (0.01)Spring K Externalizing Behaviors (Instrument) 0.04*


(0.10)Constant -1.29* -1.71* -1.52** -1.62*

(0.62) (0.86) (0.89) (0.86)

R-squared 0.67 0.70 0.72 0.71 0.62 0.49N 9363 9363 9363 9363 9363 9363

Note: * p<0.05, ** p<0.01, *** p<0.001

32


Table S15.First-Third Grade Study 2B Regressions – No Fixed Effects

Raw difference






ratings



ratings


teacher ratings


Stage 1IV –

Stage 2[1] [2] [3] [4] [5]

Female -0.17*** -0.26*** -0.23*** -0.24*** -0.17*** -0.12***(0.02) (0.02) (0.02) (0.02) (0.03) (0.03)

First Grade Math Test Score 0.77*** 0.45*** 0.43*** 0.44*** 0.17*** 0.32***(0.01) (0.02) (0.02) (0.02) (0.02) (0.03)

Age at Third Grade 0.05*** 0.04** 0.05** 0.05** 0.00 0.05**(0.02) (0.02) (0.02) (0.02) (0.02) (0.02)

Age at First Grade -0.06*** -0.05** -0.06*** -0.06*** 0.06** -0.10***(0.02) (0.02) (0.02) (0.02) (0.02) (0.02)

Spring K Math Test Score 0.18*** 0.16*** 0.17*** 0.11*** 0.09***(0.02) (0.02) (0.02) (0.02) (0.02)

Fall K Math Test Score 0.14*** 0.13*** 0.12*** 0.06** 0.08***(0.02) (0.02) (0.02) (0.02) (0.02)

Age at Spring K 0.00 0.00 0.00 -0.02 0.01(0.02) (0.02) (0.02) (0.02) (0.02)

Age at Fall K -0.02 -0.01 -0.01 -0.06** 0.03(0.02) (0.02) (0.02) (0.02) (0.02)

Third Grade Externalizing Behaviors 0.01 -0.01 0.01 0.09** -0.09**(0.02) (0.02) (0.02) (0.03) (0.03)

Third Grade Approaches to Learning 0.17*** 0.08*** 0.16*** 0.57*** -0.23***(0.02) (0.02) (0.02) (0.03) (0.06)

33


First Grade Approaches to Learning 0.05** 0.03* -0.01 0.03 -0.01(0.02) (0.02) (0.02) (0.03) (0.02)

Race = Black or African American, Non-Hispanic -0.24*** -0.28*** -0.24*** 0.27*** -0.43***

(0.04) (0.04) (0.04) (0.05) (0.05)Race = Hispanic (Race specified) 0.08 0.06 0.07 0.12* -0.01

(0.05) (0.05) (0.05) (0.05) (0.05)Race = Hispanic (Race not specified) 0.03 -0.01 0.02 0.29*** -0.18**

(0.04) (0.04) (0.04) (0.07) (0.06)Race = Asian -0.01 -0.02 0.00 0.09 -0.07

(0.04) (0.04) (0.04) (0.07) (0.06)Race = Native Hawaiian, Other Pacific Islander -0.03 -0.02 0.00 -0.03 0.01

(0.06) (0.06) (0.06) (0.09) (0.07)Race = American Indian or Alaska Native -0.21** -0.19* -0.22** -0.18* -0.10

(0.07) (0.08) (0.07) (0.09) (0.11)Race = More than one race, Non-Hispanic -0.10 -0.13 -0.11 0.17 -0.23*

(0.06) (0.07) (0.07) (0.09) (0.09)SES composite 0.07*** 0.07*** 0.07*** 0.04 0.05


(0.01)First Grade Teacher Rating of Math (Instrument) 0.10*** 0.14***

(0.01) (0.02)First Grade Externalizing Behaviors (Instrument) 0.11***


(0.09)Constant -0.01 -0.03 0.26 0.14 -1.61** 1.06**

34


(0.44) (0.60) (0.58) (0.60) (0.69) (0.67)

R-squared 0.60 0.67 0.68 0.68 0.40 0.51N 5733 5733 5733 5733 5733 5733

Note: * p<0.05, ** p<0.01, *** p<0.001

35


Table S16.First-Third Grade Study 2B Regressions – With Fixed Effects

Raw difference






ratings



ratings


teacher ratings


IV-FE –Stage 2

[1] [2] [3] [4] [5]Female -0.18*** -0.26*** -0.22*** -0.25*** -0.16*** -0.09**


(0.01) (0.02) (0.02) (0.02) (0.02) (0.03)Age at Third Grade 0.03 0.06 0.04 0.05 0.07 -0.03

(0.07) (0.07) (0.07) (0.07) (0.05) (0.07)Age at First Grade -0.04 -0.01 0.01 -0.01 -0.09 0.08

(0.07) (0.07) (0.07) (0.07) (0.05) (0.06)Spring K Math Test Score 0.23*** 0.20*** 0.22*** 0.10*** 0.12***

(0.02) (0.02) (0.02) (0.02) (0.03)Fall K Math Test Score 0.12*** 0.08*** 0.10*** 0.13*** -0.03

(0.02) (0.02) (0.02) (0.02) (0.03)Age at Spring K -0.06 -0.08 -0.06 0.06 -0.12

(0.07) (0.07) (0.07) (0.06) (0.07)Age at Fall K -0.01 0.01 0.00 0.06 0.06

(0.06) (0.06) (0.06) (0.05) (0.06)Third Grade Externalizing Behaviors 0.02 -0.01 0.01 0.09*** -0.12***

(0.03) (0.02) (0.03) (0.02) (0.03)Third Grade Approaches to Learning 0.21*** 0.07** 0.20*** 0.53*** -0.32***

(0.03) (0.02) (0.03) (0.02) (0.08)

36


First Grade Approaches to Learning 0.00 -0.01 -0.05* 0.02 -0.04(0.02) (0.02) (0.02) (0.02) (0.02)

Race = Black or African American, Non-Hispanic -0.20*** -0.19*** -0.20*** -0.05 -0.15*

(0.06) (0.05) (0.06) (0.05) (0.06)Race = Hispanic (Race specified) 0.00 0.00 -0.01 0.00 0.00

(0.05) (0.05) (0.05) (0.04) (0.05)Race = Hispanic (Race not specified) 0.01 0.02 0.01 -0.01 0.02

(0.06) (0.05) (0.06) (0.04) (0.06)Race = Asian -0.06 -0.06 -0.06 0.01 -0.07

(0.07) (0.06) (0.06) (0.06) (0.07)Race = Native Hawaiian, Other Pacific Islander -0.02 0.01 0.01 -0.09 0.09

(0.10) (0.10) (0.10) (0.09) (0.12)Race = American Indian or Alaska Native -0.18 -0.15 -0.20 -0.09 -0.09

(0.10) (0.10) (0.10) (0.08) (0.10)Race = More than one race, Non-Hispanic -0.10 -0.13 -0.11 0.10 -0.21*

(0.07) (0.07) (0.07) (0.07) (0.09)SES composite 0.07*** 0.06*** 0.07*** 0.06*** 0.01


(0.02)First Grade Teacher Rating of Math (Instrument) 0.11*** 0.11***

(0.02) (0.01)First Grade Externalizing Behaviors (Instrument) 0.08***


(0.13)Constant -0.07 -1.28 -0.47 -0.76

37


(1.66) (2.48) (2.38) (2.45)

R-squared 0.68 0.74 0.76 0.75 0.56 0.35N 5733 5733 5733 5733 5733 5733

Note: * p<0.05, ** p<0.01, *** p<0.001

38


Table S17. Balance Before and After Propensity-Score Matching for Grades K-1 in Study 2A Regressions

Unmatched sample[N = 6658]

Matched sample without teacher FE[N = 6658]

Matched sample with teacher FE[N = 6658]

VariableMale mean

Female mean

Std diff.

pvalue

Var. Ratio

Male mean

Female mean

Std diff.

p value

Var. Ratio

Male mean

Female mean

Std diff.

p value

Var. Ratio

Propensity score 0.44 0.56 -0.73 0.00 0.82 0.50 0.50 0.00 1.00 1.00 0.50 0.50 0.00 1.00 1.00

Continuous variablesAge at Fall K 68.29 67.56 0.17 <.0001 0.87 67.98 67.86 0.03 0.40 0.92 68.09 67.85 0.06 0.10 0.96Age at Spring K 74.37 73.64 0.17 <.0001 0.89 74.04 73.95 0.02 0.51 0.93 74.15 73.93 0.05 0.13 0.97Age at First Gr 86.31 85.58 0.17 <.0001 0.88 85.99 85.88 0.02 0.45 0.94 86.08 85.86 0.05 0.13 0.97Fall K Math 0.01 -0.01 0.02 0.38 0.86 0.12 0.14 -0.02 0.46 0.89 0.02 0.00 0.01 0.72 0.94Spring K Math 0.02 -0.02 0.04 0.13 0.89 0.10 0.13 -0.03 0.42 0.94 0.01 -0.01 0.02 0.50 1.02EB at Fall K 1.73 1.46 0.45 <.0001 0.65 1.59 1.59 0.01 0.83 1.04 1.60 1.62 -0.04 0.48 1.23ATL at Fall K 2.90 3.18 -0.42 <.0001 0.85 3.04 3.05 -0.02 0.63 0.97 3.03 3.04 -0.01 0.90 1.06EB at Spring K 1.77 1.50 0.45 <.0001 0.65 1.64 1.63 0.02 0.53 1.03 1.65 1.65 0.00 0.97 1.15ATL at Spring K 3.01 3.30 -0.45 <.0001 0.84 3.16 3.17 -0.01 0.83 1.05 3.17 3.16 0.01 0.77 1.12EB at First Gr 1.79 1.51 0.46 <.0001 0.65 1.66 1.65 0.01 0.84 1.01 1.66 1.66 0.00 0.93 1.06ATL at First Gr 2.89 3.20 -0.44 <.0001 0.89 3.04 3.04 0.00 0.95 1.06 3.02 3.04 -0.03 0.52 1.10SES in K 0.04 0.04 0.00 0.99 0.94 0.04 0.06 -0.03 0.37 0.95 0.06 0.05 0.01 0.77 0.89

Categorical variablesRace 0.06 0.96 0.33White 66% 63% 0.06 62% 63% -0.03 62% 61% 0.02Black 12% 14% -0.05 14% 13% 0.02 14% 13% 0.02Hisp, w/ race 7% 8% -0.03 8% 8% 0.02 7% 8% -0.03Hisp, w/o race 8% 9% -0.02 8% 8% 0.01 7% 8% -0.04Asian 2% 2% -0.01 3% 3% -0.01 5% 4% 0.07Native Haw. /PI 0% 0% -0.01 1% 1% 0.01 0% 1% -0.07Amer. Indian 1% 2% -0.01 2% 1% 0.02 1% 1% 0.01Multirace 3% 2% 0.07 2% 3% -0.03 3% 4% -0.04

K = kindergarten, Gr = grade, ATL = Approaches to Learning, EB = Externalizing Behavior Problems, SES = socioeconomic status, White = White, non-Hispanic, Black = Black or African American, non-Hispanic, Hisp. w/ race = Hispanic, race specified, Hisp. w/o race = Hispanic, race not specified, Native Haw./PI = Native Hawaiian or other Pacific Islander, Amer. Indian = American Indian or Alaskan Native, Multirace = more than one race specified, non-Hispanic.

39


Table S18. Balance Before and After Propensity-Score Matching for Grades 1-3 in Study 2A RegressionsUnmatched sample

[N = 3919]Matched sample without teacher FE

[N = 3917]Matched sample with teacher FE

[N = 3919]

VariableMale mean

Female mean

Std diff.

pvalue

Var. Ratio

Male mean

Female mean

Std diff.

p value

Var. Ratio

Male mean

Female mean

Std diff.

p value

Var. Ratio


Continuous variablesAge at Fall K 68.32 67.56 0.18 <.0001 0.89 67.73 67.82 -0.02 0.60 0.91 67.93 67.82 0.03 0.62 0.94Age at Spring K 74.38 73.64 0.18 <.0001 0.92 73.77 73.89 -0.03 0.52 0.92 73.97 73.87 0.03 0.63 0.96Age at First Gr 86.31 85.57 0.18 <.0001 0.91 85.70 85.81 -0.03 0.58 0.91 85.88 85.81 0.02 0.75 0.96Age at Third Gr 110.11 109.35 0.18 <.0001 0.92 109.49 109.60 -0.03 0.57 0.92 109.68 109.57 0.03 0.61 0.97Fall K Math 0.05 -0.04 0.09 0.02 0.86 0.00 0.04 -0.04 0.40 1.01 0.02 0.06 -0.04 0.37 1.07Spring K Math 0.04 -0.04 0.08 0.03 0.88 -0.01 0.02 -0.03 0.53 1.00 0.02 0.05 -0.03 0.60 1.07First Gr Math 0.08 -0.08 0.16 <.0001 0.86 -0.02 -0.01 -0.01 0.81 0.91 0.03 0.03 0.00 0.92 1.00EB at Fall K 1.69 1.46 0.40 <.0001 0.69 1.56 1.57 0.00 0.99 1.01 1.55 1.56 -0.02 0.73 1.08ATL at Fall K 2.96 3.20 -0.37 <.0001 0.94 3.09 3.07 0.02 0.61 1.14 3.09 3.11 -0.03 0.53 1.06EB at Spring K 1.74 1.50 0.41 <.0001 0.66 1.61 1.61 0.00 0.96 0.98 1.60 1.63 -0.06 0.38 1.13ATL at Spring K 3.09 3.34 -0.40 <.0001 0.84 3.20 3.21 -0.03 0.55 1.13 3.23 3.24 -0.01 0.78 1.01EB at First Gr 1.75 1.51 0.41 <.0001 0.68 1.63 1.63 0.01 0.89 0.98 1.62 1.64 -0.02 0.72 1.04ATL at First Gr 2.95 3.24 -0.45 <.0001 0.89 3.08 3.11 -0.04 0.51 1.08 3.08 3.14 -0.08 0.12 1.07EB at Third Gr 1.81 1.56 0.43 <.0001 0.74 1.69 1.69 0.01 0.90 1.09 1.66 1.68 -0.03 0.62 1.18ATL at Third Gr 2.92 3.23 -0.47 <.0001 0.86 3.07 3.10 -0.04 0.39 0.99 3.09 3.11 -0.03 0.61 1.10SES in K 0.10 0.08 0.02 0.57 0.88 0.11 0.14 -0.04 0.37 0.97 0.14 0.14 0.00 0.99 0.88

Categorical variablesRace 0.73 0.80 0.46White 71% 70% 0.02 70% 69% 0.02 69% 68% 0.04Black 9% 10% -0.05 10% 10% 0.01 9% 9% -0.02Hisp, w/ race 7% 7% -0.03 7% 7% 0.02 6% 7% -0.07Hisp, w/o race 7% 6% 0.03 6% 6% -0.04 6% 6% 0.03Asian 2% 2% 0.01 3% 4% -0.08 6% 5% 0.05Native Haw. /PI 1% 1% 0.01 1% 1% 0.00 1% 2% -0.16Amer. Indian 1% 1% -0.01 1% 1% 0.01 1% 1% -0.01Multirace 2% 2% 0.03 2% 2% 0.00 3% 2% 0.03


40


Table S19. Balance Before and After Propensity-Score Matching for Grades K-1 in Study 2B Regressions




VariableMale mean

Female mean

Std diff.

pvalue

Var. Ratio

Male mean

Female mean

Std diff.

p value

Var. Ratio

Male mean

Female mean

Std diff.

p value

Var. Ratio


Continuous variablesAge at Fall K 68.23 67.39 0.20 <.0001 0.86 67.79 67.81 0.00 0.90 0.96 67.89 67.71 0.04 0.20 0.95Age at Spring K 74.33 73.49 0.20 <.0001 0.87 73.90 73.90 0.00 0.98 0.97 74.00 73.81 0.04 0.18 0.96Age at First Gr 86.29 85.45 0.20 <.0001 0.87 85.85 85.87 0.00 0.87 0.96 85.94 85.78 0.04 0.21 0.95Fall K Math 0.02 -0.02 0.03 0.16 0.86 -0.01 0.00 -0.01 0.71 0.91 0.00 0.00 0.00 0.91 0.99Spring K Math 0.03 -0.03 0.05 0.02 0.90 0.01 0.00 0.01 0.60 0.95 0.01 0.01 0.00 0.99 1.03ATL at Spring K 3.02 3.30 -0.42 <.0001 0.85 3.16 3.16 0.00 0.97 1.05 3.16 3.15 0.01 0.88 1.13EB at First Gr 1.79 1.52 0.42 <.0001 0.68 1.66 1.66 0.00 0.91 1.04 1.65 1.66 -0.01 0.67 1.14ATL at First Gr 2.90 3.20 -0.44 <.0001 0.89 3.05 3.05 0.00 0.87 1.05 3.04 3.05 0.00 0.89 1.15SES in K 0.04 0.04 -0.01 0.63 0.98 0.05 0.05 0.01 0.76 0.98 0.05 0.06 -0.01 0.66 1.05

Categorical variablesRace 0.16 0.99 0.93White 66% 64% 0.06 63% 64% -0.01 62% 61% 0.02Black 13% 14% -0.04 13% 13% 0.00 13% 14% -0.01Hisp, w/ race 7% 8% -0.03 7% 7% -0.01 8% 8% -0.01Hisp, w/o race 8% 8% -0.01 8% 8% 0.00 7% 7% -0.02Asian 2% 2% -0.01 3% 3% 0.03 4% 4% 0.02Native Haw. /PI 1% 1% 0.00 1% 1% 0.01 1% 1% 0.03Amer. Indian 1% 2% -0.03 2% 2% 0.01 2% 2% 0.01Multirace 3% 2% 0.02 3% 3% -0.01 3% 3% -0.02


41


Table S20. Balance Before and After Propensity-Score Matching for Grades 1-3 in Study 2B Regressions




VariableMale mean

Female mean

Std diff.

pvalue

Var. Ratio

Male mean

Female mean

Std diff.

p value

Var. Ratio

Male mean

Female mean

Std diff.

p value

Var. Ratio

Propensity score 0.45 0.57 -0.73 <.0001 0.82 0.51 0.51 0.00 .99 1.00 0.51 0.51 0.00 1.00 1.00

Continuous variablesAge at Fall K 68.29 67.49 0.19 <.0001 0.88 67.88 67.73 0.04 .27 0.92 67.97 67.72 0.06 .12 0.90Age at Spring K 74.37 73.58 0.19 <.0001 0.90 73.96 73.81 0.04 .28 0.94 74.02 73.81 0.05 .20 0.91Age at First Gr 86.33 85.55 0.19 <.0001 0.90 85.93 85.76 0.04 .23 0.93 85.98 85.78 0.05 .21 0.91Age at Third Gr 110.16 109.36 0.19 <.0001 0.90 109.74 109.60 0.03 .32 0.94 109.81 109.60 0.05 .18 0.91Fall K Math 0.04 -0.04 0.08 .007 0.87 0.00 0.05 -0.05 .15 0.89 0.00 0.02 -0.02 .66 0.92Spring K Math 0.04 -0.04 0.08 .007 0.88 0.01 0.05 -0.04 .27 0.91 0.00 0.01 -0.01 .80 0.92First Gr Math 0.08 -0.07 0.15 <.0001 0.83 -0.01 0.04 -0.05 .14 0.81 -0.02 -0.01 -0.01 .78 0.80ATL at First Gr 2.97 3.25 -0.44 <.0001 0.87 3.12 3.13 -0.02 .60 1.04 3.13 3.12 0.01 .80 1.11EB at Third Gr 1.80 1.56 0.42 <.0001 0.73 1.68 1.67 0.02 .64 1.05 1.67 1.68 -0.01 .84 1.15ATL at Third Gr 2.93 3.23 -0.47 <.0001 0.86 3.08 3.09 -0.02 .68 0.97 3.10 3.12 -0.03 .43 1.01SES in K 0.10 0.10 0.00 .99 0.91 0.12 0.15 -0.03 .32 0.95 0.13 0.15 -0.03 .42 1.00

Categorical variablesRace .67 .96 .69White 72% 70% 0.03 69% 70% -0.02 67% 69% -0.03Black 9% 10% -0.05 10% 10% 0.01 10% 9% 0.03Hisp, w/ race 7% 7% -0.01 7% 7% -0.02 7% 8% -0.01Hisp, w/o race 7% 6% 0.02 6% 6% 0.02 6% 6% -0.02Asian 2% 2% 0.00 3% 3% 0.03 4% 4% 0.03Native Haw. /PI 1% 1% -0.01 1% 1% -0.01 1% 1% 0.03Amer. Indian 2% 2% 0.00 2% 2% -0.01 1% 2% -0.04Multirace 2% 2% -0.02 2% 2% 0.02 3% 2% 0.06


42


Table S21. Study 2A Regressions – K-1 Propensity Score MatchingWithout Fixed Effects With Fixed Effects









WLSIV –

Stage 1IV –

Stage 2 WLS-FEIV-FE –Stage 1

IV-FE –Stage 2

[model 6] [model 7] [model 6] [model 7]Female -0.16*** -0.15*** -0.10** -0.16*** -0.12*** -0.09**


(0.02) (0.02) (0.09) (0.02) (0.02) (0.04)Age at First Grade 0.08*** 0.04* 0.06*** 0.22** 0.05 0.19**

(0.02) (0.02) (0.02) (0.06) (0.07) (0.06)Age at Spring K -0.07*** 0.01 -0.08*** -0.19** 0.01 -0.18**

(0.02) (0.02) (0.02) (0.07) (0.06) (0.06)Fall K Math Test Score 0.19*** 0.14*** 0.13*** 0.21*** 0.14*** 0.12***

(0.02) (0.02) (0.02) (0.02) (0.02) (0.03)Age at Fall K -0.02 -0.06** 0.01 -0.04 -0.05 0.01

(0.02) (0.02) (0.02) (0.06) (0.05) (0.05)First Grade Externalizing Behaviors 0.01 0.07** -0.03 0.01 0.05* -0.02

(0.02) (0.03) (0.02) (0.03) (0.02) (0.02)First Grade Approaches to Learning 0.17*** 0.61*** -0.05 0.21*** 0.51*** -0.06

(0.02) (0.02) (0.06) (0.02) (0.02) (0.06)Spring K Externalizing Behaviors 0.06 0.01 0.05 0.03 0.02 0.01

(0.03) (0.03) (0.03) (0.03) (0.02) (0.03)Spring K Approaches to Learning 0.07** -0.03 0.04 0.04** 0.01 0.00

(0.02) (0.03) (0.02) (0.03) (0.02) (0.03)

43


Fall K Externalizing Behaviors -0.01 0.07* -0.04 0.03 0.05* 0.00(0.03) (0.03) (0.03) (0.03) (0.02) (0.03)

Fall K Approaches to Learning 0.04 0.02 -0.03 0.04 0.00 0.03(0.02) (0.03) (0.03) (0.03) (0.02) (0.02)

Race = Black or African American, Non-Hispanic -0.23*** 0.00 -0.23*** -0.11* -0.09* -0.06***

(0.03) (0.04) (0.03) (0.05) (0.04) (0.04)Race = Hispanic (Race specified) -0.02 0.04 -0.04 -0.06 0.02 -0.07

(0.04) (0.06) (0.04) (0.06) (0.03) (0.05)Race = Hispanic (Race not specified) 0.01 0.10* -0.05 -0.08 -0.06 -0.05

(0.04) (0.04) (0.04) (0.06) (0.04) (0.05)Race = Asian -0.10 -0.09 -0.07 -0.06 0.07 -0.10

(0.05) (0.07) (0.06) (0.08) (0.04) (0.07)Race = Native Hawaiian, Other Pacific Islander -0.10 0.05 -0.12 -0.09 0.05 -0.11

(0.08) (0.11) (0.08) (0.08) (0.09) (0.08)Race = American Indian or Alaska Native -0.12 -0.02 -0.11 -0.04 0.29** -0.21*

(0.08) (0.08) (0.08) (0.11) (0.10) (0.11)Race = More than one race, Non-Hispanic -0.04 0.01 -0.05 -0.05 0.04 -0.07

(0.08) (0.07) (0.08) (0.07) (0.05) (0.05)SES composite 0.03 0.01 0.02 -0.01 0.03 -0.02

(0.01) (0.02) (0.01) (0.02) (0.01) (0.02)Spring K Teacher Rating (Instrument) 0.16*** 0.12***

(0.02) (0.02)Fall K Teacher Rating (Instrument) -0.02 0.03*

(0.02) (0.01)Predicted First Grade (Current) Teacher Rating 0.36*** 0.53***

(0.09) (0.11)Constant -1.36 -2.03 -0.46 -2.94 -2.03

(0.32) (0.40) (0.39) (1.00) (0.40)

44


R-squared 0.65 0.53 0.63 0.80 0.53 0.60N 6658 6658 6658 6658 6658 6658

Note: * p<0.05, ** p<0.01, *** p<0.001

45


Table S22. Study 2A Regressions – 1-3 Propensity Score MatchingWithout Fixed Effects With Fixed Effects









WLSIV –

Stage 1IV –


IV-FE –Stage 2

[model 6] [model 7] [model 6] [model 7]Female -0.24*** -0.20*** -0.09 -0.24*** -0.17*** -0.04


(0.02) (0.03) (0.04) (0.03) (0.02) (0.06)Age at Third Grade 0.03 -0.02 0.06* 0.17 0.18 -0.04

(0.02) (0.03) (0.03) (0.09) (0.10) (0.14)Age at First Grade -0.03 0.06 -0.08* -0.09 -0.10 -0.02

(0.02) (0.03) (0.03) (0.09) (0.08) (0.10)Spring K Standardized Math Test Score 0.18*** 0.05 0.12*** 0.27*** 0.10*** 0.14**

(0.03) (0.03) (0.03) (0.03) (0.02) (0.04)Fall K Standardized Math Test Score 0.14*** 0.08** 0.06 0.11*** 0.11** -0.03

(0.02) (0.03) (0.03) (0.03) (0.02) (0.04)Age at Spring K -0.02 0.01 -0.03 -0.21 0.01 -0.23*

(0.03) (0.04) (0.03) (0.11) (0.08) (0.09)Age at Fall K -0.01 -0.07 0.05 0.11 -0.11 0.25*

(0.02) (0.03) (0.03) (0.09) (0.08) (0.10)Third Grade Externalizing Behaviors -0.03 0.11** -0.12** -0.03 0.08* -0.12**

(0.03) (0.04) (0.04) (0.04) (0.03) (0.04)Third Grade Approaches to Learning 0.17*** 0.55*** -0.21* 0.21*** 0.52*** -0.40**

(0.03) (0.04) (0.09) (0.03) (0.03) (0.15)

46


First Grade Externalizing Behaviors 0.10** 0.07 0.04 0.10** 0.06* 0.03(0.03) (0.05) (0.05) (0.03) (0.03) (0.04)

First Grade Approaches to Learning 0.05 0.06 -0.04 0.03 0.04 -0.05(0.03) (0.04) (0.05) (0.03) (0.03) (0.04)

Spring K Externalizing Behaviors 0.00 0.04 -0.04 0.01 0.00 0.01(0.03) (0.05) (0.05) (0.03) (0.03) (0.04)

Spring K Approaches to Learning 0.10** 0.03 0.04 0.04 0.02 0.03(0.03) (0.05) (0.04) (0.04) (0.03) (0.04)

Fall K Externalizing Behaviors 0.05 -0.02 0.05 0.03 0.00 0.03(0.03) (0.04) (0.04) (0.04) (0.03) (0.04)

Fall K Approaches to Learning -0.06 -0.04 -0.04 -0.04 -0.09* -0.05(0.03) (0.04) (0.04) (0.04) (0.03) (0.05)

Race = Black or African American, Non-Hispanic -0.23*** 0.31*** -0.45*** -0.23** -0.05*** -0.16*

(0.05) (0.07) (0.08) (0.09) (0.06) (0.07)Race = Hispanic (Race specified) 0.10 0.10 0.02 0.04 -0.01 0.04

(0.06) (0.07) (0.07) (0.05) (0.06) (0.07)Race = Hispanic (Race not specified) 0.04 0.16* -0.09 0.08 -0.01 0.08

(0.06) (0.07) (0.08) (0.07) (0.07) (0.09)Race = Asian -0.02 0.07 -0.04 -0.01 -0.01 0.00

(0.06) (0.09) (0.09) (0.10) (0.07) (0.08)Race = Native Hawaiian, Other Pacific Islander 0.11 0.00 0.13 0.13 -0.19 0.37

(0.12) (0.13) (0.12) (0.17) (0.20) (0.22)Race = American Indian or Alaska Native -0.20* -0.11 -0.11 0.03 0.04 -0.07

(0.10) (0.11) (0.12) (0.14) (0.13) (0.14)Race = More than one race, Non-Hispanic 0.03 0.02 0.00 -0.03 0.10 -0.16

(0.09) (0.12) (0.13) (0.08) (0.09) (0.11)SES composite 0.09*** 0.06 0.05 0.08*** 0.09*** -0.02

(0.02) (0.03) (0.03) (0.02) (0.02) (0.03)Spring K Teacher Rating of Math 0.06* -0.01 0.06** -0.09**

47


(0.02) (0.02) (0.02) (0.03)First Grade Teacher Rating of Math 0.13*** -0.01

(0.03) (0.05)Fall K Teacher Rating of Math 0.02 0.12

(0.03) (0.07)Interaction between First Grade and Spring K Teacher Rating 0.03*

(0.02)Predicted Third Grade (Current) Teacher Rating 0.69*** 1.14***

(0.14) (0.28)Constant -0.41 -1.19 0.56 -4.07

(0.76) (1.01) (1.04) (3.56)R-squared 0.67 0.42 0.50 0.83 0.56 0.41N 3917 3917 3917 3919 3919 3919

Note: * p<0.05, ** p<0.01, *** p<0.001

48


Table S23. Study 2B Regressions – K-1 Propensity Score MatchingWithout Fixed Effects With Fixed Effects









WLSIV –

Stage 1IV –


IV-FE –Stage 2

[model 6] [model 7] [model 6] [model 7]Female -0.14*** -0.16*** -0.08*** -0.15*** -0.16*** -0.08***


(0.02) (0.02) (0.03) (0.02) (0.01) (0.03)Age at First Grade 0.11*** 0.06*** 0.08*** 0.16* 0.01 0.16**

(0.01) (0.02) (0.02) (0.06) (0.05) (0.05)Age at Spring K -0.07*** -0.02 -0.07*** -0.12*** -0.02 -0.11*

(0.02) (0.02) (0.02) (0.06) (0.05) (0.05)Fall K Math Test Score 0.22*** 0.12*** 0.16*** 0.22*** 0.15*** 0.14***

(0.02) (0.02) (0.02) (0.02) (0.01) (0.02)Age at Fall K -0.05** -0.05** -0.02 -0.05** 0.00 -0.05

(0.01) (0.02) (0.01) (0.05) (0.04) (0.04)First Grade Externalizing Behaviors 0.03 0.12*** -0.04 0.05** 0.10*** -0.01

(0.02) (0.02) (0.02) (0.02) (0.02) (0.02)First Grade Approaches to Learning 0.17*** 0.62*** -0.09 0.21*** 0.54*** -0.04

(0.02) (0.02) (0.06) (0.02) (0.02) (0.06)Spring K Approaches to Learning 0.08*** 0.03* 0.05** 0.07*** 0.05*** 0.03

(0.02) (0.02) (0.02) (0.02) (0.02) (0.02)Race = Black or African American, Non-Hispanic -0.20*** 0.02 -0.21*** -0.07 -0.10** -0.02

49


(0.01) (0.03) (0.03) (0.04) (0.03) (0.03)Race = Hispanic (Race specified) -0.01 0.10** -0.04 -0.05 0.02 -0.06

(0.04) (0.04) (0.04) (0.05) (0.03) (0.04)Race = Hispanic (Race not specified) -0.02 0.15*** -0.08* -0.06 -0.02 -0.05

(0.03) (0.04) (0.04) (0.05) (0.04) (0.04)Race = Asian -0.05 -0.03 -0.03 -0.10 0.03 -0.11*

(0.05) (0.05) (0.05) (0.06) (0.07) (0.05)Race = Native Hawaiian, Other Pacific Islander -0.24** -0.22* -0.16* -0.16* 0.04 -0.17*

(0.07) (0.09) (0.07) (0.07) (0.07) (0.08)Race = American Indian or Alaska Native -0.19* 0.08* -0.21** -0.28* 0.14 -0.35**

(0.07) (0.07) (0.07) (0.13) (0.09) (0.11)Race = More than one race, Non-Hispanic -0.11** -0.06 -0.09* -0.11* -0.08* -0.07

(0.04) (0.06) (0.04) (0.05) (0.04) (0.05)SES composite 0.03* 0.02 0.02 -0.01 0.03* -0.02

(0.01) (0.01) (0.01) (0.02) (0.01) (0.01)First Grade (Current) Teacher Rating

Spring K Teacher Rating of Math (Instrument) 0.13*** 0.12***

(0.01) (0.01)Spring K Externalizing Behaviors (Instrument) 0.06** 0.04**

(0.02) (0.02)Predicted First Grade (Current) Teacher Rating 0.40*** 0.46***

(0.09) (0.11)Constant -1.76*** -2.58*** -0.60*** -2.16***

(0.27) (0.33) (0.37) (0.95)R-squared 0.64 0.52 0.61 0.79 0.64 0.61N 9362 9362 9362 9362 9362 9362

Note: * p<0.05, ** p<0.01, *** p<0.001

50


Table S24. Study 2B Regressions – 1-3 Propensity Score MatchingWithout Fixed Effects With Fixed Effects









WLSIV –

Stage 1IV –


IV-FE –Stage 2

[model 6] [model 7] [model 6] [model 7]Female -0.25*** -0.18*** -0.13*** -0.26*** -0.17*** -0.09*


(0.02) (0.02) (0.03) (0.02) (0.02) (0.03)Age at Third Grade 0.05** -0.03 0.07*** 0.14 0.12 0.00

(0.02) (0.02) (0.02) (0.09) (0.06) (0.08)Age at First Grade -0.05** 0.09** -0.11*** -0.09 -0.17** 0.08


(0.02) (0.03) (0.03) (0.02) (0.02) (0.03)Fall K Math Test Score 0.12*** 0.05 0.07** 0.11*** 0.15*** -0.04**

(0.02) (0.03) (0.02) (0.02) (0.02) (0.03)Age at Spring K 0.01 -0.01 0.01 -0.09 0.09 -0.18*

(0.02) (0.03) (0.02) (0.09) (0.06) (0.08)Age at Fall K -0.02 -0.08** 0.03 0.02 -0.05** 0.09

(0.02) (0.02) (0.02) (0.07) (0.06) (0.07)Third Grade Externalizing Behaviors -0.02 0.07* -0.09** 0.01 0.07** -0.11**

(0.02) (0.03) (0.03) (0.03) (0.03) (0.03)Third Grade Approaches to Learning 0.16*** 0.56*** -0.18** 0.19*** 0.54*** -0.34***

(0.02) (0.03) (0.06) (0.03) (0.02) (0.10)

51


First Grade Approaches to Learning 0.04* 0.04 -0.01 0.01 0.01 -0.02(0.02) (0.03) (0.03) (0.02) (0.02) (0.03)

Race = Black or African American, Non-Hispanic -0.24*** 0.29*** -0.41*** -0.20** -0.08 -0.11

(0.04) (0.06) (0.06) (0.06) (0.05) (0.06)Race = Hispanic (Race specified) 0.06 0.08 0.01 0.04 0.01 0.02

(0.05) (0.06) (0.05) (0.05) (0.04) (0.05)Race = Hispanic (Race not specified) 0.02 0.28*** -0.16* -0.03 -0.01 -0.02

(0.05) (0.06) (0.06) (0.06) (0.05) (0.06)Race = Asian 0.03 0.11 -0.02 -0.02 0.02 -0.05

(0.06) (0.12) (0.07) (0.07) (0.06) (0.07)Race = Native Hawaiian, Other Pacific Islander- -0.04 0.01 -0.03 0.20 0.11 0.31*

(0.08) (0.10) (0.07) (0.15) (0.12) (0.14)Race = American Indian or Alaska Native -0.27** -0.08 -0.23* -0.09 -0.19 -0.08

(0.08) (0.09) (0.10) (0.09) (0.13) (0.14)Race = More than one race, Non-Hispanic -0.06 0.20* -0.19* -0.03 0.10* -0.13

(0.06) (0.09) (0.08) (0.08) (0.07) (0.08)SES composite 0.05** 0.02 0.04* 0.07*** 0.08*** -0.01

(0.02) (0.02) (0.02) (0.02) (0.02) (0.02)Third Grade (Current) Teacher Rating

First Grade Teacher Rating of Math (Instrument) 0.15*** 0.10***

(0.02) (0.02)First Grade Externalizing Behaviors (Instrument) 0.08** 0.07**

(0.03) (0.02)Predicted Third Grade (Current) Teacher Rating 0.58*** 0.95***

(0.10) (0.16)Constant -0.24 -1.19** 0.49** -2.78

52


(0.60) (0.80) (0.72) (3.15)

R-squared 0.67 0.40 0.55 0.83 0.56 0.50N 5731 5731 5731 5733 5733 5733

Note: * p<0.05, ** p<0.01, *** p<0.001

53


A. Spring 1st grade mathematics score, Study 2A (non-matched sample)

Mediated path (a×b) = -0.07 (-0.11, -0.04)

B. Spring 1st grade mathematics score, Study 2B (non-matched sample)

Mediated path (a×b) = -0.07 (-0.11, -0.04)

54


C. Spring 3rd grade mathematics score, Study 2A (non-matched sample)

Mediated path (a×b) = -0.20 (-0.32, -0.11)

D. Spring 3rd grade mathematics score, Study 2B (non-matched sample)

Mediated path (a×b) = -0.17 (-0.24, -0.12)

Figure S1. Results of mediation analyses (Model 5, compared to Model 2) for Study 2A and Study 2B with fixed effects (with the non-matched samples). The numbers in parentheses are 95% bootstrapped confidence intervals based on 5000 bootstrapped replications (MacKinnon, 2008). See Tables 4 and 5 for additional covariates included in the models.

55


A. Spring 1st grade mathematics score, Study 2A (non-matched sample)

Mediated path (a×b) = -0.06 (-0.10, -0.03)

B. Spring 1st grade mathematics score, Study 2B (non-matched sample)

Mediated path (a×b) = -0.06 (-0.09, -0.03)

56


C. Spring 3rd grade mathematics score, Study 2A (non-matched sample)

Mediated path (a×b) = -0.18 (-0.28, -0.11)

D. Spring 3rd grade mathematics score, Study 2B (non-matched sample)

Mediated path (a×b) = -0.13 (-0.20, -0.09)

Figure S2. Results of mediation analyses (Model 5, compared to Model 2) for Study 2A and Study 2B without fixed effects (with the non-matched samples). The numbers in parentheses are 95% bootstrapped confidence intervals based on 5000 bootstrapped replications (MacKinnon, 2008). See Tables 4 and 5 for additional covariates included in the models.

57

supp.apa.orgsupp.apa.org/.../supplemental/a0035073/DEV_Robinson_… · Web view... Third Grade....

Documents

Transcript of supp.apa.orgsupp.apa.org/.../supplemental/a0035073/DEV_Robinson_… · Web view... Third Grade....