1
Math gender gaps and teacher ratings
Supplemental Online Materials
List of Figures and Tables
Tables
Table 1. Means and SDs, overall and by gender
Table 2. Correlations
Table 3. IV instrument validity information
Table 4. Study 2A results
Table 5. Study 2B results
Figures
Figure 1. Study 1 Math Teacher Ratings Figure
Figure 2. Study 1 Reading Teacher Ratings Figure
Figure 3. Conceptual Design Analyses in Study 2
Figure 4. Four Fixed Effects Mediation Figures (with the Non-matched Samples)
Figure 5. Four Fixed Effects Mediation Figures (with the Matched Samples)
Supplemental Tables
Table S1. ECLS-K teacher questionnaire for mathematics proficiency scales – Kindergarten
Table S2. ECLS-K teacher questionnaire for mathematics proficiency scales – First Grade
Table S3. ECLS-K teacher questionnaire for mathematics proficiency scales – Third Grade
Table S4. ECLS-K teacher questionnaire for mathematics proficiency scales – Fifth Grade
Table S5. Study 1 Regressions – Spring K
Table S6. Study 1 Regressions – First Grade
Table S7. Study 1 Regressions – Third Grade
Table S8. Study 1 Regressions – Fifth Grade
Table S9. Study 2A Regressions – K-1 No Fixed Effects
Table S10. Study 2A Regressions – K-1 Fixed Effects
Table S11. Study 2A Regressions – 1-3 No Fixed Effects
Table S12. Study 2A Regressions – 1-3 Fixed Effects
Table S13. Study 2B Regressions – K-1 No Fixed Effects
Table S14. Study 2B Regressions – K-1 Fixed Effects
Table S15. Study 2B Regressions – 1-3 No Fixed Effects
Table S16. Study 2B Regressions – 1-3 Fixed Effects
Table S17. Balance Before and After Propensity-Score Matching K-1 Study 2A Regressions
Table S18. Balance Before and After Propensity-Score Matching 1-3 Study 2A Regressions
Table S19. Balance Before and After Propensity-Score Matching K-1 Study 2B Regressions
Table S20. Balance Before and After Propensity-Score Matching 1-3 Study 2B Regressions
Table S21. Study 2A Regressions – K-1 Propensity Score Matching
Table S22. Study 2A Regressions – 1-3 Propensity Score Matching
Table S23. Study 2B Regressions – K-1 Propensity Score Matching
Table S24. Study 2B Regressions – 1-3 Propensity Score Matching
Supplemental Figures
Figure S1. Four Fixed Effects Mediation Figures (with the Non-matched Samples)
Figure S1. Four No Fixed Effects Mediation Figures (with the Non-matched Samples)
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.
Table S1
Kindergarten teacher questionnaire items
THIS CHILD . . . / CIRCLE ONE FOR EACH ITEMNot Yet / Beginning / In Progress / Intermediate / Proficient / Not Applicable
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
Table S2
First-grade teacher questionnaire items
THIS CHILD . . . / CIRCLE ONE FOR EACH ITEMNot Yet / Beginning / In Progress / Intermediate / Proficient / Not 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
Table S3
Third-grade teacher questionnaire items
THIS CHILD . . . / CIRCLE ONE FOR EACH ITEMNot Yet / Beginning / In Progress / Intermediate / Proficient / Not Applicable
1. 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 thensubtracts 4 when doing the mental mathproblem 467+96, or writes the algorithms orequations needed to solve a word problem,or orders steps sequentially in a multistepproblem. / 1 / 2 / 3 / 4 / 5 / N/A
3. Recognizes properties of shapes and relationships among shapes – forexample, recognizes that rectangles arecomposed of two right triangles, ordemonstrates congruence by copying theexact size and shape of a pentagon onto ageoboard. / 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, correctlyorders 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
Table S4
Fifth-grade teacher questionnaire items
THIS CHILD . . . / CIRCLE ONE FOR EACH ITEMNot Yet / Beginning / In Progress / Intermediate / Proficient / Not 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
1
Math gender gaps and teacher ratings
Table S5
Study 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)
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 / 0.80
N / 9223 / 9223 / 9223 / 9223 / 9223 / 9223 / 9223
Note: * p<0.05, ** p<0.01, *** p<0.001
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***
(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 / 0.78
N / 6658 / 6658 / 6658 / 6658 / 6658 / 6658 / 6658
Note: * p<0.05, ** p<0.01, *** p<0.001
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)
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)
R-squared / 0.42 / 0.46 / 0.67 / 0.68 / 0.74 / 0.74 / 0.76
N / 3919 / 3919 / 3919 / 3919 / 3919 / 3919 / 3919
Note: * p<0.05, ** p<0.01, *** p<0.001
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
(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)
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 / 0.75
N / 1099 / 1099 / 1099 / 1099 / 1099 / 1099 / 1099
Note: * p<0.05, ** p<0.01, *** p<0.001
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 / Conditional difference among boys and girls, after accounting for current teacher ratings / Conditional difference among boys and girls, after accounting for prior teacher ratings / Conditional difference among boys and girls, after accounting for predictedcurrent teacher ratingsWLS / 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)
Fall K Math Test Score / 0.20*** / 0.18*** / 0.19*** / 0.15*** / 0.13***
(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
(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)
R-squared / 0.60 / 0.64 / 0.64 / 0.64 / 0.52 / 0.61
N / 6658 / 6658 / 6658 / 6658 / 6658 / 6658
Note: * p<0.05, ** p<0.01, *** p<0.001
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 / Conditional difference among boys and girls, after accounting for current teacher ratings / Conditional difference among boys and girls, after accounting for prior teacher ratings / Conditional difference among boys and girls, after accounting for predictedcurrent teacher ratingsWLS-FE / WLS-FE / WLS-FE / WLS-FE / IV-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
(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) / (0.02) / (0.02) / (0.01) / (0.02)
First Grade (Current) Teacher Rating / 0.25***
(0.02)
Spring K Teacher Rating (Instrument) / 0.06*** / 0.12***
(0.02) / (0.02)
Fall K Teacher Rating (Instrument) / 0.03*
(0.01)
Predicted First Grade (Current) Teacher Rating / 0.54***
(0.12)
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 / 0.47
N / 6658 / 6658 / 6658 / 6658 / 6658 / 6658
* p<0.05, ** p<0.01, *** p<0.001
Table S11.
First-Third Grade Study 2A Regressions – No Fixed Effects
Raw difference / Conditional difference among boys and girls, before accounting for teacher ratings / Conditional difference among boys and girls, after accounting for current teacher ratings / Conditional difference among boys and girls, after accounting for prior teacher ratings / Conditional difference among boys and girls, after accounting for predictedcurrent teacher ratingsWLS / WLS / WLS / WLS / IV –
Stage 1 / IV –
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)
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
(0.10) / (0.11) / (0.10) / (0.11) / (0.17)
Race = More than one race, Non-Hispanic / -0.10 / -0.13 / -0.12 / 0.15 / -0.25
(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***
(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 / 0.41
N / 3919 / 3919 / 3919 / 3919 / 3919 / 3919
Note: * p<0.05, ** p<0.01, *** p<0.001