Using a cluster randomized trial design, we evaluated the persistence of effects of a research-based model for scaling up educational interventions. The model was implemented in 42 schools in two city districts serving low-resource communities, randomly assigned to three conditions. In pre-kindergarten, the two experimental interventions were identical, but one included follow-through in the kindergarten and first-grade years, including knowledge of the pre-K intervention and ways to build upon that knowledge using learning trajectories. Students in the experimental group scored significantly higher than control students (g = .51 for those who received follow-through intervention in kindergarten and first grade; g = .28 for non–follow-through), and follow-through students scored significantly higher than non–follow-through students (g = .24).
AgodiniR.HarrisB. (2010). An experimental evaluation of four early elementary school math curricula. Journal of Research on Educational Effectiveness, 3, 199–253. doi:10.1080/19345741003770693
2.
AkibaM.LeTendreG. K.ScribnerJ. P. (2007). Teacher quality, opportunity gap, and national achievement in 46 countries. Educational Researcher, 36, 369–387. doi:10.3102/0013189X07308739
3.
AunolaK.LeskinenE.LerkkanenM.-K.NurmiJ.-E. (2004). Developmental dynamics of math performance from pre-school to grade 2. Journal of Educational Psychology, 96, 699–713. doi:10.1037/0022-0663.96.4.699
4.
BakerE. L. (2007). Principles for scaling up: Choosing, measuring effects, and promoting the widespread use of educational innovation. In SchneiderB.McDonaldS.-K. (Eds.), Scale up in education, Volume I: Ideas in principle (pp. 37–54). Lanham, MD: Rowman & Littlefield.
5.
BallD. L.CohenD. K. (1999). Instruction, capacity, and improvement. Philadelphia, PA: Consortium for Policy Research in Education, University of Pennsylvania.
6.
BallouD.SandersW. L.WrightP. (2004). Controlling for student background in value-added assessment of teachers. Journal of Educational and Behavioral Statistics, 29(1), 37–65. doi:10.3102/10769986029001037
7.
BennettN.DesforgesC.CockburnA.WilkinsonB. (1984). The quality of pupil learning experiences. Hillsdale, NJ: Erlbaum.
8.
BormanG. D. (2007). Designing field trials of educational interventions. In SchneiderB.McDonaldS.-K. (Eds.), Scale up in education, Volume II: Issues in practice (pp. 41–67). Lanham, MD: Rowman & Littlefield.
9.
BredekampS. (2004). Standards for preschool and kindergarten mathematics education. In ClementsD. H.SaramaJ.DiBiaseA.-M. (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 77–82). Mahwah, NJ: Erlbaum.
10.
BrightG. W.BowmanA. H.VaccN. N. (1997). Teachers’ frameworks for understanding children’s mathematical thinking. In PehkonenE. (Ed.), Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 105–112). Lahti, Finland: University of Helsinki.
11.
BrobergA. G.WesselsH.LambM. E.HwangC. P. (1997). Effects of day care on the development of cognitive abilities in 8-year-olds: A longitudinal study. Developmental Psychology, 33, 62–69. doi:10.1037//0012-1649.33.1.62
12.
Brooks-GunnJ. (2003). Do you believe in magic? What we can expect from early childhood intervention programs. Social Policy Report, 17(1), 1, 3–14.
13.
CarneiroP.HeckmanJ. J. (2003). Human capital policy. In KruegerA. B.HeckmanJ. J. (Eds.), Inequality in America: What role for human capital policies? (pp. 77–239). Cambridge, MA: MIT Press.
14.
CarpenterT. P.FennemaE. H.PetersonP. L.CareyD. A. (1988). Teacher’s pedagogical content knowledge of students’ problem solving in elementary arithmetic. Journal for Research in Mathematics Education, 19, 385–401.
15.
CarpenterT. P.FrankeM. L. (2004). Cognitively guided instruction: Challenging the core of educational practice. In GlennanT. K.BodillyS. J.GalegherJ. R.KerrK. A. (Eds.), Expanding the reach of education reforms: Perspectives from leaders in the scale-up of educational interventions (pp. 41–80). Santa Monica, CA: RAND Corporation.
16.
CarpenterT. P.MoserJ. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15, 179–202.
17.
CarrM.SteinerH. H.KyserB.BiddlecombB. (2008). A comparison of predictors of early emerging gender differences in mathematics competence. Learning and Individual Differences, 18, 61–75.
18.
CaseR.GriffinS.KellyW. M. (1999). Socioeconomic gradients in mathematical ability and their responsiveness to intervention during early childhood. In KeatingD. P.HertzmanC. (Eds.), Developmental health and the wealth of nations (pp. 125–149). New York, NY: Guilford.
19.
CCSSO/NGA. (2010). Common core state standards for mathematics. Washington, DC: Council of Chief State School Officers and the National Governors Association Center for Best Practices. Retrieved from http://corestandards.org/
20.
Celedón-PattichisS.MusantiS. I.MarshallM. E. (2010). Bilingual elementary teachers’ reflections on using students’ native language and culture to teach mathematics. In FooteM. Q. (Ed.), Mathematics teaching & learning in K–12: Equity and professional development (pp. 7–24). New York, NY: Palgrave Macmillan.
21.
CicchettiD. (1994). Guidelines, criteria, and rules of thumb for evaluating normed and standardized assessment instruments in psychology. Psychological Assessment, 6(4), 284–290.
22.
ClarkeD. M.CheesemanJ.GervasoniA.GronnD.HorneM.McDonoughA.. . . RowleyG. (2002). Early Numeracy Research Project final report. Melbourne, Australia: Department of Education, Employment and Training, the Catholic Education Office (Melbourne), and the Association of Independent Schools Victoria.
23.
ClarkeD. M.ClarkeB. A. (2004). Mathematics teaching in grades K–2: Painting a picture of challenging, supportive, and effective classrooms. In RubensteinR. N.BrightG. W. (Eds.), Perspectives on the teaching of mathematics (66th yearbook) (pp. 67–81). Reston, VA: National Council of Teachers of Mathematics.
24.
ClementsD. H.SaramaJ. (2004a). Building Blocks for early childhood mathematics. Early Childhood Research Quarterly, 19, 181–189.
ClementsD. H.SaramaJ. (2007a). Early childhood mathematics learning. In LesterF. K.Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 461–555). New York, NY: Information Age Publishing.
27.
ClementsD. H.SaramaJ. (2007b). Effects of a preschool mathematics curriculum: Summative research on the Building Blocks project. Journal for Research in Mathematics Education, 38, 136–163.
28.
ClementsD. H.SaramaJ. (2008a). Experimental evaluation of the effects of a research-based preschool mathematics curriculum. American Educational Research Journal, 45, 443–494.
29.
ClementsD. H.SaramaJ. (2008b, March). Scaling-up interventions: The case of mathematics. Paper presented at the American Educational Research Association, New York, NY.
30.
ClementsD. H.SaramaJ. (2009). Learning and teaching early math: The learning trajectories approach. New York, NY: Routledge.
ClementsD. H.SaramaJ. (2012). Building Blocks software [Computer software]. Columbus, OH: SRA/McGraw-Hill. (Original work published 2007)
33.
ClementsD. H.SaramaJ.DiBiaseA.-M. (2003). Preschool and kindergarten mathematics: A national conference. Teaching Children Mathematics, 8, 510–514.
34.
ClementsD. H.SaramaJ.LiuX. (2008). Development of a measure of early mathematics achievement using the Rasch model: The Research-based Early Maths Assessment. Educational Psychology, 28(4), 457–482. doi:10.1080/01443410701777272
35.
ClementsD. H.SaramaJ.SpitlerM. E.LangeA. A.WolfeC. B. (2011). Mathematics learned by young children in an intervention based on learning trajectories: A large-scale cluster randomized trial. Journal for Research in Mathematics Education, 42(2), 127–166.
36.
CohenD. K. (1996). Rewarding teachers for student performance. In FuhrmanS. H.O’DayJ. A. (Eds.), Rewards and reforms: Creating educational incentives that work (pp. 61–112). San Francisco, CA: Jossey Bass.
37.
CooperH.AllenA. B.PatallE. A.DentA. L. (2010). Effects of full-day kindergarten on academic achievement and social development. Review of Educational Research, 80(1), 34–70.
38.
CubanL.UsdanM. (Eds.). (2003). Powerful reforms with shallow roots: Improving America’s urban schools. New York, NY: Teachers College.
39.
CurrieJ.ThomasD. (1995). Does Head Start make a difference?American Economic Review, 85, 341–364.
40.
CurrieJ.ThomasD. (2000). School quality and the longer-term effects of Head Start. Journal of Human Resources, 35(4), 755–774.
41.
Darling-HammondL. (1997). The right to learn: A blueprint for creating schools that work. San Francisco, CA: Jossey-Bass.
42.
Darling-HammondL. (2006). Securing the right to learn: Policy and practice for powerful teaching and learning. Educational Researcher, 35(7), 13–24.
43.
DentonK.WestJ. (2002). Children’s reading and mathematics achievement in kindergarten and first grade. Washington, DC: U.S. Department of Education, National Center for Education Statistics. Retrieved from http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2002125
44.
DuncanG. J.ClaessensA.EngelM. (2004). The contributions of hard skills and socio-emotional behavior to school readinessEvanston, IL: Northwestern University
45.
DuncanG. J.MagnusonK. (2011). The nature and impact of early achievement skills, attention skills, and behavior problems. In DuncanG. J.MagnusonK. (Eds.), Whither opportunity? Rising inequality and the uncertain life chances of low-income children (pp. 47–70). New York, NY: Russell Sage Press.
46.
EndersC.TofighiD. (2007). Centering predictor variables in cross-sectional multilevel models: A new look at an old issue. Psychological Methods, 12, 121–138.
47.
EngelM.ClaessensA.FinchM. (in press). Teaching students what they already know? The misalignment between mathematics instructional content and student knowledge in kindergarten. Educational Evaluation and Policy Analysis.
48.
FairchildA. J.MacKinnonD. P.TaborgaM. P.TaylorA. B. (2009). R2 effect-size measure of mediation analysis. Behavioral Research Methods, 41, 486–498.
49.
FennemaE. H.CarpenterT. P.FrankeM. L.LeviL. (1998). A longitudinal study of gender differences in young children’s mathematical thinking. Educational Researcher, 27, 6–11.
50.
FishR. (2003). Effects of attending prekindergarten on academic achievement (Unpublished master’s thesis). University of Buffalo, State University of New York, Buffalo, NY.
51.
FixsenD. L.BlaseK. A.NaoomS. F.WallaceF. (2009). Core implementation components. Research on Social Work Practice, 19(5), 531–540.
52.
FixsenD. L.NaoomS. F.BlaseK. A.FriedmanR. M.WallaceF. (2005). Implementation research: A synthesis of the literature (FMHI Publication No. 231). Tampa, FL: University of South Florida, Louis de la Parte Florida Mental Health Institute, the National Implementation Research Network.
53.
FraivilligJ. L.MurphyL. A.FusonK. C. (1999). Advancing children’s mathematical thinking in Everyday Mathematics classrooms. Journal for Research in Mathematics Education, 30, 148–170.
54.
FullanM. G. (1992). Successful school improvement. Philadelphia, PA: Open University Press.
55.
GarcesE.CurrieJ.ThomasD. (2002). Longer term effects of Head Start. American Economic Review, 92(4), 999–1012.
56.
GrayS. W.RamseyB. K.KlausR. A. (1983). The early training project 1962–1980. In Consortium for Longitudinal Studies (Ed.), As the twig is bent . . . Lasting effects of preschool programs (pp. 33–69). Mahwah, NJ: Erlbaum.
57.
GriffinS.CaseR. (1997). Re-thinking the primary school math curriculum: An approach based on cognitive science. Issues in Education, 3, 1–49.
58.
GriffinS.CaseR.SieglerR. S. (1994). Rightstart: Providing the central conceptual prerequisites for first formal learning of arithmetic to students at risk for school failure. In McGillyK. (Ed.), Classroom lessons: Integrating cognitive theory and classroom practice (pp. 25–49). Cambridge, MA: MIT Press.
59.
HallG. E.HordS. M. (2001). Implementing change: Patterns, principles, and potholes. Boston, MA: Allyn and Bacon.
HedgesL. V.HedbergE. C. (2007). Intraclass correlation values for planning group randomized trials in education. Educational Evaluation and Policy Analysis, 1, 60–87.
62.
HiebertJ. C. (1999). Relationships between research and the NCTM Standards. Journal for Research in Mathematics Education, 30, 3–19.
63.
HubermanM. (1992). Critical introduction. In FullanM. G. (Ed.), Successful school improvement (pp. 1–20). Philadelphia, PA: Open University Press.
64.
Investigations in number, data, and space (2nd ed.). (2008). Upper Saddle River, NJ: Pearson Scott Foresman.
65.
JacksonK. (2011). Exploring relationships between mathematics teachers’ views of students’ mathematical capabilities, visions of instruction, and instructional practices. Paper presented at the American Educational Research Association, New Orleans, LA.
66.
JacksonK.WilsonJ. (2012). Supporting African American students’ learning of mathematics: A problem of practice. Urban Education. Advance online publication. doi:10.1177/0042085911429083
67.
JacobsV. R.FrankeM. L.CarpenterT. P.LeviL.BatteyD. (2001). Professional development focused on children’s algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38, 258–288.
68.
JordanH.MendroR.WeerasingheD. (1997). Teacher effects on longitudinal student achievement. Paper presented at the National Evaluation Institute, Indianapolis, IN.
69.
KaserJ. S.BourexisP. S.Loucks-HorsleyS.RaizenS. A. (1999). Enhancing program quality in science and mathematics. Thousand Oaks, CA: Corwin Press.
70.
KildayC. R.KinzieM. B. (2009). An analysis of instruments that measure the quality of mathematics teaching in early childhood. Early Childhood Education Journal, 36, 365–372.
71.
KirkR. E. (1982). Experimental design: Procedures for the social scientist. Belmont, CA: Wadsworth.
72.
KleinA.StarkeyP.ClementsD. H.SaramaJ.IyerR. (2008). Effects of a pre-kindergarten mathematics intervention: A randomized experiment. Journal of Research on Educational Effectiveness, 1, 155–178.
73.
KleinA.StarkeyP.WakeleyA. (2000). Child Math Assessment: Preschool Battery (CMA). Berkeley, CA: University of California, Berkeley.
74.
KlingnerJ. K.AhweeS.PilonietaP.MenendezR. (2003). Barriers and facilitators in scaling up research-based practices. Exceptional Children, 69, 411–429.
75.
Ladson-BillingsG. (1997). It doesn’t add up: African American students’ mathematics achievement. Journal for Research in Mathematics Education, 28(6), 697–708.
76.
LawlessK. A.PellegrinoJ. W. (2007). Professional development in integrating technology into teaching and learning knowns, unknowns, and ways to pursue better questions and answers. Review of Educational Research, 77(4), 575–614.
77.
LeakJ.DuncanG. J.LiW.MagnusonK.SchindlerH.YoshikawaH. (2012). Is timing everything? How early childhood education program cognitive and achievement impacts vary by starting age, program duration and time since the end of the program. Irvine, CA: University of California, Irvine Department of Education.
78.
MacKinnonD. P.FritzM. S.WilliamsJ.LockwoodC. M. (2007). Distribution of the product confidence limits for the indirect effect: Program PRODCLIN. Behavior Research Methods, 39(3), 384–389.
79.
MacKinnonD. P.LockwoodC. M.WilliamsJ. (2004). Confidence limits for the indirect effect: Distribution of the product and resampling methods. Multivariate Behavioral Research, 39, 99–128.
80.
MagnusonK. A.WaldfogelJ. (2005). Early childhood care and education: Effects on ethnic and racial gaps in school readiness. The Future of Children, 15, 169–196.
81.
MartensR.HurksP. P. M.MeijsC.WassenbergR.JollesJ. (2011). Sex differences in arithmetical performance scores: Central tendency and variability. Learning and Individual Differences, 21, 549–554.
82.
MartinD. B. (2007). Beyond missionaries or cannibals: Who should teach mathematics to African American children?The High School Journal, 91(1), 6–28.
McLoydV. C. (1998). Socioeconomic disadvantage and child development. American Psychologist, 53, 185–204.
85.
MontieJ. E.XiangZ.SchweinhartL. J. (2006). Preschool experience in 10 countries: Cognitive and language performance at age 7. Early Childhood Research Quarterly, 21, 313–331.
86.
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education, Office of Planning, Evaluation and Policy Development.
87.
National Research Council. (2001). Eager to learn: Educating our preschoolers. Washington, DC: National Academy Press.
88.
National Research Council. (2007). Taking science to school: Learning and teaching science in grades K–8. Washington, DC: National Academy Press.
89.
National Research Council. (2009). Mathematics in early childhood: Learning paths toward excellence and equity. Washington, DC: National Academy Press.
90.
NatrielloG.McDillE. L.PallasA. M. (1990). Schooling disadvantaged children: Racing against catastrophe. New York, NY: Teachers College Press.
91.
PallasA. M.AlexanderK. L.EntwisleD. R.ThompsonM. (1987). School performance, status relations, and the structure of sentiment: Bringing the teacher back in. American Sociological Review, 52, 665–682.
92.
ParisS. G.MorrisonF. J.MillerK. F. (2006). Academic pathways from preschool through elementary school. In AlexanderP.WinneP. (Eds.), Handbook of research in educational psychology (pp. 61–85). Mahwah, NJ: Erlbaum.
93.
PellegrinoJ. W. (2007). From early reading to high school mathematics: Matching case studies of four educational innovations against principles for effective scale up. In SchneiderB.McDonaldS.-K. (Eds.), Scale up in practice (pp. 131–139). Lanham, MD: Rowan & Littlefield.
94.
PituchK. A.MurphyD. L.TateR. L. (2010). Three-level models for indirect effect in school and class randomized experiments in education. The Journal of Experimental Education, 78, 60–95.
95.
PituchK. A.StapletonL. M.KangJ. (2006). A comparison of single sample and bootstrap methods to assess mediation in cluster randomized trials. Multivariate Behavioral Research, 41, 367–400.
96.
PreacherK. J.CurranP. J.BauerD. J. (2006). Computational tools for probing interaction effects in multiple linear regression, multilevel modeling, and latent curve analysis. Journal of Educational and Behavioral Statistics, 31, 437–448.
97.
PreacherK. J.HayesA. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40, 879–889.
98.
Preschool Curriculum Evaluation Research Consortium. (2008). Effects of preschool curriculum programs on school readiness (NCER 2008-2009). Washington, DC: Government Printing Office. Retrieved from http://ncer.ed.gov
99.
RameyC. T.RameyS. L. (1998). Early intervention and early experience. American Psychologist, 53, 109–120.
100.
RaudenbushS. W. (2007). Designing field trials of educational interventions. In SchneiderB.McDonaldS.-K. (Eds.), Scale up in education, Volume II: Issues in practice (pp. 23–40). Lanham, MD: Rowman & Littlefield.
101.
RaudenbushS. W. (2008). Advancing educational policy by advancing research on instruction. American Educational Research Journal, 45, 206–230.
102.
RaudenbushS. W. (2009). TheBrownlegacy and the O’Connor challenge: Transforming schools in the images of children’s potential. Educational Researcher, 38(3), 169–180.
103.
RaudenbushS. W.BrykA. S.CheongY. F.CongdonR. (2006). HLM: Hierarchical linear and nonlinear modeling. Lincolnwood, IL: Scientific Software International.
104.
RistR. (1970). Student social class and teacher expectations: The self-fulfilling prophecy in ghetto education. Harvard Educational Review, 40(3), 411–451.
105.
RoyerJ. M.TronskyL. N.JacksonS. J.Horace MarchantI. (1999). Math-fact retrieval as the cognitive mechanism underlying gender differences in math test performance. Contemporary Educational Psychology, 24, 181–266.
106.
SandersW. L.HornS. P. (1998). Research findings from the Tennessee Value-Added Assessment System (TVAAS)database: Implications for educational evaluation and research. Journal of Personnel Evaluation in Education, 12(3), 247–256.
107.
SandersW. L.RiversJ. C. (1996). Cumulative and residual effects of teachers on future student academic achievement (Research Progress Report). Knoxville, TN: University of Tennessee Value-Added Research and Assessment Center.
108.
SaramaJ.ClementsD. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York, NY: Routledge.
109.
SaramaJ.ClementsD. H.HenryJ. J. (1998). Network of influences in an implementation of a mathematics curriculum innovation. International Journal of Computers for Mathematical Learning, 3, 113–148.
110.
SaramaJ.ClementsD. H.StarkeyP.KleinA.WakeleyA. (2008). Scaling up the implementation of a pre-kindergarten mathematics curriculum: Teaching for understanding with trajectories and technologies. Journal of Research on Educational Effectiveness, 1, 89–119.
111.
SaramaJ.ClementsD. H.WolfeC. B.SpitlerM. E. (2012). Longitudinal evaluation of a scale-up model for teaching mathematics with trajectories and technologies. Journal of Research on Educational Effectiveness, 5(2), 105–135.
112.
SaramaJ.DiBiaseA.-M. (2004). The professional development challenge in preschool mathematics. In ClementsD. H.SaramaJ.DiBiaseA.-M. (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 415–446). Mahwah, NJ: Erlbaum.
113.
SaramaJ.LangeA.ClementsD. H.WolfeC. B. (2012). The impacts of an early mathematics curriculum on emerging literacy and language. Early Childhood Research Quarterly, 27, 489–502. doi:10.1016/j.ecresq.2011.12.002
114.
SawadaD.PiburnM. D.JudsonE.TurleyJ.FalconerK.BenfordR.BloomI. (2002). Measuring reform practices in science and mathematics classrooms: The reformed teaching observation protocol. School Science and Mathematics, 102, 245–253.
115.
SchoenH. L.CebullaK. J.FinnK. F.FiC. (2003). Teacher variables that relate to student achievement when using a standards-based curriculum. Journal for Research in Mathematics Education, 34(3), 228–259.
116.
ShowersB.JoyceB.BennettB. (1987). Synthesis of research on staff development: A framework for future study and a state-of-the-art analysis. Educational Leadership, 45(3), 77–87.
117.
SieglerR. S. (1995). How does change occur: A microgenetic study of number conservation. Cognitive Psychology, 28, 255–273. doi:10.1006/cogp.1995.1006
118.
SnipesJ.DoolittleF.HerlihyC. (2002). Foundations for success: Case studies of how urban school systems improve student achievement. Washington, DC: Council of the Great City Schools.
119.
SowderJ. T. (2007). The mathematical education and development of teachers. In LesterF. K.Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 157–223). New York, NY: Information Age Publishing.
120.
StarkeyP.KleinA.WakeleyA. (2004). Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19, 99–120.
121.
StevensonH. W.NewmanR. S. (1986). Long-term prediction of achievement and attitudes in mathematics and reading. Child Development, 57, 646–659.
122.
StipekD. J.RyanR. H. (1997). Economically disadvantaged preschoolers: Ready to learn but further to go. Developmental Psychology, 33, 711–723.
123.
ThomasB. (1982). An abstract of kindergarten teachers’ elicitation and utilization of children’s prior knowledge in the teaching of shape concepts. Unpublished manuscript, School of Education, Health, Nursing, and Arts Professions, New York University.
124.
TurnerR. C.RitterG. W.RobertsonA. H.FeatherstonL. (2006, April). Does the impact of preschool child care on cognition and behavior persist throughout the elementary years?Paper presented at the American Educational Research Association, San Francisco, CA.
125.
U.S. Department of Health and Human Services—Administration for Children and Families. (2010). Head Start impact study. Final report. Washington, DC: Office of Planning, Research and Evaluation, U.S. Department of Health and Human Services.
126.
Van den Heuvel-PanhuizenM. (1996). Assessment and realistic mathematics education. Utrecht, the Netherlands: Freudenthal Institute, Utrecht University.
127.
WeilandC.WolfeC. B.HurwitzM. D.ClementsD. H.SaramaJ. H.YoshikawaH. (2012). Early mathematics assessment: Validation of the short form of a prekindergarten and kindergarten mathematics measure. Educational Psychology, 32(3), 311–333. doi:10.1080/01443410.2011.654190
128.
WeissI. R. (2002). Systemic reform in mathematics education: What have we learned?Paper presented at the meeting of the research presession of the 80th annual meeting of the National Council of Teachers of Mathematics Las Vegas, NV.
129.
WolfeB. (1991). Effective practices in inservice education: An exploratory study of the perceptions of Head Start participants (Unpublished doctoral dissertation). University of Wisconsin-Madison, WI.
130.
WoodK.FridS. (2005). Early childhood numeracy in a multiage setting. Mathematics Education Research Journal, 16(3), 80–99.
131.
WrightB. (1991). What number knowledge is possessed by children beginning the kindergarten year of school?Mathematics Education Research Journal, 3(1), 1–16.
132.
WrightB. D.StoneM. H. (1979). Best test design: Rasch measurement. Chicago, IL: MESA Press.
133.
WrightR. J.MartlandJ.StaffordA. K.StangerG. (2002). Teaching number: Advancing children’s skills and strategies. London: Paul Chapman/Sage.
134.
WrightS. P.HornS. P.SandersW. L. (1997). Teacher and classroom context effects on student achievement: Implications for teacher evaluation. Journal of Personnel Evaluation in Education, 11, 57–67.
135.
ZhaiF.RaverC.JonesS. M. (2012). Academic performance of subsequent schools and impacts of early interventions: Evidence from a randomized controlled trial in Head Start settings. Children and Youth Services Review, 34(5), 946–954.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
