and Cox (1986).
This study was conducted with 90 stu- dents in grades 6 through 8 classrooms in six schools in Texas. The mean age of the students was 13 years and 7 months, and all students were identified as having learning disabilities in mathematics. Before the intervention, the students com- pleted a pretest assessment that consisted of 25 subtraction problems that required regrouping operations. After the interven- tion, a similar assessment of 25 subtrac- tion problems was completed as a post- test. A separate reliability assessment demonstrated that the two forms of the subtraction assessment were highly cor- related (r = .82).
Students were stratified by gender and school and then randomly assigned to one of nine experimental groups. In all groups, the students received instruction for solv- ing subtraction problems in 45-minute sessions conducted over six consecutive school days. For this recommendation,
we report only on the comparison be- tween three groups. One group (n = 30) received effort feedback in addition to per- formance feedback during the first three sessions. Another group (n = 30) received effort feedback in addition to performance feedback during the last three sessions. A third group (n = 30) did not receive ef- fort feedback (received only performance feedback).314 Effort feedback consisted of
the proctor commenting to the student, “You’ve been working hard.” Students in both effort feedback groups received 15 statements of effort feedback across the entire intervention.
Results indicated significant positive ef- fects for effort feedback relative to the comparison group regardless of when the student received the effort feedback. These results suggest that effort feedback is ben- eficial for learning disabled students who may not otherwise recognize the causal link between effort and outcomes.
314. Other group distinctions were related to student verbalization and are described in the discussion of recommendation 3 (explicit instruction).
References
American Educational Research Associa- tion, American Psychological Associa- tion, & National Council on Measurement in Education. (1999). The standards for
educational and psychological testing. Washington, DC: American Educational Research Association Publications. American Psychological Association.
(2001). Publication manual of the Ameri-
can Psychological Association (5th ed.). Washington, DC: Author.
American Psychological Association. (2002). Criteria for practice guideline development and evaluation. Amer-
ican Psychologist, 57(December), 1058–1061.
Artus, L. M., & Dyrek, M. (1989). The ef-
fects of multiple strategy intervention on achievement in mathematics. Un- published master’s thesis, Saint Xavier College, Chicago.
Baker, S. K., Gersten, R., Dimino, J., & Grif- fiths, R. (2004). The sustained use of research-based instructional practice: A case study of peer-assisted learning strategies in mathematics. Remedial
and Special Education, 25(1), 5–24. Baker, S., Gersten, R., Flojo, J., Katz, R.,
Chard, D., & Clarke, B. (2002). Prevent-
ing mathematics difficulties in young children: Focus on effective screening of early number sense delays (Technical Report No. 0305). Eugene, OR: Pacific Institutes for Research.
Bangert-Drowns, R. L., Kulik, C. C., Kulik, J. A., & Morgan, M. (1991). The instruc- tional effects of feedback in test-like events. Review of Educational Research,
61(2), 213–238.
Beckmann, S., Fuson, K., SanGiovanni, J., & Lott Adams, T. (Eds.), (2009). Focus in
grade 5: Teaching with curriculum focal points. Reston, VA: National Council of Teachers of Mathematics.
Berch, D. B. (2005). Making sense of number sense. Journal of Learning Disabilities,
38(4), 333–339.
Beirne-Smith, M. (1991). Peer tutoring in arithmetic for children with learning disabilities. Exceptional Children, 57 (4), 330–337.
Bloom, B. S. (1980). All our children learn-
ing. New York: McGraw-Hill.
Bruner, J. (1966). Toward a theory of in-
struction. Cambridge, MA: Belknap Press of Harvard University Press. Bryant, B. R., Bryant, D. P., Kethley, C., Kim,
S. A., Pool, C., & Seo, Y. (2008). Prevent- ing mathematics difficulties in the pri- mary grades: The critical features of instruction in textbooks as part of the equation. Learning Disability Quarterly,
31(1), 21.
Bryant, D. P., & Bryant, B. R. (2005). Early
mathematics identification and interven- tion: Working with students at-risk for mathematics difficulties. [Power Point presentation]. University of Texas Sys- tem/TEA. Retrieved January 2007 from www.k8accesscenter.org/documents/ SERP-Math.DCAIRppt.ppt
Bryant, D. P., Bryant, B. R., Gersten, R., Scammacca, N., & Chavez, M. M. (2008). Mathematics intervention for first- and second-grade students with mathemat- ics difficulties: The effects of tier 2 in- tervention delivered as booster lessons.
Remedial and Special Education, 29(1), 20–32.
Bryant, D. P., Bryant, B. R., Gersten, R. M., Scammacca, N. N., Funk, C., Winter, A., et al. (2008). The effects of tier 2 intervention on the mathematics per- formance of first-grade students who are at risk for mathematics difficulties.
Learning Disability Quarterly, 31(2), 47–63.
Bryant, D. P., Smith, D. D., & Bryant, B. R. (2008). Teaching students with special
needs in inclusive classrooms. Boston, MA: Allyn & Bacon.
Butler, F. M., Miller, S. P., Crehan, K., Bab- bitt, B., & Pierce, T. (2003). Fraction in- struction for students with mathemat- ics disabilities: Comparing two teaching sequences. Learning Disabilities Re-
REFERENCES
Carnine, D., Jitendra, A., & Silbert, J. (1997). A descriptive analysis of mathematics curricular materials from a pedagogi- cal perspective. Remedial and Special
Education, 18(2), 66–81.
Chard, D. J., Clarke, B., Baker, S., Otter- stedt, J., Braun, D., & Katz, R. (2005). Using measures of number sense to screen for difficulties in mathematics: Preliminary findings. Assessment for Ef-
fective Intervention, 30(2), 3–14.
Clarke, B., Baker, S., Smolkowski, K., & Chard, D. J. (2008). An analysis of early numeracy curriculum-based measure- ment: Examining the role of growth in student outcomes. Remedial and Special
Education, 29(1), 46–57.
Clarke, B., & Shinn, M. R. (2004). A prelimi- nary investigation into the identification and development of early mathematics curriculum-based measurement. School
Psychology Review, 33(2), 234–248. Compton, D., Fuchs, L., & Fuchs, D. (2007).
The course of reading disability in first grade: Latent class trajectories and early predictors. Unpublished manuscript. Darch, C. (1989). Comprehension instruc-
tion for high school learning disabled students. Research in Rural Education,
5(3), 43–49.
Darch, C., Carnine, D., & Gersten, R. (1984). Explicit instruction in mathematics problem solving. Journal of Educational
Research, 77(6), 351–359.
Dehaene, S. (1999). The number sense: How
the mind creates mathematics. New York: Oxford University Press.
Deno, S. (1985). Curriculum-based mea- surement: The emerging alternative.
Exceptional Children, 52(3), 219–232. Epstein, M., Atkins, M., Cullinan, D.,
Kutash, K., and Weaver, R. (2008). Re-
ducing Behavior Problems in the Elemen- tary School Classroom: A Practice Guide
(NCEE #2008-012). Washington, DC: Na- tional Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved January 2009
from http://ies.ed.gov/ncee/wwc/ publications/practiceguides.
Espin, C. A., Deno, S. L., Maruyama, G., & Cohen, C. (1989, April). The basic aca-
demic skills sample (BASS): An instrument for the screening and identification of children at risk for failure in regular edu- cation classrooms. Paper presented at an- nual meeting of American Educational Re- search Association, San Francisco, CA. Field, M., & Lohr, K. (Eds.). (1990). Clini-
cal practice guidelines: Directions for a new program. Washington, DC: National Academies Press.
Foegen, A. (2000). Technical adequacy of general outcome measures for mid- dle school mathematics. Diagnostique,
25(3), 175–203.
Foegen, A. (2008). Progress monitoring in middle school mathematics: options and issues. Remedial and Special Education,
29(4), 195–207.
Foegen, A., & Deno, S. L. (2001). Identify- ing growth indicators for low-achieving students in middle school mathematics.
Journal of Special Education, 35(1), 4–16. Foegen, A., Jiban, C., & Deno, S. (2007). Prog-
ress monitoring measures in mathemat- ics: A review of the literature. The Jour-
nal of Special Education, 41(2), 121–139. Fuchs, D., Compton, D. L., & Fuchs, L. (2007). Innovations in identifying learn-
ing disabilities using responsiveness-to- instruction. Unpublished manuscript. Fuchs, L. S., Compton, D. L., Fuchs, D.,
Paulsen, K., Bryant, J. D., & Hamlett, C. L. (2005). The prevention, identification, and cognitive determinants of math dif- ficulty. Journal of Educational Psychol-
ogy, 97(3), 493–513.
Fuchs, L. S., & Fuchs, D. (1998). Treatment validity: A unifying concept for recon- ceptualizing the identification of learn- ing disabilities. Learning Disabilities Re-
search & Practice, 13(4), 204–219. Fuchs, L. S., & Fuchs, D. (2008). Best prac-
tices in progress monitoring reading and mathematics at the elementary grades. In A. Thomas & J. Grimes (Eds.),
REFERENCES
ed.). Bethesda, MD: National Association of School Psychologists.
Fuchs, L. S., Fuchs, D. L., Compton, D. L., Bryant, J. D., Hamlett, C. L., & Seetha- ler, P. M. (2007). Mathematics screening and progress monitoring at first grade: Implications for responsiveness to in- tervention. Exceptional Children, 73(3), 311–330.
Fuchs, L. S., Fuchs, D., Compton, D. L., Pow- ell, S. R., Seethaler, P. M., Capizzi, A. M., et al. (2006). The cognitive correlates of third-grade skill in arithmetic, algo- rithmic computation, and arithmetic word problems. Journal of Educational
Psychology, 98, 29–43.
Fuchs, L. S., Fuchs, D., Craddock, C., Hol- lenbeck, K. N., & Hamlett, C. L. (2008). Effects of small-group tutoring with and without validated classroom instruc- tion on at-risk students’ math problem solving: Are two tiers of prevention better than one? Journal of Educational
Psychology, 100(3), 491–509.
Fuchs, L. S., Fuchs, D., Finelli, R., Courey, S. J., & Hamlett, C. L. (2004). Expanding schema-based transfer instruction to help third graders solve real-life mathe- matical problems. American Educational
Research Journal, 41(2), 419–445. Fuchs, L. S., Fuchs, D., Finelli, R., Courey,
S. J., Hamlett, C. L., Sones, E. M., et al. (2006). Teaching third graders about real-life mathematical problem solving: A randomized controlled study. Elemen-
tary School Journal, 106(4), 293–312. Fuchs, L. S., Fuchs, D., Hamlett, C. L., &
Karns, K. (1998). High achieving stu- dents’ interactions and performance on complex mathematical tasks as a function of homogeneous and hetero- geneous pairings. American Educational
Research Journal, 35(2), 227–267. Fuchs, L. S., Fuchs, D., Hamlett, C. L., Phil-
lips, N. B., & Bentz, J. L. (1994). Class- wide curriculum-based measurement: Helping general educators meet the challenge of student diversity. Excep-
tional Children, 60(6), 518–537.
Fuchs, L. S., Fuchs, D., Hamlett, C. L., Pow- ell, S. R., Capizzi, A. M., & Seethaler, P. M. (2006). The effects of computer-assisted instruction on number combination skill in at-risk first graders. Journal of Learn-
ing Disabilities, 39(5), 467–475.
Fuchs, L. S., Fuchs, D., Hamlett, C. L., Thomp- son, A., Roberts, P. H., & Kupek, P., et al. (1994). Formative evaluation of academic progress: How much growth can we ex- pect? Diagnostique, 19(4), 23–49. Fuchs, L. S., Fuchs, D., Hamlett, C. L., Walz,
L., & Germann, G. (1993). Formative evaluation of academic progress: How much growth can we expect? School
Psychology Review, 22(1), 27–48. Fuchs, L. S., Fuchs, D., & Hollenbeck, K. N.
(2007). Extending responsiveness to in- tervention to mathematics at first and third grades. Learning Disabilities Re-
search & Practice, 22(1), 13–24.
Fuchs, L. S., Fuchs, D., & Karns, K. (2001). Enhancing kindergartners’ mathemati- cal development: Effects of peer-assisted learning strategies. Elementary School
Journal, 101(5), 495–510.
Fuchs, L. S., Fuchs, D., Karns, K., Hamlett, C. L., Katzaroff, M., & Dutka, S. (1997). Effects of task-focused goals on low- achieving students with and without learning disabilities. American Educa-
tional Research Journal, 34(3), 513–543. Fuchs, L. S., Fuchs, D., Karns, K., Hamlett, C., Katzaroff, M., & Dutka, S. (1998). Comparisons among individual and cooperative performance assessments and other measures of mathematics competence. Elementary School Journal,
99(1), 23–51.
Fuchs, L. S., Fuchs, D., Phillips, N. B., Ham- lett, C. L., & Karns, K. (1995). Acquisition and transfer effects of classwide peer- assisted learning strategies in mathe- matics for students with varying learn- ing histories. School Psychology Review,
24(4), 604–620.
Fuchs, L. S., Fuchs, D., Prentice, K., Burch, M., Hamlett, C. L., Owen, R., et al. (2003a). Explicitly teaching for transfer: Effects on third-grade students’ mathematical
REFERENCES
problem solving. Journal of Educational
Psychology, 95(2), 293–305.
Fuchs, L. S., Fuchs, D., Prentice, K., Burch, M., Hamlett, C. L., Owen, R., et al. (2003b). En- hancing third-grade students’ mathemat- ical problem solving with self-regulated learning strategies. Journal of Educa-
tional Psychology, 95(2), 306–315. Fuchs, L. S., Fuchs, D., Prentice, K., Hamlett,
C. L., Finelli, R., & Courey, S. J. (2004). Enhancing mathematical problem solv- ing among third-grade students with schema-based instruction. Journal of
Educational Psychology, 96(4), 635–647. Fuchs, L. S., Fuchs, D., Stuebing, K., Fletcher, J. M., Hamlett, C. L., & Lambert, W. (2008). Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition? Journal of Edu-
cational Psychology, 100(1), 30–47. Fuchs, D., Fuchs, L. S., & Vaughn, S. (Eds.).
(2008). Response to intervention. Newark, DE: International Reading Association. Fuchs, L. S., Fuchs, D., & Zumeta, R. O.
(2008). A curricular-sampling approach to progress monitoring: Mathemat- ics concepts and applications. Assess-
ment for Effective Intervention, 33(4), 225–233.
Fuchs, L. S., Hamlett, C. L., & Fuchs, D. (1998). Monitoring basic skills progress:
Basic math computation (2nd ed.). Aus- tin, TX: PRO-ED.
Fuchs, L. S., Hamlett, C. L., & Fuchs, D. (1998). Monitoring basic skills progress:
Basic math concepts and applications. Austin, TX: PRO-ED.
Fuchs, L. S., Powell, S. R., Hamlett, C. L., & Fuchs, D. (2008). Remediating computa- tional deficits at third grade: A random- ized field trial. Journal of Research on
Educational Effectiveness, 1(1), 2–32. Fuchs, L. S., Seethaler, P. M., Powell, S. R.,
Fuchs, D., Hamlett, C. L., & Fletcher, J. M. (2008). Effects of preventative tutoring on the mathematical problem solving of third- grade students with math and reading difficulties. Exceptional Chil-
dren, 74(2), 155–173.
Gardner, E. F., Rudman, H. C., Karlsen, G. A., & Merwin, J. C., (1982). Stanford
achievement test (17th edition). Cleve- land, OH: Psychological Corporation. Geary, D. C. (2003). Learning disabilities in
arithmetic: Problem-solving differences and cognitive deficits. In H. L. Swanson, K. R. Harris, & S. Graham (Eds.), Hand-
book of learning disabilities (pp. 199– 212). New York: Guildford Press. Geary, D. C. (2004). Mathematics and learn-
ing disabilities. Journal of Learning Dis-
abilities, 37(1), 4–15.
Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruc- tion for students with mathematical disabilities. The Journal of Special Edu-
cation, 33(1), 18–28.
Gersten, R., Clarke, B. S., & Jordan, N. C. (2007). Screening for mathematics dif-
ficulties in K–3 students. Portsmouth, NH: RMC Research Corporation, Center on Instruction.
Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and inter- ventions for students with mathematics difficulties. Journal of Learning Disabili-
ties, 38(4), 293–304.
Gersten, R., Keating, T., & Irvin, L. (1995). The burden of proof: Validity as im- provement of instructional practice.
Exceptional Children, 61, 510–519. Goldman, S. R., Pellegrino, J. W., & Mertz,
D. L. (1988). Extended practice of basic addition facts: Strategy changes in learning disabled students. Cognition
and Instruction, 5(3), 223–265.
Guskey, T. R. (1984). The influence of change in instructional effectiveness upon the affective characteristics of teachers. American Educational Re-
search Journal, 21(2), 245–259.
Haager, D., Klinger, J., & Vaughn, S. (2007).
Evidence-based reading practices for re- sponse to intervention. Baltimore, MD: Paul H. Brooks Publishing Company. Halpern, D., Aronson, J., Reimer, N., Simp-
kins, S., Star, J., & Wentzel, K. (2007).
Encouraging girls in math and science
REFERENCES
National Center for Education Research, Institute of Education Sciences, U.S. De- partment of Education. Retrieved Janu- ary 2009, from http://ies.ed.gov/ncee/ wwc/publications/practiceguides.
Hanich, L. B., Jordan, N. C., Kaplan, D., & Dick, J. (2001). Performance across dif- ferent areas of mathematical cognition in children with learning difficulties.
Journal of Educational Psychology, 93(3), 615–626.
Harry, B., & Klingner, J. K. (2006). Why are
so many minority students in special education? Understanding race and dis- ability in schools. New York: Teachers College Press.
Hasselbring, T. S., Bransford, J. D., & Goin, L. I. (1988). Developing math automaticity in learning handicapped children: The role of computerized drill and practice. Focus
on Exceptional Children, 20(6), 1–7. Hecht, S. A., Vagi, K. J., & Torgesen, J. K.
(2007). Fraction skills and proportional reasoning. In D. B. Berch & M. M. Maz- zocco (Eds.), Why is math so hard for
some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 121–132). Baltimore, MD: Paul H. Brookes Publishing Co.
Heller, L. R., & Fantuzzo, J. W. (1993). Re- ciprocal peer tutoring and parent part- nership: Does parent involvement make a difference? School Psychology Review,
22(3), 517–534.
Heller, K., Holtzman, W., & Messick, S. (1982). Placing children in special educa-
tion: A strategy for equity. Washington, DC: National Academies Press.
Helwig, R., Anderson, L., & Tindal, G. (2002). Using a concept-grounded, curriculum- based measure in mathematics to pre- dict statewide test scores for middle school students with LD. The Journal of
Special Education, 36(2), 102–112. Hill, H. C., Rowan, B., & Ball, D. L. (2005). Ef-
fects of teachers’ mathematical knowl- edge for teaching on student achieve- ment. American Educational Research
Journal, 42(2), 371–406.
Howard, P., Perry, B. & Conroy, J. (1995, November). Manipulatives in K-6 math-
ematics learning and teaching. Paper presented at the annual conference of the Australian Association for Research in Education, Hobart.
Howard, P., Perry, B., & Lindsay, M. (1996, November). Mathematics and manipula-
tives: Views from the secondary schools. Paper presented at the joint annual meeting of the Educational Research Association, Singapore and Australian Association for Research in Education, Singapore.
Jiban, C., & Deno, S. L. (2007). Using math and reading curriculum-based mea- surements to predict state mathematics test performance. Assessment for Effec-
tive Intervention, 32(2), 78–89.
Jitendra, A. K. (2007). Solving math word
problems: Teaching students with learn- ing disabilities using schema-based in- struction. Austin, TX: PRO-ED.
Jitendra, A., Carnine, D., & Silbert, J. (1996). Descriptive analysis of fifth grade di- vision instruction in basal mathemat- ics programs: Violations of pedagogy.
Journal of Behavioral Education, 6(4), 381–403.
Jitendra, A. K., Griffin, C. C., McGoey, K., Gardill, M. C., Bhat, P., & Riley, T. (1998). Effects of mathematical word problem solving by students at risk or with mild disabilities. The Journal of Educational
Research, 91(6), 345–355.
Jitendra, A. K., Sczesniak, E., & Deatline- Buchman, A. (2005). An exploratory validation of curriculum-based math- ematical word-problem-solving tasks as indicators of mathematics proficiency for third graders. School Psychology Re-
view, 34(3), 358–371.
Johnson, E. S., Jenkins, J. R., Petscher, Y., & Catts, H. W. (2008). How can we improve
the accuracy of screening instruments?
Manuscript submitted for publication. Jordan, N. C., Hanich, L. B., & Kaplan, D.
(2003). A longitudinal study of mathe- matical competencies in children with specific mathematics difficulties versus
REFERENCES
children with comorbid mathematics and reading difficulties. Child Develop-
ment, 74(3), 834–850.
Kaminski, R., Cummings, K. D., Powell- Smith, K. A., & Good, R. H. I. (2008). Best practices in using Dynamic Indicators of Basic Early Literacy Skills (DIBELS) for formative assessment and evaluation. In A. Thomas & J. Grimes (Eds.), Best
practices in school psychology V: Vol. 4
(pp. 1181–1204). Bethesda, MD: National Association of School Psychologists. Kavale, K., & Spaulding, L. (2008). Is re-
sponse to intervention good policy for specific learning disability? Learning
Disabilities Research & Practice, 23(4), 169–179.
Lee, J., Grigg, W., & Dion, G. (2007). The
nation’s report card: Mathematics 2007
(NCES 2007–494). Washington, DC: Na- tional Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education.
Leh, J. M., Jitendra, A. K., Caskie, G. I. L., & Griffin, C. C. (2007). An evaluation of curriculum-based measurement of mathematics word problem-solving measures for monitoring third-grade students’ mathematics competence.
Assessment for Effective Intervention, 32(2), 90–99.
Lembke, E. S., & Foegen, A. (2009). Iden- tifying early numeracy indicators for kindergarten and first-grade students.
Learning Disabilities Research & Prac- tice, 24(1), 12–20.
Lembke, E. S., Foegen, A., Whittaker, T. A., & Hampton, D. (2008). Establishing tech- nically adequate measures of progress in early numeracy. Assessment for Effec-
tive Intervention, 33(4), 206–214. Locuniak, M. N., & Jordan, N. C. (2008).
Using kindergarten number sense to predict calculation fluency in second grade. Journal of Learning Disabilities,
41(5), 451–459.
Manalo, E., Bunnell, J. K., & Stillman, J. A. (2000). The use of process mnemonics in teaching students with mathematics
learning disabilities. Learning Disability
Quarterly, 23(2), 137–156.
McCloskey, M. (2007). Quantitative literacy and developmental dyscalculias. In D. B. Berch & M. M. Mazzocco (Eds.),
Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities. Bal-
timore: Paul H. Brookes Publishing. Messick, S. (1988). The once and future is-
sues of validity: Assessing the meaning and consequences of measurement. In H. Wainer & H. I. Braun (Eds.), Test valid-
ity (pp. 33–44). Hillsdale, NJ: Lawrence Erlbaum Associates.
Milgram, R. J., & Wu, H. S. (2005). The key
topics in a successful math curriculum.
Retrieved November 26, 2008, from http://math.berkeley.edu/~wu/
National Academy of Sciences. (2002). Mi-
nority students in special and gifted education. Washington, DC: National Academies Press.
National Council of Teachers of Mathemat- ics. (2006). Curriculum focal points for
prekindergarten through grade 8 math- ematics: A quest for coherence. Reston, VA: Author.
National Joint Committee on Learning Disabilities. (2005). Responsiveness to intervention and learning disabilities.
Learning Disability Quarterly, 28(4), 249–260.
National Mathematics Advisory Panel. (2008). Foundations for success: The
final report of the national mathemat- ics advisory panel. Washington, DC: U.S. Department of Education.
National Research Council. (2001). Add-
ing it up: Helping children learn math- ematics. Washington, DC: National Academies Press.
Okamoto, Y., & Case, R. (1996). Exploring the microstructure of children’s central conceptual structures in the domain of number. Monographs of the Society for
Research in Child Development, 61(1–2), 27–58.
Organisation for Economic Co-operation and Development. (2008). Programme
REFERENCES
for international student assessment (PISA).Retrieved December 5, 2008, from http://www.pisa.oecd.org/
Parmar, R. S. (1992). Protocol analysis of strategies used by students with mild disabilities when solving arithmetic word problems. Diagnostique, 17(4), 227–243.
Peterson, P. L., Fennema, E., & Carpenter, T. (1989). Using knowledge of how stu-Using knowledge of how stu- dents think about mathematics. Educa-
tional Leadership, 46(4), 42–46.
President’s Commission of Excellence in Special Education. (2002). A new era: Re-
vitalizing special education for children and their families. Washington, DC: U.S. Department of Education.
Robert, R. S., & Jenkins, E. (1989). How chil-
dren discover new strategies. Hillsdale, NJ: Lawrence Erlbaum Associates. Robinson, C. S., Menchetti, B. M., & Torge-
sen, J. K. (2002). Toward a two-factor theory of one type of mathematics dis- abilities. Learning Disabilities Research
& Practice, 17(2), 81–89.
Schmidt, W. H., & Houang, R. T. (2007). Lack of focus in mathematics: Symptom or cause? Lessons learned. In T. Loveless (Ed.), What international assessments tell
us about math achievement. Washing- ton, DC: Brookings Institution Press. Schunk, D. H., & Cox, P. D. (1986). Strategy
training and attributional feedback with learning disabled students. Jour-
nal of Educational Psychology, 78(3), 201–209.
Shapiro, E. S., Edwards, L., & Zigmond, N. (2005). Progress monitoring of math- ematics among students with learning disabilities. Assessment for Effective In-
tervention, 30(2), 15–32.
Shinn, M. R. (Ed.). (1989). Curriculum-based
measurement: Assessing special chil- dren. New York: Guilford Press. Siegler, R. S., & Jenkins, E. (1989). How chil-
dren discover new strategies. Hillsdale, NJ: Lawrence Erlbaum Associates. Silbert, J., Carnine, D., & Stein, M. (1989).
Direct instruction mathematics. Colum- bus, OH: Merrill.
Stigler, J. W., & Hiebert, J. (1999). The teach-
ing gap: Best ideas from the world’s teachers for improving education in the classroom. New York: Free Press. Thurber, R. S., Shinn, M. R., & Smolkowski, K.
(2002). What is measured in mathematics tests? Construct validity of curriculum- based mathematics measures. School