Assessing the Instructional Level for Mathematics: A Comparison of Methods
Abstract
This study compared the mathematics performance of 434 second-, third-, fourth-, and fifth-grade students to previously reported fluency and accuracy criteria using three categories of performance (frustration, instructional, and mastery). Psychometric properties of the fluency and accuracy criteria were explored and new criteria for the instructional level were empirically derived. Two sets of mathematics probes were administered to the students and delayed alternate-form reliability coefficients were obtained from multiskill probes. Results suggested that fluency data were significantly more reliable than accuracy data. Slopes from the single-skill probes were used to categorize students as high responders, and the mean fluency scores from that group's multiskill probes were used to suggest an alternative instructional level of 14-31 digits correct per minute for second- and third-graders and 24-49 digits correct per minute for fourth- and fifth-graders. Implications for practice and suggestions for future research are discussed.
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Foegen et al. review two approaches to developing CBMs in math: curriculum sampling versus robust indicators; curriculum sampling reflects items from within a year given high curriculum specificity, while robust indicators reflect problems identifying core competence enabling growth to be modeled over multiple years.
“Foegen et al. [141] comprehensively review two approaches to developing CBMs in math: curriculum sampling versus robust indicators.Rather than a mastery approach, curriculum sampling reflects items from within a year “given the high level of curriculum specificity in mathematics” (p.122); in contrast, robust indicators reflect problems that “identify aspects of core competence in mathematics [that”
From Curriculum-Based Measurement: A Brief History of Nearly Everything from the 1970s to the Present (2013) · cites this paper as [141]
Cites
Statistical Power Analysis for the Behavioral Sciences (2nd ed.).
Lachenbruch, P. A., & Cohen, J. (1989) · Journal of the American Statistical Association · doi:10.2307/2290095 · Cited by 37,385 · see citing works
National Council of Teachers of Mathematics
(1979) · Mathematics Teacher Learning and Teaching PK-12 · doi:10.5951/mt.72.8.0637 · Cited by 8,512 · see citing works
Messick, S. (1995) · American Psychologist · doi:10.1037/0003-066x.50.9.741 · Cited by 4,198 · see citing works
Psychological Testing: Principles, Applications, and Issues
Kaplan, R. M. (1982) · Cited by 1,799 · see citing works
Best Practices in School Psychology IV
Thomas, A., Grimes, J., & McKevitt, B. C. (1995) · Medical Entomology and Zoology · Cited by 1,333 · see citing works
Vellutino, F. R., Scanlon, D. M., Sipay, E. R., Small, S. G., Pratt, A., Chen, R., & DENCKLA, M. B. (1996) · Journal of Educational Psychology · doi:10.1037/0022-0663.88.4.601 · Cited by 932 · see citing works
Curriculum-based measurement: Assessing special children.
Shinn, M. R. (1989) · Guilford Press eBooks · Cited by 919 · see citing works
Peer-Assisted Learning Strategies: Making Classrooms More Responsive to Diversity
Fuchs, D., Fuchs, L. S., Mathes, P. G., & Simmons, D. C. (1997) · American Educational Research Journal · doi:10.3102/00028312034001174 · Cited by 662 · see citing works
Behavioral Fluency: Evolution of a New Paradigm
Binder, C. V. (1996) · The Behavior Analyst · doi:10.1007/bf03393163 · Cited by 559 · see citing works
(1977) · Cited by 434 · see citing works
Advanced applications of curriculum-based measurement
Shinn, M. R. (1998) · Medical Entomology and Zoology · Cited by 386 · see citing works
Fuchs, L. S., & Fuchs, D. (1998) · Learning Disabilities Research and Practice · Cited by 367 · see citing works
School Psychology: A Blueprint for Training and Practice II.
Ysseldyke, J., Dawson, P., Lehr, C. A., Reschly, D. J., Reynolds, M. C., & Telzrow, C. F. (1997) · Cited by 254 · see citing works
A Model for Conducting a Functional Analysis of Academic Performance Problems
Daly, E. J., Martens, B. K., Witt, J. C., & Dool, E. J. (1997) · School Psychology Review · doi:10.1080/02796015.1997.12085886 · Cited by 249 · see citing works
Assessing Intervention Responsiveness: Conceptual and Technical Issues
Fuchs, L. S. (2003) · Learning Disabilities Research & Practice · doi:10.1111/1540-5826.00073 · Cited by 236 · see citing works
Explicitly teaching for transfer: Effects on third-grade students' mathematical problem solving.
Fuchs, L. S., Fuchs, D., Prentice, K., Burch, M., Hamlett, C. L., Owen, R., Hosp, M. K., & Jancek, D. (2003) · Journal of Educational Psychology · doi:10.1037/0022-0663.95.2.293 · Cited by 185 · see citing works
A Personal View of Curriculum-Based Assessment
Gickling, E. E., & Thompson, V. P. (1985) · Exceptional Children · doi:10.1177/001440298505200302 · Cited by 182 · see citing works
Daly, E. J., & Martens, B. K. (1994) · Journal of Applied Behavior Analysis · doi:10.1901/jaba.1994.27-459 · Cited by 182 · see citing works
Christ, T. J. (2006) · School Psychology Review · doi:10.1080/02796015.2006.12088006 · Cited by 174 · see citing works
Persistent arithmetic, reading, or arithmetic and reading disability
Badian, N. A. (1999) · Annals of Dyslexia · doi:10.1007/s11881-999-0019-8 · Cited by 157 · see citing works
Gickling, E. E., & Armstrong, D. L. (1978) · Journal of Learning Disabilities · doi:10.1177/002221947801100905 · Cited by 152 · see citing works
What is Measured in Mathematics Tests? Construct Validity of Curriculum-Based Mathematics Measures
Thurber, R. S., Shinn, M. R., & Smolkowski, K. (2002) · School Psychology Review · doi:10.1080/02796015.2002.12086170 · Cited by 141 · see citing works
Curriculum-Based Assessment: An Introduction
Tucker, J. A. (1985) · Exceptional Children · doi:10.1177/001440298505200301 · Cited by 126 · see citing works
Comparison of dual discrepancy criteria to assess response to intervention
Burns, M. K., & Senesac, B. V. (2005) · Journal of School Psychology · doi:10.1016/j.jsp.2005.09.003 · Cited by 111 · see citing works
Self-citationEmpirical Analysis of Drill Ratio Research
Burns, M. K. (2004) · Remedial and Special Education · doi:10.1177/07419325040250030401 · Cited by 103 · see citing works
Self-citationBurns, M. K., Dean, V. J., & Foley, S. (2004) · Journal of School Psychology · doi:10.1016/j.jsp.2004.04.003 · Cited by 102 · see citing works
Self-citationFuchs, L. S., Fuchs, D., Phillips, N. B., Hamlett, C. L., & Earns, K. (1995) · School Psychology Review · doi:10.1080/02796015.1995.12085790 · Cited by 101 · see citing works
VanDerHeyden, A. M., & Burns, M. K. (2005) · Assessment for Effective Intervention · doi:10.1177/073724770503000302 · Cited by 97 · see citing works
Self-citationDevelopment and Validation of a Process for Screening Referrals to Special Education
VanDerHeyden, A. M., Witt, J. C., & Naquin, G. M. (2003) · School Psychology Review · doi:10.1080/02796015.2003.12086194 · Cited by 94 · see citing works
Self-citationBest Practices in Curriculum-Based Assessment.
Gravois, T. A., & Gickling, E. E. (2002) · Cited by 80 · see citing works
THE EFFECTS OF INSTRUCTIONAL MATCH AND CONTENT OVERLAP ON GENERALIZED READING PERFORMANCE
Daly, E. J., Martens, B. K., Kilmer, A., & Massie, D. R. (1996) · Journal of Applied Behavior Analysis · doi:10.1901/jaba.1996.29-507 · Cited by 72 · see citing works
Identifying Growth Indicators for Low-Achieving Students in Middle School Mathematics
Foegen, A., & Deno, S. L. (2001) · The Journal of Special Education · doi:10.1177/002246690103500102 · Cited by 61 · see citing works
The Generalizability of CBM Survey-Level Mathematics Assessments: Just How Many Samples Do We Need?
Hintze, J. M., Christ, T. J., & Keller, L. A. (2002) · School Psychology Review · doi:10.1080/02796015.2002.12086171 · Cited by 58 · see citing works
Greenwood, C. R. (1991) · Journal of Reading Writing and Learning Disabilities International · doi:10.1080/0748763910070203 · Cited by 58 · see citing works
Mathematics Instruction for Students with Special Needs
Rivera, D. M., & Bryant, B. R. (1992) · Intervention in School and Clinic · doi:10.1177/105345129202800203 · Cited by 41 · see citing works
Computers and Curriculum-Based Measurement: Effects of Teacher Feedback Systems
Fuchs, L. S., Fuchs, D., & Hamlett, C. L. (1989) · School Psychology Review · doi:10.1080/02796015.1989.12085405 · Cited by 37 · see citing works
Use of Gickling's Model of Curriculum-Based Assessment to Improve Reading in Elementary Age Students
Shapiro, E. S. (1992) · School Psychology Review · doi:10.1080/02796015.1992.12085603 · Cited by 36 · see citing works
Burns, M. K., Tucker, J. A., Frame, J., Foley, S., & Hauser, A. (2000) · Journal of Psychoeducational Assessment · doi:10.1177/073428290001800405 · Cited by 30 · see citing works
Self-citationShapiro, E. S., & Ager, C. (1992) · The Elementary School Journal · doi:10.1086/461693 · Cited by 30 · see citing works
Getting It Right So They Can Get It Right: An Overview of the Special Series
Daly, E. J., & McCurdy, M. (2002) · School Psychology Review · doi:10.1080/02796015.2002.12086167 · Cited by 23 · see citing works
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Curriculum-Based Measurement: A Brief History of Nearly Everything from the 1970s to the Present
Tindal, G. (2013) · ISRN Education · doi:10.1155/2013/958530 · Cited by 59 · see citing works
- Authors
- Burns, M. K., VanDerHeyden, A. M., & Jiban, C. L.
- Affiliations
- University of Minnesota (US)
- University of California, Santa Barbara (US)
- Corresponding author
- Burns, Matthew K.
- ORCID
- Burns, Matthew K.
- Venue
- School Psychology Review
- Publisher
- Informa UK Limited
- Published
- 2006-09-01
- Volume
- 35
- Issue
- 3
- Pages
- 401-418
- ISSN
- 0279-6015 (ISSN-L)
- 2372-966X
- OpenAlex
- W1564627542
- Cited by
- 96
- References
- 40
- Citations by year
- 2026: 1 · 2025: 4 · 2024: 2 · 2023: 4 · 2022: 3 · 2021: 6 · 2020: 8 · 2019: 12 · 2018: 8 · 2017: 3 · 2016: 6 · 2015: 7 · 2014: 3 · 2013: 2 · 2012: 7
- FWCI
- 1.26
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- School Psychology Review (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Cognitive and developmental aspects of mathematical skills
- Social Sciences › Psychology › Developmental and Educational Psychology › Behavioral and Psychological Studies
- Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
- Keywords
- mathematics fluency, instructional level, elementary school students, psychometric properties, alternate form reliability, frustration level, mastery level
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