The Effects of the Explicit Inquiry Routine on the Performance of Students with Learning Disabilities on One-Variable Equations

Abstract

This study determined the effects of the Explicit Inquiry Routine (EIR), a teaching routine, on the math performance of 14 middle-school students with math learning disabilities. The routine integrates validated mathematical teaching practices from general education (inquiry, dialogue) and special education (intensive, explicit instruction) to engage students in an interactive inquiry process across multiple modes (concrete, representation, and abstract) of illustration and manipulation to develop an understanding of the one-variable equation. A multiple-baseline-across-students design was employed. Both statistical analysis and visual inspection indicated that students' scores increased and were maintained for up to 11 weeks after instruction was terminated. In addition, students transferred their skills to textbook word problems and standardized math achievement measures.

Get full access to this article

View all access options for this article.

References

Allsopp

D. H.

(1999). Using modeling, manipulatives, and mnemonics with eighth-grade math students. Teaching Exceptional Children, 32(2), 74–81.

Battista

M. T.

(1999). Fifth graders' enumeration of cubes in 3D arrays: Conceptual progress in an inquiry-based classroom. Journal for Research in Mathematics Education, 30(4), 417.

Butler

F. M.

Miller

S. P.

Crehan

Babbitt

Pierce

(2003). Fraction instruction for students with mathematics disabilities: Comparing two teaching sequences. Learning Disabilities Research and Practice, 18(2), 99–111.

Cass

Cates

Smith

Jackson

(2003). Effects of manipulative instruction on solving area and perimeter problems by students with learning disabilities. Learning Disabilities Research and Practice, 18(2), 112–120.

Cohen

(1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.

Connolly

(1998). KeyMath Revised: A Diagnostic Inventory of Essential Mathematics (Norms Updated Edition). Circle Pines, MN: American Guidance Service.

Coyne

M.D.

Kame'enui

E. J.

Carnine

D. W.

(2007). Effective teaching strategies that accommodate diverse learners (3rd ed.). Upper Saddle River, NJ: Pearson Merrill Prentice Hall.

Deshler

D. D.

Lenz

B. K.

Bulgren

Schumaker

J. B.

Davis

Grossen

(2004). Adolescents with disabilities in high school settings: Student characteristics and setting dynamics. Learning Disabilities: A Contemporary Journal, 2(2), 30–48.

Flesch

(1948). A new readability yardstick. Journal of Applied Psychology, 32, 221–233.

10.

Goos

(2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, 35(4), 258–291.

11.

Gravemeijer

van Galen

(2003). Facts and algorithms as products of students' own mathematical activity. In Kilpatrick

Martin

W. G.

Schifter

(Eds.), A research companion to principles and standards for school mathematics (pp. 114–122). Reston, VA: National Council of Teachers of Mathematics.

12.

Harris

K. R.

Graham

(1994). Constructivism: Principles, paradigms, and integration. The Journal of Special Education, 28(3), 233–247.

13.

Hiebert

(2003). What research says about the NCTM standards. In Kilpatrick

Martin

W. G.

Schifter

(Eds.), A research companion to principles and standards for school mathematics (pp. 5–22). Reston, VA: National Council of Teachers of Mathematics.

14.

Hoover

H. D.

Hieronymus

A. N.

Frisbie

D. A.

Dunbar

S. B.

(1993). The Iowa Tests of Basic Skills. Chicago: Riverside.

15.

Individual with Disabilities Education Improvement Act. (2004). P. L. 108–446.

16.

Jitendra

A. K.

Kameenui

Carnine

(1994). An exploratory evaluation of dynamic assessment of the role of basals on comprehension of mathematical operations. Education and Treatment of Children, 17, 139–162.

17.

Jitendra

A. K.

DiPipi

C. M.

Perron-Jones

(2002). An exploratory study of schema-based word-problem-solving instruction for middle school students with learning disabilities: An emphasis on conceptual and procedural understanding. The Journal of Special Education, 36(1), 23–38.

18.

Jones

E. D.

Wilson

Bhojwani

(1997). Mathematics instruction for secondary students with learning disabilities. Journal of Learning Disabilities, 30(2), 151–163.

19.

Kieran

(1992). The learning and teaching of school algebra. In Grouws

D.A.E.

(Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 390–419). New York: Macmillan Publishing Co., Inc.

20.

Larkin

M. J.

(2001). Providing support for student independence through scaffolded instruction. Teaching Exceptional Children, 34(1), 30–34.

21.

Maccini

Gagnon

J. C.

(2000). Best practices for teaching mathematics to secondary students with special needs. Focus on Exceptional Children, 32(5), 1–22.

22.

Maccini

Hughes

(2000). Effects of a problem-solving strategy on the introductory algebra performance of secondary students with learning disabilities. Learning Disabilities Research and Practice, 15(1), 10–21.

23.

Maccini

Ruhl

K. L.

(2000). Effects of a graduated instructional sequence on the algebraic subtraction of integers by secondary students with learning disabilities. Education and Treatment of Children, 23(4), 465–489.

24.

Mercer

C. D.

Jordan

Allsopp

D. H.

Mercer

A. R.

(1996). Learning disabilities definitions and criteria used by state education departments. Learning Disability Quarterly, 19(4), 217–232.

25.

Miller

S. P.

Butler

F. M.

Lee

(1998). Validated practices for teaching mathematics to students with learning disabilities: A review of literature. Focus on Exceptional Children, 31(1), 1–24.

26.

Miller

S. P.

Mercer

C. D.

(1993). Using data to learn concrete-semiconcrete-abstract instruction for students with math disabilities. Learning Disabilities Research and Practice, 8(2), 89–96.

27.

Miller

S. P.

Mercer

C. D.

(1997). Educational aspects of mathematics disabilities. Journal of Learning Disabilities, 30(1), 47–56.

28.

Montague

(1992). The effects of cognitive and metacognitive strategy instruction on the mathematical problem solving of middle school students with learning disabilities. Journal of Learning Disabilities, 25(4), 230–248.

29.

Montague

(1997). Cognitive strategy instruction in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30(2), 164–177.

30.

Montague

(2007). Self-regulation and mathematics instruction. Learning Disabilities Research & Practice, 22(1), 75–83.

31.

National Center for Education Statistics (NCES). (2005). Condition of education. Retrieved January 11, 2006, from http://nces.ed.gov/programs/coe/2005/section4/table.asp?tableID=285

32.

National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.

33.

No Child Left Behind Act of 2001. (2002). P. L. 107–110.

34.

Palincsar

A. S.

(1986). The role of dialogue in promoting scaffolded instruction. Educational Psychologist, 21, 73–98.

35.

Peressini

Knuth

(2000). The role of tasks in developing communities of mathematical inquiry. Teaching Children Mathematics, 6(6), 391.

36.

Perie

Grigg

W. S.

Dion

G. S.

(2005). The nation's report card: Mathematics 2005 (No. NCES 2006-453). Washington, DC: Institute of Education Sciences, National Center for Education Statistics.

37.

Rosenshine

Meister

(1992). The use of scaffolds for teaching higher-level cognitive strategies. Educational Leadership, 49 (7), 26–33.

38.

Scruggs

T. E.

Mastropieri

M. A.

Casto

(1987). “Meta-analysis for single-subject research: When does it clarify, when does it obscure?”: Response to Salzberg, Strain, and Baer. RASE: Remedial and Special Education, 8(2), 49–52.

39.

Sfard

(2000). Symbolizing mathematical reality into being or how mathematical discourse and mathematical objects create each other. In Yackel

Cobb

, (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design (pp. 37–98). Mahwah, NJ: Lawrence Erlbaum Associates, Publishers.

40.

Vygotsky

L. S.

(1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.

41.

Witzel

B. S.

Mercer

C. D.

Miller

M. D.

(2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research and Practice, 18(2), 121–131.

42.

Woodward

(1991). Procedural knowledge in mathematics: The role of the curriculum. Journal of Learning Disabilities, 24(4), 242–251.

43.

Woodward

, (2006). Making reformed-based mathematics work for academically low-achieving middle school students. In Montague

Jitendra

A. K.

(Eds.), Teaching mathematics to middle school students with learning difficulties (pp. 29–50). New York: Guilford Press.

44.

Zack

Graves

(2001). Making mathematical meaning through dialogue: “Once you think of it, the Z minus three seems pretty weird.” Educational Studies in Mathematics, 46(1/3), 229–271.