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  1. Effective Instructional Strategies for Correctional Education Programs Joseph Calvin Gagnon, Ph.D. George Mason University Mike Krezmien, M.A. University of Maryland Richard Krause

  2. Agenda • Technology • Graduated instruction and strategy instruction

  3. Educational Reform: • Standards-driven reform is the primary approach to assuring today’s high school graduates are internationally competitive • Prompted by the public dissatisfaction and poor performance by U.S. students on international assessments (McLaughlin, Shepard, & O’Day, 1995), educators, curriculum specialists, and national organizations have focused on development of challenging standards for over a decade.

  4. Educational Reform: • Assuring all students achieve in math is a national priority (IDEA, 1997; No Child Left Behind Act of 2001) • Success in math is considered a gateway to many educational and occupational opportunities (Jetter, 1993)

  5. Educational Reform: • Recent legislation has assisted these efforts and assured that students with disabilities are included, to the maximum extent possible • Central to this notion of reform is the assertion that all students are, “entitled to instruction that is grounded in a common set of challenging standards” (McLaughlin, 1999, p. 10)

  6. Educational Reform: • Rigorous standards are especially crucial for students with learning disabilities (LD) and emotional disturbances (ED), who are commonly included in the general education environment. • These students have historically been provided a less rigorous curriculum with IEP goals that: • Focus on computation (Shriner, Kim, Thurlow, & Ysseldyke, 1993) • Have minimal linkage to long-term general education outcomes (Nolet & McLaughlin, 2000; Sands, Adams, & Stout, 1995; Smith, 1990)

  7. Educational Reform: • Some states require students to pass assessments with open-ended problem solving tasks

  8. Real World Problem Solving and Technology: • Computer/videodisc based • Effective instruction and instructional design variables • Anchored instruction • Web based instruction (WBI) • Calculators • Standard • Graphing

  9. Real World Problem Solving and Technology: • Technology-based instructional approaches can significantly affect student learning and acquisition of higher-level math concepts; particularly when embedded within real-world problem solving tasks (Maccini & Gagnon, in press) • This approach relies on the use of a computer, calculator, or other specialized systems as the mode of instruction (Vergason & Anderegg, 1997)

  10. Real World Problem Solving and Technology: • Technology-based instruction can: • Assist teachers in moving away from a focus on memorization and routine manipulation of numbers in formulas and toward instruction and activities embedded in real-world problems (Bottge & Hasselbring, 1993) • Promote active student learning (Kelly, Gersten, & Carnine, 1990)

  11. Real World Problem Solving and Technology: • Embedding problem solving information within a real world context helps: • Activate student conceptual knowledge when presented with a real-life problem solving situation (Gagne, Yekovich, & Yekovich, 1993) • Improve student motivation, participation, and generalization (Palloway & Patton, 1997)

  12. Real World Problem Solving and Technology: Teacher Quote: “I incorporate fun activities such as timing a wave, weighing bananas, and counting chips in a cookie to acquire data. Students are included in groups and usually have successful experiences with others as they do the activities”

  13. Real World Problem Solving and Technology: • Anchored instruction is one such example of embedding problem solving situations in a real-life situation via interactive video-disc instruction (see Bottge & Hasselbring, 1993) • Students with special needs may need additional support to benefit from enhanced anchored instruction • Additional review of the videodisc • Cooperative learning strategies (Bottge et al., 2002)

  14. Real World Problem Solving and Technology: • However, “Rather than capitalizing on the insights and motivation that students bring to the classroom, schools may actually be wasting valuable time by withholding more authentic and motivating problems until ‘prerequisite’ skills are acquired” (Bottge et al., 2001, p. 312) • It is effective to use videodisc-based interventions that embed interesting and age-appropriate problem-solving situations (Bottge, 1999; Bottge & Hasselbring, 1993; Bottge et al., 2001; Bottge et al., 2002)

  15. Real World Problem Solving and Technology: Recommendations: • Incorporate di (e.g., model, guided practice, review, feedback) within technology-based interventions • Incorporate effective instructional design variables within technology-based instruction to reduce student confusion and mathematical errors

  16. Real World Problem Solving and Technology: • Discrimination: Skills are introduced, practiced, and mixed with other types of problems. Specific instruction and remediation provide for discrimination • Range of Examples: Students introduced to fractions less than one, improper fractions, and provided strategies for reading and writing both

  17. Real World Problem Solving and Technology: • Explicit Strategy Teaching: Students provided explicit problem solving strategies • Computer software should incorporate a wide range of examples and nonexamples into instruction for discrimination practice and generalization

  18. Real World Problem Solving and Technology: • One example of a series that uses technology, the noted instructional design features, and teaching practices recommended by NCTM is: • The Systems Impact Direct Instruction videodisc mathematics programs (DIV) (Mastering Fractions, Mastering Decimals and Percents, Mastering Equations, Roots, and Exponents, Mastering Ratios and Word Problems, and Mastering Informal Geometry) (Scott Foresman, 1991)

  19. Real World Problem Solving and Technology: Recommendations: • Incorporate technology-based tutorial programs that embed basic math skills and higher order thinking within problem-solving situations • This allows students to practice remedial skills within context • For example, it is recommended that computers be available to students with LD for tutorial assistance

  20. Real World Problem Solving and Technology: Example: • The Hot Dog Stand and Geometric SuperSupposer(both programs are available from Sunburst Communications at http://www.sunburst.com/index/html)

  21. Real World Problem Solving and Technology: Example: • The Adventures of Jasper Woodbury consists of 12 video-disc based adventures (plus video based analogs, extensions and teaching tips) that focus on mathematical problem finding and problem solving • Each adventure is designed from the perspective of the standards recommended by the National Council of Teachers of Mathematics (NCTM)

  22. Real World Problem Solving and Technology: • Each adventure provides multiple opportunities for problem solving, reasoning, communication and making connections to other areas such as science, social studies, literature and history (NCTM, 1989; 1991) • Jasper adventures are designed for students in grades 5 and up • Each videodisc contains a short (approximately 17 minute) video adventure that ends in a complex challenge

  23. Real World Problem Solving and Technology: • The adventures are designed like detective novels where all the data necessary to solve the adventure (plus additional data that are not relevant to the solution) are embedded in the story • Jasper adventures also contain "embedded teaching" episodes that provide models of particular approaches to solving problems

  24. Real World Problem Solving and Technology: • Geometry • Blueprint for Success, The Right Angle, The Great Circle Race • Algebra • Working Smarter, Kim’s Komet, The General is Missing http://peabody.vanderbilt.edu/projects/funded/jasper/Jasperhome.html

  25. Real World Problem Solving and Technology: • The Jasper series is currently being used in classrooms in every state in the U. S., as well as in classrooms in Canada and China. Jasper is published and distributed by LEARNING, Inc., a division of Lawrence Erlbaum Associates.

  26. Real World Problem Solving and Technology: Web-based Instruction: • A promising approach is the TRIP project (Christle et al., 2001), which: • Extends the principles of anchored instruction and contextualized learning (Cognition and Technology Group at Vanderbilt, 1990) • Includes Web-based instruction (WBI) within a universally designed environment • Students work collaboratively • Research is needed to fully realize the effects of WBI, but the future appears promising

  27. Real World Problem Solving and Technology: • Limitations to the use of technology: • The review was limited to 11 published articles that met all criteria • Although 73% (n = 8) of the studies determined significant treatment effects, three of the studies noted that the proficiency levels of students with disabilities fell below the established criterion for learning of 80%

  28. Real World Problem Solving and Technology: • Further, of the articles that obtained significant findings, only 45% (n = 5) of the interventions directly programmed for maintenance and 55% (n = 6) programmed for generalization • The generalizability of the findings may also be of concern because no information was available on new technologies (e.g., DVD and streaming video)

  29. Real World Problem Solving and Technology: Calculators: • In one study, calculator use was the most prevalent adaptation noted by teachers Maccini & Gagnon, 2002) • Consistent with Etlinger and Ogletree (1982), teacher responses involved two primary categories:

  30. Real World Problem Solving and Technology: • The "practical" function: The use of calculators to complete tedious calculations, save time, increase student motivation, and to decrease math anxiety • The "pedagogical" function: Relates to similarities between calculators, textbooks, and manipulatives in that each enhances student understanding and competence in mathematics

  31. Real World Problem Solving and Technology: • These classifications are consistent with the five primary functions of calculators as stated by the NCTM • Within the practical classification, NCTM identifies the use of calculators to • Perform tedious computations that arise when working with real data in problem solving situations • Concentrate on the problem-solving process rather than calculations associated with problems • Gain access to mathematics beyond their level of computational skill

  32. Real World Problem Solving and Technology: • Teachers noted, Daily use of calculators to eliminate arithmetic phobia (Maccini & Gagnon, 2002) • Use of calculators to increase motivation has also been noted by researchers (Deshler, Ellis, Lenz, 1996)

  33. Real World Problem Solving and Technology: • The pedagogical function coincides with two other uses identified by NCTM • To explore, develop, and reinforce concepts including estimation, computation, approximation, and properties • To experiment with math ideas and discover patterns

  34. Real World Problem Solving and Technology: • Teachers noted using calculators as an aid for students to solve problems, • Students use calculators only after attempting to solve problems • Students use calculators to help solve problems, but still must show an understanding by listing their steps

  35. Real World Problem Solving and Technology: • Calculators can be used to enhance learning by helping students to visualize connections between symbolic and graphic solutions (Milou, Gambler, & Moyer, 1997; Demana & Waits, 1990), teachers noted, • Students use calculators or graphing calculators for Algebra II

  36. Real World Problem Solving and Technology: • Salend and Hoffstetter (1996) assert the importance of: • Training students to use calculators • Using an overhead projector to teach this skill • Locating and describing the function of each key to students • Providing examples of calculator use

  37. Real World Problem Solving and Technology: • Students should be provided opportunities to practice calculations, including estimation skills and reviewing answers obtained through calculator use

  38. Real World Problem Solving and Technology: • Another important category of teacher responses related to teaching students to use calculators, • I do extensive work with students on how to use the calculator • I use an overhead calculator to assist with VAKT [i.e., visual, auditory, kinesthetic, and tactile learning]"

  39. Real World Problem Solving and Technology: • Based on teacher responses, the literature, and NCTM position statements (1998) the following recommendations for teachers are noted: • Model calculator application • Use calculators in computation, problem solving, concept development, pattern recognition, data analysis, and graphing • Integrate calculator use in assessment and evaluation

  40. Real World Problem Solving and Technology: • Remain current with state-of-the-art technology • Explore and develop new ways to use calculators to support instruction and assessment

  41. Concrete-Semiconcrete-Abstract Instructional Sequence (C-S-A) Bruner’s structure-oriented theory of learning: Enactive mode (e.g., the “doing” phase” - using concrete objects to represent problems - concrete representations) Iconic mode (e.g., the “seeing phase” visualizing representations of the problem - semiconcrete representations) Symbolic mode (e.g., using abstract symbols to represent the problem - abstract representations)

  42. C-S-A: Research: Why teach for meaning? Students with learning problems have problems with: • classifying objects or ideas • finding logical relationships/making logical deductions • generating hypotheses choosing among alternative routes

  43. C-S-A: • Empirical studies have validated CSA use with students with high incidence disabilities for: • Whole number operations • Word problems • Place value • Introductory algebra skills

  44. C-S-A: Recommendations for Practice: Teach for meaning prior to abstract representations Examples: • Guidelines for using manipulatives - In the Focus journal p. 11 • Addition Sample Problem - In the TEC journal p. 14

  45. C-S-A: Solve: 3a + 2a + 5 = 20 Concrete: Use paper plates and beans to solve: 1 bean = 1 unit 1 paper plate = variable “a” =   +  + • • • • • = • • • • • • • • • • • • • • • • • • • • = • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •  = 3 Source: Allsopp (1999, p. 78)

  46. C-S-A: Solve: 3a + 2a + 5 = 20 Semiconcrete: Use pictures of plates and beans to solve – = # less than 10; = tens variable “a” =   +  +– – – – – =   +  +– – – – – =   +  +– – – – – = – – – – – – – – – –  +  = – – – – – – – – – – – – – – – – – – – –

  47. C-S-A: Solve: 3a + 2a + 5 = 20 Abstract: 5a + 5 = 20 5a + 5 - 5 = 20 - 5 5a = 15 a = 3 Check: 5(3) + 5 = 20; 20 = 20 Yes, it checks.

  48. Strategy Instruction: Strategy instruction in math, such as a first letter Mnemonic strategy, is used to help students memorize and recall effective problem solving skills • For example, the steps in the strategy can help remind students to read the problem carefully, to obtain a whole picture of the problem (problem representation), to solve the solution, and to check your answers (problem solution)

  49. Strategy Instruction: Strategy Instruction Can Include: • Structured worksheets/cue cards to help students remember problem solving steps or strategies for solving problems • Mnemonics to help students recall problem solving steps or important facts Research: Strategy instruction that incorporated a first-letter mnemonic and structured worksheets helped students with LD learn prealgebra skills and concepts (Maccini & Hughes, 2000)

  50. Strategy Instruction: Recommendations for Practice: Refer to the “STAR Strategy Steps” as an example of how to teach both problem representation and problem solution using a first letter mnemonic strategy Example: 1. STAR - See article in TEC journal, p. 10 and instructional steps, p. 12