Mathematics Interventions

1
Mathematics Interventions

• The Access Center
• American Institutes for Research
• March 29, 2005

2
Objectives

• To describe the Information-Processing theory and
  relationship with Cognitive Strategy Instruction
  (CSI)
• To Define Cognitive Strategy Instruction (CSI)
• To review efficacy research on CSI
• To demonstrate the process of Cognitive Strategy
  Instruction

3
Learning Variables

• Strategies (procedural knowledge)
• Metacognition (knowledge about those strategies
  and about ones own thinking processes
• Knowledge base (knowledge about the world in
  general)
• Motivational Beliefs
• Cognitive Style

4
Three important implications from learning theory

• The need to help students develop background
  knowledge
• Provide extensive reading, review, practice and
  discussion
• The importance of student processing
• Initiate activities that require students to
  process and apply new information with prior
  material
• The importance of graphic organizers
• The importance of building students strategic
  knowledge
• The importance of students as active learners,
  requited to self-regulate their own
  problem-solving.

5
Definitions

• Cognitive Strategies goals directed (intended
  to perform a definite function) and consciously
  controllable process (statable)that facilitate
  performance (do things better, easier, and
  quicker). Guides that serve to support or
  facilitate the learner as they develop internal
  procedures that enable them to perform the higher
  level operations.
• Types of strategies visualization,
  verbalization, making associations, chunking,
  questioning, scanning, underlining, accessing
  cues, mnemonics
• Good strategy user one who possesses a variety
  of strategies and uses these procedures to meet
  cognitive challenges (PEMDAS)

6
Problems

• Jose and Nancy are selling greeting cards to
  raise money for the school camping trip.
  Together they sold cards totaling 88.50. Jose
  sold 67.00 worth of cards. How much money did
  Nancy make selling cards?
• On one side of a scale there are 3 pots of jam
  and a 100 oz. weight. On the other side there is
  a 200 oz. and a 500 oz. weight. The scale is
  balanced. What is the weight of one pot of jam?
• Lindsey has a total of 82.00, consisting of an
  equal number of pennies, nickels, dimes, and
  quarters. How many coins does she have in all?

7
Cognitive Strategy Instruction

• Cognitive Strategy Instruction an effort on the
  part of the teacher or the instructional
  materials to help students process information in
  meaningful ways and become independent learners.
• Founded on a broad base of research that has
  validated its effectiveness.
• Generally consist of teaching students to
  represent problems by drawing a picture,
  constructing a chart or a table, imagining the
  salient features of a problem.
• With practice, students learn to figure out which
  approaches work and which do not work for solving
  problems in the same category.

8
Research on CSI in Mathematics

• Case, Harris Graham (1992) self-regulated
  strategy on problem solving
• Hutchinson (1993) representing and solving word
  problems
• Jitendra Hoff (1995) schema-based
  instruction, distinguish type of problem
• Jitendra Xin (1997) meta-analysis
• Maccini Hughes (2000) problem-solving strategy
• Montague (1992) cognitive and metacognitive
  strategy
• Montague, Applegate Marquard (1993) cognitive
  and metacognitive strategy
• Montague, Warger Morgan (2000) Solve It!
• Woodward, Monroe, Baxter (2001) classwide
  performance tasks and ad-hoc tutoring

9
Features of CSI

• Focus on how and why specific topics are to be
  mastered
• Emphasis with how specific topic fits into an
  overall framework of related topics and skills
• Instruction is direct to the extent that the
  teacher or material makes explicit what is to be
  learned or indirect to the extent that students
  themselves make the connection between thinking
  skills and problem solutions.
• Directly addresses students comprehension and
  problem-solving deficiencies
• Teacher serves as mediator by helping to activate
  prior knowledge, represent information, select
  learning strategies, construct meaning, monitor
  understanding, assess the use of strategy,
  organize and relate ideas, summarize, and extend
  learning.

10
General Steps in Teaching Cognitive Strategy
Instruction
1.
Teach needed prerequisite skills, activate
prior knowledge
Describe the strategy to students (usually with
the help of a prompt or cue)
2.
Teach the cognitive strategy using small steps
3.
Teacher models the strategy with think alouds
4.
Students verbally rehearse the strategy,
memorize (may have checklists)
5.
Support the strategy. Students do guided
practice with corrective feedback as necessary
6.
Students have independent practice of strategy
7.
Promote generalization and self-monitoring gain
mastery
8.
pretest students as of knowledge of strategies
11
Problems

• In the Orange Bowl parade there were 50 marching
  bands. 28 bands had 660 members and the
  remainder of the bands had 45 members each. How
  many band members were in all the marching bands?

12
Conclusions

• Students with learning disabilities generally
  have greater difficulty in
• representing mathematical problems
• deriving goals for solving such problems
• choosing among appropriate strategies for problem
  solving
• engaging in self-monitoring processes, and
• Cognitive Strategy Instruction can assist with
  these areas.
• Cognitive Strategy Instruction can assist in
  students learning and improve self-esteem

13
Goal of Education

• Education is a process of developing, enlarging,
  expanding, and refining our students knowledge
  structures (Lloyd, Kameanui, Chard, 1997).
• Lloyd, J. W., Kameanui, E. J., Chard, D.
  (1997). Advances in research on instruction. In
  J. W. Lloyd, E. J. Kameanui, D. Chard (Eds).
  Issues in educating students with disabilities.
  Mahwah, NJ Lawrence Erlbaum, p. 197-221.