Effective Instructional Practices Continued…

Ashley Shahidullah

CEP 802A9/30/11

Finish Video Questions…

•Place value centers

Instructional Practice #3

•Explicit C-R-A instruction with teacher modeling and scaffolding▫Is teacher centered and focused on helping

students learn basic skills and information

CONCRETE

▫Providing students with opportunities to understand each mathematical concept by first working with concrete materials, then representations, then working at the abstract level

▫Manipulatives can be useful when teachers understand the purpose for using them

REPRESENTATIONAL

•When students begin to draw representations, some of the structure of manipulatives is removed and misconceptions are more visible

•Using illustrations to represent concrete materials, gives students an opportunity to connect their drawing of newly learned concepts to the concrete materials they are already familiar with

ABSTRACT

•The goal at this level is to ensure that students explicitly connect their conceptual knowledge gained at the concrete and representational levels to mathematical symbols and related mental processes (i.e., numbers, variables)

CHALLENGES

•Struggling learners often experience difficulty demonstrating abstract level understanding

•2 potential explanations:▫They don’t really understand the concept

or meaning behind the abstract representation

▫They have difficulty retrieving from memory previously learned math concepts and skills necessary for understanding a new concept

Consideration 1

Use appropriate and various concrete objects to teach the particular mathematical concept or skill

•Discrete objects-objects that can be counted▫Cookies▫Counting blocks▫Chips

•Continuous objects- not used for counting but are used for measurement▫Ruler▫Measuring cup▫Weight scale

Consideration 2

Use appropriate drawings or picture representations of concrete objects

Consideration 3

Use appropriate strategies for assisting students to make the transition from concrete to abstract level of understanding

Consideration 4

Determine students’ understanding at each level before moving to the next level

Level of Understanding

Mastery guideline

Concrete Accurately represents math concept or performs math skill correctly 3 of 3 times for 3 consecutive days

Representational Accurately represents mathematics concept or performs math skill 5 of 5 times for 3 consecutive days

Abstract Accurately represents math concept or performs math skill 10 of 10 times for 3 consecutive days

Explicit teacher modeling/scaffolding

•Is a well supported instructional strategy for students with high-incidence disabilities in mathematics

•Several specific modeling and scaffolding techniques are effective when helping students move through the CRA sequence of instruction

1. Link to previous knowledge2. Incorporate multi-sensory methods3. Cue key features of a target mathematics

concept1. Visual cuing (color-coding, directional

arrows, circling symbols, etc)2. Using a structured form with guiding

questions or prompts to direct student reflection

Instructional Implementation

1. Problem:____________________2. Describe with pictures or words your

way for solving the problem.

3. When I solved the problem, I got_________.

4. I used ________________to solve the problem.

Structured form with prompts

Goal: To solve a math problem.ChecklistYou are to:

Write the problem at the top of the page.

• Use a strategy to solve the problem.

• Use pictures or words to explain your strategy.

Write your answer in the blank

Write the items or ideas you used to solve the problem

Cuing sheet for activity

4. Provide examples and non-examples of a target concept

5. Scaffold/fade teacher direction from high to medium to low levels

6. Provide immediate and specific corrective feedback

7. Provide generous amounts of specific positive reinforcement

YES NO

Instructional Practice #4

Teach problem solving strategies

Strategy Instruction

•Is STUDENT centered and teaches students how to learn information and then retrieve that information when it is needed.

•The focus is primarily on the rules and the processes or global skills required to learn the required concept.

Direct Instruction

• Direct instruction is a teacher centered instructional approach that is most effective for teaching basic or isolated skills (Kroesbergen & Van Luit, 2003).

• can be a scripted program that is very systematic with a step by step format requiring student mastery at each step.

• generally fast paced instruction and often used with a small group of students.

http://www.k8accesscenter.org/training_resources/documents/DirectInstructionMathApplicationFinal_000.pdf

Swanson (2001) identified 12 criteria associated with direct instruction. When any four of these indicators are present, direct instruction is occurring:

• Breaking down a task into small steps• Administering probes• Administering feedback repeatedly• Providing a pictorial or diagram presentation• Allowing indep practice and individ paced instruction• Breaking instruction down into simpler phases• Instructing in a small group• Teacher modeling a skill• Providing set materials at a rapid pace• Providing individ child instruction• Teacher asking questions• Teacher presenting the new (novel) materials (Swanson,

2001, p. 4)

• According to researchers, using a combination of direct instruction and strategy instruction has a greater positive effect than either method alone

• Teaching basic skills to students through direct instruction and then teaching them strategies to store and retrieve the information will ensure a successful educational experience for all students (Ellis, 1993; Karp & Voltz, 2000; Swanson, 2001)

According to Swanson (2001), strategy instruction has several components:

• Advanced organizers (mental scaffolding)• Organization (have students assess own

understanding )• Elaboration (connecting new material to info

already learned)• Generative learning (making sense of new info

by summarizing)• General study strategies (outlining,

questioning, discussions with peers, and underlining)

Strategy instruction follows a sequence of events:

1. States the objective2. Review skills needed for new info3. Present the new info/skill4. Question students about events5. Provide time for group instruction and

indep practice6. Give performance assessments

(Swanson, 2001)

Strategy Instruction

What Does Strategy/Implicit Instruction Look Like for Mathematics?

•The object of strategy instruction is to teach students to use higher-order thinking skills, to problem solve, and to use techniques that they can generalize into other areas.

The Problem

•Sara saved $12.85 from her allowance. At the beach, she spent $1.75 for an ice cream cone and $4.50 in the video arcade. She wants to buy a necklace that costs $5.00. Does she have enough money left to buy the necklace?

Think Aloud Problem Solving Process

Teacher Self-DialogueWhat do they want me to find out? Hmmm…Does Sara have enough money to buy the necklace? How much does she need for thenecklace? $5.00. I’ll write that down here. OK, she needs $5.00. How much did she start out with? Oh, $12.85. Well, she had enough to start out with, but she spent some of it. How much did she spend? She bought an ice cream cone for $1.75, and she spent $4.50 in the arcade. What do I do now? I guess there are two ways I could dothis. I could subtract one amount from $12.85 and the other amount from what she had left, or I could add both of the amounts she spent and then subtract the total from $12.85.

Learning Strategies

What Are Learning Strategies? •Learning strategies are an individual’s

approach to a task. •They are how a student organizes and

uses a set of skills to learn content or to accomplish a particular task more effectively and efficiently either in or out of school (Schumaker & Deshler, 1984).

learning strategies include:• what we think about (e.g., planning

before writing• realizing when we are not understanding

something we are reading• remembering what we have learned

previously on the topic under study) •and what we physically do (e.g., taking

notes, rereading to clear up confusion, making a chart, table, or story map to capture the most important information).”

• Teachers who teach students learning strategies teach students how to learn and how to be successful in and out of the academic setting.

• Learning strategies give students a way to think through and plan the solution to a problem.

•Students who use learning strategies become more effective and independent learners.

Two Types of Learning Strategies• Cognitive

▫ Learning how to read▫ Visualize▫ Estimate▫ Compute

• Metacognitive▫ Self checking▫ Self questioning▫ Self monitoring

What Do Learning Strategies Look Like for Mathematics?

Cognitive learning strategies range from the simple to the complex and may include ▫ Adding by counting on from the first addend or the

larger addend

▫ Using mnemonics

▫ Understanding that two times any number will be even or that five times any number will always end in a zero or a 5

▫ Using a finger strategy for multiplying numbers less than 10 by 9

How to Implement Learning Strategies in the Classroom

Administrators should: ▫provide professional development about

learning strategies and ▫monitor teachers to be sure that learning

strategies are taught.

Teachers should:

• have a range of strategies from which to choose; • practice new strategies until they are

comfortable with them; • explain why learning strategies are important as

they teach them, which motivates students; • match strategies with the material; • model a variety of strategies in each

class―different students may be more successful with different strategies;

• consistently encourage students to use learning strategies in learning situations;

• monitor students’ use of learning strategies to ensure they are using them correctly; and

• encourage generalization to other subject areas.

Mnemonics

ADHD and Mathematics

•Reading response

Classroom Accommodations•Eliminate distractions•Review medications and

the effect on the student

•Be straightforward•Allow for time-out if a

student needs it•Review directions in

advance•Give undivided

attention to the student

•Allow for signaled response

•Focus on what is said, not how well it is said

•Listen patiently•Allow more time•Review lighting and

background for appropriateness

•Eliminate background noises

•Maximize availability of visual media and/or models

•Clearly label items or equipment•Allow for direct manipulation of materials•Get feedback from student•Provide a reader when appropriate•Computer, circles, dictation when appropriate

Classroom Accommodations

References

• The Access Center Improving Outcomes for All Students K-8• Kroesbergen, E. H., & Van Luit, J. E. H. (2003). Mathematical

interventions for children with special educational needs. Remedial and Special Education, 24, 97–114.

• Maccini, P., & Gagnon, J. C. (2000). Best practices for teaching mathematics to secondary students with special needs. Focus on Exceptional Children, 32, 1–22.

• Swanson, H. L. (2001). Searching for the best model for instructing students with learning disabilities. Focus on Exceptional Children, 34, 1–15

• Scruggs, T. E., & Mastropieri, M. A. (1993). Special education for the twenty-first century:Integrating learning strategies and thinking skills. Journal of Learning Disabilities, 26,392–398.

For Next Week

• Read: Steele, M. (2002). Strategies for helping students who have learning disabilities in mathematics. Mathematics Teaching in the Middle School, 8, 140-143.

• Project 4 due: Pre-CRA Assessment

• Article related to culturally responsive teaching or secondary mathematics