History

OH NO ~ Not History1. TRADITIONAL MATH (1900–1957+) Basic skills learned by continuous practice of

basic algorithms (drill). Basic skills are seen as the building blocks of mathematical thinking.

Assessment based on standard pencil and paper testing.

Teacher–directed: lecture, demonstration, question and answer.

Students work independently most of the time. Discrete content: separate courses for Algebra 1,

Geometry, Algebra II, and Trigonometry.

2. NEW MATH (approximately 1960) Basic skills learned by application of

mathematical laws, not by practicing algorithms.

Assessment based on standard pencil and paper testing.

Teacher–directed: lecture, demonstration, question and answer.

Students work independently most of the time.

Set Theory is the centerpiece of study.

2. NEW MATH (approximately 1960) Basic skills learned by application of

mathematical laws, not by practicing algorithms.

Assessment based on standard pencil and paper testing.

Teacher–directed: lecture, demonstration, question and answer.

Students work independently most of the time.

Set Theory is the centerpiece of study.

3. REFORM MATH (approximately 1975) Practice of basic skills are de–emphasized in favor of

“self–paced” and "constructed” learning. Assessment is based on portfolios, projects, rubrics, observation, and self–reflection, as well written tests.

Student–directed: “constructivist” activities, where the student “discovers” and creates mathematical constructs from activities and experiences supervised by the teacher. The teacher is no longer “the dispenser of knowledge.” Rather, the teacher is a “learning facilitator.”

Students work in cooperative learning groups much of the time.

Integrated content: Algebra 1, Geometry, Algebra II, and Trigonometry are integrated into a series of classes rather than being distinct courses of study. Emphasis is on “real– world” problems. Reform Math places great importance on the self-esteem of the student.

Results “Since World War II, math instruction in the

United States has changed course time and again --- with little improvement in test results.”

1967: Five-year study of 12 Western nations finds U.S. 13-year- olds & high school seniors far behind those in other countries. New Math is blamed.

1988: A 17-nation comparison shows America’s best students, the top 5%, last in algebra and calculus . “Back-to-Basics” is blamed.

1996: The Third International Mathematics and Science Study, comparing students in 41 countries, finds U.S. eighth- graders below average. Reform Math is blamed.

Math Humor Teaching Math in the 1950s (Traditional): A

logger sells a load for $100. His production cost is 4/5 of the price. How much is his profit?

Teaching Math in the 1970s (New Math): A logger trades a set “L” (of lumber) for a set “M” (of money). The cardinality of set “M” is 100. The cardinality of subset “C” (his cost) is 20 less than “M”. What is the cardinality of set “P” (his profit)?

Teaching Math in the 1990s (Reform): A logger sells a load for $100. Her production is $80 and her profit is $20. Your assignment: underline the number 20.

Food for Thought How much should we drill and “memorize”? How do we teach Problem Solving? When should we use manipulatives &

calculators? What about learning styles & ability groups? How do we know when a child has learned? How do we deal with self-image and self-

esteem?

Direct Instruction

direct instruction vs. Direct

Instruction The term “direct instruction” has been used

in the teacher effectiveness literature (e.g., Rosenshine, 1976) to refer to:

A. Patterns of teacher behavior correlated with enhanced academic achievement

B. The focus is on how instructional time is used in the classroom

direct instruction vs. Direct Instruction

C. Conclusions are that low achieving students will reach higher achievement if the teacher maintains high engagement rates and consistently uses:

1. demonstration 2. guided practice 3. independent practice 4. review

direct instruction vs. Direct Instruction Direct Instruction originated with

Engelmann and his colleagues at the University of Oregon:

The focus of “Direct Instruction” is on both teacher presentation techniques and on the careful design of curricular materials.

Goals of DI To accelerate student learning by

maximizing efficiency in design and delivery of instruction

Efficiency is achieved when students generalize, beyond the specific material in the lesson

DI programs Over 50 specific programs have been published

for teaching language, reading, writing, spelling, mathematics, and science Designed primarily for grades K-6 There are also remedial programs for special

education and adult education in corrective reading and corrective math.

Direct Instruction offers one of the most empirically validated and effective curricula that we have for all children--gifted, average, at-risk, developmentally delayed, disadvantaged (Adams & Engelmann, 1996). 

Project Follow Through Over 700,000 children in 170 disadvantaged

communities across the US participated in this 1 billion-dollar study

3 goals of the project: increase basic knowledge and skills (Basic Skills Models), to improve cognitive and problem-solving skills (Cognitive Models), and to promote positive self-concept (Affective Models) among the participating children

Purpose: To identify "best practices" so that the most effective methods could subsequently be applied to achieve the three core goals in the disadvantaged children across the US

Results of Project Follow Through

More Results of PFT

Direct Instruction works, but…???!!

Overall, DI was the only model that had a consistently positive effect on all 3 aspects of learning

Therefore, one would have expected that the US Office of Education would have strongly endorsed and supported the use of DI as the model of choice

BUT… Engelmann's programs were criticized

for being too rigid and for emphasizing basic skills

Schools of Education in universities, boards of education, the Ford Foundation and commercial publishers argued against the research and the data, and they won. Opinion triumphed over data (Engelmann, 1992; Adams & Engelmann, 1996)

Central Elements of DI philosophy Teachers are responsible for student

learning. “If the student hasn’t learned, the

teacher hasn’t taught.”

Curriculum design is a critical variable in student achievement.

Features of Direct Instruction

Small Group Instruction

Active Student Responding

Careful Design of Instructional Presentations and Materials Script & Format (Model, Lead, Test) Brisk Pace Signaling Choral Group Responding Corrective Feedback Reinforcement

1. Small group instruction

3-5 (greater the deficit / younger the students)

10-12 (milder disabilities / older students)

desks

chalkboard

teacher

Advantages of Small Group Instruction Increases time available for direct instruction Increases control of motivational variables Provides opportunities to facilitate

observational learning, peer interaction and communication

Enhances generalization of skill

2. Maximizes active student respondingObservations from Juniper Gardens Study, 19801. How much directed reading instruction does

the average first grade child receive each day in the regular classroom?

2. On the average, how much time does a third, fourth, or fifth grader spend practicing the basic mathematics facts (addition, subtraction, multiplication, and division) during each school day?

Observations (continued)3. What percent of the average class period

do pupils spend in transition (at the beginning and end of the period, getting ready, cleaning up, etc.)

4. How many pages of written composition does the average fourth grader write per day?

Results of Observations

(Based on preliminary observations in a relatively small number of classrooms.)

1. 20 seconds 2. Less than 5 seconds 3. From 25-50% 4. Less than one

“We keep saying that Johnny can’t read because he’s deprived, because he’s hungry, because he’s discriminated against. We say that Johnny can’t read because his daddy is not in the home. Well, Johnny learns to play basketball without daddy.”

“We do best what we do most, and for many of our children that is playing ball. One of the reasons that Johnny does not read well is that Johnny doesn’t practice reading.”

(Rev. Jesse Jackson, 1976)

2 reasons high level ASR is important

Provides practice critical to mastery. Provides feedback to teacher on student

understanding.

Strategies for increasing student responses

Use of group responding - (e.g. choral responses or response

cards) Brisk pace - ( i.e., Little time between last student

response and next task or question )

3. Careful design of instructional presentations and materials Begins by analyzing content matter and identifying central organizing ideas that enable students to learn more in less time

Instructional topics and objectives are organized into tracks that allow for systematic skill development across the length of the program

Skills are sequenced to maximize student success and minimize points of confusion

Clear communication is designed to minimize ambiguity for students

Instructional formats are designed to structure the dialogue between teachers and students

Interactions are formatted General format:

Model. (e.g., teacher touches a letter in her presentation book (m) and says the corresponding sound “My turn, this sound is /mmm/. The teacher models a few times if necessary. "Listen again, /mmm/…“)

Lead. The teacher does the task with the students. ("Say it with me /mmm/." (Note the explicit rule.) Teacher touches under the letter and says the sound with the students.)

Test. Students now do the task without help. This is understood not as a “test” of the students, but rather as information on the teacher's effectiveness and an opportunity for the children to practice. (“Do it by yourself. What sound?“) Teacher points under letter. The whole group responds until firm. **Then teacher calls on individual students.**

Re-test. Earlier material is reviewed later. This gives more practice and aids retention.

Delivery Features Scripted lessons

designed to ensure clear communication of material

Rapid pacing- active student engagement is enhanced when teachers maintain a brisk pace ability to cover more material holds student attention keeps students engaged, which in turn

can reduce behavior problems

Signaling Characteristics: CLARITY & CONSISTENCY Focus Preparation Signal Verification

Choral group responding mixed with individual turns

Corrective feedback (i.e., model>lead>test) Reinforcement

Assessing Progress Ongoing mastery is used to monitor

student progress Informal assessments

100% student responseEveryone answers on signalResponses are academically correct

Formal assessmentsMastery Test are included periodically

to determine student progress through programs.

Student-Teacher Interactions DI defines the teacher’s role more clearly

and explicitly than most other forms of instruction Scripts relieve teachers of the role of

“instructional designer” Teachers’ role is…

1) to deliver instruction in a way that is effective and motivating to students, and

2) to make critical decisions about how to adapt program based on the needs of students

Additional Information: Myths and Truths about Direct Instruction http://www.adihome.org/phpshop/articles/individualArticle.php?type=ESP&volume=17&number=1&article_num=3&username Association for Direct Instructionwww.adihome.org