History

OH NO ~ Not History 1. 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. Set Theory 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. Set Theory

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

d irect i nstruction vs. D irect I nstruction  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)Engelmann, 1992Adams & 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)  (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 responding Observations from Juniper Gardens Study, 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.) 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 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 response  Everyone answers on signal  Responses are academically correct Formal assessments  Mastery 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 individualArticle.php?type=ESP&volume=1 7&number=1&article_num=3&username individualArticle.php?type=ESP&volume=1 7&number=1&article_num=3&username  Association for Direct Instruction