Title: History
1History
2OH NO Not History
- TRADITIONAL MATH (19001957)
- 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. - Teacherdirected lecture, demonstration,
question and answer. - Students work independently most of the time.
- Discrete content separate courses for Algebra 1,
Geometry, Algebra II, and Trigonometry.
3- NEW MATH (approximately 1960)
- Basic skills learned by application of
mathematical laws, not by practicing algorithms. - Assessment based on standard pencil and paper
testing. - Teacherdirected lecture, demonstration,
question and answer. - Students work independently most of the time.
- Set Theory is the centerpiece of study.
- NEW MATH (approximately 1960)
- Basic skills learned by application of
mathematical laws, not by practicing algorithms. - Assessment based on standard pencil and paper
testing. - Teacherdirected lecture, demonstration,
question and answer. - Students work independently most of the time.
- Set Theory is the centerpiece of study.
4- REFORM MATH (approximately 1975)
- Practice of basic skills are deemphasized in
favor of selfpaced and "constructed learning.
Assessment is based on portfolios, projects,
rubrics, observation, and selfreflection, as
well written tests. - Studentdirected 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.
5Results
- 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 Americas 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.
6Math 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.
7Food 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?
8Direct Instruction
9 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
10direct 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
11direct 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.
12Goals 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
13DI 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).
14Project 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
15Results of Project Follow Through
16More Results of PFT
17Direct 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
18- 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)
19Central Elements of DI philosophy
- Teachers are responsible for student learning.
- If the student hasnt learned, the teacher
hasnt taught. - Curriculum design is a critical variable in
student achievement.
20Features 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
211. Small group instruction
- 3-5 (greater the deficit / younger the students)
- 10-12 (milder disabilities / older students)
chalkboard
desks
teacher
22Advantages 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
232. Maximizes active student responding
- Observations from Juniper Gardens Study, 1980
- 1. 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?
24- 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?
25Results 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
26- We keep saying that Johnny cant read
because hes deprived, because hes hungry,
because hes discriminated against. We say that
Johnny cant 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 doesnt practice reading. - (Rev. Jesse Jackson, 1976)
27 2 reasons high level ASR is important
- Provides practice critical to mastery.
- Provides feedback to teacher on student
understanding.
28Strategies 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 ) -
293. 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
30- Clear communication is designed to minimize
ambiguity for students - Instructional formats are designed to structure
the dialogue between teachers and students
31Interactions 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.)
32- 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.
33Delivery 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
34- Signaling
- Characteristics CLARITY CONSISTENCY
- Focus
- Preparation
- Signal
- Verification
- Choral group responding mixed with individual
turns - Corrective feedback (i.e., modelgtleadgttest)
- Reinforcement
35Assessing 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.
36Student-Teacher Interactions
- DI defines the teachers 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
37Additional Information
- Myths and Truths about Direct Instruction
http//www.adihome.org/phpshop/articles/indiv
idualArticle.php?typeESPvolume17number1artic
le_num3username - Association for Direct Instruction
- www.adihome.org