models of intervention in mathematics education daniel j. brahier
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Models of Intervention in Mathematics
Education
Daniel J. Brahier
Submitted by: Cheryl Gurney
Intervention Models
Teacher Professional Development
What does the research say?National Council of Teachers of Mathematics (NCTM,
2000)Math is a process as much as it is a content area.National Standards are: problem solving, reasoning
and proof, communication, connection and representation
State and national standards encourage teachers to use problem solving as the focal point of the lesson and promote mathematical thinking.
Children learn best in a student-centered classroom that emphasizes content that is meaningful and relevant to the learner. (Constructivist Theory)
Constructivist TheoryInstead of being a blank slate, a child has his/her
own ideas and incomplete conceptionsTeacher helps students to make their own schema
as they explore problemsTeacher is on hand to help children construct more
complete ideas.
Third International Mathematics and Science Study (TIMSS)
Indicated teachers in US over-emphasize lecture and skill development
Students are infrequently involved in realistic, high-level problem solving
Skill acquisition is given priority over conceptual understanding.
Programme for International Student Achievement (PISA, 2003)
Studied 15-year-olds achievement in mathematics in 41 different countries
U. S. Scored significantly lower than the international average.
U. S. outperformed 12 other nations.
PISA (2003) states: “Successful functioning in mathematics requires a combination of knowledge processing and application skills, which do not inevitably go together.”
Problem solving abilities of American 15-year-olds is very low.
U.S. outperformed 11 other countries.
Early Numeracy Research Project (Australia, 2003) Studied early mathematics education and the use of
individual learning plans designed to help students meet targeted goals.
Every student who is experiencing difficulty in learning mathematics can benefit from an individual learning plan.
Creating Laboratory Access for Science Students (CLASS, 1998)
Recognized Middle and High School teachers must be provided with tools to successfully teach mathematics, including Special Education programming.
Tools and professional development was provided through summer programs, mini-grants, focus groups and short courses.
Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989)
Theoretical research is not supported by curriculum being taught
Textbooks did not allow for the recommended student-centered teaching practices
National Science Foundation funded the creation of curriculum programs.
Middle Grades
Early Grades High School
Intervention Models Directly Involving Students
Within the Classroom1. Interactive Software
Allows students to make predictions, test hypothesis, visualize different representations of problems, or drill and review basic math ideas.
2. Co-operative Learning Groups Students increase achievement and long term
retention and increase high order thinking skills. Provides opportunities for at-risk students to
interact with others who are achieving at higher levels
Includes peer tutoring older : younger or peer : peer.
3. Learning Centers After strengths and weaknesses have been assessed
students can be assigned to learning centers that address their needs
Students spend time working on individual areas of need rather than assuming the whole class needs the same experiences
4. Differentiating Homework Assignments Some students may be prepared to work challenging
problems; others may need review, practice or develop basic competency
Special homework assignments meet the needs of all
5. Alternate Learning Models Auditory, visual, tactile and kinesthetic learners Large or small group or individual instruction setting Physical models, visualizing, hands-on opportunities
Outside the Classrooms1. Specialist – Push In/Pull Out
Specialist and classroom teacher work together to determine student needs and provide either push in or pull out services to provide instruction and intervention in student need area.
Small group or one-on-one instruction2. Tutoring
Elementary – provided at recess and lunch periods. Time is limited but students can build confidence.
Middle and High Schools – Tutorials during study halls by specialists. No class time missed; No after school conflicts.
Outside the School Day1. Tutoring Before or After School
Highly-qualified teachers are paid extra to provide individual or small group instruction
Cons: Not required: Students choice; Finding highly qualified teachers willing work extra hours.
2. Saturday Assistance/ Enrichment Popular in Japan – Students review and practice basic
math. Structure could include: mini-classes; tutoring
sessions; small group instruction; and informal differentiated instruction
Cons: funding, attracting students
3. Summer School Provide enrichment and intervention Teacher identifies areas that need intervention at the end of
the year Summer school is built around the needs of the student.
4. Internet Tutoring Ask Dr. Math – math forum Count Me Smart – Elementary tutorial Individual Teacher pages
5. Personal Tutor Tutoring session with a paid professional even for one hour
per week can make major differences for individual students Caution: Careful communication between the teacher and
tutor is a must to be sure instruction will be consistent. Cons: Scheduling, funding.
Issues Related to Intervention Models
1. Communication Intervention teams
Assess goals and needs of at-risk students
Design intervention strategies Regular communication with parents
and caregivers reviewing academic needs and sharing progress reports.
2. FundingIntervention in any form is expensiveTeacher/Specialists need to be paid for
their work
Suggested solutions: Realigning SchedulesFlexible School DayCommunity VolunteersPD ConsortiumsGrants
3. Duration and Content Short term targeted tutoring vs long term support that
allow rapport to be built Basic skill building vs Real world problem solving
4. Co-ordination with Classroom Teacher Pull out programs deny classroom interaction time Any type of intervention needs to support the
instructional methods of the classroom teacher. Classroom teachers need to be involved in designing
intervention programs.
5. Structure of the School Day Elementary School – intervention can be extended into
other subject area time. Middle and High School – Block Schedules
1. 4 X 4 Block – 4 classes per semester; 90 minute classes
2. A/B Block – 7-8 classes meeting every other day for 90 minute classes.
Caution: 90 minute classes cannot be viewed as 2- 45 minute classes. Time must be used for intervention and extension allowing students to engage in hands on exploration and learning center activities
ReferencesBrahier, D. J. (2005). Models of intervention in
mathematics education. Proceedings of the prompt intervention in mathematics intervention, http://ohiorc.org/for/math/prime.aspx
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