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Models of Intervention in Mathematics Education Daniel J. Brahier

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.

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Models of Intervention in Mathematics Education Daniel J. Brahier

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  1. Models of Intervention in Mathematics EducationDaniel J. Brahier Submitted by: Cheryl Gurney

  2. Intervention Models

  3. Teacher Professional DevelopmentWhat 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)

  4. Constructivist Theory • Instead of being a blank slate, a child has his/her own ideas and incomplete conceptions • Teacher helps students to make their own schema as they explore problems • Teacher is on hand to help children construct more complete ideas.

  5. 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.

  6. 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.

  7. 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.

  8. 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

  9. National Science Foundation funded the creation of curriculum programs. • Middle Grades • Early Grades • High School

  10. Intervention Models Directly Involving Students • Within the Classroom • Interactive Software • Allows students to make predictions, test hypothesis, visualize different representations of problems, or drill and review basic math ideas. • 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.

  11. 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

  12. Outside the Classrooms 1. 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 instruction 2. 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.

  13. Outside the School Day 1. 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

  14. 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.

  15. Issues Related to Intervention Models • 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.

  16. 2. Funding • Intervention in any form is expensive • Teacher/Specialists need to be paid for their work Suggested solutions: • Realigning Schedules • Flexible School Day • Community Volunteers • PD Consortiums • Grants

  17. 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.

  18. 5. Structure of the School Day • Elementary School – intervention can be extended into other subject area time. • Middle and High School – Block Schedules • 4 X 4 Block – 4 classes per semester; 90 minute classes • 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

  19. References Brahier, D. J. (2005). Models of intervention in mathematics education. Proceedings of theprompt intervention in mathematics intervention, http://ohiorc.org/for/math/prime.aspx

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