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