Components of the Mathematics Class
· The mathematics class should be organized to include the following elements: Oral Drill and Mental Exercises,
· Maintenance Quiz, Homework Check, Developmental Lesson and Reinforcement/Evaluation Activities.
1. Oral Drill and Mental Exercises
· A brief period at the beginning of the math class should be devoted to developing mental math skills through oral drill and mental exercises. The content of these exercises should include skills which the students have already evidenced understanding. New skills should not be introduced at this time. Students should progress through these exercises quickly and should apply mental math skills throughout the exercises.
2. Guidelines for Drill
1. Children should attempt to memorize material they reasonably understand.
2. Children should begin to memorize basic math facts soon after they demonstrate an understanding of symbolic statements.
3. Children should participate in drill with the intent to memorize.
4. During drill sessions, the teacher should emphasize remembering—not explaining!
5. Keep drill sessions brief!!! (…but have drill every day!!!)
6. Teachers should have students try to memorize only a few facts in a given lesson and should constantly review previously memorized facts.
7. Express confidence in your students’ ability to memorize—encourage them to try memorizing and see how fast they can be.
8. Emphasize verbal drill activities and provide feedback immediately.
9. Vary drill activities and be enthusiastic.
10. Praise students for their good efforts—keep a record of their progress.
3. Maintenance Sheet
A maintenance quiz, consisting of about 5 examples should reinforce skills previously presented in class.
· The examples should be mixed practice rather than focusing on one particular skill as this gives the student practice in shifting focus to answer a variety of questions on different skills in a testing situation.
· The content should include material previously taught for mastery and previously tested.
· For evaluation purposes, maintenance grades should not be considered on an equal par with major test grades.
· Teachers should make use of maintenance results to plan for re-teaching and individual or small-group reinforcement activities.
4. Homework Check
Assignment of homework is necessary for reinforcement. However, it is important to keep the following points in
mind when doing so:
· Homework is intended as a vehicle for practice and reinforcement of skills. Therefore, skills which have not been thoroughly presented and practiced in class, should not be completed as homework
· The emphasis should be on quality rather than quantity.
o a child who completes five exercises correctly would most likely be able to complete the rest of the examples on the page correctly.
o a student who completes a whole page of exercises incorrectly has practiced and learned an incorrect process which will be more difficult to break once it is learned.
o Secondly, whatever is assigned as homework should be checked, and should be able to be checked in a relatively short period of time. Again, the teacher can make good use of the results to assist with future planning.
o Checking of homework can be done in a variety of ways: using projection equipment, at the board or with the assistance of a teacher’s aide.
5. Developmental Lesson
The developmental lesson should take a major portion of the mathematics period. This includes a well-planned presentation and development of the skill to be mastered.
o This part of the math lesson should include extensive use of
concrete objects, and the board or projector with non-reliance on the textbook by the teacher as well as the student.
o The textbook should not be the determiner of pacing, sequencing, timing or scope of content. These areas are determined by the guidelines taking into consideration the needs of the students.
o Following the concept continuum of progressing from the concrete to the abstract, concepts should be introduced through a problem-solving or real-life situation in order to give purpose to the lesson and to identify the need to acquire the presented skill.
o It is important that the teacher make an effort to give the students purpose for learning each skill.
CONCEPT CONTINUUM
Semi-Concrete Abstract
Concrete à Pictorial à Diagrammatic à Symbol à Mental
Organizational Ideas for Manipulatives in the Math class
· Make sure the materials are organized and can be stored easily
· Make students responsible for the care and storage of the materials
· Prepackage materials—Use”baggies”, boxes, storage containers
· Have groups self-manage materials. Appoint a “materials manager” in your learning groups
· Involve students in obtaining manipulatives.
· Use “noiseless” manipulatives—foam pieces, erasers, cardboard, etc.
· Use inexpensive manipulatives. Many inexpensive substitutes can be found in dollar stores and discount stores
· Use the manipulatives yourself first.
8. Evaluation/Reinforcement
The last ten or fifteen minutes of the math class should be used for practice and reinforcement of skills. Students working independently might use notebooks, technology, centers or workbooks. Teacher-directed reinforcement for
individuals or flexible groups might take place. Homework should be assigned.
The daily math class, then might follow the following time organizational pattern:
15 Minutes / 5 Minutes / 25-30 Minutes / 10-15 MinutesOral Drill
Mental Exercises / Homework
Check / Developmental Lesson / Evaluation/
Reinforcement
9. Assessment
Assessment is an integral part of mathematics instruction. Students are expected to show their mastery of concepts and skills presented through the results of a variety of assessment methods.
The following principles should be taken into consideration with regard to math assessment
1. Instruction and assessment are closely linked.
2. Teachers constantly assess students informally.
3. Assessments, as part of instruction, are important sources of information for instructional decisions made by teachers
4. Students must be part of goal setting and evaluation, with self-assessment a vital part of learning.
5. Formal assessments are stronger if they relate closely to what is taught in the classroom
6. Documentation of assessment is important in connecting classroom work to evaluation.
In keeping with these principles, teachers should model more formal testing formats and teach students to interpret questions in a variety of testing styles.
Coordinator’s Checklist
· o - Does each teacher have a copy of the appropriate guidelines?
· www.allentowndiocese.org -click on "Diocesan Administration"
· -click on "Catholic Education"
· -At the bottom - "Teach" as the user name ; "User" as the password –enter
· -Scroll down and select the math guideline and Priority Topics
o Do the teachers use the math guidelines as a foundation for their planning?
o Are the Priority Topics reviewed quarterly by the coordinator and principal
o Do the teachers use the grade skills master paper
o Do the teachers teach the appropriate problem solving from the Priority Topics
o Does a plan for merging of math series with the guidelines exist?
o Is each teacher aware of the Organizational pattern for the math class?
o Does each teacher provide for drill and maintenance of skills on a daily basis?
o Do teachers make use of the Iowa testing results as a part of their planning?
o Are manipulatives available at every level?
o Are a variety of assessment types being used?
o Does the teacher keep a file with samples of level math tests and answer keys for tests
o Is there evidence of student self-assessment?
o Is there a problem solving file for each student?
o Is there evidence of the use of writing skills in math?
o Is there evidence of the use of a problem-solving method?
o Are teachers aware that the Allentown Diocese Math Guidelines are based on State Standards
o Are teachers incorporating technology into their math lessons?
o Are calculators being used for the appropriate skills at each level?
o Is software being used for instructional purposes?
o Are manipulatives available at every level?
o Do teachers make use of in-service opportunities?
o Are new teachers given direction for implementing the school’s math program?