# CREATING A RESULTS-ORIENTED MATH CLASSROOM >> ORGANIZING LESSONS FOR SUCCESS

To have a results-oriented mathematics classroom, we must organize lessons with key mathematics ingredients and components.

## results-oriented lesson:  7 elements

1. Mental Arithmetic/Mathematics (10 minutes) [Entire Class]

The teacher establishes a strong number sense at each grade level.  She achieves these through students counting, estimating, using benchmark numbers ('good' numbers), understanding properties of numbers, using mental arithmetic, and understanding the effect of arithmetic operations on numbers.

2. Linking Concepts and Procedures (10 minutes) [Entire Class]

A mathematics lesson begins with the incorporation of the perspective and knowledge that students bring to the topic. The teacher builds the new concepts and procedures from students’ intuitive and prior knowledge. Each lesson aims at developing multiple, cognitive strategies and focus on depth of the concept, instead of just the quantity of problems.  It is better to devote an entire class period to two or three problems from many angles and in-depth, rather than to work on many problems using the same procedure or ‘recipe.’

3. Prerequisite Skills (Embedded in the lesson) [Entire Class and Individuals]

Every lesson includes the development of the following prerequisite and support skills for the concepts being taught:

·4. New Language, Concept, and/or Procedure (30 minutes) [Entire Class]

The teacher approaches the concept through patterns that show students how to solve problems and see relationships and connections between different concepts and procedures. She uses manipulatives, models and other representations to demonstrate the problem situation, and then links concrete to symbolic and abstract representation.  The classroom activities, book exercises and skills pages complement each other and the stated objectives. The teacher accepts multiple correct solutions, and also emphasizes that the answers should aim at the developmental sequence from estimated solutions to exact answers, then to efficient strategies, and, finally, to reach elegant solutions.  Enrichment activities are multi-sensory and challenge students.

(a) Concept Building: Levels of Knowing

(b) Models:

The teacher is aware of and accommodates different mathematics learning

personalities in a classroom, and plans lessons accordingly.

That means the models include:

5.  Mathematics as a Second Language (Integrated in the lesson)

The teacher bases instruction of the new concept or procedure on situational story problems.  From that she brings out the

6.  Review and Consolidation (5 minutes) [Whole Class]

The teacher emphasizes cumulative follow-through in the form of mixed problem-solving, reviews and tests (in multiple forms and modalities) that check on the mastery of specific objectives at different levels of knowing, and makes them accessible to as many students as possible. There is a careful balance between linguistic, conceptual, and procedural knowledge.

The teacher uses ongoing assessments to guide instruction and timeline.

7.  Homework

Each homework assignment has the following components:

Author Contact Information:

Mahesh C. Sharma: Mahesh@mathematicsforall.org

508-877-4089 (H) | 508-494-4608 (C)

Center for Teaching/Learning of Mathematics, Inc.

754 Old Connecticut Path, Framingham, MA 01701

508 494 4608 (T); 508 788 3600 (F).