#PICTORIAL MODELS IN MATH HOW TO#

Blends conceptual and procedural understanding in structured way.

By linking learning experiences from concrete-to-representational-to-abstract levels of understanding, the teacher provides a graduated framework for students to make meaningful connections.

Teaches conceptual understanding by connecting concrete understanding to abstract math process.

Helps passive learner to make meaningful connections.

How Does This Instructional Strategy Positively Impact Students Who Have Learning Problems? After students master performing the skill at the abstract level of understanding, ensure students maintain their skill level by providing periodic practice opportunities for the math skills.Provide many opportunities for students to practice performing the skill using only numbers and symbols.

#PICTORIAL MODELS IN MATH HOW TO#

When students demonstrate mastery drawing solutions, describe and model how to perform the skill using only numbers and math symbols (abstract level of understanding).

Provide many practice opportunities where students draw their solutions or use pictures to problem-solve.

When students demonstrate mastery of skill by using concrete objects, describe & model how to perform the skill by drawing or with pictures that represent concrete objects (representational level of understanding).

Provide students many practice opportunities using concrete objects.

When initially teaching a math concept/skill, describe & model it using concrete objects (concrete level of understanding).

When teaching at each level of understanding, use explicit teaching methods (see the instruction strategy Explicit Teacher Modeling).

Use appropriate strategies for assisting students to move to the abstract level of understanding for a particular math concept/skill (see Abstract Level of Understanding/Potential barriers to abstract understanding for students who have learning problems and how to manage these barriers).

Teach representational understanding second.

Use appropriate drawing techniques or appropriate picture representations of concrete objects (see Representational Level of Understanding/Examples of drawing solutions by math concept area).

Use appropriate concrete objects to teach particular math concept/skill (see Concrete Level of Understanding/Understanding Manipulatives-Examples of manipulatives by math concept area).What are the critical elements of this strategy? As a teacher moves through a concrete-to-representational-to-abstract sequence of instruction, the abstract numbers and/or symbols should be used in conjunction with the concrete materials and representational drawings (promotes association of abstract symbols with concrete & representational understanding).Students are provided many opportunities to practice and demonstrate mastery at the abstract level before moving to a new math concept/skill.The math concept/skill is finally modeled at the abstract level (using only numbers and mathematical symbols).Students are provided many opportunities to practice and demonstrate mastery by drawing solutions.tallies, dots, circles, stamps that imprint pictures for counting)

The math concept/skill is next modeled at the representational (semi-concrete) level which involves drawing pictures that represent the concrete objects previously used (e.g.Students are provided many opportunities to practice and demonstrate mastery using concrete materials.chips, unifix cubes, base ten blocks, beans and bean sticks, pattern blocks). Each math concept/skill is first modeled with concrete materials (e.g.When students who have math learning problems are allowed to first develop a concrete understanding of the math concept/skill, then they are much more likely to perform that math skill and truly understand math concepts at the abstract level. The purpose of teaching through a concrete-to-representational-to-abstract sequence of instruction is to ensure students truly have a thorough understanding of the math concepts/skills they are learning.

Pictorial models in math