Chapter 13. 13 | 2 Copyright © Cengage Learning. All rights reserved. Reaching Exceptional Learners Geometrical & Spatial Reasoning

Chapter 13

13 | 2Copyright © Cengage Learning. All rights reserved.

Reaching Exceptional LearnersGeometrical & Spatial Reasoning


Mathematical Routine:Shape puzzles


Conversation in Mathematics• Discuss how the lesson was accessible to all the

students in the class. What did the teacher do to differentiate the lesson?


Exceptionality

• Pedagogy


How We Learn


Access and Equity

• Equal access versus identical instruction• High expectations• Providing modifications for students with an IEP

versus unidentified students• Importance curriculum and instruction plays• Teachers of students of special needs must be

familiar with the grade level curriculum and practices of general education students


Role of Assessment

• Individual assessments provide the most information

• Modification of assessments for children with language difficulties (are we testing language or math?)


Differentiating Instruction


Advanced Learners or Gifted Students


Struggling Learners


Specified Learning Disabilities & ADD/ADHD

• For a child to be considered having a specific learning disability, there must be a significant gap between his intelligence and achievement in one ore more of the following areas:– Oral Expression– Listening comprehension– Written expression– Basic reading skills– Reading comprehension– Math calculations– Math reasoning


Possible Barriers• Memory• Self-regulation• Visual procession• Language processing• Related academic skills• Motor skills


Removing Barriers

Specific barrier Possible indicators Possible strategy

Memory(visual memory,

verbal/auditory memory, working memory)

•Inability to retain math facts or new information

•Forgetting steps in an algorithm•Performing poorly on review lessons•Difficulty telling time•Difficulty solving multi-step word problems

•mnemonic devices•rehearsal strategies•make student aware of his specific learning strategy and

teach him how to use it to memorize information•make the calculator, multiplication chart and other study

aids available


Self-regulation (excitement/ relaxation,

attention, inhibition of impulses)

•Difficulty maintaining attention to steps in algorithms or problem solving•Difficulty sustaining attention to critical instruction•Blurting out answers•Difficulty waiting for their turn

•minimize distractions in the environment•allow students to work in short blocks or shorten assignments•incorporate more breaks and opportunities for movement•provide a quiet corner in the room such students can go to work•provide constant and explicit feedback (i.e., using a reward system for on-task behavior)•provide visual organizers with important information or directions highlighted

Visual processing(visual memory, visual

discrimination, visual/spatial organization, visual-motor

coordination)

•Loses place on the worksheet•Difficulty differentiating between numbers, coins, operation symbols and clock hands•Difficulty writing across paper in a straight line•Difficulty aligning numbers and other aspects involving directionality•Difficulty using a number line

•provide oral directions•in a story problem, write numbers using words•provide options, written or drawn, so students can cross them out when they have used them up•ensure use of lots of manipulatives•provide many organizational tools to help visualize quantities (i.e., ten frames, hundred chart, base ten blocks)•do not use transparencies to present important information. Once removed the students is lost. Provide information on charts or the white board that can remain posted the entire class.


Language processing(expressive language,

vocabulary development, receptive

language, auditory processing)

•Difficulty with oral drills•Unable to count on from within a sequence•Difficulty carrying out multi-step directions•Difficulty with word retrieval•Difficulty explaining how they solved a problem

•Simplify language•maintain quiet, calm environments•allow lots of opportunities to manipulate•act out story problems •explicitly discuss key vocabulary•use cloze sentences or sentence starters (The____has____and _____) to help students reflect•encourage lots of talk with partners and small groups

Related Academic Skills •reading•writing•study skills

•allow students to demonstrate understanding in a variety of ways•explicitly teach how to study using different modalities: saying, listening, writing, etc.

Motor Skills •Student writes numbers illegibly, slowly , and inaccurately•Student has difficulty writing numbers in small spaces and aligning columns•Difficulty with one-one-correspondence•Difficulty working with small manipulatives.

•allow a peer to write down thinking process of the student•provide access to technology •provide larger manipulatives•provide number and symbol cards student can manipulate to show thinking•orally interview child


Dyscalculia

• Disorder in calculation• May perform inconsistently from one year to the

next - quality of instruction is critical!• May perform at grade level in other subject

areas, such as reading.


Students with Severe Learning Needs

• All students need to pass through the same steps: concrete/semi-concrete/abstract.

• They basically need to make the same generalizations, but they may take much longer to do so.


Geometric & Spatial Reasoning

• Content


The Four Geometric Systems

• Topological Geometry• Transformational Geometry• Euclidean Geometry• Coordinate Geometry


Spatial Reasoning

• A combination of Topological and Transformational Geometry– symmetry– flip– slide– rotation (rotational point outside the shape; rotational

point inside the shape)


Tessellations


Euclidean Geometry(two and three-dimensional figures)

• Polygon sort• Three-dimensional solids (always use actual solids

before introducing pictures - each pair of children need to be able to manipulate their own set of solids).


Coordinate Geometry• The Cartesian Plane• Ordered Pairs• Translations

Documents

Chapter 13. 13 | 2 Copyright © Cengage Learning. All rights reserved. Reaching Exceptional Learners Geometrical & Spatial Reasoning