SPED 780 Class 10 Memory and Cognition Math

SPED 780 Class 10 Memory and Cognition Math Disabilities Judith Mack, MSEd, MSW Adjunct Lecturer Department of Special Education

Agenda • Learning Disabilities and Life Stories discussion • Memory & Cognition lecture • Math Key Points • Math Activity

Small Group Discussion Small group discussion: • What stood out to you about Lynn’s story? Why? • Lynn writes of several different class situations and tutors who worked with her. What seemed to be most effective for Lynn? What didn’t work? • Lynn writes of going to the room labeled “RR” for “Remedial Reading” which she and others thought stood for “Retard Room. ” How does this relate to your own practice, and how can we ensure our students don’t feel stigmatized because of their LD?

Learning and Memory: Guiding Questions • How can we explain learning and memory? • What do we know about the learning and memory of students with learning disabilities? • How can learning, memory, and motivation needs be addressed?

How Can We Explain Learning and Memory? • Learning and memory include: • • Cognition Metacognition Attention Motivation • Though many theories exist, informationprocessing theory is the current dominant theory of learning and memory.

Information Processing Theory • In this theory, incoming information enters the sensory register and, if attention is paid to it, travels through these information-processing systems: • • • Short-term memory Working memory Long-term memory – stores information in a variety of ways • • • Episodic memory Semantic memory Procedural memory Executive control or metacognitive processes Motivation

Information Processing Theory • Short-term memory • Working memory

Information Processing Theory • Long-term memory – stores information in a variety of ways • Episodic memory • Semantic memory • Procedural memory

Information Processing Theory • Executive control or metacognitive processes • • • Task analysis Strategy control Strategy monitoring • Motivation “internal process that activates, guides, and maintains behavior over time” (Slavin, 2003, p. 329)

Cognitive Styles • Cognitive styles are ways of approaching problem-solving tasks. • Field independence—field dependence – the degree to which people are influenced by their environment when asked to make decisions on perpetual tasks. • Children who have learning disabilities are generally more field dependent than their nondisabled peers.

Cognitive Styles • Reflectivity-impulsivity – degree to which a person takes time to reflect on alternatives before making a choice. • Students with learning disabilities are more apt to be impulsive than their nondisabled peers.

Memory Abilities • Many students with learning disabilities display difficulties with memory: • Short-term memory • Students with learning disabilities perform auditory short -term memory tasks poorly • Working memory • Even more important than short-term memory problems in the reading and math difficulties

Metacognitive or Executive Control Abilities • Metacognitive areas students with learning disabilities can be deficient in: • Metamemory – strategies for thinking about and remembering major points of material • Metalistening – strategies for thinking about and remembering major points of material as one listens • Metacomprehension – strategies for thinking about and remembering major points of material as one reads

Metacomprehension: Reading • Clarifying the purposes of reading • Focusing attention on important parts of a passage • Monitoring one’s level of comprehension • Rereading and scanning ahead • Consulting external sources

Motivation • Motivational problems of students with learning disabilities stem from three interrelated areas: • External locus of control – these students wait for others to motivate, organize, and evaluate th • Negative attributions – these students don’t take pride in success and more readily accept responsibility for their failures • Learned helplessness – the belief that your efforts will not result in the desired outcomes

How Can Learning, Memory, and Motivation Needs Be Addressed? • Cognitive training involves: • Changing the thought process of students • Providing students with strategies for learning • Teaching students self-initiative • Specific cognitive training techniques include: • • Self-instruction Self-monitoring of academic performance Self-determination Mnemonic strategies

Self-Instruction and Self-Monitoring of Academic Performance • Self-instruction – verbalizing the steps in a task • Teaches students to guide their own actions in completing tasks • Self-monitoring – keeping track of one’s own work and making a record of it • Teaches students to understand their strengths and weaknesses

Math Strategy Steps (Self. Instruction) Text page 240 • READ (say, ask check) • PARAPHRASE • VISUALIZE • HYPOTHESIZE • ESTIMATE • COMPUTE • CHECK

Self-Determination and Mnemonic Strategies • Self-determined behavior – making one’s own decisions about important aspects of one’s life • Self-determination skills often must be directly taught to students with learning disabilities • Mnemonic strategies – ways to enhance memory and retrieval skills using visual or acoustic representations • • Letter strategies Keyword method Pegword method Reconstructive elaborations

Keyword Method for Buncombe

Pegword Method for Garnet

Attribution Training • Attribution training – teaching students to recognize the relationship between hard work and success • Pointing out that when students do well, it is due to having tried hard and not giving up • Research on attribution training’s effectiveness has been mixed

Cognitive Strategies • Cognitive strategies combine self-instruction, mnemonic strategies, and attribution training to help students complete various tasks • Two examples of cognitive strategies: • Test-taking strategy – an approach to taking a test that reduces anxiety and helps students show what they know of the content • Content textbook strategy – an approach to completing reading texts successfully in content area textbooks

General Teaching Practices to Activate Learning and Memory • Certain teacher behaviors can help students with learning disabilities better develop their learning capacities, such as: • • • Providing advanced organizers Activating background knowledge Providing distributed practice Engaging students in dialogue Setting appropriate expectations Use of assistive technology devices

Memory and Cognition Wrap-Up Turn & Talk How have you seen difficulties with memory in your students? What strategies have been helpful? What strategies would you like to try?

Math: Key Questions • How does mathematical knowledge develop normally? • What problems in mathematics do students experience? • How are mathematics abilities assessed? • What interventions help students with mathematics difficulties?

How Does Mathematical Knowledge Develop Normally? • Conservation – the preservation of a physical quantity during transformation or reactions • Normally developing young children usually come to school with some informal knowledge. • Most students develop number sense, a conceptual structure critical for mathematics learning, before kindergarten.

How Does Mathematical Knowledge Develop Normally? • Typically, young children come to school having already developed addition skills and the ability to think about numbers as wholes that are composed of parts. • During school years, children gradually develop more sophisticated strategies to solve problems: • • From counting of manipulatives to more efficient strategies Place value – the ability to conceptualize numbers as multiples of ten; also called the decimal, or base-10, system

The Mental Number Line Concept

Cognitive Abilities and Math Skills • Number sense • Neurological deficits • Memory deficits • Language Abilities • Spatial Abilities • Non-verbal learning disabilities

Problems with Math Performance • Performance on basic arithmetic tasks • Mistakes are not random • Errors are usually systematic and indicate a mistaken strategy • Difficulties with story problems • Reading problems negatively affects performance • Features of story problems that cause students difficulties: • • Extraneous information Complex syntactic structures Change of number and type of noun used Use of verbs such as “purchased” or “bought” instead of “was given”

Types of Math Disabilities • Conceptual understanding • Language of math • Written number symbol system • Procedural steps of computation • Application of arithmetic skills • Basic number facts • Problem solving • Lack of Automaticity • Poor word-problem strategies • Poor calculation strategies • Poor number sense • Counting sequences

How Are Mathematics Abilities Assessed? • Teacher referrals due to a specific student’s difficulties • Screening tests can then be administered to determine whether further assessment is needed • Another type of assessment includes testing used to guide program planning • Assessment continues in the form of progress monitoring

Achievement Tests • Schools may screen large groups of students in mathematics to determine who might need additional services. • Common screening tests include most general achievement batteries, such as the California Achievement Test. • Some screening instruments may provide preliminary diagnostic information.

Formal Diagnostic Testing • Diagnostic tests should allow the teacher to determine in which areas of mathematics a student is having difficulty. • The student may be having difficulties in one or more of the following areas: • Basic information, computation skills, problem solving • Fractions, measurement, money • Algebra, geometry

Informal Inventories • Informal inventories – the student completes different kinds of problems so the teacher can determine which kinds of mathematics problems are appropriate for each student • Can be commercially developed or created by teachers • Should be aligned with the curriculum in use • Are administered without time limits or teacher assistance

Error Analysis and Progress Monitoring • Teachers can analyze students’ mistaken answers to determine what to teach. • Instruments such as the Diagnostic Inventory of Basic Arithmetic Skills provide examples and interpretation of mistakes. • Evaluation of students’ progress can be accomplished through: • Achievement tests, diagnostic tests, and informal inventories • Assessment of students’ performances on curricular materials • Adoption or creation of a set of short tests

What Interventions Help Students with Mathematics Difficulties? • Choices of instructional methods should be based on whether the methods are effective. • Developmental programs introduce basic skills such as addition, subtraction, multiplication, and division. • Basal programs – programs used for teaching beginners fundamental math concepts • Examples include Connecting Math Concepts, DISTAR Arithmetic, and the Structural Arithmetic program

Remedial Interventions • Similar characteristics as developmental programs • Critical features include: • Introducing new concepts systematically • Providing adequate practice and review • Teaching big ideas • Examples include the Computational Arithmetic Program (CAP) and the Corrective Mathematics program

Technology • Arithmetic and mathematics lend themselves well to the use of technology. • Debates continue with respect to how calculators should be used. • Computer software can provide the practice opportunities many students with learning disabilities need.

Effective Teaching Procedures • Modeling • Providing a demonstration and permanent model of a correct solution to a problem • Reinforcement • Beneficial when prerequisite skills are in place • Use of mental images • Anchoring math in real world situations

Effective Teaching Procedures • Strategy training – a broad range of methods whereby students are taught component skills required to attack a given type of problem • A task analysis of a cognitive operation is performed • Self-instruction training • Self-instructional techniques – cognitive training techniques in which the teacher and then the student verbalize questions or instructions for performing a task

Task Analysis of Math Problems

Math Activity

For Tomorrow Reading: • Hallahan, Chapter 9 • Barkley • Salend