Key ideas about information processing & math learning

Don’t confuse “knowledge” with “memory” “Knowledge” = understanding & relating “Memory” = retaining & recalling knowledge However, the way information is processed by the learner has a DRAMATIC affect on BOTH!

EVERYTHING WE TEACH BOILS DOWN TO… The learner… Facts Basic Concepts Associated Concepts Processes Strategies What would be an example from math curriculum of… Fact Dichotomous information (right or wrong) Basic concept Idea that must be experienced to understand – cannot be defined with words Associated concept Requires a explanation using words Process Series of consistent steps to follow Strategy Loosely structured plan of attack that requires on-going decision making about the application of different processes, monitoring, & reflection

The learner… Facts Basic Concepts Associated Concepts Processes Strategies So which kind of knowledge is Calvin struggling with? Fact Basic concept Associated concept Process Strategy

The learner… Facts Basic Concepts Associated Concepts Processes Strategies Fact Basic concept Associated concept Process Strategy So which kind of knowledge does this picture address?

The learner… Facts Basic Concepts Associated Concepts Processes Strategies Which kind of knowledge is illustrated in this cartoon? Fact Basic concept Associated concept Process Strategy

The learner… Facts Basic Concepts Associated Concepts Processes Strategies Which kind of knowledge is illustrated in this cartoon? Fact Basic concept Associated concept Process Strategy

The learner… Facts Basic Concepts Associated Concepts Processes Strategies Fact Basic concept Associated concept Process Strategy

The learner… Facts Basic Concepts Associated Concepts Processes Strategies One more time… Fact Basic concept Associated concept Process Strategy

The learner… Makes many connections to other ideas Can explain how idea is affected by various phenomena Can explain impact of idea on the world Makes effective comparisons with other ideas Has sufficient knowledge of relevant facts Can identify different manifestations of idea Can summarize or explain gist of idea in own words SEMANTIC KNOWLEDGE Facts Basic Concepts Associated Concepts Processes Strategies PROCEDURAL KNOWLEDGE CONDITIONAL KNOWLEDGE how to do it what it is about & why it’s relevant when to use / not use 3 BASIC KINDS OF KNOWLEDGE different ways to do it UNDERSTANDING A MATH ASSOCIATED CONCEPT

The learner… Can perform the process smoothly and accurately Can explain why the process is necessary to perform certain kinds of problems Makes effective comparisons with other processes Has sufficient knowledge of relevant mathematical facts Knows WHAT the steps to the process are SEMANTIC KNOWLEDGE Facts Basic Concepts Relational Concepts Processes Strategies PROCEDURAL KNOWLEDGE CONDITIONAL KNOWLEDGE how to do it what it is about & why it’s relevant when to use / not use 3 BASIC KINDS OF KNOWLEDGE different ways to do it UNDERSTANDING A MATH COMPUTATION Recognizes when it is appropriate and not appropriate to apply the process

The learner… SEMANTIC KNOWLEDGE Facts Basic Concepts Relational Concepts Processes Strategies PROCEDURAL KNOWLEDGE CONDITIONAL KNOWLEDGE how to do it what it is about & why it’s relevant when to use / not use different ways to do it UNDERSTANDING A MATH COMPUTATION How do you get students to have good computation skills & knowledge?

The learner… SEMANTIC KNOWLEDGE Facts Basic Concepts Relational Concepts Processes Strategies PROCEDURAL KNOWLEDGE CONDITIONAL KNOWLEDGE how to do it what it is about & why it’s relevant when to use / not use different ways to do it UNDERSTANDING A MATH COMPUTATION How do you get students to have good computation skills & knowledge?

The learner… SEMANTIC KNOWLEDGE Facts Basic Concepts Relational Concepts Processes Strategies PROCEDURAL KNOWLEDGE CONDITIONAL KNOWLEDGE how to do it what it is about & why it’s relevant when to use / not use different ways to do it UNDERSTANDING A MATH COMPUTATION How do you get students to have good computation skills & knowledge? PERFECT PRACTICE = PERFECT LEARNING IMPERFECT PRACTICE = IMPERFECT LEARNING SCAFFOLDED I DO IT WE DO IT Y’ALL DO IT YOU DO IT Instruction must be… DEVELOPMENTALLY APPROPRIATE

The learner… SEMANTIC KNOWLEDGE Facts Basic Concepts Relational Concepts Processes Strategies PROCEDURAL KNOWLEDGE CONDITIONAL KNOWLEDGE how to do it what it is about & why it’s relevant when to use / not use different ways to do it UNDERSTANDING A MATH COMPUTATION How do you get students to have good computation skills & knowledge? SCAFFOLDED Instruction must be… DEVELOPMENTALLY APPROPRIATE SUFFICIENT TO CREATE BRAIN PATHWAYS PERIODICALLY REVIEWED Most appropriate math homework is practicing previously learned skills to build fluency…. …NOT working problems that address new concepts or skills just introduced in class!

EVERYTHING WE TEACH BOILS DOWN TO… The learner… SEMANTIC KNOWLEDGE Facts Basic Concepts Relational Concepts Processes Strategies PROCEDURAL KNOWLEDGE CONDITIONAL KNOWLEDGE how to do it what it is about & why it’s relevant when to use / not use different ways to do it UNDERSTANDING A MATH COMPUTATION How do you get students to have good computation skills & knowledge? ELABORATION

! Remember Short-term memory Hold on to the information long enough for working memory to process the information Role How Rote – no meaning given to info; sub-vocalizing Affected by Fatigue, stress, multi-tasking, brain functions Improved by Medicine; no evidence that training/education helps There is nothing teachers can do to strengthen short-term memory There are plenty of things teachers can do to make the situation worse! There are some things teachers can do help circumvent the problem e.g., writing instructions on board rather than telling them orally SHORT TERM WORKING LONG TERM So how does memory fit into this?

Brain elaborates information to develop “relational understanding” Generative strategy training helps a LOT! Medications; meaningful brain-exercise Quality of short-term memory; degree of acquired knowledge; language development, emotions, time to process, stress; intentional behaviors & intentional learning, complexity of info Improved by 7 Key ELABORATION Strategies summarizingorganizing visualizingcomparingpredicting questioning evaluating NOTE! Many students with LD or related learning language problems experience working memory deficits Make meaning; connect/integrate ideas to existing knowledge; evaluate info; monitor comprehension Role How Affected by Working memory Short-term memory

Unclear; stagnant “filing” metaphor is too simplistic; evidence that information in memory is in constant state of reconstruction. Unclear whether medicine improves long term memory, (may be due to positive impact of drug on short-term, & working memory processes, as well as executive functions) Quality of elaboration that occurred when info processed by working memory; the more info is patterned via neural pathways, more accessible info is for retrieval; the more semantic information is linked to episodic memory, the better the long-term memory Improved by Store & retrieve information Role How Affected by Working memory Long-term memory Short-term memory

Characteristics of students with learning disabilities that affect math learning Do not know basic math facts, thus hugely struggle learning sophisticated processes that require this knowledge Lack of reading skills Tend to be rote learners, use verbal rehearsal rather the visualization of math concepts

Characteristics of students with learning disabilities that affect math learning Typically fail to link new learning with background knowledge or previously learned skills IMPLICATIONS: Advance organizers, Review perquisite knowledge & skills, Cue students to make links Cue real-world connections

Characteristics of students with learning disabilities that affect math learning Typically non-strategic; very poor at monitoring IMPLICATIONS: Explicit instruction in strategies; Write the steps on board & handout. Touch step, say out load, then do it. Using think-alouds to model monitoring

Characteristics of students with learning disabilities that affect math learning Most are very poor at using elaboration as a learning tool; poor relational understanding IMPLICATIONS: Employ “low-risk” elaboration activities Cue use of specific elaboration strategies…“Picture in your mind…”“How are these different?” “Explain the steps to me.” Use concrete analogies Use think-sheets & graphic organizers

Characteristics of students with learning disabilities that affect math learning Difficulty maintaining attention IMPLICATIONS: Employ direct instruction that results in high frequency correct responding Provide explicit feedback frequently

Characteristics of students with learning disabilities that affect math learning Some experience difficulty with short-term memory and/or auditory processing =dramatically affects board to paper note-taking IMPLICATIONS: Reduce the amount of language students must process. Pre-teach vocabulary Employ think-sheets & graphic organizers.

LOTTERY: A tax on people who are bad at math

Use this think-sheet to plan a unit about a math problem-solving process or strategy The Strategy Unit Plan

Skills to review StudentsObjective or re-teach MaterialsOutcomeLearning Level OPENING - Anticipatory Set Set goals and/or plot goal on progress chartInformation about relevance of strategy Re-visit what students did best on last practice activity Steps to performing the strategySituations where the strategy can be used Review student progress toward strategy generalization Course of Study Standard Best at… Needs to learn … Introductory Simple practice Applied practice Generalization I do it We do it Y’all do it You do it Best at… Needs to learn … Introductory Simple practice Applied practice Generalization I do it We do it Y’all do it You do it Best at… Needs to learn … Introductory Simple practice Applied practice Generalization I do it We do it Y’all do it You do it BODY Forecast future learning & generalization Facilitate student reflection about strengths & weakness associated with performing the strategy CLOSING Use this think-sheet to plan specific lessons that address a math problem- solving process or strategy The Strategy Lesson Plan