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The Critical Importance of Instruction & The Language of Mathematics -…
The Critical Importance of Instruction & The Language of Mathematics
Models of Instruction
Direct
Concentrates on observable behavior and clearly defined tasks and methods for teaching and assessing students
Clearly defined tasks
Teacher modeling
Explicit directions
Immediate feedback
Reinforcement
Direct instruction
Explicit instruction
Cognitive
Demonstrates efficient methods for presenting organized information, with scaffolds and examples for students
Teacher think-alouds
Modeling
Self-Regulation
Scaffolded instruction
Strategy instruction
Metacognitive strategy instruction
Self-regulation
Social
Facilitates the development of productive ways of interacting and norms that support engaged student learning
Positive interdependence
Individual accountability
Group processing
Social skills
Face-to-face interactions
Cooperative learning
Peer Tutoring
Group investigation
Information-Processing
Provides learners with information and concepts to develop hypothesis testing and creative thinking to approach learning
Student choice
Student-centered
Whole-part-whole approach
Authentic purpose for learning
Case-based learning
Critical thinking
Critical inquiry
Problem-based learning
Instructional Methods for Grouping Students
Whole class
Students spend time being instructed by the teacher
Small group: same skill level
Students are divided into groups on the basis of their ability to perform a skill; teacher instructs each group separately
Small group: mixed skill level
Students are divided into groups randomly; teacher instructs each group separately
One-to-one
A student works on a one-ton-one basis with a teacher or computer; students proceed at their own pace on their own ability level
Peer tutoring
Pairs of students, at the same or different grade levels, are formed; students in each pair instruct one another
Cooperative learning
Students work in small mixed-ability groups; each group with a shared learning goal
Classwide peer tutoring
Students work in small mixed-ability groups, each group with a shared learning goal
Considerations
Positive interdependence
Members of the team have a set goal to achieve
Individual accountability
Group processing
Social skills
Specific student skills are expected so that students can work and communicate with each other to achieve the goal
Team members actively work together to achieve the established goal
Each member of the group has a role
Components of Explicit and Systematic Instruction
Focus instruction on critical content
Sequence skills logically
Task-analyze complex skills into smaller steps
Design focused lessons
Set the expectation to start the lesson
Review prior skills
Demonstrate stepwise instructions
Use clear and concise language
Provide examples and nonexamples
Provide students with guided practice
Require frequent responses
Monitor student performance closely
Deliver instruction at a brisk pace
Connect information across lessons and content
Provide abundant time for practice and cumulative review
Levels of Instruction
Concrete
Utilizing manipulatives
Representational
Objects are replaced with representations, such as pictures
Abstract
Arabic numbers, mathematical symbols, and accompanying explanations
Instructional Enhancements
Anchored instruction
Use authentic problem situations in both conventional and digital environments
Modifications to text
Change text to match the background and reading level of your students
Text-to-speech conversions
Record textbooks for students, or have students record their work through digital pictures with spoken explanations
Use of manipulatives
Use concrete objects that match the purpose of the lesson at the level where students should understand it
Simulations/virtual reality
Interacting with various media that show the concept to a student allows the student to see the relevance of a standard and learn how mathematics is used
Technological tools
Use technology to increase students' interactions with mathematical skills
Concept maps and models
Graphic organizers and explicit models may be used to help students make connections between mathematical concepts and skills
Metacognitive Strategies
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Make sense of problems; persevere in solving them
Differentiated Instruction
Ongoing assessment and adjustment
Clarity in the standards and in the curriculum's learning goals
Use of flexible grouping
Tasks that are respectful of each learner
Accommodations on Interactive Assessment Systems
Highlighting or coloring
Magnification
Oral administrations
Graphic organizers
Masking to minimize distractors
Contrast enhancement
Word Problems
Prepare problems and use them in whole-class instruction
Present word problems to the whole class and show the necessary steps to solve them
Choose problems with contexts that are familiar to students
Change the problem types
Assist students in monitoring and reflecting on the problem-solving process
Give students prompts
Students must be taught problem-solving steps
Model using thinking-aloud
Expose students to multiple problem-solving strategies
Teach students how to use visual representations
Metacognitive strategies used to mediate the effects of working memory deficits
Schema-based problem solving
Highly structured
Use modeling and student think-alouds
Based on motivational principals
Highly visual
Engage students in metacognitive processes
Group
Two or more smaller groups are grouped to make up a larger group
Change
Two or more sequential actions lead to an increase or decrease in total quantity or value
Compare
Two items are compared, using a common unit or referent
Help students recognize and articulate mathematical concepts and notation
Techniques to Build Understanding of Terminology
Total physical response
Connecting spoken words with physical gestures
Frayer models
Define in own words
List facts and characteristics
Provide examples and nonexamples
Keyword approach
Use a word that is acoustically similar and can be illustrated
Mathematics sentence structure
Have students write an expression to match the literacy sentence
Contextual Relationships
Connect context and math vocabulary within problem solving
Intensive practice of vocabulary
Teach vocabulary in context and synthetically
Use vocabulary consistently
Language Demands of Mathematics
Vocabulary
Sentence structure
Contextual relationships
Katie Mynar
Intensive Interventions
If visuals don't work, then use...
Other concrete manipulatives
Proportionate sentence strips
Provide fully-worked examples to analyze and explain
Use a rubric to assess to understand where the student's difficulties are
OPTIMIZE
Plan lessons and curriculum in order to develop a progression of learning based on prior knowledge and understanding
O - order the skills before teaching
P - pair your sequence with the textbook
T - take note of commonalities and differences
I - Inspect other chapters to see if differences are covered
M - match supplemental guides to see if they cover the differences
I - identify additional instruction to complement current text and curriculum
Z - zero in on optimal sequence
E - evaluate and improve sequence every year