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Capacity Development and School Reform Accountability
Dale Carothers, Mathematics SpecialistAltoria Henley, Mathematics Specialist
Our Group Expectations:
• Silence cell phones.
• Participate and share.
• Listen with an open mind.
• Ask questions.
• Work toward solutions.
• Use time effectively.
Session GoalsTeachers will understand how to optimize
instructional time by learning how to use the components of an effective classroom.
Teachers will be able to plan how to adapt the components of an effective classroom in their school setting.
Session Outcomes
Components of an Effective Mathematics Classroom
Focus on Curriculum Identify the Sunshine State Standards Strands and Content
Objective Focus on Instruction Focus on the Learner Focus on Classroom Environment Evidence of different learning styles being met
FCIM Plan – Do – Check – Act (PDCA) Cycle
55
PDCA Instructional Cycle
PLAN
ACT
DO
CHECK
• Data Disaggregation
• Calendar Development• Direct Instructional
Focus
• Tutorials
• Enrichment
• Assessment
• Maintenance
• Monitoring
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PLAN: Design or revise the mathematics learning process components to improve results
DO: Implement the plan and measure its performance
CHECK: Assess the measurements and share the results with stakeholders
ACT: Decide on changes needed to improve the mathematics learning process
Plan
Opening Activity
What is your perspective of an effective classroom?
1.Journal it.
2. After your journal writing, write a strategy on a sticky for each chart.
Components of a Model Classroom
Focus on CurriculumAsk yourself is the following evident, not
evident, or unable to determine.
What is the learning objective for lesson?Is the learning objective(s) evident to
students? Is the learning objective grade level
appropriate?
Identifying the Sunshine State Standards Strands for Teacher and Students
Number Sense, Concepts, OperationsMeasurementsGeometry and Spatial SenseAlgebraic ThinkingData Analysis and Probability
Focus on InstructionIdentify instructional practicesIdentify grouping formatIdentify research-based instructional strategiesFocus on the learnerFocus on Classroom Environment
Focus on InstructionIdentify the instructional practices used
during instruction.
Instructional Practices
Coaching Modeling Teacher Directed Q and A
Discussion Presentations Student Directed Q and A
Hands on experiences
Providing directions/Instructions
Technology Demonstrations
Learning Centers
Lecture Providing opportunity for practice
Grouping FormatWhole GroupSmall GroupPaired Individual
Focus on LearnerStudent ActionsInstructional MaterialsLevel of Student WorkLevel of Class Engagement
Student ActionsWhat are your students doing?
ListeningReading SpeakingWorking with hands-on manipulativesWriting in journal
Instructional Materials Easily Accessible
Computer Software
Lab/activity Sheet
Real-world objects
Websites
Content-specific manipulatives
Overhead/board/flip chart
Student Created materials
Videos
Hand-held technology/Calculators
Published print materials
Textbook Resource Books
Level of Student Work Bloom’s Taxonomy
EVALUATION-Making judgments and justifying positions
SYNTHESIS-Putting information together in new ways
ANALYSIS-Breaking down information into parts
APPLICATION-Using information in a new way
COMPREHENSION-Understanding information
KNOWLEDGE-Recalling informationEx. Basic Math Facts
Depth of Knowledge & Complexity Level
“Knowledge Sort Activity”
DOK & Complexity Level Key Words / Tasks
Level 1
(Low)
Recall
Level 2 (Moderate)
Skill/Concept
Level 3
(High)
Strategic Thinking
Level 4
(High)
Extended Thinking
“Identify” “Classify” Requires reasoning, planning, using evidence, and a higher level of
thinking than the previous levels.
Requires complex reasoning, planning,
developing, and thinking most likely over an extended
period of time
“Recall” “Organize”
“Recognize” “Estimate”
“Use” “Make Observations”
“Measure” “Collect and Display Data”
Drawing Conclusions
Task demands should be high
Requires rote response
“Compare Data” Citing Evidence Work should be complex
Performing an algorithm
“Explain”,”Describe”, “Interpret”
(depending on the object of the action
Logical argument
Following a procedure
Level of Engagement
Focus on EnvironmentMaterials are availableModels/exemplars of quality student workRoutines and procedures are evident.Scoring rubrics are displayed/provided.Students interact with classroom
environment.Student Success Walls and Word Walls
Word Wall PurposeA word wall is a systematically organized
collection of words displayed in large letters on a wall in the classroom (Cunningham,1995).
Word walls serve many purposes. Teachers can use them to facilitate word analysis; provide models of commonly misspelled words; or to build vocabulary for a unit of study.
“
Education Not DecorationDr. Darla Shaw, Coordinator of Graduate Reading, Western Connecticut State University
It’s no longer enough for classroom walls to be attractive.”
“A working word wall, if developed properly, can bring real life to a classroom.”
“Children who learn in a classroom with a working word wall, have a distinct advantage over students who don’t have such a resource in their room.”
Word walls need to…Type of Word Walls
be specific to the math content being studied.
be connected to words with their visual cues.
be arranged by strands, topics or categories.
be student interactive.
•High frequency mathematics words
•Common patterns, phrases related to signs and symbols
•Content Specific
•Math Genres
•Reinforcement of current skills and concepts
Floor Plan
All classroom areas should be visible to the teacher.
Designate whole, small and independent student work areas.
Determine the technology area and the number of students per computer.
Make sure that portfolios, assessments and math centers are accessible to students.
Mathematics ClassroomFloor plan will depend on the grade level
you are teaching. (It should maximize classroom space and focus on student instruction.)
Instructional and purposeful visual aids are key components of an effective classroom. (Curriculum focused word walls, math content charts and math center activities)
Mathematics Word Wall
Working Word Wall
The Language IN MathematicsStrategies for Developing Mathematics Vocabulary
Helping students become independent learners is an important goal Connecting Mathematics
strategies to high student achievement. Activity #2
Evidence of Different Learning Styles Needs Being Met
Rotational ModelSmall Group InstructionsStep by Step Handouts Visual Representations of ContentLanguage TranslationsComputer Instruction
Research states the following interventions
are found to be effective…
Research –Based Instructional Strategies for Interventions
Scaffolding InstructionConcrete-Representation-
Abstract InstructionDirect/Explicit InstructionVerbalization while problem
solving5 Step Process to Solving
Problems
DRAW StrategySTAR StrategyTeaching Skills to
MasteryMetacognitive
Strategies
Exploration ActivityEach group will have an intervention strategy
with a description. Create a lesson using the strategy on your
description card.
Technology com.Destination MathFCAT ExplorerFlorida AchievesGizmosLearning VillageNettrekker (Learning Village)Brain Pop
Print Rich Environment “The moment one steps foot inside a
classroom one can usually tell what is
important to the teacher in terms of the
type of working literacy (Mathematical)
environment he or she sets up for the
students.”
P-Child
39
Elements of a Print Rich Environment Word Walls Bulletin Board Displays Graphic Organizers Mathematics Vocabulary Student Generated Work Classroom Libraries Mathematics Work Stations
A Print-Rich Environment Doesn’t Contain:Coloring WorksheetsUnrelated Math WorksheetsPuzzles and games that doesn’t relate to the
curriculum.Stale word wallsWords on every object in the room
Suggestions from Marzano
1. Present explanation or description of words
2. 5-7 Vocabulary Words per Unit of Study
3. Present pictorial examples
4. Students generate explanations or descriptions
5. Students create pictorial examples
6. Frequently, ask students to review words in their own explanations, definitions, and/or examples
What should students know & be able to do?
DefinePronounceGive examplesUse in Writing (Short
& Extended Responses)
Use verbally
Recognize as sight words
Identify in real-lifeCompare/contrastVisualizeIntegrate
Instructional Strategies for Vocabulary Development
Techniques from Supplemental Education Instruction (SEI)
Frayer ModelGraphic OrganizersMath JournalsMath Word BanksBingo/Wordo
Techniques from SEISing or Chant wordsUse physical gesture and/or act out
Make up gestures Act it out & Verbalize Verbalize & Act it out
Illustrate wordsCreate posters using student representationsSystematic Review Activities
Charts That Support Learning
Functional Charts Anchor Charts
Teacher-createdProcedural information SchedulesRubricsRotational
Co-authoredReinforce concept
learningVisual reminders of
incidental learningTeaching tool
Some samples of anchor charts…
What types of math anchor charts could be used in your content area? Create your own.
Frayer Model Video
Frayer Model Instructional VideoActivity #1Graphic Organizer Video Activity #2
Word Sort ActivityThere are two types of word sorts: closed and open.
1. In closed word sorts the teacher defines the process for
categorizing the words. This requires students to engage in
critical thinking as they examine sight vocabulary,
corresponding concepts, or word structure.
2. In open word sorts the students determine how to
categorize the words, thereby becoming involved in an
active manipulation of words.
Mathematics is a Language Math vocabulary
development is an essential piece of language instruction when teaching mathematics in the classroom.
Marilyn Burns, 2005
“The standard for mathematics should be the same as the standard for reading-bringing meaning to the printed symbols. In both situations, skills and understanding must go hand in hand. The challenge is, how do we help students develop meaning and make sense of what they do?”
Benefits of Math and Literature Integration
The story provides structure for children to explore math concepts.
Math and literature are interrelated and not separate entities.
Literature provides the connection between the “real world” experience and the highly structured discipline of mathematics.
How We Teach in Mathematics
Mathematics Standards
Numbersand OperationsAlgebraGeometryMeasurementData Analysis/Probability
Mathematics Processing Standards
Problem SolvingReasoning and ProofCommunicationConnectionsRepresentation
Math Classroom Libraries Provide a variety of math literature books
Library is well organized and displayed.
Change literature as the year progresses based on math content introduced/reinforced.
Have a space where students can review books.
Have an area where students can review books, read or listen to books on tape.
Provide vocabulary words and activities aligned to the skills identified in the literature.
Connections to Mathematics
The Curriculum ConnectionMaking “Real-World” Connections
The literature selection creates the environment for students to use:
Mathematics skillsReading skills
Writing skillsCritical thinking skills
Math vocabulary development-”Word Walls”
Daily graphing activitiesEstimation (guessing) jar
activitiesMath learning
centers/gamesIntegrating math and
literatureUsing math journals
Mathematics Library Your Thoughts and Reflections
Vocabulary Journals
Spiral notebooks/steno padsComposition books/3-ring binders Personal favorites -organize by strandSimple form -4 boxesGraphic organizer –Frayer modelCommercial -grid paper & lines
Math Journal StructureDate every entry so that student growth or lack of
it is evident.
Entries include vocabulary words, sentences of explanation, equations, diagrams, charts, graphs, etc.
Journal entries stay in the journal and are not torn out.
Math Journal PossibilitiesVocabulary-words, pictures and numbersFormulas, algorithms, proceduresAnchor problemsProblems of the Day/WeekOn-going formative assessment of skills,
concepts and connectionsSmall group feedback
Student Portfolios “Portfolios themselves do not have a profound
effect on student progress; rather it is the use of constructive, precise and frequent feedback that has the strong effect on student learning.”
Bob Marzano (1998)Mid-Continent Regional Educational Library
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Student Portfolios DefinedA student portfolio can be defined as:
“A cumulative and ongoing collection of
entries that are selected and commented on by
the student, the teacher and/or peers, to assess
the student’s progress in the development of a
competency .
(Simon, & Forgette-Giroux, 2000).
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Portfolio ComponentsRequired Artifacts:
Student Data Checks (Current FCAT, Fall Diag., Winter Diag.-Student Goal Worksheet)
Embedded Assessment Data
Evidence of Remediation Mastery/Enrichment based on Embedded Assessment Data
Portfolio Feedback Sheet
Short and Extended Response for specified benchmarks in appropriate grade levels
End of Year Reflection
Suggested Artifacts:
Solutions to difficult problems that detail problem solving abilities.
Use of mathematics in another discipline
Problems created by the student
Responses to challenging questions and problems
Project based learning samples
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Another definition…“A purposeful collection of student work that
tells the story of student achievement or growth.”
J. Arter, 1995
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Important factors to consider…Purpose to be served
by the portfolio.
Specific skills to be assessed or developed by the portfolio.
How you will manage the portfolio (include time for student self-assessment and conferencing)?
What sections will be included in the portfolio?
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ReflectionsLooking back at today’s presentation, what
mathematics background knowledge must children know in order to complete the activities?
How will you utilize instructional strategies to support conceptual depth and understanding in mathematics?
What other math skills are related to today’s presentation?
In what ways will you revise your current instructional strategies to incorporate more in-depth understanding and critical thinking?
How will you assess student’s understanding of the math skills and concepts?
Michael Fullan and Andy Hargreaves
“It is what teachers think, do, and are, at the level of the classroom, that ultimately shapes the kind of learning that young people get.”
Spring 2008 67
Questions and Concerns
67
Mathematics Capacity Development TeamMichelle White, Mathematics Manager
Shabana [email protected]
Bobbie Brooks [email protected]
Dale [email protected]
Cara Hayden [email protected]
Altoria Henley [email protected]
Sharon [email protected]
Carol [email protected]
Thank you for all that you do for our students!
