Components of an Effective Mathematics Classroom

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Components of an Effective Mathematics
Classroom

• Capacity Development and School Reform
  Accountability
• Dale Carothers, Mathematics Specialist
• Altoria Henley, Mathematics Specialist

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Our Group Expectations

• Silence cell phones.
• Participate and share.
• Listen with an open mind.
• Ask questions.
• Work toward solutions.
• Use time effectively.

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Session Goals

• Teachers 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.

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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

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FCIM Plan Do Check Act (PDCA) Cycle
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Applying FCIM to School-based processes for
Data-Driven Results
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
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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.

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Classroom Learning environment

• Components of a Model Classroom

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Focus on Curriculum

• Ask 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?

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Identifying the Sunshine State Standards Strands
for Teacher and Students

• Number Sense, Concepts, Operations
• Measurements
• Geometry and Spatial Sense
• Algebraic Thinking
• Data Analysis and Probability

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Focus on Instruction

• Identify instructional practices
• Identify grouping format
• Identify research-based instructional strategies
• Focus on the learner
• Focus on Classroom Environment

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Focus on Instruction

• Identify the instructional practices used during
  instruction.

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Grouping Format

• Whole Group
• Small Group
• Paired
• Individual

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Focus on Learner

• Student Actions
• Instructional Materials
• Level of Student Work
• Level of Class Engagement

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Student ActionsWhat are your students doing?

• Listening
• Reading
• Speaking
• Working with hands-on manipulatives
• Writing in journal

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Lets Talk!
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Instructional Materials Easily Accessible
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Level of Student Work Blooms Taxonomy
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Depth of Knowledge Complexity LevelKnowledge
Sort Activity
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DOK Complexity Level Key Words / Tasks
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Level of Engagement
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Focus on Environment

• Materials are available
• Models/exemplars of quality student work
• Routines and procedures are evident.
• Scoring rubrics are displayed/provided.
• Students interact with classroom environment.
• Student Success Walls and Word Walls

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Word Wall Purpose

• A 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.

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Education Not DecorationDr. Darla Shaw,
Coordinator of Graduate Reading, Western
Connecticut State University

• Its 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 dont have such a resource in their
  room.

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• Word walls need to

• Type of Word Walls

• High frequency mathematics words
• Common patterns, phrases related to signs and
  symbols
• Content Specific
• Math Genres
• Reinforcement of current skills and concepts

• 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.

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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.

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Mathematics Classroom

• Floor 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)

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Mathematics Word Wall
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Working Word Wall
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The Language IN MathematicsStrategies for
Developing Mathematics Vocabulary
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Helping students become independent learners is
an important goal Connecting Mathematics
strategies to high student achievement. Activity
2
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Evidence of Different Learning Styles Needs Being
Met

• Rotational Model
• Small Group Instructions
• Step by Step Handouts
• Visual Representations of Content
• Language Translations
• Computer Instruction

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Research Based Instructional Strategies for
Interventions
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• Research states the following interventions are
  found to be effective

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Research Based Instructional Strategies for
Interventions

• Scaffolding Instruction
• Concrete-Representation-Abstract Instruction
• Direct/Explicit Instruction
• Verbalization while problem solving
• 5 Step Process to Solving Problems

• DRAW Strategy
• STAR Strategy
• Teaching Skills to Mastery
• Metacognitive Strategies

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Exploration Activity

• Each group will have an intervention strategy
  with a description.
• Create a lesson using the strategy on your
  description card.

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Technology com.

• Destination Math
• FCAT Explorer
• Florida Achieves
• Gizmos
• Learning Village
• Nettrekker (Learning Village)
• Brain Pop

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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

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Elements of a Print Rich Environment

• Word Walls
• Bulletin Board Displays
• Graphic Organizers
• Mathematics Vocabulary
• Student Generated Work
• Classroom Libraries
• Mathematics Work Stations

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A Print-Rich Environment Doesnt Contain

• Coloring Worksheets
• Unrelated Math Worksheets
• Puzzles and games that doesnt relate to the
  curriculum.
• Stale word walls
• Words on every object in the room

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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

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What should students know be able to do?

• Define
• Pronounce
• Give examples
• Use in Writing (Short Extended Responses)
• Use verbally

• Recognize as sight words
• Identify in real-life
• Compare/contrast
• Visualize
• Integrate

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Instructional Strategies for Vocabulary
Development

• Techniques from Supplemental
  Education Instruction (SEI)
• Frayer Model
• Graphic Organizers
• Math Journals
• Math Word Banks
• Bingo/Wordo

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Techniques from SEI

• Sing or Chant words
• Use physical gesture and/or act out
• Make up gestures
• Act it out Verbalize
• Verbalize Act it out
• Illustrate words
• Create posters using student representations
• Systematic Review Activities

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Charts That Support Learning

• Functional Charts

• Anchor Charts

• Teacher-created
• Procedural information
• Schedules
• Rubrics
• Rotational

• Co-authored
• Reinforce concept learning
• Visual reminders of incidental learning
• Teaching tool

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Some samples of anchor charts
What types of math anchor charts could be used in
your content area? Create your own.
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Frayer Model Video

• Frayer Model Instructional Video
• Activity 1
• Graphic Organizer Video
• Activity 2

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Word Sort Activity

• There 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.

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Mathematics is a Language

• Math vocabulary development is an essential
  piece of language instruction when teaching
  mathematics in the classroom.

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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?

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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.

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How We Teach in Mathematics

• Mathematics Standards
• Numbers
• and Operations
• Algebra
• Geometry
• Measurement
• Data Analysis/Probability

• Mathematics Processing Standards
• Problem Solving
• Reasoning and Proof
• Communication
• Connections
• Representation

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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.

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Connections to Mathematics

• The Curriculum Connection

• Making Real-World Connections

• The literature selection creates the
  environment for students to use
• Mathematics skills
• Reading skills
• Writing skills
• Critical thinking skills

• Math vocabulary development-Word Walls
• Daily graphing activities
• Estimation (guessing) jar activities
• Math learning centers/games
• Integrating math and literature
• Using math journals

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Mathematics Library Your Thoughts and Reflections
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Vocabulary Journals

• Spiral notebooks/steno pads
• Composition books/3-ring binders
• Personal favorites -organize by strand
• Simple form -4 boxes
• Graphic organizer Frayer model
• Commercial -grid paper lines

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Math Journal Structure

• Date 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.

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Math Journal Possibilities

• Vocabulary-words, pictures and numbers
• Formulas, algorithms, procedures
• Anchor problems
• Problems of the Day/Week
• On-going formative assessment of skills, concepts
  and connections
• Small group feedback

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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 Defined

• A 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
  students progress in the development of a
  competency .
• (Simon, Forgette-Giroux, 2000).

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Portfolio Components

• Required 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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Reflections

• Looking back at todays 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 todays
  presentation?
• In what ways will you revise your current
  instructional strategies to incorporate more
  in-depth understanding and critical thinking?
• How will you assess students understanding of
  the math skills and concepts?

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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.

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Questions and Concerns
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Mathematics Capacity Development Team
Michelle White, Mathematics Manager Michelle.white
_at_palmbeach.k12.fl.us

• Altoria Henley altoria.henley_at_palmbeach.k12.fl.us
• Sharon Martinez
• martinezs_at_palmbeach.k12.fl.us
• Kim Pirtle
• pirtlk_at_palmbeach.k12.fl.us
• Carol Sheffield
• sheffic_at_palmbeach.k12.fl.us

Shabana Ahmad-Farook farook_at_palmbeach.k12.fl.us
Bobbie Brooks brooksb_at_palmbeach.k12.fl.us Dale
Carothers carothers_at_palmbeach.k12.fl.us Cara
Hayden haydenc_at_palmbeach.k12.fl.us
Thank you for all that you do for our students!