Strategies for Successful Teaching

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Strategies for Successful Teaching

• Mathematics Staff Development
• 2007

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Introductory Activity

• Find a blank index card on your desk and answer
  the following two questions on the card.
• What does differentiated instruction mean to you?
• What types of assessments do you use with your
  students?

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Partners Please!

• Find your new partner.
• Turn to your partner, and give them a hearty
  welcome.
• Tell your partner This stinks. I would really
  like to go homehow about you?
• Once more turn to your partner.
• Thank them for their honesty.
• Have a seat with your new partner.

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Group Sharing Time

• What do you think differentiated instruction is?
• Contributions from the group.
• OFFICIAL definition of differentiated
  instruction

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Differentiated Instruction

• To differentiate instruction is to recognize
  students varying background knowledge, readiness,
  language, preferences in learning, interests, and
  to react responsively. Differentiated instruction
  is a process to approach teaching and learning
  for students of differing abilities in the same
  class. The intent of differentiating instruction
  is to maximize each students growth and
  individual success by meeting each student where
  he or she is, and assisting in the learning
  process.
• 
  Tracey Hall, Ph.D

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Learning Cycle and Decision Factors Used in
Planning and Implementing Differentiated
Instruction
                                               
                                                  
                                                  
                                       
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Follow-up Question

• What strategies are you using to help your
  students be successful? (List 2 or 3 things.)
• Other strategies we might want to look at?

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What are students doing/not doing that keeps them
from being successful?
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So What Does the Research Tell Us?
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Instruction for at-risk students is a failure
because.

• Students are robbed of interesting, stimulating
  assignments. There is a preponderance of
  worksheets, seatwork, etc.
• Interaction with teachers and peers is reduced
  because of rote learning methods.
• Sorting students into homogenous groups reduces
  cognitive involvement.
• Intensive instruction confines students to a
  passive role and encourages learned
  helplessness.
• Barbara
  Presseisen, At-Risk Students and Thinking, 1998

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When I dieI hope it occurs during a
lecturebecause the transition from life to
death will be so slight that I will hardly
notice it.
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What do we know aboutour adolescent learners?
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What do we know aboutour adolescent learners?

• Students learn best in an emotional climate that
  is supportive and marked by mutual respect (Caine
  Caine, 1991).
• The activities and contexts in which students are
  engaged should be meaningful to them so they will
  make connections between school learning and the
  world beyond school.
• Students near the top of their class know about
  four times as many vocabulary words as their
  lower performing classmates.

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Extrinsic Motivation in NOT the Key!

• Schools that are especially successful in
  promoting resiliency build on students' intrinsic
  motivation. These schools actively engage
  students in a variety of rich and experiential
  curricula that connect to their interests,
  strengths, and real world activities (Anderman
  Maehr, 1994 Weinstein et al., 1991). In
  addition, they count on students' active
  participation and decision-making in the daily
  life of the classroom and school to build
  responsibility and ownership for learning. These,
  in turn, become intrinsic motivators for further
  learning and resiliency."

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• Youth who are succeeding against the odds talk of
  being respected and of having their strengths and
  abilities recognized (McLaughlin et al., 1994
  Mehan et al., 1994).

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High Expectations!

• Within the last ten years, research on successful
  programs for youth at risk of academic failure
  has clearly demonstrated that high
  expectations--with simultaneous support--is a
  critical factor in decreasing the number of
  students who drop out of school and in increasing
  the number of youth who go on to college (Mehan
  et al., 1994).

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(Marzano, Pickering, Pollack)
Classroom Instruction That Works
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Partner A Turn to your partner and restate some
of the ideas listed in the slides thus far.
Partner B What did your partner leave out?
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Promote Higher Order Thinking by.
Construct questions that make students think
creatively and critically. Practice
brain-compatible lesson design Lecture less and
plan opportunities for students to engage. Make
the content relevant to students daily lives.
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Higher Order Thinking means

• Construct questions that make students think
  creatively and critically.

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Divergent Questioning Strategies
Fluency Flexibility Originality Elaboration
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Forced Association Model

• How is __________________ like a
  _________________?
• How can you get ideas from _________ to help you
  work on _________?
• How can thinking about _________ help us solve
  this problem?

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Examples

• How is an equation like friendship?
• How is a polynomial like a pizza?
• How is division of numbers like cutting a cake?
  How is it different?
• How is a polygon like a person?
• How are supplementary angles like a friendship?

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Reorganization Model

• What would happen if . . . . .?
• Suppose ____________________occurred? What would
  be the consequences?

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Examples

• Given the equation y mx b. What would happen
  if m were positive (or negative or zero or
  undefined)?
• Given the equation y mx b. What would happen
  if b were 5? 3? 0?

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Examples

• What would happen if an equilateral triangle were
  stretched at only one of its vertices.

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What would happen if.

• A rhombus was stretched along two parallel sides?

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Suppose..

• The figure below was reflected across a line of
  your choice. What would be the consequences of
  this action?

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Brainstorming Model

• How many ways . . . . .?
• List the reasons for. . . .
• List all of the . . . . .
• The answer is ____. How can we arrive at that
  answer?

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Examples

• The answer is 42.75. What are some questions you
  can think of to get that answer?
• The answer ½. What are three different ways to
  get this answer?
• How many lines of symmetry can you find in the
  figure?

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Examples

• The answer is 55 m.p.h. What are all the
  questions you can think of to get that answer?
• How many different ways can the number 5 be used
  in a linear function, and with what meaning?

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List all of the

• Similarities between a square and a rectangle.
• Differences between a square and a rectangle.
• Similarities between a triangle and a trapezoid.
  
• Differences between a triangle and a trapezoid.

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Viewpoint/Involvement Model

• How would this look to a . . . .?
• What would this look like to a . . . .?
• What would __________________ think about
  _____________?
• You are a ______. How can _____ use you?

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Examples

• You are a right angle. Why cant builders get
  along without you?
• You are a meter. How many times to you need to
  move to measure the room?
• You are an equation. What would a variable think
  about you?
• You are a variable. What would a coefficient
  think about you?

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Examples

• You are slope. Why cant builders get along
  without you?
• You are an equation. How can you help me analyze
  data?
• You are a function. How can you be used to model
  a procedure for finding a solution?

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Write out your questions before hand.

• Two reasons
• It takes a few minutes to think through what you
  want the question to be based on the content you
  are working with and
• If you think you will just do it when it feels
  right, it will never get done. Divergent
  questioning is rarely spontaneous.

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Questions to avoid..

• What is the answer to 10
• Instead.how can you find a solution to 10?
• Can you solve this problem?
• Where do you want to begin to solve this problem?
• Ask questions that do not require a student to
  know the answer, or force them to admit they do
  not know how to solve the problem.

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Dont try to use all the questioning models in
the same lesson.

• Pick a model a day or
• Insert one kind of question per lesson.

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PRACTICE.

• Select one lesson within the next two weeks to
  focus on these questioning techniques.
• Look at your lesson and write some probing
  questions for each category using that lesson.
• Be prepared to share some of your questions next
  time.

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End of Part 1
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HAPPY PI DAY!!
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THINGS YOU NEED TO KNOW

• We will be sending the SOL packets home with
  students again this year, so please DO NOT use
  that material in class before then.
• Benchmark tests are close to completion
• Algebra 1 (using the same test as last year?)
• Math 8 done with review questions also
• Math 7 Adv different from Math 8 coming soon
• Math 7 coming soon with review questions also

GRCTM Spring Conference April 17 at Manchester
Middle School
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Share with the group.

• Examples of questions used in lessons.
• What worked well?
• What didnt work so well?
• What would you do different next time?

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Brain-Compatible Lesson Design

• You cant teach a student anything until you have
  his/her attention.
• Engage the multiple intelligences (all eight ways
  of knowing), giving all learners ways to excel.
• Recognize and accommodate student's preferred
  learning styles - especially the hard to reach

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• learning is more meaningful when students are
  given the opportunity to play with, apply,
  manipulate and assimilate new ideas into their
  own schema.
• teach by giving students the opportunity to
  collect a wide variety of information on a topic,
  apply what they've learned to some situation, and
  then critique or analyze that information to see
  how it fits into what they already know.

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Multiple Intelligences

• Verbal-Linguistic--The ability to use words and
  language
• Logical-Mathematical--The capacity for inductive
  and deductive thinking and reasoning, as well as
  the use of numbers and the recognition of
  abstract patterns
• Visual-Spatial--The ability to visualize objects
  and spatial dimensions, and create internal
  images and pictures
• Body-Kinesthetic--The wisdom of the body and the
  ability to control physical motion
• Musical-Rhythmic--The ability to recognize tonal
  patterns and sounds, as well as a sensitivity to
  rhythms and beats
• Interpersonal--The capacity for person-to-person
  communications and relationships
• Intrapersonal--The spiritual, inner states of
  being, self-reflection, and awareness
• Howard Gardner

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What is your favorite of the multiple
intelligences? Which of these would you find most
difficult to use in your classroom?
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Instruction should be student centered rather
than teacher centered.
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• Lecture less and plan opportunities for students
  to engage.
• Make the content relevant to students daily
  lives.

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No Connections.No Meaning!

• The brain is continually trying to make sense
  out of the world, attempting to determine what is
  meaningful in what it experiences.

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Meaning orMaking Connections
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What Factors Influence Attention?
Intensity of Stimuli
Meaning
Need
Cognitive Dissonance
Novelty
Music Rhythm
Expectations
Social Interaction
Emotion
Symbols, Icons, Images
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Novelty

• Storytelling
• Use of props
• Presenting content with a new twist

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The Number Devil

• In twelve dreams, Robert, a boy who hates math,
  meets a Number Devil, who leads him to discover
  the amazing world of numbers infinite numbers,
  prime numbers, Fibonacci numbers, numbers that
  magically appear in triangles, and numbers that
  expand without . As we dream with him, we are
  taken further and further into mathematical
  theory, where ideas eventually take flight, until
  everyone-from those who fumble over fractions to
  those who solve complex equations in their
  heads-winds up marveling at what numbers can do.

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Square Numbers
1 2 3 1
4 9
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1
1
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Instructional techniques associated with
brain-based learning

• Orchestrated immersion--
• Relaxed alertness--
• Active processing--

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Orchestrated immersion

• Creating learning environments that fully immerse
  students in an educational experience

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Quadrilateral SORT.
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Relaxed Alertness

• Trying to eliminate fear in learners, while
  maintaining a highly challenging environment
• One way of making the class less threatening is
  by providing choices.  For example, allow
  students to participate in the activity, mind-map
  it, outline its key concepts, or share
  observations.

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Choice Board or Tic-Tac-Toe

• This assessment strategy allows students to
  select their own preferences but still achieve
  the targeted essential knowledge and skills.

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Choice Board or Tic-Tac-Toe

• This assessment strategy allows students to
  select their own preferences but still achieve
  the targeted essential knowledge and skills.
• Algebra Choice Board

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Active processing

• Allowing the learner to consolidate and
  internalize information by actively processing it
  

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Active Processing Example

• To remember the names of polygons
• Triangle make a triangle with your arms and
  body.
• Quadrilateral Draw a square in the air
• Pentagon Salute your government offices
• Hexagon Wave a wand over the desk
• Heptagon Play tug of war - heave
• Octagon Act like an octopus
• Nonagon Shake your head NO
• Decagon Wiggle your ten fingers.

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Discuss with a partner how you might use this for
your classroom instruction.
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If they cant read the question, it doesnt
matter how much math they know!

• Essential vocabulary used on assessments and
  lesson plans must originate from Understanding
  the Standard contained in the Virginia Curriculum
  Framework.
• This vocabulary must be directly taught and
  learned.
• Students must be provided with strategies to
  make meaning of the term by drawings or
  expressing definitions in their own words.
• Teachers must spiral essential vocabulary
  throughout the year with engaging activities.

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Vocabulary Card Activities

• Video Clip on Frayer Model
• Practice Select a vocabulary word from the bag
  and try this yourself.
• Vocabulary Sort activities

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Name That Category

• Partner A faces the board
• Partner B faces away from the board
• Clue giver lists terms that pertain to a category

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Rules THE PYRAMID GAME

• Steps
• Students form groups of 2 players per team.
• Each team is provided with a ziplock bag
  containing 6 cards.
• Each card contains a category and 6 words from
  the Curriculum Framework associated with the
  category.
• One player selects a card, reads the category to
  their partner and is provided with 30 seconds to
  1 minute to provide clues to their partner so
  they will say each word.

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Levels of Thinking
Application
200 POINTS
Knowledge Evaluation
100 POINTS 100 POINTS
Comprehension Analysis Synthesis
50 POINTS 50 POINTS 50 POINTS
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BLIND SequencingPurpose To provide an
opportunity for students to communicate (in their
own words) their understanding of a process.

• Directions
• Deal out the problem cards face down.
• Each person takes a turn describing their card to
  their team.
• The team determines what the cards represent and
  how to sequence the cards.

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Rules BLIND SEQUENCING (Adapted from Spencer
Kagan Associates)

• Objective A team of students must correctly
  sequence essential steps in any process requiring
  procedural knowledge using verbal descriptions
  only.
• Teacher prepares a set of cards containing the
  steps in a procedure (the order of the steps
  matters).
• Each participant is assigned a number in the
  team.
• ALL cards are dealt to the members of the team.
• Students are instructed to NOT show anyone the
  information contained on the card(s).
• Team member 1 begins by describing the
  information on her/his card and places the card
  on the table FACE DOWN.
• Team member 2 describes the information on
  her/his card and decides the correct location of
  the card in the sequence. The card is then placed
  in the correct spot in the sequence FACE DOWN.
• Continue the process until the team places the
  cards FACE DOWN in what the team believes to be
  the correct sequence.
• The team turns over the cards to check for
  correctness.

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Solving a word problem

• Read the problem.
• Highlight the key words and numbers in the
  problem.
• Plan how to solve the problem.
• Solve the problem.
• Check your answer to see if it makes sense.
• Reread the problem to be sure you answered the
  question asked.

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Order of operations Solving word problems
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TIERED INSTRUCTION

• A PLANNING STRATEGY FOR MIXED ABILITY CLASSROOMS

A Different Spin on an Old Idea.
SOURCE based on work by Carol Ann Tomlinson
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WHAT CAN BE TIERED?

• ASSIGNMENTS
• ACTIVITIES
• CENTERS STATIONS
• LEARNING CONTRACTS
• ASSESSMENTS
• MATERIALS
• EXPERIMENTS
• WRITING PROMPTS
• HOMEWORK

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What is Tiered Instruction?
By keeping the focus of the activity the same,
but providing routes of access at varying degrees
of difficulty, the teacher maximizes
the likelihood that 1) each student comes away
with pivotal skills understandings 2) each
student is appropriately challenged.
Teachers use tiered activities so that all
students focus on essential understandings and
skills but at different levels of complexity,
abstractness, and open-endedness.
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Creating Multiple Paths For Learning
Key Concept or Understanding
Understand The Concept
Struggling With The Concept
Some Understanding
READINESS LEVELS
Reaching Back
Reaching Ahead
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IDENTIFY OUTCOMES WHAT SHOULD THE STUDENTS KNOW,
UNDERSTAND, OR BE ABLE TO DO?
THINK ABOUT YOUR STUDENTS PRE-ASSESS READINESS,
INTEREST, OR LEARNING PROFILE
INITIATING ACTIVITIES USE AS COMMON EXPERIENCE
FOR WHOLE CLASS
GROUP 1 TASK
GROUP 2 TASK
GROUP 3 TASK
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THE TEACHERS CHALLENGE

• Developing--
• Respectful Activities
• Interesting
• Engaging
• Challenging

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Planning Tiered Assignments
Concept to be Understood OR Skill to be Mastered
Create on-level task first then adjust up and
down.
Below-Level Task
On-Level Task
Above-Level Task
Adjusting the Task
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When Tiering

• Adjust---
• Level of Complexity
• Amount of Structure
• Materials
• Time/Pace
• Number of Steps
• Form of Expression
• Level of Dependence

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The Equalizer
5. Smaller Leap
1. Foundational
Transformational
Greater Leap
6. More Structured
More Open
2. Concrete
Abstract
7. Clearly Defined Problems
Fuzzy Problems
3. Simple
Complex
8. Less Independence
Greater Independence
4. Fewer Facets
Multi-facets
9. Slower
Quicker
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Tiers of Instruction

• C Layer Basic knowledge, understanding. The
  student builds on his/her current level of core
  information.   
• B Layer Application or manipulation of the
  information learned in the C layer. Problem
  solving or other higher level thinking tasks can
  be placed here.
• A Layer Critical Thinking and Analysis. This
  layer requires the highest and most complex
  thought. Create leaders, voters.

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ANNOUNCEMENTS

• GRCTM SPRING CONFERENCE Registration forms on the
  tablefill one out and turn in to me.
• MSC Engineering Program
• Still one slot left for a teacher
• Next department meeting to discuss benchmark
  assessments and course outlines, etc. - APRIL 18
  at 3 pm in library.
• Last department meeting of the school year May
  16, at 3 pm in library.

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What role does assessment play in all of this?

• Are tests, quizzes, and homework the only kind of
  valid assessments?
• What about homework?
• I pass all of the tests and quizzes, but because
  I dont do my homework, I am failing the class.
• The teacher gives me all these problems that are
  the same.I dont know how to do the first ones
  so I give up.

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Every Student Has a Right To

• Know the well-defined and clearly stated criteria
  for assessment or grading.
• Get genuine and frequent feedback, both for right
  now and for long-term progress toward the exit
  level
• Take part in grading or scoring that will give
  chances to improve performance, with assessment
  being recursive and continual.
• Have plenty of opportunity to do work of which he
  or she can be proud of, with revisions,
  self-assessment, and self-correction.
• Be able to show, often and in many ways, how well
  he or she is doing, especially to demonstrate
  strengths.

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Assessment..

• How do you assess your students?
• What forms of assessment do you use?
• What alternate assessments do you use?
• Do the students do any self-assessment?

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Some tips

• Dont score every piece of student work.
• Dont panic when you encounter a piece of student
  work that you dont understand. Ask to explain
  further.
• Accept the fact that there will NEVER be enough
  time.
• Ask Why? Or How do you know? or Explain what
  you did often.

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Rubrics

• You cannot be too clear when it comes to
  expectations.
• Make sure your students (and their parents) are
  very clear on what your expectations are for
  every assignment.
• Students need to know, going in, what your
  expectations are.
• You as a teacher also need to know what your
  expectations are.

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• Write down your criteria. Share it with the
  students ahead of time.
• Make criteria or "rubrics" for all the different
  types of assignments you offer.
• Post those rubrics on the wall around the room,
  color coded based on the assignment type.

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• Schools that motivate young people to learn use
  several assessment approaches, including
  authentic assessments that promote student
  reflection, critical inquiry, and
  problem-solving, and assessments that validate
  children's different intelligences, strengths,
  and learning styles.

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Standard Assessments

• Homework
• Quizzes
• Tests
• Worksheets
• 9-week tests

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Quick Assessment..

• On a sheet of paper, number from 1 to 10.
• Next to each number, respond with A, B, C or D as
  if you were answering a multiple choice test.

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Answers.

• C
• D
• B
• A
• C

• B
• C
• B
• D
• A

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Make them better!

• Less assigning of 1-39 odd.
• Less multiple choice questioning, more open-ended
  questioning
• Allow for requizzing retesting should be
  formative not summative
• 9-week tests and SOL test should be the ONLY
  summative assessments.

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Alternate Assessments

• Journals
• Pair Share
• Projects
• Presentations to the class
• Activities
• Open-ended questions
• Student-created questions

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Virginia Math Standards of Learning, Blooms
Taxonomy, and Research-Based Strategies For
Increasing Student Achievement
MATH 6
2006-2007
Dan Mulligan, 2007
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Virginia Math Standards of Learning, Blooms
Taxonomy, and Research-Based Strategies For
Increasing Student Achievement
MATH 7
2006-2007
Dan Mulligan, 2007
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Virginia Math Standards of Learning, Blooms
Taxonomy, and Research-Based Strategies For
Increasing Student Achievement
MATH 8
2006-2007
Dan Mulligan, 2007
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Standards Verbs

• PROBLEM SOLVING
• Analyze Derive Discover Evaluate Explore
• Predict Solve Survey Verify Investigate
• REASONING
• Categorize Classify Compare Contrast Differentiat
  e
• Describe Estimate Explain Generalize Interpret
• Justify Order Hypothesize Predict Infer
• Prioritize Rank Validate Summarize
• COMMUNICATION
• Clarify Correspond Describe Discuss Demonstrate
• Exhibit Explain Express Persuade Portray
• Restate Show Speak State Write

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• Restate the Question say it in a different
  way.
• Answer the Question
• Reason for the answer
• Explain your solution

RARE
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2001 Released Test Question

• Johanna rented a car. Rental costs
• were 29.00 per day plus 0.49 for
• each mile driven. If she kept the car
• for 1 day and drove 50 miles, how
• much did she owe?

RARE
Find 2 different ways to solve this problem.
Explain your reasoning for both.
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Explain why you chose a particular answer. What
properties do the other choices demonstrate?
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A to Z Review uses the letters of the alphabet as
an organizer for tapping prior knowledge
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Cubing

• Topic___________________________
• Describe it___________________
• What does it look like?
• Compare it ___________________
• What is it similar to or different from?
• Associate it ___________________
• What does it make you think of?
• Analyze it ___________________
• How is it made or what is it composed of?
• Apply it ___________________
• What can you do with it? How is it used?
• Argue for or against it ___________________
• Take a stand and list reasons for supporting it.
• Spend only 5 minutes on each side of the cube.

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Build A City.Using Polygons
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Enhanced Scope Sequence

• PLENTY OF ACTIVITIES that you should be using
  with ALL students, not just those doing VGLA.

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NCTM Illuminations Website

• http//illuminations.nctm.org/

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Cinquains

• a short, simple poem.
• It is a creative outlet for reflecting on the
  meaning of a concept of information just learned.

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Guidelines

• The first line is a one word title (usually a
  noun).
• The second line is a two word description of the
  topic (usually two adjectives).
• Line three is three words expressing action of
  the topic (usually three ing
• words).
• The fourth line is a four word phrase showing
  feeling for the topic.
• The fifth line (last line) is a one word synonym
  that restates the essence of the
• topic.

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6th Grade Cinquain

• Integer
• Positive, Negative
• Opposing, Counting, Numbering
• Whole and its opposite
• Signed

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7th Grade Cinquain

• Mean
• Central Number
• Summing, Averaging, Middle
• Sum divided by count
• Statistic

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Algebra 1 Cinquain

• Slope
• Steepness, direction
• Rising before running
• Measures rate of change
• Pitch

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Write your own Cinquain.

• Polygon
• Probability
• Circle
• Inequality

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Why use CINQUAINS in the classroom

• Synthesizes information for greater understanding
• An evaluation tool as an alternative to a regular
  assignment or quiz
• Creative expressionget students involved more

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Working with Graphs

• Select a graph card from the deck.
• Roll a die to identify the task.
• Read the task to your team.
• Answer the question and justify your proposed
  solution.
• Ask team members to verify your solution.
• Pass the die to the next team member.
• Go to step 2.

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3, 2, 1 Write three things you learned today
write 2 connections to your real life write one
question for tomorrow.
Using pictures only, summarize three key points
of todays lesson.
Summarize todays lesson with a content Cinquain.
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Remember we are teaching the thinkers of
tomorrow.
The teachers of our childrens children. The
finders of cures for our illnesses. The
decision-makers for global peace. The
problem-solvers of our future.