Bridging the Gap A

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					A Simple Question of
Weight Ratios

A Simple
Question of
Weight Ratios
  Helpful Strategies for Differentiation using the CSCOPE
             Scope and Sequence and Exemplar Lessons
                                         Chris Miller, MS
                                             Sanger ISD
Promises, promises
           Monty Python Clips
          Algebra 1 Examples

Characteristics of Students who Struggle
     with Mathematics Problem Solving
       What causes students to
 Generallack of consensus in research as
                       to specific causes.
    Many studies focus on math facts and
                simple math computations
       Few studies focus on the cognitive
            dimensions of problem solving
                         (Wendling & Mather, 2009)
   What causes students to
 Findings   of studies for 1st – 3rd graders
                     Poor nonverbal reasoning
                         Slow processing speed
             Poor short-term memory retrieval
              Difficulties with working memory
               Deficient oral language abilities
         (Swanson & Beebe-Frankengerber, 2004; Fuchs,
                          Fuchs Stuebing, et al., 2008)
Working Memory and Executive
    Difficultiesin Working Memory and
   Executive Function may account for a
 larger group of people characterized as
                having “math difficulties”
     Also may explain why over 30% of
students with ADHD are also diagnosed
           with math learning disabilities
                    (Wendling & Mather, 2009)
     Executive Function
    The  executive functions are a set of
       processes that all have to do with
managing oneself and one's resources in
order to achieve a goal. It is an umbrella
  term for the neurologically-based skills
        involving mental control and self-
  Executive Function: The Basics
  The executive functions all serve a "command
 and control" function; they can be viewed as the
                  "conductor" of all cognitive skills.
 Executive functions help you manage life tasks
 of all types. For example, executive functions let
       you organize a trip, a research project, or a
                                  paper for school.
           Often, when we think of problems with
                 executive functioning, we think of
   disorganization. However, organization is only
                      one of these important skills.
         Working Memory
   Working memory is the executive and attentional
aspect of short-term memory involved in the interim
    integration, processing, disposal, and retrieval of
  Most theorists today use the concept of working
  memory to replace or include the older concept of
      short-term memory, thereby marking a stronger
            emphasis on the notion of manipulation of
 information instead of passive maintenance. (More
   than just remembering, it’s where you manipulate
                           information in your head.)
  Characteristics of Good Problem
 Use  a variety of strategies, including self-
                        monitoring strategies
      Read the problem for understanding
                       (reread as necessary)
                    Paraphrase the problem
 Identify key information (may underline or
                                   highlight it)
    Ask themselves, “What is the question
      being asked? What am I looking for?”
 Characteristics of Good Problem
           Visualize – create a schematic
 Formulate a plan to solve problems using
        both verbal and visual information
           Estimate a reasonable answer
         Compute and check the answer
 Understand the language of mathematics
 Characteristics of Poor Problem
    Solvers in Mathematics

                  Poor    Number Sense
 Little or no use of varying strategies
 Little or no use of visualization (may
                   create limited pictorial
                    Little or no planning
          Little or no use of estimation
   Characteristics of Poor Problem
      Solvers in Mathematics
     Limited   mathematical vocabulary
  May compute prior to understanding
                             the problem
 Little or no checking of procedures or
                  answers for accuracy.
 Evidenced-Based Instructional Features
        that Improve Math Achievement

You do the math!
   Clarity of objectives: Objectives state specific
                and measurable student behaviors.
 One skill or concept: The focus is on only ONE
  new skill or concept so that adequate resources
    of working memory are available for learning.
 Use of manipulatives or representations: These
     techniques are used to increase conceptual
                understanding, understanding, and
          Instructional approach: Explicit instructional
   procedures are used that employ modeling and an
                                   explanation of steps.
    Teacher examples: Examples are presented for
          teachers to teach the target skill or concept.
           Provision of adequate practice: Sufficient
                 opportunities to practice are provided.
 Review of adequate math skills: Review is provided
                                of important prior skills.
  In other words: The research favors good teaching
                 strategies - what we’re already doing.
            Error correction and feedback: Corrective
           instructive feedback is provided that allows
               students to analyze their performances.
       Vocabulary: Key vocabulary is introduced and
      Strategies: Cognitive strategies are taught and
   Progress Monitoring: Procedures are described for
               ensuring student progress and mastery.
           Wendling, Barbara J. and Wendy Mather.
              Essentials of Evidence-Based Academic
             Interventions. Rapid Reference 9.1 p 197
      Four Effective Instructional
    Practices for Teaching Math and
             Their Benefits

             Teach   within authentic contexts
  (demonstrates significance of math for real-
       life problem solving, promotes interest)
 Build meaningful student connections (links
          new learning to previous knowledge)
                             explicit Concrete-
                         Provide
            Representational-Abstract (CRA)
         instruction with modeling/scaffolding
      (matches instruction to student’s current
                       level of understanding)
           Teach problem-solving strategies
    (develops metacognitive skills and fosters
   Wendling, Barbara J. and Wendy Mather. Essentials of Evidence-
          Based Academic Interventions. Rapid Reference 9.5 p 203
       Using the CSCOPE Scope and
Sequence Effectively with Students Who
            Struggle with Mathematics

        Reading Is FUNdamental
                  Read the Year-At-a-Glance.
                 Read the Exemplar Lessons.
                  Read the Unit Assessment.

 It   seems redundant, but I still catch myself
         not reading carefully, and that leads to
Vocabulary of Instruction
Key Understandings
       Key Understandings and
       Questions to Check for

   Found   within each lesson. Scaffold
        these heavily for your students.
           Consider typing them up in a
    worksheet for them to complete as
                           you go along.
 Also include the Key Understandings
                     in your scaffolding.
Scaffolding Questions

                  Try It B4 You Buy It

    the lesson on yourself. Go through the
 Try
     teaching cycle as well as trying it as a
  Time intensive at first, but saves time in
                                 the long run.
  Helps you to identify potential difficulties
                              or roadblocks.
  Don’t Throw Out the Baby with
         the Bath Water

    Avoid   the temptation to throw out the
curriculum when you encounter obstacles.
  Using a textbook or another curriculum
   that is not created in alignment with the
 CSCOPE scope and sequence seems to
 be very successful in confusing students.
(Modifying the CSCOPE
    Exemplar Lessons)
     Modifying the CSCOPE Exemplar

 Go  through the lessons and break them
    up according to the following domains:
                  One skill or concept at a time
     Explicit instructional procedures are used
     Employ modeling and explanations of the
 Provide enough opportunities to practice each
   Concrete-Representational-Abstract
    (CRA) instruction is vital. Struggling
learners have a harder time generalizing
           new skills to abstract concepts.
 Set up intermediate steps between the
     concrete and abstract to scaffold the
      transference of these skills into new
     Stealing, not Cheating
                                    UT DANA Center
 You’ll find similar problems oftentimes with additional
                   scaffolding questions and examples.
                Region IV’s remediation materials
        Objective based, easy to teach, often scripted.
                                    World Wide Web
                       I steal from the Khan Acacemy
                           Beth Loughry (Region X)
 Use and abuse the wonderful people at your Regional
          Service Center. Excellent source for help and
• Slow down and cut your food into small
       enough bites so you don’t choke.

   Schema-Based Instruction
  Focus on teaching students to search for
                   more than just key words.
 Teach them to recognize specific problem
   types as they would recognize a person,
                   movie, or perhaps a song.
    Recognizing schema helps the student
   transfer their acquired knowledge, skills,
        and strategies to a new situation or
  Schema-Based Instruction
                               The   student:
    Identifies the problem type (schema).
 Represents the problem by diagramming
              or illustrating key information.
       Plans how to solve the problem by
  selecting the appropriate operations and
                     writing out the equation.
                        Solves the problem.
Hey, Chris! Stop and Pull up
     some examples!

          Modifying Lessons
   Go through lessons and break them up
       according to the following domains:
 One skill or concept at a time
 Explicit instructional procedures are used
 Scaffolding
 C-R-A
 Provide enough opportunities to practice
  each skill
 Palatable chunks

 Have Faith in the Process
  Fightthe tendency to cover a particular
concept until you are sure that they “get it”
   Learning occurs through out the year.
   The “light bulb” comes on for different
    students at different times in different
          Teaching for breadth vs. depth
             Quit whipping a dead horse.
Other Obstacles that Impede
           Math Instruction
  • Environmental or Emotional factors
   can impede the quality of instruction
         and learning in any classroom.
• Being aware of these factors can help
              you take the emotional or
      environmental “temperature” of a
   given class, or a given student, on a
                              given day.

Maslow’s Hierarchy of Needs

Chris Miller
                 Sanger ISD
  601 Elm St. Sanger, TX 76266


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