Teaching%20Vocabulary%20and%20Language%20Skills

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Teaching Vocabulary and Language Skills
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Two Areas

• Language of instruction
• Mathematics-related vocabulary and language skills

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Language of Instruction

• Terms commonly used in directions given by
  teachers (directions, actions, names of objects,
  names of colors).
• Students should be screened to ensure they
  possess the language concepts and if not they
  should receive remediation.
• Remediation
• Place in math program with carefully controlled
  teacher wording and provide supplementary
  language instruction

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Math-related Vocabulary and Language Skills

• Terms used to describe characteristics of objects
• e.g., square, circle, dime,
• Terms used to describe relationships between
  objects
• e.g., parallel, similar, near, far

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Math-related Vocabulary and Language Skills

• Terms used to describe numbers in an operation
  and the operations themselves
• e.g., sum, addend, difference, add, subtract
• Classification terms
• e.g., 6 boys, 7 girls, 3 cats

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Guidelines

• Need to integrate brief vocabulary-oriented
  instructional activities into math curriculum
• Sequence of instruction depends on necessity of
  term. Some terms must be taught as preskills,
  others can wait until strategy is taught.
• Preskill -- end with, side, equal, same, other
• Later -- denominator, numerator, subtrahend

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Vocabulary Teaching Procedures

• Modeling positive and negative examples
• Using synonyms
• Giving definitions

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Modeling Positive and Negative Examples

• Model positive and negative examples of the new
  word
• Test the students on their mastery of the
  examples
• Present examples of the new word along with
  examples of other previously taught words

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Presentations

• Quickly paced
• Stress important words (this is not)
• Present until all students are able to respond
  correctly to a group of three positive and three
  negative examples

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Teaching Vocabulary with Synonyms

• Teacher links new word with previously learned
  words rather than modeling examples
• Must carefully select word used as a synonym --
  be sure word is familiar
• Tests with positive and negative examples
• Provide practice in applying several recently
  taught synonyms

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Format

• Model and immediate acquisition
• Here is a new word. Subtract. Subtract means
  minus. What does subtract mean?
• Positive and negative examples
• Write 4 2 on the board. Do we subtract in this
  problem?
• Write 6-3 on the board. Do we subtract in this
  problem?
• Review in context of other words.
• What does ADD tell us to do? (plus)
• What does SUBTRACT tell us to do? (minus)

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Teaching Vocabulary with Definitions

• Teach definition
• Must carefully select words used in definition --
  be sure word is familiar (i.e., a preskill).
• Show positive and negative examples
• Contrast it with previously learned definitions

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Format

• Model and immediate acquisition
• A sum is the answer when you add. What is the
  sum?
• Positive and negative examples
• Write 4-13. Ask, Is 3 a sum? How do you know?
• Write 426. Ask Is 6 a sum? How do you know?
• Review in context of other words
• What is the DIFFERENCE of 5 and 2?
• What is the SUM of 5 and 2?

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Critical Preskills

• Equality
• More-Less

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Equality

• Teach first in a context other than addition
• Teach functional definition
• Present series of positive and negative examples

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More-Less

• Important in story problems
• Introduce as synonym (bigger, not bigger)
• Present series of positive and negative examples

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Counting
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Instructional Analysis

• Questions to ask yourself for each type of
  counting
• What are the preskills?
• What is this a preskill for?
• What sequencing guidelines apply?
• What are potential errors?
• How do I correct them (remediation)?

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Preskills

• What are preskills?
• Give an example of a skill that is a preskill for
  a more advanced skill.

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Sequence Integration

• General Guidelines
• Preskills are taught before they are needed in
  strategies.
• Easy skills are taught before more difficult
  ones.
• Strategies and information that is likely to be
  confused are spaced or separated.

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Types of math knowledge errors

• Fact
• Component
• Strategy
• Incorrect operation
• Random errors

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Fact Error

• Student incorrectly responds to a memory task in
  which s/he is asked to tell the answer to one of
  the 100 addition, multiplication, subtraction
  facts or the 90 division facts.
• For example,
• 2 2 5
• 7 x 3 14
• 5 - 2 2
• 4 / 2 4

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Component Error

• Student makes error on previously taught skill
  that has been integrated as a step in a problem
  solving strategy.
• For example
• counts incorrectly or forgets the name of a
  numeral while completing an addition problem in
  lower grades.
• forgets to rewrite fractions as equivalent
  fractions in an addition problem or forgets to
  put a zero in the ones column when completing a
  multi-digit multiplication problem in upper
  grades.

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Strategy Error

• Student demonstrates that s/he does not know
  steps in strategy.
• For example,
• Student doesnt attempt to rename in a
  multiplication or subtraction problem.
• Student multiplies top number by bottom number in
  a multi-digit multiplication problem rather than
  both top numbers by each of the bottom numbers
  separately.

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Incorrect Operation

• Student uses wrong operation -- fails to
  discriminate between operations.
• For example,
• 25 - 12 37
• 13 x 3 16

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Random Error

• Student makes random, inconsistent errors across
  different problem types.
• May be related to motivation.
• Becomes a concern when accuracy drops below 85 to
  90.

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General Diagnosis and Remediation

• Four step procedure
• Teacher analyzes worksheet errors and
  hypothesizes what the cause might be.
• Teacher interviews student to determine cause of
  the error if its not obvious.
• Teacher provides reteaching through board or
  worksheet presentations.
• Teacher tests student on a set of problems
  similar to the problematic ones.

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Specific Remediation

• Fact
• Provide more practice, motivation.
• Component
• Reteach specific skill, provide additional
  practice.
• Strategy
• Reteach strategy.
• Incorrect operation
• Precorrect, prompt.
• Random errors
• If accuracy below 85, observe closely and work
  to increase motivation.

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Counting

• Why is counting important?
• What is rote counting?
• How is it different from rational counting?
• (What is the preskill for rational counting?
  Which sequencing guideline?)
• (Rational counting of 2 groups is a preskill for
  what? Which sequencing guideline?)

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Counting

• What is counting from a number?
• (What is counting from a number a preskill for?
  Which sequencing guideline is this?)

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Counting

• What is skip counting?
• Why should skip counting by 10 be taught early?
• What other skill does skip counting facilitate?
• Which of the sequencing guidelines do these
  exemplify?

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Rote Counting

• How do you determine where to start rote counting
  with young children?
• How do you teach rote counting?
• (See Summary Box 4.1 and Format 4.1)

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Rote Counting Error Correction

• How do you correct students who leave out a
  number when rote counting?

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Correction Procedures

• Stop
• Model, lead, test the hard part (2 numbers
  prior to the error)
• Test the whole sequence
• Delayed test

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Rote Counting Practice and Review

• How can a teacher provide enough practice in
  order for lower performing students to master
  rote count?

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Rational Counting

• Again, what is it?
• Why start with pictures rather than
  manipulatives?
• Format 4.2How is rational counting taught?

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Rational Counting Error Correction

• What 2 types of errors can students make?

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Rational Counting Error Correction

• How do you correct coordination errors?
• How do you correct rote counting errors?

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Rational Counting Error Correction

• How do you correct coordination errors?
• Tell the students to count only when they touch
  (you can model too).
• Testrepeat the exercise.
• Continue until students can count correctly
  several (3) times.
• Delayed testrepeat the exercise later.
• (Provide lots of practice and review.)

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Rational Counting Error Correction

• How do you correct rote counting errors?
• Model the hard part.
• Lead students on the hard part.
• Testrepeat the exercise (from 1).
• Continue until students can count correctly
  several (3) times.
• Delay testrepeat the exercise later.
• (Provide lots of practice and review.)

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Rational Counting Two Groups

• Why?
• What error might students make?
• How do you correct?

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Counting from Different Numbers

• Why?
• How?
• What error might the students make?
• How do you correct this error?

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Counting Backwards

• Why?
• How?

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Rote Counting by 1s from 30 to 100

• Preskills Rote counting from a number other
  than 1 skip counting by 10s
• Important skill to practice is counting across
  "decades."
• Demonstrate the relationship between tens
  groupings (i.e., sequence of numerals 1, 2, 3. .
  .21, 22, 23).

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Instructional Sequence

• Count numbers higher than 100, stay within
  centuries and decades,
• Count numbers higher than 100, stay within
  centuries, but count across decades,
• Count across centuries beginning and ending at
  number ending with 5
• After mastery, change examples to promote
  generalization.

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Skip Counting Count-by Series

• Why?
• Why should counting by 10 be taught early?
• What other skill do count by series facilitate?
• Which of the sequencing guidelines do these
  exemplify?

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Skip Counting Count-by Series

• Why is it suggested by we put count-by series in
  the following order (sequencing guideline)
• 10, 2, 5, 9, 4, 25, 3, 8, 7, 6

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Skip Counting Count-by Series

• The format (4.5) has 2 parts. What are they for?
• How do you teach a new series?
• When can the next series be started?

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Symbol Identification and Place Value
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Symbol Identification and Place Value

• Three major areas
• reading and writing numerals
• column alignment
• expanded notation

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Terms

• What do the following terms mean
• Number
• Numeral
• Place value
• Expanded notation
• Column alignment

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Introducing the Concept

• Concepts for kindergarten through early 1st grade
• Numeral identification (0-10),
• Numeral writing (0-10),
• Symbol identification (, -, , q),
• Equation reading and writing,
• Numeral and line matching.

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Introducing Numeral Identification

• When do you start?
• What sequencing guideline is critical in
  determining the order in which numerals are
  introduced?

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Introducing Numeral Identification

• Order of introduction what numerals would you
  separate?
• Rate of instruction how fast can we introduce
  new numerals?
• How do you introduce new numerals?

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Introducing Numeral Identification

• Write review numerals (how many times?) and new
  numeral (how many times?) on board.
• Introduce new numeral.
• (This is __. What is it?)
• Discrimination practice.
• (What order?)
• Individual turns.

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Introducing Numeral Identification

• Why do you need to signal?
• How do you signal when students are looking at
  the numerals on the board?
• How long should you spend on this task?

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Introducing Numeral Writing

• When can you introduce numeral writing?
• Rate of introduction?
• What are the stages of introduction
  (scaffolding)?
• What is numeral dictation? What order do you
  dictate numerals?
• How do you correct student errors?

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Introducing Symbol Identification and Writing

• -
• How do you introduce symbols?

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Introducing Equation Reading and Writing

• What is equation reading a preskill for?
• When is equation reading introduced?
• How do you teach equation reading?

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Introducing Equation Writing

• When is equation writing introduced?
• How do you teach equation writing?
• How do you correct if students write numerals out
  of order?

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Numeral/Object Correspondence

• Students identify the symbol (numeral) and write
  that number of lines.
• Students count the objects and write the numeral.
• Preskills for addition and subtraction using
  equality strategy.

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Numeral/Object Correspondence

• When can you introduce these numeration skills?

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Numeral/Object Correspondence

• Before teaching students to identify the symbol
  and write the lines, what preskill must students
  have?
• See format 5.3.
• What errors might students make in 5.3?

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Numeral/Object Correspondence

• Why is writing numerals to represent a set of
  objects important?
• 4 2
• llll ll

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Numeral/Object Correspondence

• Format 5.4 teaches students to count the objects
  and write the numeral.
• What are the preskills?
• What errors might students make?

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Numeral/Object Correspondence

• What should you do if students make a counting
  error?
• What should you do if the students make an error
  in numeral identification or writing?
• When do you introduce manipulatives?

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Place Value

• Reading and Writing Numerals
• Column Alignment
• Expanded Notation

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Reading and Writing Teen Numerals

• When is reading teens numerals introduced?
• What is the order of introduction?
• See format 5.5.
• When are irregular teens introduced?
• What is the rate of introduction for irregular
  teens?

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Reading and Writing Teens Numerals

• When is writing teens numerals introduced?
• See format 5.6.
• When might manipulatives be used?

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Reading Numerals20-99

• What are the preskills?
• Format 5.7

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Writing Numerals20-99

• When is this introduced (that iswhat are the
  preskills)?
• See format 5.8.
• When dictating numerals in step E, what is the
  example selection guideline?

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Writing Numerals20-99

• What pattern of errors might students make
  (diagnosis)?

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For a Diagnosis and Remedy

1. State the diagnosis.
2. State the formats that you would reteach.
3. State the examples that you would emphasize.

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Remediation for Written Reversals (such as 71 for
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• Reteach writing teens format. At the same time,
  reteach writing tens numbers format (without 1s
  in the ones placelike 31).
• Then teaching writing format with minimal
  discriminations21 12, 41 14, etc.

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Reading and Writing Numerals100-999

• Reading hundredsWhat are the preskills?
• See format 5.9.
• Sequencing What is avoided initially?
• Then, what examples are used?

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Reading and Writing Numerals100-999

• Sequencing What is avoided initially?
• (0 in the tens place)
• What examples are used when 0 in the tens place
  is included?

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Reading and Writing Numerals100-999

• Writing hundreds numeralsFormat 5.10

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Reading and Writing Numerals1,000-999,999

• What is the sequence for introducing these
  numerals?
• What are the example selection guidelines when
  zeros are introduced?

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Column Alignment

• Why is this an important skill?
• See format 5.13

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Expanded Notation

• What is expanded notation?
• See Format 5.14.

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Curriculum Evaluation