Teaching Vocabulary and Language Skills

1. Teaching Vocabulary and Language Skills

2. Two Areas: • Language of instruction • Mathematics-related vocabulary and language skills

3. 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

4. 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

5. 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

6. 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

7. Vocabulary Teaching Procedures • Modeling positive and negative examples • Using synonyms • Giving definitions

8. 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

9. 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

10. 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

11. 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)

12. 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

13. Format • Model and immediate acquisition • A sum is the answer when you add. What is the sum? • Positive and negative examples • Write 4-1=3. Ask, “Is 3 a sum? How do you know?” • Write 4+2=6. 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?

14. Critical Preskills • Equality • More-Less

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

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

17. Counting

18. 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)?

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

20. 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.

21. Types of math knowledge errors • Fact • Component • Strategy • Incorrect operation • Random errors

22. 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

23. 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.

24. Strategy Error • Student demonstrates that s/he does not know steps in strategy. • For example, • Student doesn’t 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.

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

26. 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%.

27. 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.

28. 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.

29. 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?)

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

31. 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?

32. 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)

33. Rote Counting: Error Correction How do you correct students who leave out a number when rote counting?

34. Correction Procedures • “Stop” • Model, lead, test the “hard part” (2 numbers prior to the error) • Test the whole sequence • Delayed test

35. Rote Counting: Practice and Review How can a teacher provide enough practice in order for lower performing students to master rote count?

36. Rational Counting Again, what is it? Why start with pictures rather than manipulatives? Format 4.2—How is rational counting taught?

37. Rational Counting: Error Correction What 2 types of errors can students make?

38. Rational Counting: Error Correction How do you correct coordination errors? How do you correct rote counting errors?

39. Rational Counting: Error Correction How do you correct coordination errors? • Tell the students to count only when they touch (you can model too). • “Test”—repeat the exercise. • Continue until students can count correctly several (3) times. • Delayed “test”—repeat the exercise later. (Provide lots of practice and review.)

40. Rational Counting: Error Correction How do you correct rote counting errors? • Model the hard part. • Lead students on the hard part. • “Test”—repeat the exercise (from 1). • Continue until students can count correctly several (3) times. • Delay “test”—repeat the exercise later. (Provide lots of practice and review.)

41. Rational Counting: Two Groups Why? What error might students make? How do you correct?

42. Counting from Different Numbers Why? How? What error might the students make? How do you correct this error?

43. Counting Backwards Why? How?

44. 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).

45. 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.

46. Skip Counting: Count-by Series Why? • Why should countingby 10 be taught early? • What other skill do count by series facilitate? • Which of the sequencing guidelines do these exemplify?

47. 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

48. 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?

49. Symbol Identification and Place Value

50. Symbol Identification and Place Value • Three major areas: • reading and writing numerals • column alignment • expanded notation