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Mathematics and Reading in Mathematics or If you cant read the problem, its hard to get the answer.

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Title: Mathematics and Reading in Mathematics or If you cant read the problem, its hard to get the answer.


1
Mathematics and Reading in Mathematics or If
you cant read the problem, its hard to get the
answer.
  • Research and Evaluation
  • August 2006

2
Reading Looks Far Better Than Mathematics on the
TAKS
  • Looking at TAKS, one might think the district
    isnt doing very well in math but is doing much
    better in reading
  • Across grades, 72 of students pass reading while
    59 pass math
  • 13 of 18 Unacceptable secondary schools are so
    because of math (4 also have reading as a problem
    and 1 is reading only)
  • 25 of 29 schools missed AYP because of math (9
    missed because of reading as well and 4 schools
    missed reading only)

3
But, It Aint So
  • When ITBS results are examined, we see that the
    district does far better in math than in reading
  • Mathematics results are dramatically higher than
    reading comprehension in 8 out of 9 grades
  • In every subgroup, students do significantly
    better in math than reading comprehension

4
Percent At or Above 40th Percentile Reading and
Math ITBS 2005
5
OK, Why Does TAKS Math Look So Bad?
  • TAKS math performance looks much worse than TAKS
    reading performance for two reasons
  • The TAKS math tests are far more difficult than
    TAKS reading tests, and
  • The TAKS math tests have such a large reading
    component that poor student reading skills pull
    down math scores
  • (Note This does not say that reading is the only
    problem with TAKS math)

6
How Do We Know TAKS Math is a Harder Test?
  • When the reading Lexiles of reading items and
    math items are compared, math items are at a much
    higher reading level
  • When TAKS reading and math passing values are
    compared with ITBS percentiles, passing TAKS math
    is much harder at all but one grade

7
Reading Lexiles of TAKS Math and Reading Test
Items
  • A Lexile is a measure of reading level. The
    higher the Lexile, the harder the reading
    passage.
  • Lexiles of 2006 released 9th grade TAKS items in
    mathematics and reading were examined for reading
    level

8
Lexile Results
  • The median Lexile for 9th grade TAKS math items
    was 985, about a 6th or 7th grade reading level.
  • The median Lexile for 9th grade TAKS reading
    items was 580, about a 3rd grade reading level.

9
Lexile Results
  • 23 of 9th grade math items had reading levels
    above the 9th grade level
  • 8 of 9th grade math items had reading levels
    above the 12th grade level
  • Only 6 of 9th grade reading items had reading
    levels above the 9th grade level

10
Lexile Results
  • 85 of the 9th grade reading Lexiles were below
    the median Lexile for math
  • Only 6 of 9th grade math items were below the
    reading median Lexile

11
Here is a 9th grade reading item at the TAKS
reading Lexile median
  • Paragraph 42 is mainly about
  • A. Matthew and Sundance becoming acquainted
  • B. What horses like to eat while in the corral
  • C. Fences and their usefulness on ranches
  • D. Matthew leaving the corral with the others

12
Here is a 9th grade math item at the TAKS math
Lexile median
  • 38. Brandon has a budget of 58 to spend on
    clothes. The shirts he wants to buy are on sale
    for 9 each, and the pair of pants he wants costs
    21. All prices include tax. Which inequality
    could be used to determine s, the maximum number
    of shirts Brandon can buy if he also buys the
    pair of pants?
  • F. 21s 9 lt 58
  • G. 9s 21 58
  • H. 30s lt 58
  • J. 9s - 21 58

13
Here is a 9th grade TAKS math item at a 9th grade
Lexile level.
  • 36. Heidi has a main-course choice of a
    hamburger, a hot dog, an egg roll, a taco, a fish
    sandwich, or a chicken sandwich. She has a
    side-order choice of french fries, corn chips,
    potato chips, or a salad. Heidis beverage choice
    can be a soda, fruit punch, milk, or water. Which
    is the best method to determine how many
    different combinations Heidi could choose?
  • F. Add the total number of items in the 3
    categories together
  • G. Multiply the total number of main-course
    choices by the total number of side-order choices
    and add the product to the total number of
    beverage choices
  • H. Multiply the sum of the total number of
    main-course choices and the total number of
    side-order choices by the total number of
    beverage choices
  • J. Multiply the total number of items in each
    of the 3 categories together

14
ITBS Evidence
  • ITBS evidence shows the relative difficulty of
    the TAKS reading and math tests even more clearly
  • We computed percentile levels where students had
    a 50/50 chance of passing reading or math and
    percentile levels for reaching commended on
    reading or math

15
ITBS Evidence
  • In 7 of 8 grades, passing TAKS math is more
    difficult than passing reading by at least 13
    percentile points and at 3 of 8 grades by 20
    percentile points

16
ITBS Evidence
  • In 6 of 8 grades, reaching commended on math is
    more difficult than reaching commended on reading
    by at least 10 points and at 3 of 8 grades by 20
    points

17
TAKS Passing by ITBS Percentile
18
TAKS Commended by ITBS Percentile
19
So, What Makes the Math Tests Harder?
  • You may have guessed it already. The answer, in
    part, is
  • Reading Level

20
What Type of Reading Is In Math (and Science)
Items?
  • These items use a type of reading we will call
    expository (some add the term formal) reading
  • Expository reading differs from general reading
    in significant ways and calls for many skills not
    found in general reading
  • We will come back to this idea in our
    Recommendations and Next Steps

21
What Part Does Reading Play in Math Performance?
  • Research just completed looked at the
    relationship of reading to mathematics.
  • The 9th grade 2005 TAKS reading and math scores
    were studied.

22
Significant Reading-Related Components of Math
Scores
  • Two reading-related components of 9th grade TAKS
    math scores stood out
  • LEP status LEP reading achievement was lower
    than non-LEP and it was significantly related to
    math achievement

23
Significant Reading-Related Components of Math
Scores
  • Two reading-related components of 9th grade TAKS
    math scores stood out
  • The Classroom Effectiveness Index of a students
    reading teacher was significantly related to math
    achievement. The higher the CEI in reading, the
    higher math achievement.

24
Significant Reading Components in Math Tests and
Items
  • Using 2006 ITBS results, students were divided
    into low, average, and high reading achievers and
    low, average, and high math achievers and we
    graphed the TAKS results
  • Lets look at the graph of the 9th grade test
    results using this approach

25
Grade 9 TAKS by Reading and Math Achievement
Levels
26
Grade 9 TAKS by Reading and Math Achievement
Levels
  • Looking at the graph we see that, at all three
    math levels, increasing reading achievement helps
    math achievement
  • Since most of the districts students are in the
    lower reading achievement group, there is great
    potential for increasing math by increasing
    reading

27
Significant Reading Components in Math Items
  • Items were grouped into 4 categories
  • A reading effect at all math levels
  • A reading effect for low math achievers
  • A reading effect for high math achievers
  • Math items with no particular reading effect
  • Lets look at one of the graphs

28
Grade Nine Math Item 43
29
Grade Nine Math Item 43
  • 43. Narongs family bought 3 shirts, 2 pairs of
    jeans and 2 pairs of shoes. Each shirt cost 18
    and each pair of shoes cost 35. The jeans were
    marked down from their original price of 40.
    What other information, if any, is needed to find
    the total cost of the 7 items before tax?
  •  
  • A. The percent markdown for the shirts
  • B. The original price of the jeans
  • C. The percent markdown for the jeans
  • D. No additional information is needed.
  •  

30
How Many Ninth Grade Items Have Strong Reading
Components?
  • An analysis of the items for grade 9 math shows
    that
  • 27 have strong reading components at all levels
  • 23 have strong reading components for high math
    achievers
  • 27 have strong reading components for low math
    achievers
  • Thus, better readers achieve at higher levels on
    75 of the items on the ninth grade TAKS

31
How Do Math Items Do Relative to Reading at Some
Other Grades?
  • At grade 3, 58 of the items have strong reading
    components
  • At grade 5, 39 of the items have strong reading
    components
  • At grade 8, 80 of the items have strong reading
    components

32
Anecdote
  • A principal told us recently that we again did
    poorly on the measurement objective at grade 9 in
    2006, so we investigated the items
  • Of the 6 items for the measurement objective, 5
    had strong reading components as well as math
    components
  • Clearly, better readers will help the measurement
    objective regardless of math ability

33
Obvious Facts About Math and Reading
  • Kihneman corollary 1 If you help students do
    better in reading you get an automatic boost on
    TAKS math
  • Kihneman corollary 2 If you stop extra help in
    reading when a student just passes TAKS reading,
    you leave the student far short of the necessary
    reading level to pass math

34
Think About Corollary 2 For a Moment
  • If a student just passes reading, how far short
    does that leave him/her of the reading level of
    the math test?

..Pass a test with a reading level here?
Will a student reading here.?
35
What We Know About Reading
  • The most effective reading teachers teach
  • More higher order skills
  • More writing including editing and rewriting
  • The best measure of a reading teachers
    effectiveness is that teachers CEI

36
Recommendations
  • This information does not imply that we need to
    put less of an emphasis on mathematics
  • NEVER stop extra reading assistance to a student
    who has ever failed TAKS reading
  • Extra help in reading needs to continue beyond
    passing TAKS reading until a student is at least
    at a score level of 2250 or at the 40th
    percentile on the ITBS

37
Recommendations
  • More expository reading in the form of
    math-oriented reading passages and questions
    needs to be added to reading instruction
  • Science shows the same relationship to reading as
    math in our preliminary work. More expository,
    science-oriented reading passages and questions
    need to be added to reading instruction

38
Recommendations
  • Even high achieving math students who are below
    the high achievement level in reading need extra
    reading assistance, preferably in expository
    reading. That help will benefit TAKS math
    performance

39
Bottom Line
  • Working on math alone to improve math scores,
    wont get you where you want to go. Youve got
    to work on expository reading and keep working on
    it.

40
Next Steps
  • Examine the reading curriculum and add expository
    math (and science) reading instruction and
    examples at all grades
  • Build expository math and science reading into
    the reading scope and sequence

41
Next Steps
  • Construct staff development modules on expository
    reading in math and science for reading, math,
    and science teachers (and coaches)
  • Provide schools with profiles of combined math
    and reading levels of their students individually
    and by grade

42
Next Steps
  • Assure that reading, math, and science coaches
    stress expository reading in math and science and
    can demonstrate it
  • Build expository reading in math and science into
    before- and after-school programs and into
    tutoring for low achieving readers and see that
    it is implemented
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