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Preparing Students for Math ISAT

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Title: Preparing Students for Math ISAT


1
Preparing Students for Math ISAT
2
Illinois Assessment Framework
  • All test items on the ISAT align to the Illinois
    Mathematics Assessment Framework
  • see IAF Handout
  • Percentages chart
  • Numbering system
  • Pp 20-21 some topics are not measured at all
    grade levels

3
IAF - Frequently asked questions and
misconceptions
  • referents (7.3.05 pp 20)
  • convert within the same measurement system p.
    21
  • Most Graphs in Goal 10 not 8 (Algebra)
  • Net p. 27

4
Align Curriculum and local testing to the IAF
  • Templates for aligning math curriculum
    http//www.roe41.org/handouts/framework/default.ht
    mlM
  • Sample of aligning a textbook to the IAF

5
ISAT Mathematics SessionsGrades 3-8
Test Window March 2-13, 2009
6
Non-Multiple Choice Items
  • The 2 short-response items will contribute 5 to
    the scale score.
  • The 1 extended-response item will contribute 10
    to the scale score.
  • Short- and Extended-Response items are scored
    using a rubric. (www.isbe.net/assessment/math.htm)
  • Item-specific rubrics are developed for each item
    before scoring.

7
Short and Extended Response
8
The answer space for each extended-response item
is 2 pages. Page 1 has a blank space, and page 2
has faint grid lines.
9
Short and Extended Response
  • Directions for how students are to respond will
    be given in the item itself (e.g., show your
    work, label your answer).
  • Use previous years released ISAT short- and
    extended-response sample items from grades3
    through 8 to practice this format.
  • ISBE website http//www.isbe.net/assessment/htmls/
    math_released_er.htm released items from previous
    years including samples of student work and how
    they were scored.

10
Report formats
  • Tied directly to the IL Assessment Framework
  • Are VERY SPECIFIC (related to objectives on the
    Framework) about strengths and weaknesses
  • Will help you make School Improvement Plans, make
    curricular decisions, plan staff development

11
Reporting
Illinois Student ReportMathematics
Results(Page 3)
12
Claire wanted to buy some of each kind of
bookmark at the book fair. The bookmarks with
animals on them cost 15, and the bookmarks with
the solar system on them cost 10. Claire spent
1.00. How many of each kind of bookmark did she
buy? Show all your work. Explain in words how you
got your answer and why you took the steps you
did to solve the problem.
  • For this response make sure you
  • show all your work in solving the problem,
  • clearly label your answer,
  • tell in words how you solved the problem,
  • tell in words why you did the steps you did to
    solve the problem, and
  • write as clearly as you can.

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17
A two-day lesson model used by Mary Modene in
Belleville
  • Day 1
  • Define Extended Response.
  • Review How to Solve a Problem
  • Review the ISBE scoring rubrics.
  • Elaborate on Mathematics Knowledge
  • Elaborate on Strategic Knowledge
  • Elaborate on Explanation
  • Stress the importance of showing work.
  • Model solving an ER problem.

18
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19
THINK,PAIR,SHARE!
20
Between Day 1 and Day 2Think
  • Present a problem for students to work on
    independently.
  • Instruct students to find a solution to the
    problem and to show all of their work.

21
Pair..
  • After finding solutions, students work with a
    partner to share their solutions, determine
    whether they are correct, and share their
    strategies with each other.
  • Finally, students must choose one solution, and
    working together, try to perfect it and write the
    explanation so that their response could receive
    a score of 4-4-4.

22
Day 2.SHARE!
  • Review the information from Day 1 and what has
    happened since..
  • Review the 3 dimensions of the scoring rubric..
  • Review the problem.
  • Share correct solutions.
  • Discuss possible strategies.

23
And finally,
  • Score some papers!

24
The Big Picture
  • All teachers at every grade level in the school
    should know about and use open-ended questions
    with their students.
  • Start verbally in your classroom discourse
  • Search for, collect, create, and trade with
    colleagues Extended Response questions and tasks.
  • Have Writing Become an Integral Part of Your
    Mathematics Curriculum

25
II. Start verbally in your classroom discourse
  • When you ask questions orally in class, ask more
    authentic questions and less testing questions.

26
Testing Questions
  • Questions in which you already know the answer
    and are just testing to see if your students know
    the answer
  • What is 12x2
  • What's the definition of parallel lines?
  • More examples??

27
Authentic Questions
  • Questions in which you don't know the answer?
  • What patterns do you notice in the table?
  • What are you finding out?)
  • What are you thinking?
  • Others (think about some of the questions we use
    in Lang. Arts?) What if?

28
Questioning (continued)
  • Pose questions that have more than one correct
    answer. (i.e. What's a whole number between -4
    and 4? What are some of the coin combinations I
    could use to make 80 cents? How could I measure
    this?)...Others?
  • Always ask, "Did anyone else do it a different
    way?"
  • Ask students to solve problems in more than one
    way.
  • Ask students to explain their answer. Ask them
    to explain how they solved the problem and why
    they did it that way.

29
Answer questions with questions (a la Socrates).
  • When a student says "How do I do this problem?"
    You respond "What do you know about the problem
    that may help you get started? What have you
    tried?

30
Reverse your questions
  • Rather than What is 5x7? Ask If 35 is the
    answer, what could the question be?
  • Instead of saying "What's the perimeter of this
    figure?" give students a piece of graph paper
    and say "Can you draw figures that have the
    perimeter of 20 centimeters? What do you notice
    about their areas? Do you think the same thing
    would happen if we kept the perimeter constant at
    28 centimeters? Investigate the problem and
    report what you found out.
  • Other Examples?

31
A Practice Problem(Marilyn Burns technique)
  • Amy is paid 4 per hour for her first 10 hours of
    work one week.
  • She earned 8 per hour for an additional 6 hours
    of overtime work.
  • What do you think the question will be?

32
Creating Practice Problems
  • Write a simple addition word problem on your
    post-it note
  • Classification of word problems
  • Final unknown
  • Change unknown
  • Initial unknown
  • Post your problem in one of the three categories

33
III. Search for, collect, create, and trade with
colleagues Open-ended questions.
  • Professional publications (NCTM has 3 monthly
    grade level publications--The Mathematics
    Teacher, Mathematics Teaching in the Middle
    School, and Teaching Children Mathematics). These
    monthly publications all have collections of
    Extended Response questions.
  • Enrichment sections of your text books.
  • Ask your students to create some open-ended
    problems for you.

34
Websites
  • ISBE website http//www.isbe.net/assessment/htmls/
    math_released_er.htm released items from previous
    years including samples of student work and how
    they were scored.

35
Some Curricular Materials with Open-ended
Questions/Activities
  • Written materials for manipulatives (for instance
    The Super Source by ETA/Cuisenaire)
  • Published materials for calculators
  • Open-ended, interactive software programs (for
    instance Geometer's Sketchpad Key Curriculum
    Press)
  • The enrichment sections of your textbook series

36
Some Curricular Materials with Open-ended
Questions/Activities
  • Math and Literature Books NCTM has several books.
    Also Math and Literature series by Marilyn
    Burns mathsolutions.com or at ETACuisenaire.com)
  • Math Tantalizers (180 questions for each of 6
    levels) by Tom OBrien, from the ETA catalog

37
Use the CUT strategy
  • C Circle the question
  • U Underlined the important facts
  • T Throw out the rest!

38
IV. Have Writing Become an Integral Part of Your
Mathematics Curriculum
  • Begin slowly if your students are not accustomed
    to writing in their math class.
  • During the first semester just have students show
    their work. Second semester concentrate on the
    Why.
  • Use math word problems as your daily oral
    language exercise.
  • Talk with students about the purpose of their
    writing
  • Establish an audience
  • for their writing

39
Tell students to use words, pictures and numbers
to explain their thinking
Words
40
IV. Have Writing Become an Integral Part of Your
Mathematics Curriculum (cont.)
  • When the students play a math game or do a math
    activity, have them record what is happening as
    they play or do the activity. (i.e. rolling dice,
    sorting, making patterns, etc.)
  • Provide a context for the problem

41
IV. Have Writing Become an Integral Part of Your
Mathematics Curriculum (cont.)
  • Model writing the appropriate notation when you
    are working on a problem with the whole class.

42
IV. Have Writing Become an Integral Part of Your
Mathematics Curriculum
  • Always brainstorm with the class before writing.

43
IV. Have Writing Become an Integral Part of Your
Mathematics Curriculum
  • Use Marilyn Burn's technique of having the
    children have their thoughts come out of their
    pencils rather than their mouths.

I used unifix cubes to keep track
I used unifix cubes to keep track
44
Have Writing Become an Integral Part of Your
Mathematics Curriculum
  • Post Math Words on chart paper as they are
    introduced in the context of a problem. Leave
    them posted. (Math Word Wall)

Numerator Radius Parallel
45
IV. Have Writing Become an Integral Part of Your
Mathematics Curriculum (cont.)
  • Give a prompt "I think there is a total of _____
    possibilities because"
  • Have students start with a blank piece of paper
    then collect data, organize it, and explain
    their process so other students can see and hear
    multiple ways to organize and analyze
    information.
  • Show samples of student work from ISBE Sample
    books

46
IV. Have Writing Become an Integral Part of Your
Mathematics Curriculum (cont.)
  • Use lower grade levels problems to practice with
    so your students can concentrate on the
    "explaining" rather than the math
  • Put an open-ended question on some of your
    classroom assessments throughout the year

47
IV. Have Writing Become an Integral Part of Your
Mathematics Curriculum (cont.)
  • Train your students to use the scoring rubric so
    they understand what is being expected.
  • Score samples as a group first, then in pairs.
    Use the specific wording from the rubric to
    explain how they arrived at their score
  • Underline why phrases in sample work
  • Show a 4,4, 2 paper and make it a 4,4,4

48
IV. Have Writing Become an Integral Part of Your
Mathematics Curriculum (cont.)
  • Solve a problem as a class and write together an
    explanation that would be scored a 4,4,4 using
    the ISAT Rubric
  • Try using a graphic organizer to help students
    with the Why part of their explanations
  • Generate a list with the students of good phrases
    to use for the why
  • Close to the testing time practice answering
    Extended Response questions using the two-page
    ISAT format with the grid background

49
Space for calculations and drawings
What I did
Why I did it
50
My Explanation
Why I Did It
What I Did (examples)
to find the question because so that to see So I
could see To show to organize To keep track in
order to to find out To look for trends so I
know I already know that__ so
First, I read the problem counted drew a
picture, drew a line, drew a shape added,
subtracted, multiplied, divided took half of (or
a fourth of etc) made a chart made a
list circled made tally marks, made a graph,
added a key found the middle (median),mode found
the average (mean)
51
Indicate what the answer is!!
  • When students are finished writing their
    explanation indicate what the answer is by one of
    these
  • Circling it
  • Underlining it
  • Putting ans. or answer by it
  • Or just state the answer is in the written
    explanation

52
Possible Accommodations for IEP and 504 Students
(MUST be included in IEPs and 504 paperwork)
  • May use calculators for third graders
  • May read multiple choice, SCR and Extended
    response items to the student
  • May extend time beyond the 55 minutes or give in
    short increments
  • May allow students to dictate their explanation
    to the extended response items. Teacher must
    write word for word
  • May enlarge items and paper for the visually
    impaired and then the teacher can transcribe to
    the official answer sheet

53
Contact Information
  • Joan Barrett
  • 692-6200 ext. 6448
  • jbarrett_at_roe41.org
  • ISBE Mathematics Assessment
  • 217/782-4823
  • www.isbe.net/assessment
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