Preparing Students for Math ISAT

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Preparing Students for Math ISAT
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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

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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

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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

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ISAT Mathematics SessionsGrades 3-8
Test Window March 2-13, 2009
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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.

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Short and Extended Response
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The answer space for each extended-response item
is 2 pages. Page 1 has a blank space, and page 2
has faint grid lines.
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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.

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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

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Reporting
Illinois Student ReportMathematics
Results(Page 3)
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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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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.

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THINK,PAIR,SHARE!
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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.

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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.

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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.

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And finally,

• Score some papers!

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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

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II. Start verbally in your classroom discourse

• When you ask questions orally in class, ask more
  authentic questions and less testing questions.

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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??

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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?

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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.

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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?

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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?

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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?

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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

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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.

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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.

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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

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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

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Use the CUT strategy

• C Circle the question
• U Underlined the important facts
• T Throw out the rest!

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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

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Tell students to use words, pictures and numbers
to explain their thinking
Words
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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

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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.

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IV. Have Writing Become an Integral Part of Your
Mathematics Curriculum

• Always brainstorm with the class before writing.

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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
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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
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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

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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

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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

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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

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Space for calculations and drawings
What I did
Why I did it
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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)
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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

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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

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Contact Information

• Joan Barrett
• 692-6200 ext. 6448
• jbarrett_at_roe41.org

• ISBE Mathematics Assessment
• 217/782-4823
• www.isbe.net/assessment