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
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
Align Curriculum and local testing to the IAF • Templates for aligning math curriculum http://www.roe41.org/handouts/framework/default.html#M • Sample of aligning a textbook to the IAF
ISAT Mathematics SessionsGrades 3-8 Test Window: March 2-13, 2009*
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.
The answer space for each extended-response item is 2 pages. Page 1 has a blank space, and page 2 has faint grid lines.
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 year’s 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 releaseditems from previous years including samples of student work and how they were scored.
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
Reporting Illinois Student ReportMathematics Results(Page 3)
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 eachkind 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.
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.
Between Day 1 and Day 2…Think…… • 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.
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.
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.
And finally, Score some papers!
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
II. Start verbally in your classroom discourse • When you ask questions orally in class, ask more authentic questions and less testing questions.
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??
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…?
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.
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?
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?
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?
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
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.
Websites • ISBE website http://www.isbe.net/assessment/htmls/math_released_er.htm releaseditems from previous years including samples of student work and how they were scored.
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
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 O’Brien, from the ETA catalog
Use the “CUT” strategy • “C” – Circle the question • “U” – Underlined the important facts • “T” – Throw out the rest!
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
Tell students to use words, pictures and numbers to explain their thinking Words
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
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.
IV. Have Writing Become an Integral Part of Your Mathematics Curriculum • Always brainstorm with the class before writing.
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
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
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
IV. Have Writing Become an Integral Part of Your Mathematics Curriculum (cont.) • Use lower grade level’s 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
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
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
Space for calculations and drawings What I did Why I did it
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)