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In-service program documentation
Exploring implications for assessment (D5.3)
Facilitator's plan (by Constance Smith) -- for the experience
of solving an item from an innovative statewide exam only (From Implementation
D)
Time: about 1 1/2 hour
Materials: Newsprint, Item on prepared handout, NYS tests (Math 8 & Math A)
Rationale: we want to give the participants an opportunity to familiarize themselves with the Learning: Standards for Mathematics, Science and Technology published by the New York State Education Department and the corresponding tests and to make connections between what these new materials are asking and what is possible in mathematics education using the inquiry approach they have been experiencing. The participants should recognize and delineate what could/should be learned about doing mathematics when engaging in inquiry. They need to take a closer look at the 'simple ' and familiar' problems on the MA TH 8 test to recognize that there is potential for decision making, questioning, interpreting and analyzing with even the simplest problems but they need to do them and look carefully at what they would expect from students.
1. (30 min) Set the stage by talking about other reflections on how the learn in tessellations and the mathematics goals in area. Consider again their experiences AND what they have learned from them. Consider the thinking that was made public in the What is Mathematics? session we began this exploration of inquiry with on Monday. What have you learned about doing mathematics from your engagement in these inquiry experiences? What do you think/hope middle school students would learn as well?
Generate list on newsprint.
If difficulty in starting, point out some of things participants have said during their work - we need to clarify for ourselves the definition of this figure (when working on star formula.)
Possibly also ask teacher representatives to share what they have expected their students to learn.
2. (5 min) In light of these things that you say you've reamed and/or are important for students to learn from inquiry DO this interesting question:
(From one of the Grade 8 New York State pilot tests)
The local sports complex charges different prices for their tickets to different sporting events. The table below shows their current prices. [Anyone under 16 years of age would pruchase a child's ticket.]
Ticket Prices
| Child | Adult | |
| Hockey | $4.50 | $7.00 |
| Basketball | $5.00 | $9.00 |
| Football | $6.25 | $11.50 |
Ken's Scout Troop earned money in order to go to Saturday's football game. His father bought 8 tickets for the scouts and one ticket for himself as the Scoutmaster.
When Ken's father pays for the tickets, how much change will he receive from a $100 bill?
Note: reproduce this item on a separate sheet of paper, with no "box" for the answer, so that participants may be more inclined to give answers other than simply a numerical one.
Do individually with little direction as to what is required. The list generated should include such things as questioning, making and clarifying assumptions and justifying solutions and thus that is what we would expect to see at least on many of the papers.
3. ( 10 min) Share responses by reading (and/or recording on newsprint is desired/necessary)
If a single numerical answer is given ask: In light of these ideas about what you said about doing math, is this an acceptable answer? Why? What would be an acceptable answer?
4. (35 - 40 min)This is the first question on the Math 8 test! (show it and pass out MST Standards) It is important to look at these questions carefully before making to many judgements about them. NYS has created these tests to reflect a certain thinking about mathematics reaming -- in fact mathematics, science and technology reaming. Is NYS asking for thinking similar to what we have been engaged in this week? I'd like you to take a look at the MST Standards in particular Standard 1 elementary and intermediate level all analysis, inquiry and design and Standard 3 Mathematics intermediate level reasoning, numeration, operations (that is pages 2,3, 4, 5, 18, 19) (Refer to entire list of standards on page l and the format.) with the question you've just worked and our sense of the potential of inquiry in mind. Will giving the students an opportunity to learn through inquiry help them to reach the goals set forth by NYS.
Suggest they work in school based groups because of any additional questions or mission statements that they might also want to consider. But keep the groups to 3 or 4 is possible.
5. ( 10 min) Come back and answer the question: Is NYS asking for thinking similar to what we have been engaged in this week? Be sure in discussion to make the bridge to inquiry.
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