Facilitator's Packet Content Teachers · Training for Trainers & Materials Provided by ODE ... growth in math skills. xMaterials: ... good place to talk about key concepts for each

Facilitator’s Packet for

Using the Mathematics

Scoring Guide: Level 2

An Introduction for

High School Content

Area Teachers

This packet contains the following:

Facilitator’s Agenda PowerPoint Slides with Facilitator’s notesParticipant Handouts

Oregon Department of Education 2011 12 Office of Assessment and Information Services

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intentionally left blank.

Design for Mathematics Essential Skill Workshops Training for Trainers & Materials Provided by ODE

The workshops described below are designed to be delivered by school district personnel who have received training and materials from ODE through “Training of Trainer” WebEx sessions.

Level 1

Overview of the Essential Skill of Mathematics (30 – 45 minutes)

General audiences – posted on ODE Website at http://www.ode.state.or.us/search/page/?id=2666

Level 2

Introductory Training – Using the Mathematics Scoring Guide Content Area Teachers with math

emphasis(2 hours)

Introduces Math Scoring Guide and provides practice scoring student

papers; emphasis is on classroom use

Mathematics Teachers (3 hours)

Introduction to new Math Scoring Guide with practice scoring student

papers; emphasis is on updating scoring accuracy for Essential Skills

work samples and classroom use

Level 3

In-Depth Training – Using the Mathematics Scoring Guide for Essential Skills Work Samples

Content Area Teachers Mathematics Teachers

In-depth Training on Scoring Guide – Expand understanding of scoring

guide and increase accuracy in scoring papers with examples from

content areas classes (3 to 3 ½ hours)

In-depth Training on Scoring Guide – Expand understanding of

scoring guide and increase accuracy in scoring papers with

emphasis on Essential Skills proficiency

(3 ½ to 4 hours)

Level 4

In-Depth Training – Creating Mathematics Work Samples (3 ½ to 4 hours)

Hands-on workshop showing characteristics of effective Mathematics Problem Solving Tasks for both Content Teachers and Mathematics Teachers; review of Guidelines for Work Samples, and opportunity for participants to draft a work sample for use in their classrooms.

*Estimated time needed for trainer to deliver the workshop to district/school participants

Training of Trainer WebEx Sessions

Level 1 training for presenters is provided in a one hour WebEx session which includes reading, writing and mathematics. It is designed to be delivered to general audiences by anyone with a basic understanding of the Essential Skills. No content expertise is required. Level 1 workshop materials are also available on the ODE website at http://www.ode.state.or.us/search/page/?id=219. Select the desired Essential Skill and go to Resources and Promising Practices.

Levels 2 – 4 provides training for presenters with expertise in high school mathematics. Level 2 Training of Trainers is delivered in one 2-hour WebEx session, Level 3 in another 2-hour WebEx session and Level 4 in a final 2-hour WebEx session. All workshop materials, including ready-to-print handouts, are provided to attendees following each WebEx Training of Trainers session.

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Information provided by Oregon Department of Education Office of Assessment and Information Services 2011-12

Using the Mathematics Scoring GuideFacilitator’s Agenda -- Introductory Session for Content Teachers – Level 2

Time: 2 - 2 ½ HOURS

5 – 10 minutes

1. Welcome and Introductions May be done by the host or by the presenter. Focus on making participants feel welcome and let

them know what to expect Take care of any housekeeping details

Handout: Participant’s Packet

7 - 10 minutes Small Group Discussion (or whole group if workshop number is small)

2. Students who are currently sophomores and freshmen will have to demonstrate proficiency in the Essential Skill of Mathematics to earn a diploma. What options can we implement for the approximately 43% of students who have not yet met the standard? (Based on state data of students who did not meet the OAKS standard of 236 in 2009-10)

3. Reminder: these teachers were chosen or self-selected to attend because there is some math emphasis in their courses. You may need to steer discussion toward how courses other than math courses can support student’s growth in math skills.

Materials: Easels with chart paper, white board, document camera or small groups report out verbally.

10 minutes 4. Introductory Mathematics Work Sample and Scoring Guide presentation

Go through Slides 1 – 7 – these slides introduce the Essential Skills requirements and the options for Essential Skills proficiency. Focus of this workshop will be on using the scoring guide in classroom activities and math work samples in content classes. Materials: Laptop with PowerPoint & projector

15 minutes 5. Slides 8 - 17: Overview of the Scoring Guide This section introduces the scoring guide and scale. This is a good place to talk about key concepts for each dimension and about the scale. Use the Facilitator’s Guide to Leading the Scoring Session when discussing each dimension OR give a broad overview and then focus on each dimension as you get into scoring papers.


20 - 30 minutes

6. Slides 18 – 25 Looking at the 1st Task Have participants work the Mr. Gerard’s Oil Tank task (full version is in their handout packet). Be aware that some content teachers may not have the math skills at their fingertips to solve this problem. You can offer assistance or tips, or let participants work for a short time and then begin to share solutions they have or the approaches listed in your facilitator’s packet. Discuss differences in approaches & point out that some authentic tasks in content areas may not have the multiple approaches, but it is important not to set up the problem as a fill in the blank step-by-step activity.

7. Use the Facilitator’s Guide to Leading the Scoring Session tohelp you lead the discussion on each paper.

8. Read each of the sample papers in sequence, scoring papers as a group.

9. Discuss each paper, helping participants to see why each paper received the scores it has. Commentaries in the Facilitator’s Packet will help you understand important points about each paper.

Materials: Highlighters for participants

20 – 30 minutes

10. Slides 26 - 30 Looking at the 2nd Task Have participants work the Roof Vents task (full version is in their handout packet). Again, not all teachers may have these particular math skills, so adjust your strategy as needed. Share results and discuss differences in approaches. Use the Facilitator’s Guide to Leading the Scoring Session along with the commentary for each student sample to help you.

15 - 20 minutes

1. The next set of slides (30-39) focuses on helping teachers recognize how they can incorporate math problem solving activities in their classes.

2. One of the most effective ways teachers can support student growth in math skills is by using the scoring guide when math activities are assigned. For classroom work, teachers can choose to use one, two or more of the dimensions.

3. The Student Language version of the scoring guide and the Student Problem Solving Tips in the packet will help students to understand the target and see the connection between assignments in content classes and what they are learning in math class.


4. The Guidelines for High School Mathematics Work Samples applies more to Essential Skills Work Samples, but can provide some helpful pointers. (More information about developing math work samples will be available in a future workshop – Level 4.)

5 Minutes 5. Slides 40 - 41 close out the presentation. Insert your

information in slide 40. There is a resource list for supporting math instruction and assessment in the handout packet.

Slide 41 is a humorous quote to close the presentation

Optional – 10-20 minutes

6. Have participants brainstorm what kinds of assistance they need to integrate more math into their courses, especially math activities that can be scored with the scoring guide.

Materials: Easel with chart paper, white board, or small groups report out.

10 minutes 7. Optional Question & Answer or Summary Be sure to identify future training opportunities for

participants Total = 2 – 2 ½hours

Participant Packet:PowerPoint handouts to take notes Scoring Guide Various handouts Official Math Scoring form

Sample Student Papers: Oil Tank

TRCM1TRCM2TRCM3TRCM4TRCM5

Roof Vents TRCM6TRCM7TRCM8TRCM9TRCM10

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This introductory workshop is targeted to high school content area teachers who havemath emphasis in their courses.A companion introductory workshop is available for high school math teachers.

1

These are the three goals for this session. Explain that this session will acquaintparticipants with the newly adopted math scoring guide and with the expectations forEssential Skills proficiency.

There will be a in depth training session (Level 3) available to provide increased depth ofknowledge and experience applying the scoring guide to student papers. Teachers whotake the in depth training session should feel confident scoring papers to demonstrateproficiency in the Essential Skill of Mathematicsproficiency in the Essential Skill of Mathematics.

Remind participants that they have the PowerPoint slides in their handout to take notes on,if they wish.

2

This is the Oregon Administrative Rule, adopted by the State Board of Education, that sets the diploma requirements for the Essential Skills. These Essential Skills are also required for subsequent entering freshmen classes. The Essential Skill of Apply Math will be implemented beginning with students who first enrolled in 9th

grade in 2010-11 (most will be sophomores this year) and all future cohorts of students.

3

This is the definition adopted by the State Board for the Essential Skill of Mathematics. Thebullets, describing what it means to apply mathematics, are clearly reflected in thedimensions of the scoring guide.

4

Students have three options to demonstrate proficiency in the Essential Skill ofMathematics. Achieving a score of 236 on the high school OAKS Mathematics test is oneway. Students can also use scores achieved on various standardized tests approved by theState Board of Education. Currently approved tests are shown in the table.AP tests include AP Statistics, Calculus AB, and Calculus BC – all of which require aminimum score of 3. International Baccalaureate tests are Mathematics HL, MathematicsSL, and Math Studies. IB tests require a minimum score of 4. While these options mayhelp some students more students may choose option 3 – the work sample which ishelp some students, more students may choose option 3 the work sample which isexplained on the next slide.

5

To demonstrate proficiency in the Essential Skill of Mathematics using work samples,students must meet all three criteria listed here – 2 work samples, one each in any of twoof three content areas listed, with scores of 4 or higher in all dimensions on the mathscoring guide.

6

Work Samples require equal rigor but provide a different format to demonstrateproficiency.

7

Remind participants that this will be an introduction to the scoring guide. More detailedtraining is available in an in depth workshop (Level 3).

8

This slide explains the history and recent revision process for the Mathematics Scoring Guide. Bring out your sales skills! Oregon has lots of reasons to be proud of our scoring guide andto recognize that it can be an important classroom tool for instruction, formativeassessment, and summative assessment.

Refer to Official Scoring Guide in Handout Packet.

9

These are the 5 dimensions of the math scoring guide.

10

Refer to the handout in the Participant’s Packet Introduction to the Scoring Guideand to Suggestions for Use of Student Papers in the Facilitator’s Packet fordiscussing each dimension.

The student translates the words from the problem into appropriate mathematics.The key concepts are addressed. Evidence that makes a paper more thoroughlydeveloped or insightful may include extending their thinking to other mathematicalideas or making connections to other contexts.

11

The strategies chosen by the student are effective and complete for this task.Evidence that makes a paper more thoroughly developed or insightful may includegeneralizing a strategy using an algebraic representation versus a numeric or tabularrepresentation.

12

Communication of the reasoning refers to the connections among all of thedimensions, and the identifiable solution – allowing the flow of the paper to helpthe reader understand the path from one part to another. A clear path does notrequire a linear sequence of thoughts or communication. The student uses mathvocabulary and labels appropriately.

13

It is critical that students who are “close” to having a proficient response, withminor errors or partial answers, be given an opportunity to rework the problemgiven the scoring feedback, but no further instruction.

Evidence that makes a paper more thoroughly developed or insightful may includeextending the solution by asking new questions leading to new problems. Althoughpossible, it is a rare occurrence to get a 5 or 6 in accuracy.

14

The student states the solution within the context of the problem. This requires thestudent to review the task and reflect on what was asked. There should beevidence on the student has reviewed ALL the dimensions in solving the task.

The reflection (a second look) could be embedded in the original work or afterarriving at a solution and/or a combination of both.

Evidence that makes a paper more thoroughly developed or insightful may includesolving the task from a different perspective. Students evaluating their approachesmay include addressing the efficiency of an approach or the relative use of aprocedure.

15

This shows the continuum of scores students may achieve. Point out that the Official Scoring Guide contains detailed descriptions for each dimension. Descriptions for the 1 & 2 level are combined as are descriptions for the 5 & 6 level. However, all score points may be awarded.

16

This provides another “shorthand” way of looking at the different score levels. Refer to theStudent Tips handout in the Participant’s Packet as a way to help students understand thescoring guide and score levels. A student level version of the scoring guide is also includedin the Participant’s Packet.

17

The next slides will show some work samples and lead into scoring student papers. Animportant part of the message is that work samples can be used in a variety of waysespecially in content classes. Any time students use mathematics and receive feedbackusing the scoring guide creates important learning and connections across content areas.Students do not need to be scored on all 5 dimensions on all papers. It is fine to give anassignment and score one, two or three dimensions.

18

This definition stresses that problems are complex and generally cannot be presented in amultiple choice test format.

“There is a distinction between what may be called a problem and what may beconsidered an exercise. The latter serves to drill a student in some technique orprocedure, and requires little if any, original thought… No exercise, then, can alwaysbe done with reasonable dispatch and with a minimum of creative thinking. In

i bl if i i d f i l l h ld icontrast to an exercise, a problem, if it is a good one for its level, should requirethought on the part of the student.”Howard Eves

19

Mathematics Content Standard Assessed by This Task: H.1G.5Language From Achievement Level Descriptors for Meets which Describes the RequiredSkills: Determine area, surface area, and/or volume. Solve for missing dimensions. Solverelated context based problems.Participants have full size copy of task in their handout packet. Ask them to workindividually to solve this task.

20

You may want to have participants pair and share, share in small groups or share with thewhole group. Ultimately, you should have several different approaches to the problem thatarrive at the correct solution. (If the group does not arrive at multiple approaches, thepresenter should suggest alternatives. Some alternatives are included in the Facilitator’sPacket.)

21

Paper TR 16 received all 4’s. Lead participants through a discussion to help them find thedescriptions in the scoring guide that best match this paper in each trait. Use theSuggestions for Use of Student Papers to help you lead this part of the training.

22

Paper TR 17 received a mixture of 1’s, 2’s, and 3’s. Again, have participants identify specificphrases that describe this paper.

23

Discussion! Have participants use highlighters to emphasize key points between a 3 and a4. In general, it is not difficult to recognize high papers or very low papers. The keydecision point for many papers will be between a 3 or a 4, so raters must become proficientin making this distinction. Remind the participants that revisions are allowed and moredetail on this will be provided later in the workshop. This can help participants move pastdebating the “3” vs. “4” issue and focus on how the student could improve the answer.

24

Walk the participants through scoring each of the remaining student papers, using thecommentary to help you in leading the discussion of each paper and dimension. TR 18received a mix of 3’s & 4’s with one score of 1; TR 19 received mostly 4’s with one 5 andone 1. TR 20 received 4’s with one 5. Point out the importance of students understandingthe scoring guide in order to show the work necessary to be scored. In the handout packetis a Student Problem Solving Tips document.

25

Have participants complete this task and discuss prior to scoring papers. A full size copy isincluded in their packets.

26

Again, have participants pair and share, share in small groups or share with whole group –looking for multiple approaches to reaching the correct answer. Additional approaches areincluded in the Facilitator’s Packet.

27

Paper TR 11 received three 4’s, one 3 and one score of 1. Lead participants through adiscussion to help them find the descriptions in the scoring guide that best match thispaper in each trait. What would this paper need to meet the standard

28

Paper TR 12 received four 3’s and one 1. Again, have participants identify specific phrasesthat describe this paper. Use the Suggestions document to help you.

29

Walk the participants through scoring each of the remaining student papers, using thecommentary to help you in leading the discussion of each paper and dimension. TR 13received one 4, one 3, two 2’s and one 1. TR 14 received one 5, two 4’s, one 3, and one 1.The Suggestions document will help you lead a discussion for each of these papers.

30

Have participants brainstorm ways they can use the scoring guide in their classes. Reinforcethat not all dimensions need to be scored every time and that practice tasks (even if theyare not as complex or at the needed difficulty level for Essential Skills) will help studentsincrease math problem solving skills at the same time that they learn important contentspecific math issues.

31

Talk about importance of Math Scoring Guide as a powerful instructional tool. Haveparticipants discuss how they could use the math scoring guide in their classrooms. Thisdiscussion empowers teachers to incorporate work samples in addition to the schoolassessment plan or where no assessment plan exists yet. Depending on the size of thegroup you may want to have them pair/share or form small groups to discuss this.

32

Teachers can use Math Work Samples to determine student progress throughout theircourses or on a planned schedule. They do not have to assign all parts of the work sampleor score all dimensions.“Research has clearly shown that good formative assessment practices lead tomore effective instruction and increased student achievement. “Larry Berger

33

As students become familiar with the math scoring guide (point out student language version) they will begin to understand what they need to do in order to improve their scores and to increase their understanding of the application of math in the particular content area.

34

This is summary reminder of the requirements for a student to demonstrate mastery of theEssential Skill of mathematics using work samples. (repeated from earlier in thepresentation)

Refer to Handout – Guidelines for Math Work Samples.

35

Refer to Handout: Guidelines for High School Math Work SamplesExplain that there is an entire workshop devoted to developing good problem solving tasksfor the purpose of assessing proficiency in the Essential Skills. However, for practicepurposes, teachers should feel free to develop and try out work samples in their classes.Again, in content classes if the work sample is being used for instruction or formativeassessment, it does not have to meet the criteria for an Essential Skills work sample.

36

Students should be allowed time to do their best work.

37

Teachers who rate student work samples for the purpose of demonstrating proficiency inthe Essential Skill of Math, must be well trained in using the scoring guide. Additional indepth workshops will be available for those who wish to extend their knowledge

38

Refer to Handout: Official Mathematics Scoring Form.

Students may receive feedback after a work sample has been scored and they may revisethe work sample (in a supervised setting) and resubmit it to be scored again for EssentialSkills purposes. Typically, this would be offered to students whose paper nearly meets thestandard of all 4’s rather than for papers in the 1 & 2 range where more instruction may beneeded. Classroom teachers may want students to revise papers in order to reach anaccurate solution and to demonstrate various skills called for in the scoring guideaccurate solution and to demonstrate various skills called for in the scoring guide.

39

Please adjust this slide to reflect your information. You can either list dates if you havespecifically scheduled future workshops, or you can leave it blank with just “Follow upworkshops” and indicate that additional workshops are available on request or will bescheduled later.A handout in the Participants’ Packet provides a comprehensive list of Oregon resources.

40

This slide provides a humorous closing.

41

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To meet the graduation requirement for the essential skill of ““apply mathematics” follow these steps. 1. Student takes the OAKS Mathematics Assessment.

1a: If the student receives a ssof 236, he has met the graduation requirement standard for readin

core

g.

2b. If the student receives a score lower than 236, he/she can meet the graduation requirement standard in one of three ways:

2a. If the student receives a score of 236, he/she has met the graduation requirement standard for mathematics.

3a. The student studies and retakes the OAKS Mathematics Assessment and receives a score of 236.

REVISION IS POSSIBLE: Work samples that nearly meet the standard (scoring a mix of 4s and 3s) may be returned to students for revision. Teachers may mark areas on the scoring guide or Official Scoring Form to show students in what areas they need to work (no other instructions are allowed). The work sample is then rescored.

4b. If the student attains a score of 3 or lower on any trait, he/she does not meet the graduation requirement standard for mathematics.

4a. If the student attains a score of 4 or higher for each trait on each work sample, he/she has met the graduation requirement standard for mathematics.

3c. Complete 2 mathematics work samples that are: scored using the Official State Mathematics Scoring Guide; receive a score of 4 or higher in 5 traits for each work sample.

In addition the work samples will be drawn from: Content Strands: Algebra, Geometry and Statistics Traits: Making Sense of the Problem, Representing & Solving the Task, Communicating & Reasoning, Accuracy, Reflecting & Evaluating.

3b. Take one of a number of approved standardized tests and receive the following scores: ACT: 19 PLAN: 19 SAT: 450 PSAT: 45 ASSET: 41 Compass: 66 Work Keys: 5 AP or IB: varies

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Introduction to the Scoring Guide

The scoring guide maintains vertical consistency at each number through each of the dimensions.

6: Work is insightful 5: Work is thoroughly developed 4: Work is complete and effective (not necessarily perfect) 3: Work is partially effective or partially complete 2: Work is underdeveloped or sketchy 1: Work is ineffective, minimal, or not evident

Making Sense of the Task (MS) Interpret the concepts of the task and translate them into mathematics The student translates the words from the problem into appropriate mathematics. The key concepts are addressed. Evidence that makes a paper more thoroughly developed or insightful may include extending their thinking to other mathematical ideas or making connections to other contexts. Representing and Solving the Task (RS) Use models, pictures, diagrams, and/or symbols to represent and solve the task situation and select an effective strategy to solve the taskThe strategies chosen by the student are effective and complete for this task. Evidence that makes a paper more thoroughly developed or insightful may include generalizing a strategy using an algebraic representation versus a numeric or tabular representation. Communicating Reasoning (CR) Coherently communicate mathematical reasoning and clearly use mathematical language. Communication of the reasoning refers to the connections among all of the dimensions, and the identifiable solution – allowing the flow of the paper to help the reader understand the path from one part to another. A clear path does not require a linear sequence of thoughts or communication. The student uses math vocabulary and labels appropriately.

A significant gap is when the reader is using his/her own knowledge about the problem and mathematics to infer why a student might have moved from one part of the work to another.

Evidence that makes a paper more thoroughly developed or insightful may include additional graphics or examples to help the reader move easily through the student work.

Accuracy (AC) Support the solution/outcome. The student’s solution is correct, mathematically justified, and supported by the work.

It is critical that students who are “close” to having a proficient response, with minor errors or partial answers, be given an opportunity to rework the problem given the scoring feedback, but no further instruction.

Evidence that makes a paper more thoroughly developed or insightful may include extending the solution by asking new questions leading to new problems. Although possible, it is a rare occurrence to get a 5 or 6 in accuracy.

Reflecting and Evaluating (RE) - State the solution/outcome in the context of the task. Defend the process, evaluate and interpret the reasonableness of the solution

The student states the solution within the context of the problem. This requires the student to review the task and reflect on what was asked. There should be evidence on the student has reviewed ALL the dimensions in solving the task.

The reflection (a second look) could be embedded in the original work or after arriving at a solution and/or a combination of both.

Evidence that makes a paper more thoroughly developed or insightful may include solving the task from a different perspective. Students evaluating their approaches taken may include addressing the efficiency of an approach or the relative use of a procedure.

Additional considerations:

It is important to consider each of the dimensions as a separate entity. The weakness in the work should only reduce the score for the dimension in which the weakness occurred. On the other hand, strength in one dimension may improve a score in another dimension. An answer that is not correct may still have strong work in some or all other dimensions. Likewise, a paper with a correct solution still needs careful consideration for success in each dimension.

Because a single scoring guide is used for a variety of tasks, the student work is not always expected to exactly match the criteria described at each numbered level. It will, however, have characteristics similar to those described in the criteria.

Guidelines for using the scoring guide:

It is important to prepare for the scoring process by doing the following;

Work the task yourself State the answer within the context of the problem List the key concepts necessary to complete the task Anticipate alternative solutions and strategies

Although different scorers may use different styles, here is a typical process for using the scoring guide:

Scan the student papers and find a sample of papers that represent the spectrum of student work

Possibly sort the student work so that you will score all work with similar approaches one after another

Carefully read all through one student’s work. Read the criteria for a score of 3 on one dimension. Review the student work again. If it seems stronger than a 3, read the 4 through

6 criteria. If is weaker than a 3, consider the 1 and 2 criteria. Assign a score for that dimension Repeat the process for the other 4 dimensions

Additional scoring hints or considerations include the following:

Any scores that you are uncertain about should be set aside to look at again after scoring the rest of the papers (these papers might also be good candidates for collegial discussions).

A score of 4 meets the standard, and a 3 nearly meets – so this is a critical distinction

As a way of validating your scores, it is very helpful to have a colleague score a few of your papers without seeing the scores you gave, then having a discussion about any differences in your scores. When double scoring, as a general rule, scores that are within 1 point in any given dimension are considered “aligned” but a discussion to agree on the same score can help to “calibrate” your scoring.

Reworking “official” work samples

When time allows and if no discussion of the task has taken place in class, it is encouraged that students with 4’s or better in some dimensions, and a few scores of three, or possibly lower, should be given an opportunity to revise their work (no further instruction is allowed if this response is to be used as evidence of proficiency for the purpose of the Essential Skill of Mathematics)

2011-2012 Mathematics Problem Solving Official Scoring Guide 2011-2012 Apply mathematics in a variety of settings. Build new mathematical knowledge through problem solving. Solve problems that arise in mathematics and in other contexts.

Apply and adapt a variety of appropriate strategies to solve problems. Monitor and reflect on the process of mathematical problem solving.

For use beginning with 2011-2012 Assessments Office of Assessment and EvaluationOregon Department of Education Adopted May 19, 2011

Process Dimensions **6/ 5 4 3 *2 / 1 Making Sense of the Task Interpret the concepts of the task and translate them into mathematics.

The interpretation and/or translation of the task are

thoroughly developed and/or enhanced through connections and/or extensions to other mathematical ideas or other contexts.

The interpretation and translation of the task are

adequately developed and adequately displayed.


partially developed, and/or partially displayed.


underdeveloped, sketchy, using inappropriate concepts, minimal, and/or not evident.

Representing and Solving the Task Use models, pictures, diagrams, and/or symbols to represent and solve the task situation and select an effective strategy to solve the task.

The strategy and representations used are

elegant (insightful), complex,enhanced through comparisons to other representations and/or generalizations.

The strategy that has been selected and applied and the representations used are

effective and complete.

The strategy that has been selected and applied and the representations used are

partially effective and/or partially complete.

The strategy selected and representations used are

underdeveloped, sketchy, not useful, minimal, not evident, and/or in conflict with the solution/outcome.

CommunicatingReasoningCoherently communicate mathematical reasoning and clearly use mathematical language.

The use of mathematical language and communication of the reasoning are

elegant (insightful) and/or enhanced with graphics or examples to allow the reader to move easily from one thought to another.

The use of mathematical language and communication of the reasoning

follow a clear and coherent path throughout the entire work sample andlead to a clearly identified solution/outcome.

The use of mathematical language and communication of the reasoning

are partially displayed with significant gaps and/or do not clearly lead to a solution/outcome.

The use of mathematical language and communication of the reasoning are

underdeveloped, sketchy, inappropriate,minimal, and/or not evident.

AccuracySupport the solution/outcome.

The solution/outcome is correct and enhanced by

extensions,connections,generalizations, and/or asking new questions leading to new problems.

The solution/outcome given is correct,mathematically justified, and supported by the work.

The solution/outcome given is incorrect due to minor error(s), or a correct answer but work contains minor error(s) partially complete, and/or partially correct

The solution/outcome given is incorrect and/or incomplete, or correct, but

o conflicts with the work, or o not supported by the work.

Reflecting and EvaluatingState the solution/outcome in the context of the task.

Defend the process, evaluate and interpret the reasonableness of the solution/outcome.

Justifying the solution/outcome completely, the student reflection also includes

reworking the task using a different method, evaluating the relative effectiveness and/or efficiency of different approaches taken, and/or providing evidence of considering other possible solution/outcomes and/or interpretations.

The solution/outcome is stated within the context of the task, and the reflection justifies the solution/outcome completely by reviewing

the interpretation of the task concepts, strategies,calculations, and reasonableness.

The solution/outcome is not stated clearly within the context of the task, and/or the reflection only partially justifies the solution/outcome by reviewing

the task situation, concepts, strategies,calculations, and/or reasonableness.

The solution/outcome is not clearly identified and/or the justification is

underdeveloped, sketchy, ineffective, minimal, not evident, and/or inappropriate.

**6 for a given dimension would have most attributes in the list; 5 would have some of those attributes. *2 for a given dimension would be underdeveloped or sketchy, while a 1 would be minimal or nonexistent.

2011-12 Mathematics Problem Solving Scoring Guide: Plain Language Student Version 2011-12 (To be used with students instead of or in addition to the official scoring guide. May not be used to score papers for Essential Skills proficiency.)

**6 for a given dimension would have most of the list; 5 would have some of the list. *2 for a given dimension would be inadequate in some of the list; while a 1 would be inadequate in most of the list.

Process Dimensions **6/5 4 3 2/1* Making Sense of the TaskUnderstand the ideas and change them into a math task WHAT?

The problem is changed into thoroughly developed ideas that work. The ideas are connected to other math ideas.

The problem is changed into a math task with ideas that can work.

Parts of the problem are changed into a math task with ideas that can work.

OR Only parts of the problem are understood.

Only a small portion of the problem is understood.

OR No understanding is shown.

Representing and Solving the TaskChoose the strategy that works best for this problem.

HOW?

A thoroughly developed plan is used that contains pictures, charts, words, graphs and/or numbers. A thoroughly developed plan may contain more than one step.

A plan using pictures, charts, words, graphs and/or numbers is used to solve the problem.

The plan could solve some parts of the problem.

OR The plan has a few missing parts.

The plan has many missing parts.

OR The plan cannot work.

OR No work is shown.

Communicating ReasoningUse the language of math (words, equations, graphs, charts) to make your ideas clear to others.

WHY?

The steps to complete the work are very clear. An explanation connecting each part is given.

The path through the work can be followed to a clearly identified solution.

AND Some attempt is made to explain why one step followed another.

The path is not clear. OR

The path leaves out important parts of the work.

The steps to complete the work are just started.

OR No steps are shown.

Accuracy

The answer is…

IS IT RIGHT?

The solution is correct and may be extended. The solution is correct and the problem is solved another way.

The answer given is correct and matches the work shown.

The answer given may have a small error. Otherwise the main parts of the work are good.

The answer given is not correct or not finished.

OR The answer given doesn’t match the work.

Reflecting and EvaluatingState and check your answer, and explain why it makes sense.

CHECK?

A different way is used to solve the problem. Different methods used are compared to each other.

The answer is written in a complete sentence and answers the question that was asked.

AND A second look has been taken to completely check the work and shows why the answer makes sense.

The answer is not written in a complete sentence or does not answer the question that was asked.

OR Some, but not all of the work is checked.

The check doesn’t work. OR

The check is barely started. OR

The check is not there at all.

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Student Problem Solving Tips You may use manipulatives or a calculator to work on your problem.

To receive the highest score in each of the five areas, you will want to be certain your work SHOWS each of these parts of a successful solution.

1. Making Sense of the Task I turned important information into numbers, symbols and/or diagrams. The mathematics I used fits the problem.

If possible, I showed connections and/or extended my work to other math ideas.

2. Representing and Solving the Task I used strategies that fit the problem. I showed all my work (diagrams, pictures, models, numbers, symbols and/or words).

If possible, I was able to make generalizations and/or compare my work to other ways the task could have been completed.

3. Communicating Reasoning The path leading through my complete solution has no gaps for the reader to fill in. I used mathematical language/labels appropriately. My answer is clearly identified.

If possible, I used graphics and/or examples to enhance my work.

4. Accuracy My final answer is complete and justified. The work shown on my paper leads to my answer.

If possible, I extended my solution by asking new questions leading to new problems. .

5. Reflecting and Evaluating My solution matches what the problem was asking. I reviewed ALL of my work (interpretation of the problem, concepts, strategies, and

calculations) to show that my answer makes sense and it is correct. If possible, I worked the entire problem a second way.

RECAP:Show your answer and all of your work

so everything is clear to the reader

Oregon Department of Education 2011-12 Office of Assessment and Information Services

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Oregon Department of Education Guidelines for Mathematics Work Samples 2011-12

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Guidelines for High School Mathematics Work Samples

Definition: A Mathematics Work Sample is individual student work used to provide students with the opportunity to demonstrate problem-solving skills and/or to demonstrate proficiency in the Essential Skill of Applying Mathematics.

Purposes:1. To meet requirements for one local performance assessment in high school in mathematics 2. To demonstrate proficiency in the Essential Skill of Mathematics in order to earn an Oregon High

School Diploma

Required assessment instrument: Oregon’s Official Mathematics Scoring Guide

Requirements for mathematics work samplesNumber

1. One work sample for local performance assessment (any of three math subjects: algebra, geometry, statistics )

2. Two work samples for Mathematics Essential Skill proficiency (any two of three math subjects above). One math work sample may also count as the local performance assessment.

Required scores and traits For local performance assessment, there are no required scores. For Mathematics Essential Skill Proficiency, a minimum score of 4 out of 6 in each of the five scoring guide dimensions is required.

Making Sense of the ProblemRepresenting and Solving the TaskCommunicating ReasoningAccuracyReflecting and Evaluating

For Mathematics Essential Skill Proficiency, student work must demonstrate proficient application of high school level mathematics knowledge and skills.

Individual work must represent what the individual student can do with no outside assistance, teacher or peer feedback no collaborative group projects or products are allowed Appendices L & M of the 2011-12 Test Administration Manual contain more information (http://www.ode.state.or.us/search/page/?=486)

Opportunities for revision: work samples that nearly meet the achievement standard (scoring a mix of 4s and 3s) may be returned to students for revision In addition to scores, the only allowable feedback to students is highlighting phrases on the Official Mathematics Scoring Guide and/or using the Official Mathematics Scoring Form provided by ODE (http://www.ode.state.or.us/search/page/?id=2704)

Oregon Department of Education Guidelines for Mathematics Work Samples 2011-12

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Guidelines for High School Mathematics Work Samples (continued)

Who should complete mathematics work samples?Local Performance Assessments: All students must have the opportunity to complete at least one mathematics work sample during high school.

Essential Skill Proficiency: Students who have not demonstrated proficiency by meeting the mathematics standards with a score of 236 on the OAKS Mathematics Assessment may use work samples as evidence of their proficiency in the Essential Skill of Mathematics. (Typically, these would be students in the “nearly meets” category: students whose assessment scores or classroom work indicate that they may have the necessary mathematics skills, but are not demonstrating those skills on the OAKS assessment. Students who need significant additional instruction to reach a high school level of mathematics proficiency are not likely to benefit from the work sample option until their skills have improved.)

Who should score mathematics work samples? One trained classroom teacher or other district employee trained on Oregon’s Official Mathematics Scoring Guide. (Some schools may choose to use more than one rater or to score work samples in a group setting for anonymity and to facilitate discussion of close scores.)

Recommendations for Developing Mathematics Work Samples

Problem-Solving Tasks: Complex problems requiring multi-step solutions and reflecting content from the mathematics standards are appropriate for work samples. These work samples may be “stand-alone” tasks that provide students with opportunities to practice and demonstrate their problem- solving skills or they may arise naturally in the curriculum as part of a particular unit of study in a math or other content class. Mathematics tasks released by the Oregon Department of Education may be used as practice activities and as models to develop local math problem solving tasks http://www.ode.state.or.us/search/page/?id=281

Choice: Whenever possible, work samples should be designed to offer student choices, among several different problem-solving situations.

Recommendations for Administering and Scoring Mathematics Work Samples

Allow adequate time for students to show their best work. If students need more than one session to complete a work sample, all student materials in progress must be collected and kept secure between sessions.

Provide access to appropriate tools such as calculators and formula tables from the OAKS Mathematics Assessment.

Student Name: ___________________________________________ Date: ________________ Task Title: ____________________________________________ Grade Level:_____________

The Student Work Demonstrates:

_____Algebra _____Geometry ______Statistics/Probability

Essential Skills Requirement for Oregon Diploma

_____ Uses High School or Advanced High School level mathematics and

_____ Meets at “4” level or above in all scoring dimensions

Standard(s) Addressed: ___________________________________________

Bullets describe a score of 4. indicates areas that meet the standard. No other feedback beyond the Official Scoring Guide may be provided.

Making Sense of the Task 6 5 4 3 2 1

Important information was changed into mathematical ideas. The way the problem is changed into mathematics fits what was asked.

Representing and Solving the Task 6 5 4 3 2 1

The strategies used fit the problem. All pictures, models, diagrams, and/or symbols used to solve the problem are shown.

Communicating Reasoning 6 5 4 3 2 1

The path leading to a complete solution is shown with no gaps for the reader to fill in. The work connects all the parts (i.e. concepts, strategies, reflection, answer and reasoning). Mathematical language/labels are used appropriately throughout.

Accuracy 6 5 4 3 2 1

The final answer is complete and justified. The answer is supported by the work. The solution/outcome is correct.

Reflecting and Evaluating 6 5 4 3 2 1

The solution/outcome matches what the problem was asking. The defense of the solution reviews the interpretation of the task, concepts, strategies, calculations and reasonableness.

Raters may mark the boxes and circle specific words to explain reasons for the current scores.

Rater ID Number, Initials, or Name: Date of revision: ________________ Revised scores: MS___ RS___ CR____AC____RE___

Oregon Department of Education Math Work Sample Feedback Form Office of Assessment and Information Services

Suggestions for using the Oregon Department of Education Feedback form.

The feedback form was designed as a consistent tool for teachers to use with the state scoring guide to give students more specific feedback than dimension scores alone can provide. Although the form can be used for all students with all work samples, it isn’t often feasible to do so.

This is meant to provide feedback to students in two categories: Those who have earned scores of 3 in some dimensions and have a good

chance of editing their work in order to earn scores of 4 in all dimensions.

Those who have produced successful work samples (scores of 4 in all dimensions) but not at the level of high school or advanced standards.This information is critical when work samples are used to provide evidence of meeting the essential skills requirement for the Oregon Diploma in lieu of a passing score on the OAKS test.

1. Score the student work using the official state scoring guide. 2. Circle the scores in each dimension on the feedback form. 3. Check the boxes corresponding to what the student did well and need no revision. 4. For areas that need revision, circle key words that will give the student more

specific guidance. 5. Determine the strand (Algebra, Geometry, or Statistics) used in the solution and

indicate it in the box near the top of the form. 6. Indicate whether the student has addressed a high school or advanced standard

and identify the standard (more than one standard may be addressed).

Teachers should be familiar with the high school and advanced standards.

Resources for Supporting Mathematics Instruction in Content-Area Classes

WEBSITESThe following websites contain information specific to Oregon:

Work Sample Resource Page (ODE) http://www.ode.state.or.us/search/page/?id=219News releases and work sample resources by subject area.

Work Sample Tasks for Problem Solving: http://www.ode.state.or.us/search/page/?id=281 Links to tasks that have been aligned to the 2011-2012 scoring guide and the 2007/2009 math standards.

Assessment of Essential Skills Toolkit: http://assessment.oregonk-12.net/A web-based interactive planning system that will help districts and high schools develop a local plan for assessing the essential skills by guiding them through a series of 10 Ste

Moving Math Education Forward (MMEF): http://www.ode.state.or.us/search/page/?id=2702Workshop components and resources focus on elements of effective instruction, analyzing cognitive demand, and formative assessment. Access to materials from professional development workshops provided during the summer of 2009 to mathematics educators across Oregon.

Oregon Council of Teachers of Mathematics (OCTM) Math Links: http://www.octm.org/mathlinks.html Links to numerous k-12 math resources on a variety of math topics including; problem solving, task banks, and practice tests.

Oregon Diploma: http://www.ode.state.or.us/search/results/?id=368 Find up to date information about Oregon requirements needed to earn a diploma, including credit requirements, Essential Skills, and the personalized learning requirements.

Portland Public Schools Mathematics Curriculum: http://www.pps.k12.or.us/departments/curriculum/1476.htm From here you can select elementary, middle, or high school resources developed by Portland Public Schools, including assessments.

Salem-Keizer Curriculum, Instruction, and Assessment Online Resources: https://salkeiz-cia.orvsd.org/math Includes a number of resources for the current Oregon math standards, including deconstructed standards and pacing guides.

Test Administration Manual: http://www.ode.state.or.us/search/page/?=486 Contains specific procedures and guidelines for assessment of OAKS, local performance assessments, and work samples. See Appendices L,M, and N.WEBSITESThe following websites contain information specific to Social Studies:

http://www.thinkfinity.org/lesson-plans Thinkfinity has a search application where teachers can find lessons and materials in a variety of subjects. It’s even possible to combine content areas in the search.

http://www.jumpstart.org/search.html The Jump$tart Clearinghouse has lots of financial literacy materials.

http://www.councilforeconed.org/resources/ The Council for Economic Education provides tons of resources and lesson plans.

http://www.councilforeconed.org/ea/program.php?pid=1 EconEdLink includes CEE’s lesson plan bank.

http://education.nationalgeographic.com/education/ National Geographic’s education resources are full of math as applied to geographic studies.

WEBSITESThe following websites contain information specific to Career and Technical Education (CTE):

Mathematics for Manufacturing – http://www.uic.edu/cuppa/techbridge/PDF/MathforManufacturing_100300.PDF

CORD has a STEM Transitions project that includes 61 integrated curriculum projects. Users must register, but the material is free. These materials were developed for community colleges, but are also appropriate for high school use in my opinion - http://www.stemtransitions.org/

Rogue Community College has developed a technical math course that is problem-based. They have started piloting the course at high schools in their area. They may be willing to share the “textbook” that was developed for the course. My contact for this is Serena Ota St. Clair ([email protected]).

I also found the following sample math for automotive - http://www.cordonline.net/michigan/integrated_examples.htm. Many of these examples could be turned into worksamples but the way they are currently structured is too leading in my mind.

Lesson plans developed by Oregon teachers can be found at these sites:

http://www.lanecareerfocus.org/mathincte/index.html

http://www.ctemathlessons.com/

WEBSITEThe following website contains monthly updates from ODE on various content areas. Many resources are included:

http://www.ode.state.or.us/search/page/?id=1843

Documents

Facilitator's Packet Content Teachers · Training for Trainers & Materials Provided by ODE ... growth in math skills. xMaterials: ... good place to talk about key concepts for each