facilitator’s packet for using the mathematics scoring

Facilitator’s Packet for

Using the Mathematics

Scoring Guide: Level 2 An Introduction for High School

Math 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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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 Guide Facilitator’s Agenda -- Introductory Session – Level 2

Time: 2 ½ - 3 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 are we going to do about 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)

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

15 minutes

3. Introductory Mathematics Work Sample and Scoring Guide

presentation • Go through Slides 1 – 11 – these slides introduce the

Essential Skills requirements, the CCSS connection, and the options for Essential Skills proficiency. Focus of this workshop will be on using scoring guide with math work samples.

• Materials: Laptop with PowerPoint & projector

15 minutes

4. Slides 12 - 21: Overview of the Scoring Guide This section introduces the scoring guide and scale in a broad general way at first. 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.

30 - 40 minutes

5. Slides 22 - 29 Looking at the 1st Task Have participants

work the Farmer Brown task (full version is in their handout packet). Share results and discuss differences in approaches. Examine Scoring Guide closely for each dimension, beginning with Making Sense of the Problem and working through all dimensions. Have participants highlight key words, especially at the 3 and 4 level score points. Use the Facilitator’s Guide to Leading the Scoring Session. Materials: Highlighters for participants


6. In the separate scoring packet, have participants read each

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

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

8. In the main packet is an example of a work sample revision for Farmer John. The facilitator’s packet includes instructions for leading participants through the steps from the first student work, to the Official Feedback Form to the student revised work. (Note: you may wish to include this here or wait until you have finished scoring all student work for the remaining tasks to return to the main packet.)

20 – 30 minutes

9. Slides 30 - 34 Looking at the 2nd Task Have participants work the Bike Rental task (full version is in their handout packet). Share results and discuss differences in approaches.

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

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

12. 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 15 - 20 minutes

13. The next set of slides (35 - 41) focuses on helping teachers recognize different types of assessments they use and building a common vocabulary to talk about assessment. Emphasize the connections to instruction and the ability to adjust or target instruction for individuals or groups based on work sample data.

• Slide 41 is an individual, pair or small group discussion. Encourage participants to fill in the information for their school in their participant packet. Share results with large group.

14. Point out the Student Language Version of the Scoring Guide and the Student Problem Solving Tips in the handout packet. Teaching students to use the scoring guide and to check their work for fidelity to the scoring dimensions will help students achieve higher scores on work samples.

15. The Guidelines for High School Mathematics Work Samples has good information about work sample administration and scoring. (More information about developing math work


samples will be available in a future workshop – Level 4.)

10 minutes 16. Slides 42 – 46 Review the requirements for Essential Skills Work Samples and key issues in implementation. This is a repeat, but important to be sure participants remember these key issues.


5 Minutes

17. Slides 47 & 48 close out the presentation. Insert your information in slide 47. There is an extensive resource list for supporting math instruction and assessment in the handout packet.

• Slide 48 is a powerful quote about the importance of problem solving for students and is both a good closing slide as well as something you can leave on the screen while answering questions or moving on to the next activity.

Optional – 10-20 minutes

18. Have participants brainstorm or share instructional needs

related to the scoring guide and work samples – particularly issues around communicating and reflecting/evaluating. Refer to additional handouts in Participant’s Packet.

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

10 minutes 19. Optional Question & Answer or Summary

• Be sure to identify future training opportunities for participants

Total = 2 ½ – 3 hours

Participant Packet: • PowerPoint handouts to take notes • Scoring Guide • Various handouts • Summary Common Core State Standards • Official Math Scoring form

Sample Student Papers: Farmer Brown

• TR – 1 • TR – 2 • TR – 3 – 5

Bike Rental • TR – 6 • TR – 7 • TR – 8 - 10

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This introductory workshop is targeted to high school math teachers.A companion introductory workshop is available for content area teachers with mathemphasis in their classes.

1

These are the four goals for this session. It may be helpful to have a show of hands toknow which teachers have been trained in using a previous version of the scoring guide andhow many use a scoring guide regularly in their classes. Be sure that participants know thatthis session will acquaint them with the newly adopted scoring guide and with theexpectations for Essential 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 whoknowledge 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 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).

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

The State Board of Education has also adopted the Common Core State Standards forMathematics. The next few slides will illustrate how the intent of the CCSS is carried out inwork samples and how the Oregon Mathematics Problem Solving Scoring Guide connectsto the CCSS. This is a paraphrase of information from the introduction to the Common CoreState Standards for Mathematics. The entire quote is in the participant’s packet.

The reference to NCTM standards is made in the introduction to the CCSS and should befamiliar to Oregon teachers since Oregon math standards have long relied on NCTMfamiliar to Oregon teachers since Oregon math standards have long relied on NCTM.

5

More from CCSS for high school level students. Complete quote is in participants’ packet.

6

Purpose of CCSS information is to raise teacher’s awareness that these standards areadopted and will be implemented. They will eventually be tested using a new multi stateSMARTER Balanced Common Core Assessment. Work samples will continue from nowthrough the early implementation years of the new assessments and will help teachers andstudents be better prepared for the new assessments.

7

Participants can access the full text of the Mathematics Common Core State Standards athttp://www.ode.state.or.us/search/page/?=1527. The handout with the full text of quotesin their packet also has this link where a variety of resources is available.

8

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.A handout in the packet showing a flowchart for the Essential Skill of Mathematicsproficiency options may help further explain these slides

9

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 subject areas listed, with scores of 4 or higher in all 5 dimensions on the mathscoring guide.

10

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

11

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

12

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.

13

These are the 5 dimensions of the math scoring guide.

14

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

15

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.

16

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.

17

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.

18

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.

19

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

20

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.

21

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 ways.

22

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

23

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 participants to work first individually to solve this task, then share with a partner, thenshare with whole group on next slideshare with whole group on next slide.

24

Ultimately, you should have several different approaches to the problem that arrive at thecorrect solution. (If the group does not arrive at multiple approaches, the presenter shouldsuggest alternatives. Some alternatives are included in the Guide to Leading the ScoringSession in the Facilitator’s Packet.)

25

Paper TR 1 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.

26

Paper TR 2 received some 4’s and some 3’s. Again, have participants identify specificphrases that describe this paper.

27

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.

28

Walk the participants through scoring each of the remaining student papers, using thecommentary and Suggestions for Use of Student Papers to help you lead the discussion ofeach paper and dimension. Begin with TR 3 – a low paper; then TR 4 – a paper thatreceived all 5’s; then TR 5 – a very high paper.

29

Have participants complete this task individually first and then discuss prior to scoringpapers. A full size copy is in their packets.

30

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 Guide to Leading the Scoring Session in the Facilitator’s Packet.

31

Paper TR 6 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 document to assist you.

32

Paper TR 7 also received all 4’s. Again, have participants identify specific phrases thatdescribe this paper.

33

Walk the participants through scoring each of the remaining student papers (TR 8, 9, and10), using the commentary to help you in leading the discussion of each paper anddimension. TR 8 & 9 are both mixed scores – very good for discussion. TR 10 is a highpaper.

34

Math teachers can use the scoring guide in all the ways listed here. Reinforce using thescoring guide frequently and for different purposes. Next slides go into more depth. Pointout Student Language Scoring Guide in Participant’s Packet and Student Problem SolvingTips as resources that can be used in instruction.

35

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.

37

Depending on time available, you may want to have participants discuss how variousassessments in their schools are used.

38

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.

39

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.

40

This slide focuses on the importance of a school or district assessment plan. High schoolMath departments may want to consider developing such a plan if one does not exist atthe school level.

Does your school have a plan as to who gets assessed and when they are assessed?

Does your school have a plan as to who analyzes the data, how the data are analyzed,when the data are analyzed and how the information from the analysis is used?

Have participants use page in handout packet to fill in what they can & then discuss what isHave participants use page in handout packet to fill in what they can & then discuss what ismissing/ needed, etc.

Where is information about the assessment plan kept and who has access/knowledgeabout it?

Is the assessment plan written and made available to all staff in the school?

41

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 in packet – Guidelines for High School Mathematics Work Samples. Use itas a reference as you go through the next several slides.

42

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.

43

Students should be allowed time to do their best work.

44

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

45

Refer to Handout in packet: Official Mathematics Work Sample Feedback 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. Typically, thiswould be offered to students whose paper nearly meets the standard of all 4’s rather thanfor papers in the 1 & 2 range where more instruction may be needed.Refer to the Text Administration Manual for further information on these issues:http://www ode state or us/search/page/?=486 Appendix M & Khttp://www.ode.state.or.us/search/page/?=486 Appendix M & K

Specific information on feedback is listed in Appendix A of the Test Administration Manual.

46

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 lengthy list of additional resources.

47

This slide provides a nice closing and a focal point.

48

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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

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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

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

From the Introduction to the Common Core State Standards for Mathematics

“These Standards define what students should understand and be able to do in their study of mathematics. Asking a student to understand something means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b) (x + y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y). Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness.”

“The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).”

“Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.”

Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.

Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem.

Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?”

The Common Core Standards for Mathematics can be found at the following link: http://www.ode.state.or.us/search/page/?=1527

There are a variety of resources to assist Oregon educators at this link and additional resources will be added over time.

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 Task Understand 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 Task Choose 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 Reasoning Use 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 Evaluating State 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.

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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Instructions for Farmer John Example of Revision Materials These materials were assembled to show participants what might happen when a student successfully completes a math problem solving task, but does not use high school level math to do so. The student may be given an opportunity to revise the task if the teacher believes the student could complete the task using high school strategies. Take participants through these materials page by page, explaining how the revision process worked.

1. Pages 1-2 contain the original student work for the Farmer John task. The student uses a guess and check method and illustrations to solve the problem.

2. Page 3 contains the scores and commentary this paper originally received. Note

that the paper scored 4 in all dimensions, but should not be used as a demonstration of proficiency in the Essential Skill of Apply Mathematics because of the lack of high school level math.

3. Page 4 is the Official Math Problem Solving Work Sample Feedback Form that was returned to the student with the original work and possibly a highlighted copy of the scoring guide. The teacher may have also stated that the problem is the lack of demonstration using high school math – but no other instruction or coaching was given.

4. Pages 5-6 show the student’s second version of solving the problem using appropriate mathematical strategies.

5. Page 7 shows the revised Official Scoring Form with the new scores recorded at the bottom of the page.

6. Page 8 is the second version of the scores and commentary so that participants can see exactly how the rater interpreted the student work.

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Mathematics: Essential Skills Scores and Commentary

Work Sample Title: Farmer John Paper Number: R1 Algebra Geometry Statistics

High School Content Standard: H.1G.5 Determine the missing dimensions, angles, or area of regular polygons, quadrilaterals, triangles, circles, composite shapes, and shaded regions.

MS RS CR AC RE4 4 4 4 4

Making Sense of the Problem:

The interpretation of the task into increasing the dimensions by the same amount until reaching the desired area was adequate and complete. The mathematics is not connected or extended to other mathematical ideas.

Representing and Solving the Problem:

The strategy of making a systematic list adding 1 square yard to each original dimension and checking the area until reaching 176 was effective and complete. The strategy is not complex nor is the student able to generalize the situation.

Communicating Reason:

The student clearly represents the two rectangular pens and labels their dimensions. Although the student does not explain what he/she is specifically doing with the table, it is clear that he/she is adding 1 unit to each dimension and then multiplying to find area. However, using a systematic list or guess and check table are not considered elegant or insightful at high school level.

Accuracy:

The solution of adding 6 yards to each side is correct and supported by the work. The work does not include extensions, connections, or generalizations.

Reflecting and Evaluating:

The student summarizes the answer in a sentence at the bottom of the page, indicating they have answered the question asked and did not just give the dimensions. The review is complete, since the student basically re-did the problem again on the second page (adding an additional set of numbers), although they did not restate the solution of adding 6 yards to each side.

**Note: This is a good example of a case where a student earns a "4" in all dimensions for problem solving but does not demonstrate proficiency for Essential Skills.

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G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure tosatisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

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Mathematics: Essential Skills Scores and Commentary

Work Sample Title: Farmer John Revised Paper Number: R2 Algebra Geometry Statistics

High School Content Standard: H.1G.5 Determine the missing dimensions, angles, or area of regular polygons, quadrilaterals, triangles, circles, composite shapes, and shaded regions. G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

Achievement Level Descriptor: Determine area, surface area, and/or volume. Solve for missing dimensions. Solve related context-based problems.

MS RS CR AC RE6 6 5 6 6

Making Sense of the Problem:The interpretation of the task into generalizing the amount being added to both dimensions as “x”, and using a quadratic equation to represent the situation is enhanced. The student thoroughly develops the meaning of the x verbally and in the diagram and also looks at the mathematics thoroughly (he/she gets two answers: -21 and 6 but comments why 6 is the only one that makes sense). He/she also describes how to use a graphing calculator to solve the problem, indicating that the student has made sense of this problem in several ways.

Representing and Solving the Problem:The strategy of assigning “x” to the additional amount needed and writing, solving, and interpreting the solution for a quadratic equation makes this paper complex. The additional information on the back about how to use the graphing calculator to solve the problem adds elegance and insightfulness, and connects the problem to another representation.

Communicating Reason:The work follows a clear and coherent path and the student uses mathematical language precisely (I will solve this equation algebraically, Let y1 represent the product of the, set the window so the domain….). The reader is able to move easily from one thought to another through the use of words, symbols and the diagram to the right. The diagram of the two pens helps explain the origin of the equation (10 + x)(5 + x) = 176 but clearly shows that there would be “x” added to both sides of the pen according to the way it is labeled. There is a slight gap between the diagram and the equation (why is it 5 + x instead of 5 + 2x?). The student also does a good job describing the process used with the graphing calculator, but a sketch of the graph and more details in the description would have helped this paper become a 6 in this dimension

Accuracy:The solution of adding 6 yards to each side is correct and justified. It is also extended through the use of technology, since the student uses the technology to check if the intersection is truly the solution they arrived at using the system. The student also thought about the two solutions obtained from solving the system and commented that “6 is the only answer that makes sense”, although they do not say why.

Reflecting and Evaluating: The solution is clearly stated within the context of the task. He/she reworks the task using a graphing calculator (and if you include the original method of making a systematic list, the student has worked the problem 3 ways). He/she also considers the solution of -21 and dismisses this as possible. The approach used with the graphing calculator shows that the student reflected on his/her solution and realized that if 6 is the solution, then it should be one coordinate of the intersection point of the two lines. This evidence moves the score for this dimension to a 6.

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School Math Problem Solving Assessment & Data Analysis Plan

Assessment Describe your school’s math problem solving assessment plan?

Describe your school’s data analysis & use plan?

Benchmark

Formative

Interim and Predictive

Summative

Introduction to the Math Problem Solving Scoring Guide Workshop – Level 2

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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 WEBSITES The following websites contain information specific to Oregon: 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 Steps.

Common Core State Standards Crosswalk (ODE) http://www.ode.state.or.us/search/page/?id=3211 Identifies matches between individual Common Core standards with Oregon standards in mathematics and includes rater comments that highlight the similarities and differences between the standards.

Mathematics Achievement Standards: http://www.ode.state.or.us/search/page/?id=3182 A detailed explanation of the standard setting process and rationale for the new cut scores is provided along with links for additional resources, tools, and materials.

Moving Math Education Forward (MMEF): http://www.ode.state.or.us/search/page/?id=2702 Workshop 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.

OAKS Online Practice Test: http://www.ode.state.or.us/search/page/?id=441Helps students prepare for OAKS Online by providing sample tests for grades 3-8 and high school with the same look and feel as the actual test.

OAKS Test Specifications and Blueprint Documents:http://www.ode.state.or.us/search/page/?id=496 These documents explain how the Oregon mathematics standards will be assessed. Included are the content standards, accessible content and vocabulary, achievement level descriptors, and scoring guides.

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.

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.

The following websites contain information that is NOT specific to Oregon: AAAMath: http://aaamath.com/ a comprehensive set of interactive arithmetic lessons and unlimited practice is available on each topic, K-8.

Common Core State Standards Webpage (ODE): http://www.ode.state.or.us/search/page/?id=2860 This site has links to Common Core State Standards for Math and English Language Arts, Resources for teachers, Communication Tools, Timelines and Transitions, Assessment and more.

Mathematics Assessment Resource Service (MARS): http://www.nottingham.ac.uk/education/MARS/ Site contains samples of balanced assessment tasks including solutions, student work, and commentaries.

NCTM Illuminations: http://illuminations.nctm.org/ Direct link to NCTM’s lessons and activities. National Council of Teachers of Mathematics (NCTM): http://www.nctm.org/Contains information about standards, conferences, professional development, journals,research, and lessons and activities. PBS Teachers - Math: http://www.pbs.org/teacherline/catalog/browse/?sa=1Multimedia resources and professional development are made available for Pre-K through 12 educators. Silicon Valley Mathematics Initiative: http://www.svmimac.org/ Resources include coaching materials, performance assessment, lesson study, reports, and presentations.

Texas Assessment of Knowledge and Skills: http://www.tea.state.tx.us/student.assessment/taks/ This site contains released assessments and answer keys. Some of the materials include a Spanish version.

TI Education Technology: http://education.ti.com/us/home/down/ae This Texas Instruments site has calculator and technology-related lessons and activities for math and science.

WEBINARS A Closer Look at the Common Core State Standards for Mathematics (Education Northwest) http://educationnorthwest.org/event/1346 Archived webinar from December 13, 2010 featuring Dr. William McCallum an focusing on the progression and connection of key concepts across grades.

Common Core Standards Initiative: Preparing America’s Students for College and Career (Carnegie Learning) http://www.carnegielearning.com/webinars/common-core-standards-initiative-preparing-americas-students-for-college-and-career/ Archivedwebinar from October 27, 2010 featuring Chris Minnich. Chris leads the standards and assessment work at CCSSO, where they are currently working on implementing common standards across states.

National Council of Supervisors of Mathematics (NCSM) Webinar Series http://ncsmonline.org/events/webinars.html has two archived webinars, one from November 30, 2010 and one from February 23, 2011. The first is a getting started webinar and the other is a diving deeper webinar - both focusing on Common Core State Standards. Includes pdfs of the presentation and handouts.

WORKSHOPS, TRAININGS, AND CONFERENCES

Annenberg Learner http://www.learner.org/index.html Annenberg Learner's multimedia resources help teachers increase their expertise in their fields and assist them in improving their teaching methods. Many programs are also intended for students in the classroom and viewers at home. All Annenberg Learner videos exemplify excellent teaching. Resources can be accessed for free at learner.org.

Essential Skills Work Samples Training of Trainers (ODE) http://www.ode.state.or.us/search/page/?id=2042 ODE has scheduled Training of Trainer WebEx sessions to assist districts in implementing work samples for the Essential Skills of Reading, Writing and Mathematics. These sessions are designed to help district staff prepare to conduct workshops training teachers to use the Official Scoring Guides to assess work samples for the purpose of determining proficiency in the Essential Skills. Mathematics and Science Services (Education Northwest) http://educationnorthwest.org/services/math-science Provides educators with top-

quality professional development, technical assistance, evaluation, and research services.

National Council of Supervisors of Mathematics (NCSM) http://ncsmonline.org/events/index.html NCSM offers various seminars, workshops, and conferences throughout the school year. Please check the website for current offerings.

National Council of Teachers of Mathematics (NCTM) Conference Page: http://www.nctm.org/conferences/default.aspx?id=52 Lists current, available conferences and workshops available, including NCTM’s annual meeting and exposition.

Northwest Mathematics Conference October 13-15, 2011 http://www.northwestmathconf.org/NWMC2011/ Strands will include best practices in instruction and assessment, standards and NCTM Focal Points, historical perspectives in mathematics, and future trends in mathematics.

OCTM Professional Development Cadre: Math Workshopshttp://www.octm.org/pdc.html Workshops targeting effective instruction, including:oregon math standards, Higher order thinking, questioning strategies, lesson leverage, assessment for learning, problem solving, and common core state standards.

PRISM (Preparation for Instruction of Science and Math) Courseshttp://www.pdx.edu/ceed/prism a collaborative effort of seven Oregon universities to offer graduate level courses and professional development modules in math and science that are available online, in weekend workshops, at summer institutes, or combinations of these formats.

Teacher’s Development Group http://www.teachersdg.org/ A non-profit organization dedicated to increasing all students’ mathematical understanding and achievement through meaningful, effective professional development.

The Math Learning Center http://www.mathlearningcenter.org/development/workshopsEach year hundreds of educators attend Math Learning Center workshops for practical teaching strategies and insights into how children learn. Whether it focuses on a broad topic or a specific set of materials, an MLC workshop offers a rich learning experience.

TIPS (Teachers Inspiring Problem Solvers) http://www.math-tips.com/ Works with teachers and students to help deepen their understanding of mathematics while developing the habits and characteristics of a successful problem solver.

Problem Solvers (TIPS) is to work with teachers and students, helping deepen their understanding of mathematics while developing the habits and characteristics of a successful problem