1. The Essential Skill of Mathematics
Using the New Math Scoring Guide:
An Introduction for High School Math Teachers
This introductory workshop is targeted to high school math teachers.
A companion introductory workshop is available for content area teachers with math emphasis in their classes.

2. Goals for this workshop
1. Review
Oregon’s Math Problem Solving Scoring Guide
Classroom uses of the Math Scoring Guide
Supporting colleagues in using math work samples in content classes
2. Understand
Options for Demonstrating Proficiency in the Essential Skill of Mathematics for the Oregon Diploma
3. Score student papers and calibrate to scoring standards
4. Set the stage for follow-up training
These are the four goals for this session. It may be helpful to have a show of hands to know which teachers have been trained in using a previous version of the scoring guide and how many use a scoring guide regularly in their classes. Be sure that participants know that this session will acquaint them with the newly adopted scoring guide and with the expectations for Essential Skills proficiency.
There will be a in-depth training session (Level 3) available to provide increased depth of knowledge and experience applying the scoring guide to student papers. Teachers who take the in-depth training session should feel confident scoring papers to demonstrate proficiency in the Essential Skill of Mathematics.
Remind participants that they have the PowerPoint slides in their handout to take notes on, if they wish.

3. OAR:
For students first enrolled in grade 9 during the school year [and subsequent years], school districts and public charter schools shall require students to demonstrate proficiency in the Essential Skills listed
(A) Read and comprehend
a variety of text; and
(B) Write clearly and
accurately
(C) Apply mathematics
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 (most will be sophomores this year).

4. Essential Skill Definition
Apply Mathematics
in a variety of settings
Interpret a situation and apply workable mathematical concepts and strategies, using appropriate technologies where applicable.
Produce evidence, such as graphs, data, or mathematical models, to obtain and verify a solution.
Communicate and defend the verified process
This is the definition adopted by the State Board for the Essential Skill of Mathematics. The bullets, describing what it means to apply mathematics, are clearly reflected in the dimensions of the scoring guide.

5. The Common Core State Standards For Mathematics
describe varieties of expertise... that rest on important “processes and proficiencies” …[including the] NCTM process standards of
problem solving
reasoning and proof
communication
representation
and connections
The State Board of Education has also adopted the Common Core State Standards for Mathematics. The next few slides will illustrate how the intent of the CCSS is carried out in work samples and how the Oregon Mathematics Problem-Solving Scoring Guide connects to the CCSS. This is a paraphrase of information from the introduction to the Common Core State 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 be familiar to Oregon teachers since Oregon math standards have long relied on NCTM.

6. Make sense of problems and persevere in solving them
“Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution….
More from CCSS for high school level students. Complete quote is in participants’ packet.

7. They analyze givens, constraints, relationships, and goals
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.”
Purpose of CCSS information is to raise teacher’s awareness that these standards are adopted and will be implemented. They will eventually be tested using a new multi-state SMARTER Balanced Common Core Assessment. Work samples will continue from now through the early implementation years of the new assessments and will help teachers and students be better prepared for the new assessments.

8. Mathematical Practices
1. Make sense of problems and persevere in
solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique
the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
Participants can access the full text of the Mathematics Common Core State Standards at The handout with the full text of quotes in their packet also has this link where a variety of resources is available.
From Common Core State Standards for Mathematics

9. Essential Skill Proficiency Three options for diploma requirement
OAKS Statewide Mathematics Assessment
Score of 236 or higher
Other approved standardized assessments
Test
Score
ACT or PLAN
19/19
WorkKeys 5
Compass
66 (College Alg. test)
Asset
41 (Int. Alg. test)
SAT/PSAT
450/45
AP & IB
various
Students have three options to demonstrate proficiency in the Essential Skill of Mathematics. Achieving a score of 236 on the high school OAKS Mathematics test is one way. Students can also use scores achieved on various standardized tests approved by the State 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 a minimum score of 3. International Baccalaureate tests are Mathematics HL, Mathematics SL, and Math Studies. IB tests require a minimum score of 4. While these options may help some students, more students may choose option 3 – the work sample which is explained on the next slide.
A handout in the packet showing a flowchart for the Essential Skill of Mathematics proficiency options may help further explain these slides

10. Option 3 Math Work Samples
Students must earn
a score of 4 or higher
in each dimension
for each work sample
Two Mathematics Work Samples Required: algebra, geometry, statistics
Mathematics Work Sample scored using Official State Scoring Guide
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 two of three subject areas listed, with scores of 4 or higher in all 5 dimensions on the math scoring guide.

11. Level of Rigor
Work samples must meet the level of rigor required on the OAKS assessment.
Work samples provide an optional means to demonstrate proficiency not an easier means.
Work Samples require equal rigor but provide a different format to demonstrate proficiency.

12. Let’s Review the scoring guide !
Remind participants that this will be an introduction to the scoring guide. More detailed training is available in an in-depth workshop (Level 3).
Let’s Review the scoring guide !

13. The Math Problem Solving Scoring Guide
Background
In use since 1988 (minor revisions in 2000)
new version based on Oregon Mathematics Content Standards
aligned to the Common Core State Standards
Adopted by Oregon State Board of Education May 2011
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 and to recognize that it can be an important classroom tool for instruction, formative assessment, and summative assessment.
Refer to Official Scoring Guide in Handout Packet.

14. Mathematics Problem Solving Scoring Guide
Making Sense of the Problem
Representing and Solving the Problem
Communicating Reasoning
Accuracy
Reflecting and Evaluating
These are the 5 dimensions of the math scoring guide.

15. Making sense of the problem
Interpret the concepts of the task and translate them into mathematics
Refer to the handout in the Participant’s Packet Introduction to the Scoring Guide and to Suggestions for Use of Student Papers for in the Facilitator’s Packet for discussing each dimension.
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.

16. Representing and solving the problem
Use models, pictures, diagrams, and/or symbols to represent the problem and select an effective strategy to solve the problem.
The 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.

17. Communicating Reasoning
Communicate mathematical reasoning coherently and clearly use the language of mathematics.
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.

18. Accuracy Clearly identify and support the solution.
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.

19. Reflecting and Evaluating
State the solution in the context of the problem.
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 may include addressing the efficiency of an approach or the relative use of a procedure.

20. Simplified Mathematics Scoring Guide
Beginning 1 2 3 4 5
Emerging
Developing
Proficient
Strong 6
Exemplary
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.

21. Another way to look at scores
6 −Enhanced or connected to other mathematics
5 – Thoroughly developed
4 – Work is proficient (not perfect)
3 – Work is partially effective or partially complete
2 – Work is underdeveloped or sketchy
1 – Work is ineffective, minimal,
or not-evident
This provides another “shorthand” way of looking at the different score levels. Refer to the Student Tips handout in the Participant’s Packet as a way to help students understand the scoring guide and score levels. A student level version of the scoring guide is also included in the Participant’s Packet.

22. What does a Math Work Sample look like?
The next slides will show some work samples and lead into scoring student papers. An important part of the message is that work samples can be used in a variety of ways.

23. Mathematics Problem Solving Work Samples
Present complex, multi-step tasks
Are designed to judge student abilities to apply specific knowledge & skills
Allow a variety of problem-solving approaches
May simulate real-word mathematics problems
This definition stresses that problems are complex and generally cannot be presented in a multiple-choice test format.
“There is a distinction between what may be called a problem and what may be considered an exercise. The latter serves to drill a student in some technique or procedure, and requires little if any, original thought… No exercise, then, can always be done with reasonable dispatch and with a minimum of creative thinking. In contrast to an exercise, a problem, if it is a good one for its level, should require thought on the part of the student.”
- Howard Eves

24. Farmer John
The Task: Farmer John has a rectangular holding pen that measures 10 yards long and 5 yards wide to contain his cattle. He is acquiring more cattle from the neighboring farmer and wants to add the same amount of fencing to each side to create a new holding pen that encloses 176 square yards. How much should Farmer John add on to each side of his existing holding pen to achieve his goal?
Mathematics Content Standard Assessed by This Task: H.1G.5
Language From Achievement Level Descriptors for Meets which Describes the Required Skills: Determine area, surface area, and/or volume. Solve for missing dimensions. Solve related 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, then share with whole group on next slide.

25. Share your solution! Share your solution
Ultimately, you should have several different approaches to the problem that arrive at the correct solution. (If the group does not arrive at multiple approaches, the presenter should suggest alternatives. Some alternatives are included in the Guide to Leading the Scoring Session in the Facilitator’s Packet.)
Share your solution!

26. Scoring the First Anchor Paper
This anchor paper met the achievement standard in each trait.
Why did this paper earn these scores?
Paper TR 1 received all 4’s. Lead participants through a discussion to help them find the descriptions in the scoring guide that best match this paper in each trait. Use the Suggestions for Use of Student Papers to help you lead this part of the training.

27. Scoring the 2nd Anchor Paper
This anchor paper did not meet the achievement standard.
Paper TR 2 received some 4’s and some 3’s. Again, have participants identify specific phrases that describe this paper.
What scores did this paper earn?

28. Scoring Within the Traits . . . What differentiates a 3 and a 4?
Discussion! Have participants use highlighters to emphasize key points between a 3 and a 4. In general, it is not difficult to recognize high papers or very low papers. The key decision point for many papers will be between a 3 or a 4, so raters must become proficient in making this distinction. Remind the participants that revisions are allowed and more detail on this will be provided later in the workshop. This can help participants move past debating the “3” vs. “4” issue and focus on how the student could improve the answer.

29. Scoring Papers 3, 4, & 5 Use the scoring guide to rate each paper.
What scores did these papers earn?
Walk the participants through scoring each of the remaining student papers, using the commentary and Suggestions for Use of Student Papers to help you lead the discussion of each paper and dimension. Begin with TR 3 – a low paper; then TR 4 – a paper that received all 5’s; then TR 5 – a very high paper.

30. Bike Rental
A local bicycle rental company charges $12 to rent a bicycle. They normally have 300 rentals per month. The company owner has determined that each increase in price of $2 will decrease the number of rentals by 15. What price will maximize the revenue?
Have participants complete this task individually first and then discuss prior to scoring papers. A full-size copy is in their packets.

31. Share your solution!
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 are included in the Guide to Leading the Scoring Session in the Facilitator’s Packet.

32. Scoring the First Anchor Paper for Bike Rental
This anchor paper met the achievement standard in each trait.
Why did this paper earn these scores?
Paper TR 6 received all 4’s. Lead participants through a discussion to help them find the descriptions in the scoring guide that best match this paper in each trait. Use the Suggestions document to assist you.

33. Scoring the 2nd Anchor Paper
For Bike Rental
This anchor paper also met the achievement standard.
Paper TR 7 also received all 4’s. Again, have participants identify specific phrases that describe this paper.
What scores did this paper earn?

34. Scoring Papers 8, 9, & 10 Use the scoring guide to rate each paper.
What scores did these papers earn?
Walk the participants through scoring each of the remaining student papers (TR 8, 9, and 10), using the commentary to help you in leading the discussion of each paper and dimension. TR 8 & 9 are both mixed scores – very good for discussion. TR 10 is a high paper.

35. The Mathematics Scoring Guide
Purposes
Instructional Tool
Formative Assessment
Summative Assessment
Demonstrate Proficiency in the Essential Skill of Apply Math to earn an Oregon Diploma
Math teachers can use the scoring guide in all the ways listed here. Reinforce using the scoring guide frequently and for different purposes. Next slides go into more depth. Point out Student Language Scoring Guide in Participant’s Packet and Student Problem-Solving Tips as resources that can be used in instruction.

36. Building Consensus on Definitions of Assessments
Purpose
When Administered?
Screening
Identify students at risk of mathematics difficulties & provides info to target instruction for all students
Beginning of year or semester; when new students arrive
Formative
Supports learning and informs instruction
Embedded directly in instruction to inform teacher decisions

37. Multiple Uses for the Scoring Guide
Instructional Tool
Makes targets explicit to students
Opportunities to show students models from website or other examples
Screening Tool
Help determine likelihood of reaching proficiency – on target, need assistance, at risk
Help determine which
students need additional
instruction and coaching
Talk about importance of Math Scoring Guide as a powerful instructional tool. Have participants discuss how they could use the math scoring guide in their classrooms. This discussion empowers teachers to incorporate work samples in addition to the school assessment plan or where no assessment plan exists yet. Depending on the size of the group you may want to have them pair/share or form small groups to discuss this.

38. Building Consensus on Definitions of Assessments
Purpose
When Administered?
Interim and Predictive
Determine the progress of individuals or groups of students based on focused elements of content
Occasional, based on curriculum & other instructional milestones
Summative
Determine how much knowledge and skills individuals or groups of students (e.g. programs, schools, districts and states) have acquired.
Periodically after a substantial period of time (e.g. end of the year and end of course).
Depending on time available, you may want to have participants discuss how various assessments in their schools are used.

39. Multiple Uses for the Scoring Guide
Formative & Interim Assessments
Inform instructional strategies
Provide data on student progress
Classroom/ Summative Assessment
End of unit, course, etc. or Essential Skills
Teachers can use Math Work Samples to determine student progress throughout their courses or on a planned schedule. They do not have to assign all parts of the work sample or score all dimensions.

40. Formative Assessment
The Scoring Guide can help to identify math strengths and weaknesses.
Students learn where to focus to improve math skills.
Teachers learn where additional instruction is needed.
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.

41. Does your school have an assessment plan? Explain
Does your school have a data analysis & use plan? Explain
Benchmark
Formative
Interim and Predictive
Summative
This slide focuses on the importance of a school or district assessment plan. High school Math departments may want to consider developing such a plan if one does not exist at the 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 is missing/ needed, etc.
Where is information about the assessment plan kept and who has access/knowledge about it?
Is the assessment plan written and made available to all staff in the school?

42. Requirements for Essential Skill Proficiency Using Math Work Samples
Algebra, geometry, or statistics
Score of 4 or higher in all dimensions on Official Scoring Guide
This is summary reminder of the requirements for a student to demonstrate mastery of the Essential Skill of mathematics using work samples. (repeated from earlier in the presentation)
Refer to handout in packet – Guidelines for High School Mathematics Work Samples. Use it as a reference as you go through the next several slides.

43. Work Sample Design
Math Problem Solving Tasks must be carefully designed to provide opportunities for students to demonstrate skills in all dimensions of the scoring guide.
Math tasks must be at the appropriate difficulty level and address high school content standards.
Refer to Handout: Guidelines for High School Math Work Samples
Explain that there is an entire workshop devoted to developing good problem solving tasks for the purpose of assessing proficiency in the Essential Skills. However, for practice purposes, teachers should feel free to develop and try out work samples in their classes.

44. Work Sample Implementation
Administration
Work samples must be the product of an individual
Work samples must be supervised by an authorized adult;
Students may not work on work samples outside a supervised setting.
Students should be allowed time to do their best work.

45. Work Sample Implementation
Scoring
All work samples must be
scored using Oregon’s Official Math Scoring Guide.
All raters must have been
trained to use the Scoring Guide.
Only one set of scores is required for a work sample. (Districts may want more than one rater for borderline papers.)
Teachers who rate student work samples for the purpose of demonstrating proficiency in the 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 their knowledge

46. Work Sample Implementation
Feedback and Revision
FEEDBACK: Only 2 options
Oregon’s Official Scoring Form
Oregon’s Scoring Guide (highlight/underline)
STUDENT REVISION:
Students are allowed to revise and resubmit their work samples following scoring/feedback.
Most papers should be revised
only once.
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 revise the work sample (in a supervised setting) and resubmit it to be scored again. Typically, this would be offered to students whose paper nearly meets the standard of all 4’s rather than for papers in the 1 & 2 range where more instruction may be needed.
Refer to the Text Administration Manual for further information on these issues: Appendix M & K
Specific information on feedback is listed in Appendix A of the Test Administration Manual.

47. Resources & Coming Attractions
ODE Website:
OCTM Website:
Follow-up workshops
(List any scheduled)
Contact information
(List your information here)
Please adjust this slide to reflect your information. You can either list dates if you have specifically scheduled future workshops, or you can leave it blank with just “Follow-up workshops” and indicate that additional workshops are available on request or will be scheduled later.
A handout in the Participants’ Packet provides a lengthy list of additional resources.

48. A Parting Thought
It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.
- Paul Halmos
This slide provides a nice closing and a focal point.