## Informational Guide for the Mathematics Portfolio Appeals Process

To fulfill the mathematics assessment component of New Jersey high school graduation requirements, a student must demonstrate proficiency in mathematics. Any grade 12 student in the class of 2024 who has not yet met the high school graduation assessment requirement for mathematics may do this through the portfolio appeals process by demonstrating competency in Constructed Response Tasks (CRTs) evidencing the mathematical practices aligned to the high school mathematics content areas.

Each of the content areas encompasses knowledge and skills articulated in the New Jersey Student Learning Standards for Mathematics (NJSLS-M). Through the portfolio appeals process, evidence is gathered of a student’s ability to demonstrate the mathematical practices through **reasoning** and **modeling** within the high school content areas.

The appeals process must provide evidence from two mathematical practice categories as follows:

**Expressing Mathematical Reasoning:**Express appropriate mathematical reasoning by constructing viable arguments, critiquing the reasoning of others and/or attending to precision when making mathematical statements.- Base explanations and reasoning on knowledge and skills articulated in the Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability content areas.

**Modeling:**Apply knowledge and skills to solve real-world problems, engaging particularly in the modeling practice and, where appropriate, making sense and persevering to solve them, reasoning abstractly and quantitatively, using appropriate tools strategically and making use of structure.- Solve multi-step contextual problems requiring application of knowledge and skills articulated in the Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability content areas.

Districts should use New Jersey Student Learning Assessments (NJSLA) and New Jersey Graduation Proficiency Assessment (NJGPA) practice items and released Items as examples of the kinds of questions that should be included but **may not** use the actual items for their appeals.

The following FAQs will help guide districts in creating the evidence needed for the student appeal process.

#### 1. What are CRTs?

CRTs are open-ended questions that are designed, administered, and graded locally. CRTs must be designed to demonstrate that the student holds core mathematical competencies equivalent to the expectations of the NJSLA and NJGPA Evidence Statements. CRTs must be completed and scored in district. The content of a CRT must be aligned to Reasoning or Modeling Evidence Statements found in the Algebra I, Geometry, and/or Algebra II Evidence Statements Tables.

#### 2. How many CRTs should be submitted per student?

A total of four CRTs must be submitted per student: two reasoning tasks and two modeling tasks. Each task is from a different conceptual category area.

#### 3. Where can I find Evidence Statements Tables that align to the Reasoning and Modeling practice categories?

You can find the Evidence Statement Tables in the Test Content and Other Information section of the New Jersey Assessments Resource Center. Here are direct links to the Evidence Statement Tables for Algebra I, Geometry, and Algebra II and the NJGPA Evidence Statement Tables included in the Mathematics Content Guide for NJGPA. These are the **only** Evidence Statement Tables to be used.

Reasoning Evidence Statements are shaded in lavender beginning on page 16 of the Algebra I Evidence Statement Document and have a prefix of “HS.C.” The Algebra I Evidence Statement Document has eleven Reasoning Evidence Statements. The Geometry and Algebra II Evidence Statement Documents also have Reasoning Statements that are similarly arranged and coded.

Modeling Evidence Statements are shaded in aqua on page 18 of the Algebra I Evidence Statement Document and have a prefix of “HS.D.” The Algebra I Evidence Statement Document has seven Modeling Evidence Statements. The Geometry and Algebra II Evidence Statement Documents also have Modeling Statements that are similarly arranged and coded.

#### 4. How many CRTs must be in a completed math portfolio appeal? How do I select what statements to use?

A completed mathematics portfolio appeal must contain **four** student-completed CRTs, each of which must be accompanied by a Constructed Response Item Cover Sheet and an item specific scoring rubric.

The four CRTs in a portfolio appeal must be aligned to any two unique Reasoning Evidence Statements and any two unique Modeling Evidence Statements from the Algebra I, Geometry and/or Algebra II Evidence Statements. No Evidence Statement may be used twice.

When selecting evidence statements, also consider mathematical conceptual categories, which can be found in the third column, Evidence Statement Text, of the Evidence Statement Table. The NJSLS-M contain content from five Conceptual Categories:

- Number and Quantity (N).
- Algebra (A).
- Functions (F).
- Geometry (G).
- Statistics and Probability (S).

The four Reasoning and Modeling Evidence Statements you select must reflect four **unique** Conceptual Categories. This is best accomplished by using the Content Scope associated with the Reasoning and Modeling Evidence Statements. For example, in the Algebra I Evidence Statement Document the third Reasoning Evidence Statement found on page 16 is “HS.C.5.6” and has a Content Scope of “A-REI.5.” This Content Scope is part of Conceptual Category A or Algebra.

A portfolio appeal may include four CRTs all aligned to Algebra I Reasoning and Modeling Evidence Statements, or Geometry, or Algebra II Evidence Statements; this is a district decision. Perhaps the student is currently in an Algebra II course and you would like the portfolio appeal to reflect content that the student is currently studying. You may also use Evidence Statements from all or any Evidence Statement Documents.

Districts may use Evidence Statements that have a Content Scope from the middle school standards (securely held knowledge). For example, the Algebra I Evidence Statement Document includes HS.C.18.1 with Content Scope “8.EE.B.” This Content Scope easily fits within the Conceptual Categories A or F, however, the reasoning required for a CRT aligned to this Evidence Statement should be of the high school level.

#### 5. What should each CRT consist of?

Each CRT should have the following:

- A cover sheet that lists the following (a blank cover sheet can be downloaded from the website for your use):
- The student’s name.
- The Evidence Statement to which the task aligns (use the coding found in the Evidence Statement tables).
- The actual Evidence Statement.
- The content scope in the Evidence Statement that is being assessed.
- The conceptual category being assessed (N, F, A, G, or S).
- The type of item: Reasoning or Modeling.
- The student’s score.
- The constructed response task.
- The student’s response and score.
- The constructed response rubric.

#### 6. Can I assess the students in their native language?

Yes. However, districts will need to do the following:

- Write the CRT in English.
- Have the CRT translated into the student's native language, using a district selected process for translation services.
- After the student has responded in his/her native language, the student response
**must**be translated into English. - For more information, please review the Special Populations Guidance for Portfolio Appeals.

#### 7. Can I see a sample set of CRT selections for a particular student?

Below is a sample set of four Reasoning/Modeling Evidence Statements that would fulfill the requirements. This selection of Evidence Statements includes two from Reasoning (C), two from Modeling (D), and covers four distinct Conceptual Categories: A, N, G, and F:

- From the Algebra I Evidence Statement Document: HS.C.5.6 Content Scope A-REI.5.
- Also, from the Algebra I Evidence Statement Document: HS.D.2-5 Content Scope: N-Q.
- From the Geometry Evidence Statement Document: HS.C.13.2 Content Scope: G-GPE.5.
- From the Algebra II Evidence Statement Document: HS.D.2-10 Content Scope: F-IF.7.

#### 8. What would a sample CRT look like?

Below is a sample CRT:

**Evidence Statement Code**: HS.C.6.1

**Evidence Statement**: Base explanations/reasoning on the principle that the graph of an equation and inequalities in two variables is the set of all its solutions plotted in the coordinate plane.

**Content scope**: A-REI.D, excluding exponential and logarithmic functions.

**Conceptual Category Assessed:** Algebra (A)

**Type of Item**: Reasoning (C)

**Student Score**: 3

##### CRT:

Let | *x *| + | *y *|, where *c *is a real number.

Determine the number of points that would be on the graph of the equation for **each **given case:

Case 1: *c *< 0

Case 2: *c *= 0

Case 3: *c *> 0

Justify your answers.

##### Student Response:

Please note: The student’s response may be on separate pages from the task. Please make sure the student’s name is on each page of their response.

##### Sample Scoring Rubric

Score | Description |
---|---|

3 | Student response includes each of the following three elements:
- One reasoning point: Correct justification of the number of points on the graph for c < 0
- One reasoning point: Correct justification of the number of points on the graph for c = 0
- One reasoning point: Correct justification of the number of points on the graph for c > 0
Sample Student Response: | There are no solutions and no points on the graph when c < 0. If c = 0, there is only one solution, (0, 0). The graph consists of only one point. If c > 0, there are infinitely many solutions, which means that there are infinitely many points on the graph. |

2 | Student response includes two of the three elements. |

1 | Student response includes one of the three elements. |

0 | Student response is incorrect or irrelevant. |

#### 9. What other sources can I use to develop a CRT?

Additional examples of CRTs can be found among the released items for Algebra I, Geometry, and Algebra II. Districts should consider updating, refreshing, and developing new CRTs based on feedback gathered from educators in the district who are working with currently active CRTs.

CRTs should reflect high school-level Reasoning, Modeling, and content. For example, a CRT that merely requires a student to add up a food bill would not allow a student to demonstrate proficiency in high school level Modeling and content.

#### 10. How do I score a CRT? What is the minimum requirement for a qualifying CRT?

- CRTs aligned to Reasoning Evidence Statements should be worth a total of 3 or 4 points to be consistent with the NJSLA-M).
- CRTs aligned to Modeling Evidence Statements should be worth a total of 3 or 6 points to be consistent with the NJSLA-M.
**At least half**of the available points in each CRT must be for Reasoning or Modeling. Any remaining points can be for computation.- Score points should
**not**be awarded in half-points. - Only student scores of 50% or more of the available points should be submitted to NJDOE. If your district is using a CRT with a total of 3 available points, only student portfolio appeals with scores of 2 or 3 demonstrate student proficiency of the NJSLS-M.
- The score the district awards to a student-completed CRT must be consistent with the uniform scoring rubric that the district is using. CRTs not scored in this manner will be returned to the district.

#### 11. Can I send my CRTs for review by the NJDOE before I administer them to my students?

You may send the CRTs to the NJDOE for review. It is not required, but it is recommended. Having the CRTs reviewed will help eliminate issues when the appeal is submitted. It is far easier to correct issues with the CRTs before they are administered to students than to find out there are issues after the appeals have been received at the NJDOE.

#### 12. If I sent in CRTs for review last year, should I send them in again?

Districts may choose to have CRTs reviewed again by the NJDOE. However, this is recommended only if you feel, after reviewing this updated information guide and the further clarifications mentioned, that some CRTs from last year don’t exactly match one of the Evidence Statements, or do not focus on the primary content of an Evidence Statement**.**

#### 13. Are there common mistakes a district can avoid when developing CRTs?

The NJDOE recommends checking for common mistakes such as:

- The cover sheet is missing or is not correctly filled out for each CRT.
- There is more than one Evidence Statement listed.
- There is more than one content scope listed.
- The content of the CRT does not align to the Evidence Statements and content scope.
- The content of the CRT is below the content level and rigor of the content scope.
- The CRT is not graded and does not show where the student made an error.
- The rubric does not show the points delineated for modeling/reasoning and computation, if any.
- The rubric is missing a sample student response.

It is very important to review your CRTs, cover sheets and rubrics for accuracy when compiling your documentation.

#### 14. What do we need to keep in district for each Math appeal?

Districts should maintain the following in district for each student:

- A completed Education Proficiency Plan (EPP) that includes the most current student transcript, documentation of performance on New Jersey Graduation Proficiency Assessment (NJGPA) and/or substitute competency assessments, and an intervention plan implemented to ensure the student met the graduation assessment requirement.
- CRTs in mathematics in which the student is attempting to meet the graduation assessment requirement.
- Four graded responses to CRTs for mathematics (2 modeling, 2 reasoning).
- A completed Mathematics Portfolio Appeal Cover Sheet for each graded student response. The Mathematics Portfolio Appeal Cover Sheet is available for download on the website.

Note: All documents can be found on the Graduation Assessment Requirement webpage under the section Graduation Portfolio Appeal.

#### 15. What do I do if I have further questions?

If you have any questions, please contact the NJDOE’s Office of Assessments at assessment@doe.nj.gov or (609) 376-3960.