Introduction For the past two years, the secondary Academic Leadership Team (ALT) and the Secondary Curriculum, Instruction, and Staff Development Department have been examining our grading practices in an effort to make sure our practices support our beliefs about learning, assessment, and grading. This process has included professional learning, research, book studies, interactions with national educational specialists, action research, and input from teachers, administrators, and parents. At the heart of this work were two underlying questions. Do our grades accurately reflect student learning? Do our grading practices build confidence in our students’ belief that they can learn? This document is intended to define the philosophy, purpose, and procedures behind the changes in secondary grading practices in the core content areas adopted by Denton ISD. Some previous procedures and guidelines have been expanded, some clarified, and others changed or eliminated altogether. As you read this document, focus on the common understanding that grades should only convey what a student knows and is able to do as related to the academic standards. Grades are for the purpose of providing students and parents meaningful feedback on student learning, documenting academic progress, and informing instructional decisions to support student achievement. High schools and middle schools will begin implementation of all grading practices and guidelines starting with the 2014-2015 school year. Standards referenced grades and assessments will be phased in throughout the year with an expectation of full implementation in 2015.

Beliefs and Practices Statements As secondary educators in Denton ISD, we are committed to grading practices that support the learning process, encourage student success, and accurately reflect student progress toward mastery of the state standards, Texas Essential Knowledge and Skills, (TEKS). Our beliefs about learning and grading practices are grounded in the following statements.

All students can learn.

Students learn in different ways.

Students learn in different time frames.

Errors are inherent in the learning process.

Assessment is a process for providing feedback that influences learning.

Grades should accurately reflect mastery of the standards (TEKS or AP/IB course standards).

As evidence of our commitment to these beliefs, the following grading and assessment practices will be implemented beginning in the 2014-15 academic year.

All assignments and assessments will be referenced to the standards.

Grades will not be inflated or deflated for student nonacademic behaviors.

Grades will not be reduced for failure to meet deadlines.

Zeros will not be used to indicate missing or incomplete work.

All students will be given the opportunity for reassessment of all summative assessments, excluding semester exams.

Standard-Referenced Grades and Assessments Because we believe assessment is a process for providing feedback that influences learning and that grades should reflect mastery of the standards, Denton ISD will support accuracy in grading through standards referencing assignments and assessments.

Grades will be determined on achievements of course standards. o Texas Education Code, 28.0216 (1) A district grading policy must require a

classroom teacher to assign a grade that reflects the student’s relative mastery of an assignment. Texas code requires that granting course credit be based on academic achievement and demonstrated proficiency of the standards.

o In a standards-referenced system, a student's status is reported (or referenced) relative to the standard for each area of knowledge and skill on the report card. (Marzano, p. 18-19)

o “…the primary purpose of grades is to communicate a summary of student achievement… as a result of their learning.” (O’Connor, p. 106)

Denton ISD will enact a grading procedure that requires secondary classroom teachers to assign grades that reflect students’ mastery of the TEKS or AP/IB course standards. This procedure is designed to communicate accurate information to parents and students regarding progress towards mastery.

o It is “essential that all teachers in every school teaching the same grade or same subject/course should determine grades in similar ways.” (O’Connor, p. 5)

o It is important to ensure that student grades are accurate and that what teachers report is clear and meaningful. (Schimmer, p. 123)

Summative and Formative Assessments Because we believe errors are inherent in the learning process, all grades will be calculated using summative assessments only. Summative Assessment is the process of evaluating and grading the learning of the student at the end of a unit or instructional period. Before a summative grade is assigned, the teacher is to have adequately taught the concept, and the student is to have had a sufficient opportunity to master the concept being evaluated. Summative assessment is generally used as part of the grading process.

Definition of Summative Assessment: Assessments designed to provide information to be used in making judgments about student’s achievement at the end of a sequence of instruction. (Assessment OF learning) (adapted from O’Connor, 2011, p. 107)

Examples of Summative Assessments: final drafts/attempts, quizzes, tests, exams, projects, performances, common assessments, essays, presentations, portfolios.

Formative assessments are instructional activities designed to allow students to develop content knowledge and/or practice content skills with teacher feedback that is accurate, helpful and timely. Formative assessment is done while students are still learning. Grades should be a reflection of the mastery of the standards, so it would not be appropriate to use formative assessments for grading since students are in the learning process.

Definition of Formative Assessment: Assessments designed to provide direction for improvement and/or adjustment of teaching and learning activities for individual students or for a whole class. (Assessments FOR learning) (adapted from O’Connor, 2011, p. 107)

Examples of Formative Assessments: teacher observation, class discussions, lesson practice, practice homework, instructional questions, initial drafts/attempts, progress checks, checks for understanding, independent practice, daily work. The key is to think of summative assessment as the game/performance and formative assessment as the practice/rehearsal.

Grading Practices Grading Practice: All assignments and assessments will be referenced to the standards. As students and parents view the grade postings in the on-line Home Access Center (HAC), each posting will be followed by the course standard code. This clearly connects the work to the standard it is addressing.

Examples:

ELA – Romeo and Juliet – Make and defend inferences TEKS: 9(C)

Math – WS4-1 #2-20 evens (uses completing the square) TEKS: 5(E)

Science – Drift Worms Lab TEKS: B.7(F)

Social Studies – Columbian Exchange AP: 1.2 I (C)

World Languages – Paraphrase TEKS: 2(C) Grading Practice: Grades will not be inflated or deflated for student nonacademic behaviors. Non-academic behaviors include but are not limited to: attendance, attitude, bringing supplies/materials to class, incorrect headings, lack of neatness on an assignment, returning progress reports, etc. Even though these behaviors are important, they are not a part of our

academic standards and will not be a part of the student grade since grades reflect mastery of the standards. When concerns arise regarding these non-academic types of behaviors, they will be communicated in a form other than the students grades. Grading Practice: Grades will not be reduced for failure to meet deadlines. Meeting deadlines and turning in an assignment on time is a critical behavior that contributes to a student’s sense of responsibility, but it does not represent a student’s mastery of the standards. Our goal is to accurately report grades that represent what a student knows, understands and can do. Teachers will ask for parent support and guidance if a student develops chronic late work behavior. Grading Practice: Zeros will not be used to indicate missing or incomplete work. The use of zeros to indicate missing work allows students to “opt out” of required and essential work. The expectation is that students will complete and receive credit for all essential work in an effort to demonstrate mastery of the standards. In order to give parents accurate information, zeroes are only used to indicate that there was no mastery of the standards. If work is missing or incomplete, there is not enough evidence to communicate mastery of the standards. Using a zero in this case would give an inaccurate portrayal of the child’s knowledge. Grading Practice: All students will be given the opportunity for reassessment of all summative assessments, excluding semester exams. Because we believe that errors are inherent in the learning process, all students will be given the opportunity for reassessment of all summative assessments, excluding semester exams. It is only by reporting the most current of assessment results that a grade accurately reflects student mastery. Example: If the first score is 40 and the second score is 80, an accurate report of student mastery would be 80, not 60. Students will not be penalized for errors on the first assessment, which a mean averaging of the grades does. The opportunity for reassessment encourages students to deepen their learning on different standards, and the reassessment itself allows demonstration of the increased knowledge. If it takes a student longer to learn a standard, and the assessment comes before the student has completed the learning, there is no reason for further learning if there is no chance for reassessment. With reassessment opportunities, students actually work harder because they have taken advantage of additional learning opportunities, such as group tutorials, alternative assignments, and individual conversations with teachers. It is by participating in these additional opportunities, students earn the privilege of reassessing. An exception is made for

semester exams because, by design, they are already reassessments of all the work done during the semester. The practice of allowing students to reassess is consistent with other important assessments such as the SAT, ACT, and even a driver's license. In all of these situations, the number of times one takes the test is inconsequential. In fact, the highest score is the only score that is kept on the final record. Each secondary campus will develop reassessment guidelines so that students will know exactly how to qualify for a reassessment opportunity.

Grading Categories

Course Major Summative Minor Summative

Regular 70% 30%

Pre-AP/AP/IB 80% 20%

Major Summative Examples (examples only, not an exhaustive list)

Minor Summative Examples (examples only, not an exhaustive list)

Unit tests Projects Research papers Final drafts Essays Presentations Common assessments Lab practical Written response Performance tasks Portfolios

Quizzes Graphic organizers Rough Drafts Short pieces of writing Oral questions in class Exit tickets Learning Logs Journal entries Performance tasks Laboratory write-ups

One grade cannot count more than 1/3 of the final grade for the grading period.

The end of the grading period grade should reflect an adequate sampling of summative assessments to accurately reflect mastery of the targeted standards.

Progress reporting periods should include both minor and major summative grades.

To determine the grade at the end of the grading period, teachers will use professional judgment when considering the body of evidence from minor and major summative grades. The most recent achievement data should be considered when assessing mastery of the standards.

Teachers will record the actual grade earned as there is no minimum grade to be assigned.

Final semester grade calculations: The average of the two grading periods will count 80% of the final semester grade, and the final exam will count 20% of the final semester grade.

Grade Book Codes The following codes will be used to better communicate to parents and students entries in the grade book when viewed on-line through the Home Access Center:

INC = insufficient evidence to give a grade; used at the end of the grading period; must be removed within a specified time. Incompletes create UIL ineligibility.

R = Reassess

EXC = excused as nonessential because other evidence is sufficient to determine mastery; does not calculate into the grade

MSG = work not turned in at all; calculates as a grade of zero in the ongoing grade period calculation until completed

Zeros = only used to indicate no mastery of the standards

TEKS Code = references the course standard aligned to the assignment or assessment

Note: Sections to be included in this document which are still under development:

Homework

Academic dishonesty

References O’Connor, K. (2011). A Repair Kit for Grading: 15 Fixes for Broken Grades. Boston, MA: Pearson Education, Inc.

Marzano, R. (2009). Formative Assessment and Standards-Based Grading. Centennial, CO: Marzano Research Labs.

Schimmer, T. (2014). Ten Things That Matter From Assessment To Grading. Boston, MA: Pearson Assessment Training Institute.

The Academic Leadership Team (ALT) is in the process of examining our beliefs about learning and

assessment to determine if any grading practices need to be adjusted or changed to support our beliefs.

Teacher feedback is essential in this process. Please take the time to complete this survey by March 8th.

This survey will take less than 10 minutes to complete. We need and value your input and comments.

All responses are anonymous.

The following items focus on beliefs. Please rate your agreement/disagreement using the scale

provided.

450 surveys returned

% Agree

1

% Somewhat

Agree 2

% Somewhat Disagree

3

% Disagree

4

Students learn in different timeframes. 79.33% 19.56% 0.67% 0.44%

Students learn in different ways. 90.44% 9.33% 0.22% 0.00%

All students can learn. 82.00% 15.56% 1.78% 0.67%

Errors are inherent in the learning process. 78.22% 20.44% 1.33% 0.00%

Assessment is a process for providing feedback that influences learning. 76.89% 21.56% 1.11% 0.44%

Grades should reflect mastery of the standards (TEKS). 46.00% 43.11% 6.44% 4.44%

The following items focus on grading practices. Please rate your use of the practices using the scale provided.

Almost Always

1

Frequently

2

Sometimes

3

Never

4

I reduce points/grades for work submitted late.

21.78% 17.78% 38.89% 21.56%

I include grades of zeros for missing work.

43.11% 18.67% 24.67% 13.56%

I reduce grades for cheating.

54.89% 14.00% 17.33% 13.78%

I allow students to redo assessments without penalty if they have not done well. 32.89% 22.44% 32.00% 12.67%

I allow students to redo assessments with partial credit if they have not done well. 35.56% 25.56% 27.56% 11.33%

I allow new evidence (improved grades) to replace, not simply to be added to, old evidence (original grade). 33.56% 29.78% 28.67% 8.00%

I include performance on homework in the six weeks grade.

49.33% 18.00% 17.11% 15.56%

I provide detailed comments to students about strengths and weaknesses in their work. 22.22% 44.22% 29.33% 4.22%

I limit the number of students who receive grades of A.

0.22% 1.56% 1.56% 96.67%

The following items focus on grading practices and their supporting beliefs. Please respond to the

questions with yes or no.

Yes No

If you believe that students learn in different timeframes, can you support the practice of retaking a test for full credit provided that the student demonstrates preparedness for the retake first?

73.56% 26.44%

If you believe that students learn in different timeframes, can you support the practice of accepting “late-work” for full credit?

57.56% 42.44%

If you believe that students learn in different ways, can you support the practice of using different types of assessments to measure achievement?

90.89% 9.11%

If you believe that assessment is a process for providing feedback that influences learning, can you support the practice of standards-referenced grading?

82.22% 17.78%

If you believe that grades should reflect mastery of the standards, can you support the practice of removing “extra credit” or bonus points?

69.33% 30.67%

If you believe that grades should reflect mastery of the standards, can you support removing grades for non-academic performance (bringing supplies, effort, behavior, attendance, etc.)?

76.22% 23.78%

If you believe that grades should reflect mastery of standards and acknowledge that missing work gives you no information about mastery, can you support replacing zeros with incompletes?

67.78% 32.22%

Thank you for taking this survey. We have provided a space for you to offer comments that you feel

would be valuable to our discussions on learning and grading.

Comments Section:

Academic Leadership Team Examining Our Grading Practices

Summer 2012 Book Study: A Repair Kit for Grading: 15 Fixes for Broken Grades by Ken O’Connor Social Studies Department Chairs Elements of Grading: A Guide to Effective Practice by Douglas Reeves Science Department Chairs Transforming Classroom Grading by Robert Marzano Math Department Chairs Grading and Learning by Susan M. Brookhart English Department Chairs How to Grade for Learning by Ken O’Connor World Language Department Chairs Classroom Assessment and Grading that Work by Robert Marzano CTE Department Chairs

Fall Semester 2012 Activities: Reflected on summer reading: What three things did you discover from your reading that you agreed with and want to

be part of our grading discussions this year? What three things did you discover from your reading that challenged your thinking and

you want to part of our grading discussions this year? What three things did you discover from your reading that you do not agree with and just

can’t let go of?

Separated grades for academic and non-academic behaviors

Reviewed state grading policy, local grading policy, and local grading guidelines and procedures

Developed a process for determining our beliefs about grading and assessment

“Buried” grading practices we will give up in the spirit of Halloween !

Formed work teams to gather information and to research best practices for grading to help establish our belief statements: Research other districts Have a round table discussion with principals and central level administrators Survey teachers, students, and parents

Attended the Sound Grading Practices: Linking Quality Assessment and Grading

Conference, December 6-7, Portland, Oregon. This conference is hosted by the Assessment Training Institute originally begun by Rick Stiggins and now owned by Pearson. A group from Denton High School joined our team including teachers, Dan Ford and Renee Koontz as well as Joel Hays, associate principal at Ryan High School.

Reviewed research on what other districts are doing in the area of grading and assessment: o What stands out? What trends do you see? o What do you see that you would like incorporated into our district’s belief

statement? o What do you see that you do not want included in our district’s belief statement?

Spring Semester 2013 Activities: Held a round table discussion with Principals: Listed below are the guiding questions which

drove our discussion and acted as a spring board for sharing our thoughts. o What grading issues do you deal with most often as an administrator? o How has your perspective on grading changed when you moved from the

classroom to administration? o What would you change if you were to go back to the classroom? o Texas Education Code, 28.021, has required decisions on promotion or course

credit to be based on “academic achievement or demonstrated proficiency”. What should that look like?

Developed a rough draft of belief statements about learning, assessment, and grading which

began with each member writing a minimum of two of their own beliefs. From those personal beliefs, a more comprehensive document was created.

Developed a teacher survey for teacher feedback and insights regarding our beliefs about learning and assessment as one way to determine what teachers are practicing and what changes would they support.

Held a round table discussion with Dr. Wilson: The same guiding questions we used with the

principals were used to drive this discussion and act as a spring board for sharing our thoughts.

Administered the Teacher Survey

Analyzed teacher survey data using a data analysis tool that asks the following questions:

(1) What?...What is the data telling you? How would you put the data into measurable terms? (2) So What?...What are the implications for you / your department / campus? What will your focus be? (3) Now What?...What do you and your department / campus need to do now? What is your plan?

Determined from the teacher survey analysis which grading practices had the most support, which would need additional time for reflection by teachers, and which practices would teachers find the most difficult to change.

Met with campus ALT colleagues and examined their campus teacher survey data about

grading practices. They were asked to select 2-3 grading practices to propose to their principal for next year as the beginning steps in moving toward a different grading and assessment approach. They were also asked to give their rationale for what they chose and how it connected to their data.

Met with principals to go over their proposal and developed a plan of action for next year. Shared their plan with ALT at the last meeting of the year.

Fall Semester 2013 Activities: Shared each campus plan which targeted several grading practices to change for this

school year which will be the focus of our work regarding grading and assessment. These were determined separately by each campus, but all campuses included at least one nonacademic behavior to be eliminated from grades.

Created rubrics for use with the nonacademic behaviors that will no longer be included in the grade since the grade can only reflect mastery of the standards.

Tried the rubrics with at least one class and reported back how using the rubric worked.

Decided, after much feedback and discussion, not to ask teachers to use rubrics for

nonacademic behaviors because it is time consuming. Most agreed that the number of students not turning work in on time or not participating in class for example is small and individual contact about the issue is the best plan of action. Feedback and communication with student and parent is still expected.

Developed talking points to explain to their departments the decision not to use rubrics to

report nonacademic behaviors. Continued to shared articles with departments and bring feedback for discussion at each

meeting. Focused on two underlying questions, how accurately do our grades reflect mastering of the

standards, and how do our grading practices build confidence in our students that they can learn.

Looked at the MIT grading model and discussed what it means to prepare students for

college. What college experience are we basing that statement on…our own college biographies?

Continued analyzing ways to support teachers throughout this change process. Asking

students in high school to change their focus to learning rather than on earning points is not easy since we have trained them in a system that adds or subtracts points for nonacademic behaviors.

Developed possible procedures to be put in place to replace grade penalty as a way to get students to understand the importance of meeting deadlines, the relevance of meeting deadlines, and the consequences that occur when deadlines are not met.

Identified what guidelines and supports needed to be in place at the department level,

campus level, and district level to support the changes in grading practices.

Spring Semester 2014 Activities: Worked with Tom Schimmer, author of Ten Things that Matter from Assessment to Grading,

on leading the change process involved in examining our grading practices with an emphasis on how to support teachers and have the often difficult conversations that are part of the process.

Developed first draft of the district framework for grading procedures and practices.

Identified talking points to help teachers understand and support the district framework as well as identified professional learning targets in preparation for the changes.

Read and discussed articles and selected some to share with their departments

Created content specific examples for referencing the standards in the grade book.

Identified questions already being asked by parents of students in classes where teachers

are trying a new approach to grading and assessment. Wrote answers to parent questions and created a draft FAQ document for parents.

Worked with technology to create new grade book codes to use next year to better inform

parents when they check their child’s grades on HAC. Created examples for teachers of the types of assignments or tasks that could be used for

formative and summative assessments. Reviewed second draft of the district framework for grading procedures and practices.

Supporting Activities 2012 - 2014 Throughout this two year process, principals have met together and discussed examining

our grading practices, have led sessions with their staff, have read articles and books, have attended conferences, and have provided input and feedback from their teachers and administrators to help shape this journey.

Throughout this two year process, high school departments have met and discussed examining our grading practices, read articles, and provided feedback.

Throughout this two year process, middle school teachers have had opportunities to

participate in professional development, explore and try new practices , provide constructive

feedback, use standard-referenced grading, and implement and reflect on assessment strategies.

Tom Schimmer, author of Ten Things that Matter from Assessment to Grading, met with all high school math and science teachers on the October 2012 staff development day focusing on the accuracy and confidence building of our grading practices.

Debra Pickering, Senior Scholar with the Marzano Research Laboratory and co-author with Marzano on numerous books and articles, met with all social studies and ELA middle school teachers to examine their grading practices and assessments on the October 2012 staff development day.

Debra Pickering met with all middle school math and science teachers to examine their grading practices and assessments in November 2012.

Debra Pickering met with all at risk campus middle school teachers on three separate days in 2012-2013 to continue the work on assessment and grading.

Assistant Principals participated in an on-line Moodle book study as part of their Secondary Curriculum and Instruction Leadership Academy for 2012-2013. They were in groups focusing on a book of choice from four books on grading and assessment practices.

Additional teachers and administrators attended the Sound Grading Practices: Linking Quality Assessment and Grading Conference, Portland, Oregon, in the summer of 2013.

Tom Schimmer met with all middle school non-at-risk campuses on October 7, 2013

focusing on the accuracy and confidence building of our grading practices. Ken O-Connor, author of A Repair Kit for Grading: 15 Fixes for Broken Grades, met with all

Denton High School teachers on October 7, 2013 focusing on examining our grading practices.

Middle school teachers who were interested in trying new practices in grading and

assessment met on two different days with the Secondary Curriculum Department first semester of 2013 to develop a plan of action, supporting documents, and ways to communicate with parents about the changes they were going to implement throughout the year. Among most of these teachers, providing quality feedback to students was a critical component of their plan.

Dan Ford and Renee Koontz at DHS led their teachers through a process to develop new guidelines for grading and assessment for their campus that support the district process which they implemented as a pilot second semester 2014. They have had two parent meetings visiting with parents about the changes. The feedback from DHS teachers has been invaluable to our work as we developed our grading frame work.

Tom Schimmer led the Secondary Assistant Principals’ Curriculum and Instruction Leadership Academy in 2013-2014 focusing on leading the change in grading practices and assessment.

Tom Schimmer met with the Bettye Myers Middle School teachers on Saturday, January 11,

2014 focusing on the accuracy and confidence building of our grading practices. The Technology Department has been very supportive working with us to develop new

codes for the grade book program and figuring out how to standard reference grades in the grade book so it is helpful to parents.

Middle school principals have met and discussed grading practices, read articles, attended training, led discussions with their teachers, and supported teachers who are trying new practices in grading and assessment throughout 2013-2014.

High school principals met in March 2014 and reviewed the draft of the district grading framework developed by the ALT. Based on where their teachers are in this change process, they decided that we would implement, starting in August 2014, no inflating or deflating of grades practice, no zeros, reassessment for full credit, and no penalties for late work. Providing teachers with additional training on standard referencing their grades and assessments in the fall, teachers would practice standard referencing grades with an expectation of implementation starting the second semester.

High school and middle school principals met together in April 2014 for a final review of the district framework for grading and assessment and discussed plans for leading the implementation of new grading practices for 2014-2015.

FAQ Regarding Grading and Assessments

(1) Why are we giving students opportunities to reassess on summative

assessments?

Our focus is on student learning, and we know that students learn at different rates. Reassessment opportunities allow students to reflect on their learning and demonstrate their increase in knowledge of the standards.

(2) Why are students able to earn the full value on reassessments?

A student’s grade should accurately reflect their mastery of the standards and not the speed in which they were able to demonstrate that mastery.

(3) Why are semester exams not eligible for reassessment?

Semester exams are, by design, reassessments , and the grade reflects the cumulative mastery of the standards.

(4) How does my student earn the opportunity to reassess?

Students can qualify for the opportunity to reassess by participating in additional learning opportunities that demonstrate that new learning has occurred in preparation for the summative assessment, such as, but not limited to:

attending group tutorials attending individual tutorials completing web-based instruction completing work already assigned completing new work discussing with teacher orally about the content demonstrating mastery of the standards through an

alternative method such as project, essay, report, demonstration, etc.

Each campus will develop reassessment guidelines so that students will know exactly how to qualify for a reassessment opportunity.

(5) Why is there no longer a grade reduction for late work?

Our goal is to accurately report grades that represent what a student knows, understands, and can do. While meeting deadlines and turning in an assignment on time is a desirable behavior, it does not communicate whether or not a student knows the standard.

(6) Why are zeroes no longer being used to indicate missing or incomplete

work?

In order to give parents accurate information of their child’s mastery of the standards, zeros are only used to indicate that there was no mastery of the standards. If work is missing or incomplete, there is not enough evidence to communicate mastery of the standards. Using a zero in this case would give an inaccurate portrayal of the child’s knowledge.

(7) How will the entries into HAC be different as a result of these changes?

The following codes will be used to better communicate to parents and students entries in the grade book:

INC = insufficient evidence to give a grade; used at the end of the grading period; must be removed within a specified time. Incompletes create UIL ineligibility

R = Reassess

EXC = excused as nonessential because other evidence is sufficient to determine mastery; does not calculate into the grade

MSG = work not turned in at all; calculates as a grade of zero in the ongoing grade period calculation until completed Zeros = only used to indicate no mastery of the standards TEKS Code = references the course standard aligned to the assignment or assessment

(8) Why did we change from a 6 week grading period to a 9 week grading

period?

The nine week grading period allows for more time to provide students with meaningful feedback from formative assignments in preparation for summative

assessments. It also allows for more time for reassessing, so students can

demonstrate new learning before grades are calculated.