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Does the calculator have the ability to program functions? Here is a handout about numerical integration for the TI-82.[1] I assume they’re relatively similar but I haven’t used a calculator for a while.It goes over the basic methods[2] you’d learn which areMidpoint ruleSimpsons methodTrapezoidal methodIf you know the basic definition of a Riemann sum[3] it should be straight forwardThe Riemann sum of f(x) on some interval is given as[math]S = \displaystyle \sum_{i=1}^{n} f(x_{i}^{*}) \Delta x[/math]where [math]\Delta x = x_{i} - x_{i-1}[/math]The basic idea is to take an interval and uniformly divide it into these small partitions then evaluate the function at the points in those regions and sum the intervals. There are more advanced and accurate forms of quadrature but the basic ones are pretty easy to implement and fairly accurate most of the time.Footnotes[1] https://orion.math.iastate.edu/rymartin/RUcourses/RU152/ti82numint.pdf[2] Numerical integration - Wikipedia[3] Riemann sum - Wikipedia

The question is impossible to answer, partly because under the new system it islikely both would have had very different programs. Partly because figure skating judging always has an element of subjectivity to it.But assuming both skated the same programs, I would argue it’s possible that some parts of Kwan’s program would have given her an edge - pun unintended. This is because COP helps judges to look at the whole program’s difficulty, including subtle skills or skills that look easy but in reality are anything but. Kwan’s back to back spins, for example, would be rewarded. This is very difficult, requiring a high level of coordination, control, gradation of speed and precision. In fact this movement sequence is so complex and difficult it is rarely seen even today. And Kwan did her back-to-back spins with good extension, posture and position. This emphasis on the subtler elements of skating technique - depth of edge, edge control and quality, spin and spiral positions, coordination in footwork, line and fluid transitions - would have worked in Kwan’s favor. Her sense of style and line would also have boosted her artistic mark, as it did in the actual competition. Little things like the sound of skates can make a big difference in a performance artistically, as well as show off technical virtuosity; under 6.0 however, the technical mark was, if not dominated solely by jumps, at least heavily controlled by them. Though jumps remain very important, in some ways one of the (debatable) benefits of COP has been to rehabilitate and re-emphasize such skills as spins, footwork, choreographic complexity, and basic stroking. Under 6.0 it was easier for judges and fans alike to get swept off their feet by the dazzling virtuosity of an exciting jump or other display of raw athletic ability.Kwan’s change of edge spiral, deep and flowing edges, sensuous classical style, footwork and Ina Bauer sequence would have been valued highly. Her elegance, lines and up-and-down, buoyantly floating rhythm across the ice in footwork would have worked to her benefit, especially in the valuation of her step sequences. Of course, her edge quality and mastery of the blade to ice relationship would also be clearer when judges were specially looking for it. The intricacy and precision of her steps and the wit and formal invention of the choreography would give her a bump in both the technical and artistic scores. I don’t much like COP, partly because the anonymity removes accountability and partly because I think at times its heavy mathematization of the scoring discourages judges from looking at the bigger picture of the whole program. In favor of focusing on high-risk technical tricks, relatively minor technical nuances, and bizarre new expectations (e.g., all kinds of new contortionist spin positions, often aesthetically unappealing), a judge’s gut instinct about the beauty or appeal of a program (or lack thereof) is sometimes demoted in importance, or even discarded. However the good side of it is that it does make judges zero in on subtle aspects of skating technique, not only the raw athleticism and high risk high reward tricks that the technical mark in the 6.0 era commonly rewarded. COP actually mandates that judges look at edge quality, footwork, and choreographic quality as well as skill, complexity, and seamlessness of transitions. Much of this gets included in the technical scores - not only the artistic mark.Kwan’s layback spin was also superior to Ms. Lipinski’s, especially earlier in her career. Her arch, extension and strong spin position would have helped her. And of course, her superior depth and steadiness of edge would have made a difference in her favor as well. For all its problems, COP does sometimes better reward the intricacy and technical difficulty of footwork and moves in the field, and it also tends to more highly value challenging or striking choreographic transitions - both in footwork, and before jumps or as part of larger movement sequences. All of which Kwan had greater mastery than her rival. While her “Lyra Angelica” wasn’t especially full of complex transitions, the program showed off the edging and skating skills, as well as mastery of a diverse array of skating vocabulary, beautifully. And the footwork sequence in her “Rachmaninoff” short program was rather complex and difficult - probably slightly harder than Lipinski’s equivalent sequence in her short program. Though Lipinski performed hers with admirable power and speed.Kwan’s music - a classical piece called “Lyra Angelica” - was more subtle and restrained than Lipinski’s - the film soundtrack to “The Rainbow.” Lipinski’s music had, if not more emotion, then more flamboyance and overt drama to it; it’s possible that her music choice influenced some judges to prefer her program. In which case it would have influenced some judges to prefer her program under COP as well.Overall, I think if the judges chose to examine the subtler aspects of technique, flexibility, and extension as well as line and positioning, Kwan would be better placed to win. If they were focusing primarily on jumps and raw power the winner would be Lipinski. Since in the actual competition, three judges placed Kwan first, I think Kwan would have had a decent chance of winning, but as with all counterfactuals it’s impossible to know.If you’re asking about my personal preference, artistically it’s Kwan for me as it was for most fans. Though I think it’s fair Ms. Lipinski won that night - she gave the performance of her life under great pressure, performed exceptional technical feats, and skated with great joy and spontaneity. She had the technical edge, especially after Kwan had a very slightly shaky jump (I believe it was a flip), and while not known for her artistry Tara brought enough musical interpretation to the table to create an exciting performance.However, if you’re interested in learning more about the skating of that era I must recommend Kwan’s silver-medal winning performance as well, plus the gorgeous Rachmaninoff short program Lori Nichol and she created to match it. Not to mention her gloriously musical and stylistically gorgeous rendition of the “Lyra Angelica” program at the 1998 National Championships, a historic achievement. She won the championship, and earned a slew of record-breaking 6.0s. Kwan’s prior programs had represented a character; here she focused on movement, flow, energy and the purity of skating itself. It took her skating to new depths; and is part of the reason why a famous sports commentator could look at her and say she “translates the feeling of flight” the best of any skater (Sandra Bezic). Although her Olympic performance of that program was also very beautiful her 1998 Nationals performance is widely acknowledged to be one of her best and arguably one of the greatest in the sport. Willam Alwyn’s “Lyra Angelica” has a proud formality as well as tender romanticism and she captured both, with a performance that left some teary-eyed. The port de bras, the lines, the flowing lightness and ease of her steps, the intense focus and eerie energy of the back to back spins that flow into “harp” arms positions - the whole piece is a real work of beauty. Those back to back opposing direction spins are also exceedingly difficult and she remains one of the few figure skaters to have performed such a move in competition. And very subtle too; over almost before you’ve noticed the emotion and drama of the music rise. The music was perfectly suited to her steady concentration, confidence and calm elegance on the ice, and she brought it to life powerfully. Kwan’s skating that night recalled Janet Lynn’s bubbly ease and strange ethereal power, whom she and her choreographer had watched and used as inspiration for the program. They almost decided to use a signature piece of music for Lynn - but then realized it was too associated with her. Still, Kwan’s skating captured and even elevated to new heights Lynn’s silky grace and otherworldly classicism.Here are some photos of the lovely Michelle Kwan, skating Lyra Angelica:And here is Tara Lipinski in the same competition:You can watch their 1998 programs online on YouTube if you’re interested. Both their Nationals and Olympics performances of their “Lyra Angelica” and “The Rainbow” (Lee Holdridge) are available. It’s interesting to see the evolution and contrast between both versions, as well as the many contrasts between the two top skaters themselves - both stylistically and artistically, and technically/athletically.For more information on the judging systems and how they’re different, you can also read their criteria online. They’re fairly similar, with the main difference being that COP has broken down the precise numerical, technical and aesthetic value and provides more nuanced criteria. But the basic concepts are the same.Hope that helps. Or at least, is stimulating.Here’s some information on the 6.0 system:In the 6.0 judging system the judges are required to evaluate the following technical elements: If jumps are sufficiently rotated, havecorrect take off and landing edges, height, speed into and out of jumps, body positions (form/style) Holding spins for the minimum num- ber of rotations in position, centered (no traveling or recentering), con- trolled exit The difficulty of spiral sequences, spi- ral positions are held for minimum time, number of feet, speed, edges The difficulty of footwork sequences, turns, edges, changes of rotations, covering minimum ice surface (end to end in straight line and completing circular pattern), good carriage, speedJudges in the 6.0 system award a per- formance mark based the skater’s ability to perform a well-balanced program whose technical highlights are coordi- nated with the musical score. The overall performance needs to be visually pleas- ing to watch and should involve a sympa- thetic response from the audience.The judges evaluate the following area of the skater’s presentation skills: Skating skills Transitions Performance and execution  Choreography InterpretationThe judging system was designed to rank national senior competitors using an absolute range from zero (0.0) to six (6.0) – 6.0 mark is considered error free (per-fect) 5.0 is "very good"  4.0 is "good" 3.0 is "fair" 2.0 is "poor" Is "very poor" Is "not skated"Judges use a midpoint that coincides with the minimum "passing average" for the test level of the event. For example, in a Pre-Juvenile event a judge compares the first skater to the passing mark of a Pre-Juvenile test or 2.7. Judges mark the first skater of an event by comparison to the mid point.Here’s some information on COP:Positive Aspects of Step SequencesGood energy and executionGood speed or acceleration during sequence: This concerns skating skills and overlaps with the Skating Skills score in PCS. Skaters with good skating skills maintain their speed even when they are not doing crossovers and are executing difficult steps and turns instead (see below at Skating Skills for details).Use of various steps during the sequenceDeep clean edges: See what "deep edges" mean below at Skating Skills.Good control and commitment of the whole body maintaining accuracy of stepsCreativity and originalityEffortless throughoutElement enhances the musical structured. Positive Aspects of Choreographic SequencesGood energy and executionGood speed or acceleration during sequenceGood clarity and precisionGood control and commitment of whole bodyCreativity and originalityEffortless throughoutReflecting concept/character of the programElement enhances the musical structurefrom :TumblrI

Assessments in higher educationAn overview of assessments in higher educationWhat is an AssessmentAssessment, is a series of measurements that uses various methods and techniques, to collect data on student learning in order to refine teaching programs and improve student learning capabilities. It includes conventional examinations, projects, classroom performance analysis, practical/laboratory activities, extracurricular activities, etc. The term “assessment” is so broadly defined because it needs to include any outcome or goal in any activity or discipline that can be a part of this process.For the sake of this article, and it’s expected audience, we will mostly cover core learning-related aspects of assessments here. If you are interested in the broader definition, we’re only happy to discuss it with you in the comments.It is a continuous process fixated on measuring student learning outcomes forproviding enough learning opportunities to achieve these outcomes,implementing a systematic way of teaching,analyzing achievements,collecting evidence to determine how well students’ learning matches expectations, andusing the collected information to take informed decisions and improvement in student learning.Assessments are always cyclical and are revised to meet requirements.How does it fit inside the higher education systemAssessments is what comes after setting learning objectives and expectations. Every program, course, subject, chapter, and topic should contain certain learning objectives that the student should achieve, after completion.Each question in an assessment should ask:What is the purpose of this question?,What specific knowledge will be gained about that shall be useful to improve the teaching-learning experience and course delivery?Outcome Based Education is the foundation of assessmentsIt is simply a learning paradigm that focuses on the outcomes or goals instead of results. The educators set a certain number of necessary skills and knowledge that the learner should possess at the end of education and they are identified as the outcomes. The assessments like exams, assignments, and projects are then defined to measure the achievement of these outcomes, and their results indicate whether the students have achieved them or not.Every assessment is designed to find out how well these outcomes are achieved. Each piece of an assessment are mapped with various, sometimes multiple, outcomes so that the result of that assessment tells us if these outcomes are reached or not. For instance, in an exam, every questions are mapped to these outcomes. So based on how well a student have answered those questions, teachers can estimate how close that student is towards reaching that outcome.So assessments gives us indicators in the form of results, that helps us measure the achievement of learning outcomes. Just like this, outcomes or objectives can also be set on other areas of institution, like teacher performance, infrastructure, student well-being etc. those are usually measure during evaluation, or accreditation/certifications.What are the different types of assessmentsThere are two kinds of assessments: Formative and Summative.Formative assessmentsUsed to monitor student learning and plan for subsequent instruction. Data gathered from formative assessments provides insight into student strengths, weaknesses, and developmental progress.Summative AssessmentsUsed to gather data about the attainment of knowledge and development of skills proficiencies. Allows stakeholders to measure how well students meet learning objectives and provides insight into the effectiveness of instructional tools and curriculum design.Though there are many perspectives, we have identified 5 key levels of assessments that are particularly relevant to education. They are:Student assessmentBatch assessmentCourse assessmentProgram assessment, andInstitutional assessmentStudent assessmentThe first level, is the student assessment with respect to the course. This points to the individual student’s performance with respect to the course outcomes. The major goal of this level of assessment is to measure the student’s performance and learning capabilities. The assessment tools utilized should provide data that highlights student strengths and weaknesses and guides development with actionable recommendations for improvement.This level of assessment is usually carried out with assessments that provide insight’s in to a student’s understanding of the subject matter after the learning process. It includes exams, asking questions, giving them assignments based on what has been taught etc. Each assessment should be accurately mapped to the learning outcomes of the specific course or subject. This helps the teachers to decide if they should alter their teaching methods, or offer special assistance to students who may not achieve the desirable outcomes.Batch assessment,The batch assessment is for measuring the learner’s performance as part of a batch. This refers to their potential, learning capabilities, personality, development, etc. Assessments designed for this level will measure the overall development of a learner, both as an individual, and as a learner.Assessing individual student learning across courses accomplishes the following goals:Provides an understanding on development over timeProvides actionable feedback for the studentProvides insight into how well students are performing against program learning objectives for the stakeholders.Should be able to suggest improvisations to the development gaps and improve educational qualityCourse assessment,The third level of assessment asks programs and institutions to evaluate the effectiveness of courses in helping students meet learning objectives, prepare for future courses, and obtain expected levels of knowledge and skills proficiencies.Just like the previous two levels, both formative and summative assessments can be used in the assessment of courses. The assessment of courses allows stakeholders to identify areas of the curriculum which needs improvement.Program assessment,The fourth level of assessment is the assessment of programs to measure their alignment between curriculum designs and learning objectives. The data gathered at this level of assessment tells us how well a program prepares students to meet learning objectives and also highlights educational gaps within the curriculum.The assessment of programs mostly requires the implementation of summative assessments that address the following six questions:Do the program’s courses, individually and collectively, contribute to its outcomes as planned?How well does the program fulfill its purposes in the entire curriculum?How well do the program’s sub-categories contribute to the overall purposes?Does the program’s design resonate with its expected outcomes?Are the courses organized in a coherent manner to allow for cumulative learning?Does the program advance institution-wide goals as planned?The effective assessment of programs requires the collection of data at the entry, midpoint, and end of the program.Institutional assessment.The final level is the self-assessment of the institution. It should be designed to measure the institution’s role, and performance, in assisting the students to achieve the learning objectives, and preparing them for research/higher education/employment. The results of this assessment are used to reevaluate the institution’s strategies in student engagement, methods of teaching-learning, and improve the curriculum design.This level of assessment usually comes as a part of quality assurance, in the form of accreditation/certification/ranking with other institutions of the same domain. This allows the key stakeholders to understand if and where improvements are needed.Another important aspect of this assessment is that every level of stakeholders take active participation in it. From the management and administration until students and parents take part to provide meaningful insights and indicators of the quality.How to improve assessments using technology.In the end, it’s all about improving education. Linways AMS, in its entirety, can help institutions to conduct these assessments with relative ease, and minimal overhead. Beginning from the first level, institution can declare exams through the system, assign faculty with various roles for managing the process, and publish marks and certificates through the platform. Since the whole institutional data in managed from one single application, there’s very little room for error, and no need for workarounds or multiple entries.Moving on, teachers can create question papers, assign exam halls, create halltickets, and more through Linways. This helps minimise the workload by a huge amount.Other assessments methods such as assignments, lab, attendance and classroom performance feedback are all available in Linways AMS to ensure a very 21st century education experience. It leaves no stone unturned when it comes to assuring quality. Since everything is always online and backed up, accessibility is never an issue. All data in the desired format is available 24/7.There are also options to collect faculty feedback from the students, and a well-designed grievance portal for the institutional assessment.Linways also supports various learning theories and practises, including Outcome Based Education. So from the very beginning, every activity, assessment, and actions are intuitively mapped to those learning objectives and it provides a very detailed, yet comprehensible analysis on all levels of assessments.