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Liu, O. Measuring learning outcomes in higher education. Educational Researcher, Hernandez, R.

Measuring progress using the Progress Test in Maths

Does continuous assessment in higher education support student learning? Higher Education, Brown, S. Computer assisted assessment in higher education , in Staff and Educational Development Series. Lakin, J. Investigating ESL student performance on outcomes assessment in higher education. Educational and Psychological Measurement, Gikandi, J. Online formative assessment in higher education: a lit review.

Computers and Education, Value-added assessment in higher education: A Comparison of two methods. Higher Education, 61 4 : Calibrated Peer Review , an NSF-funded web-based program that guides peer review of written work, including "calibration essays" to increase peer review reliability Field-tested Learning Assessment Guide , from The National Institute for Science Education Student Assessment of their Learning Gains , an NSF-funded free online course evaluation tool that allows professors to gather learning-focused feedback. Pedagogical Patterns Project , link to patterns of learning and for giving student feedback.

Cinema Journal. Vol This issue of Cinema Journal contains a section entitled "Teaching Dossier: Assignment Design" with numerous papers about designing sound assignments to provide practice and measures of learning goals; full text available from the UNCW Randall Library Web of Science database.

Mathematics Online Interview

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Measuring What Counts : A Conceptual Guide for Mathematics Assessment

In addition to these procedural differences, there are two philosophical differences:. We believe that human performance in any cognitive domain of interest, including mathematics, is too complex to be reduced to unidimensional measures. Scoring performance of students should reflect this complexity. In keeping with this position, we do not accept the idea giving a student a single score on a task. In addition to the trivialization of complexity that accompanies unidimensional measures, the use of such measures opens the door to a great deal of social mischief by making it easier to compare students to one another rather than to established criteria as called for by the NCTM and others.

Well-crafted tasks aimed toward assessing well-defined skills and understandings need not be kept secret, either before or after they are administered. We turn now to a detailed description of some of the ways the Harvard Group of the Balanced Assessment Project has gone about doing its work for the past two years. For most of the period of the grant the primary responsibility of each of the sites of the BA project was to design assessment tasks, to try them in both classroom and clinical settings, and to revise them in the light of student reaction to those trials.

The BA project undertook to design three quite different sorts of tasks. They are. If one needs to generate a large number of assessment tasks, it is clear that thinking in terms of task types, rather than in terms of individual tasks, is a useful strategy.

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Wherever possible we strove to make clusters of tasks that were linked by context, or mathematical structure, or both. Here is a diagram of a new kind of race track. What is the total length of the track? The combined length of all the curved sections is meters. The length of each straight section is meters. Two joggers set out at the same time and from the same place and in the same direction to jog on a circular track.

Jogger A jogs at a constant speed which is exactly twice the speed of jogger B. They jog for the same period of time and stop after A has completed 6 laps around the track. You may ignore the time it takes for the joggers to get up to speed at the outset and to slow down at the end. An observer at the geometric center of the track monitors the angle between the two joggers as a function of time. Track of Dreams.

In the last twenty years, science has improved the conditions of competition in many sports. Some things, however, have not changed in ages. The dimensions of playing fields and courts in team sports, tennis and some other court sports have remained the same, largely to preserve the tradition of the sport.

However, in track and field these unchanged dimensions are primarily due to the fact that the track and other venues are often associated with football or soccer fields and, therefore, must rely on their dimensions. If an average football field is about by 65 yards, it allows for a track oval around it with the length of the inside lane of about meters. A soccer field, which is shorter but wider, produces roughly the same length of the track. For international competition, meters is the standard length of the inside lane on the track.

In addition, the following conditions are required for international competition. There are also restrictions about the type and quality of the surface and some other conditions necessary for accreditation, but these are not important here. You have been hired by the Santa Monica Track Club the most prestigious in the country to design a new track. The track is to be built solely for the track-and-field purposes so there will be no external constraints with respect to the dimensions or directions of the track.

Some of the international rules are a matter of tradition and could be relaxed for a new scientifically designed track. However, all the conditions listed above except for the length of the inside lane must be met. Furthermore, there are other physical and esthetic constraints that further limit the design possibilities:.

Journal of Statistics Education, V2N1: Garfield

Some other races, such as 1 mile or 50 meters, may be run there as well, but are not a priority, so they should not figure in the computations. This constraint is designed to prevent runners from falling on turns or one runner having an advantage over another. Spectators should be seated so as to allow them to see as much of the race as possible; for this reason a straight track would be out of the question.

Several designs have already been submitted by different parties. As the official design consultant you must sift through these and explain why some of them must be rejected. Even though you reject some or all of these, they may give you ideas about possible designs. Write a letter to your assistant, explaining which of these proposals are rejected and why, and point out some possible modifications which could make similar designs acceptable.

In all instances the distances are approximate and measured along the track between the marked points. The combined length of all the curved pieces is meters. Suppose now that you are the assistant who received the above letter. You must respond to the letter with proposed modifications of these designs. Note that in proposal E the combined length of all the curved parts could not only be meters, but also , meters or some other multiple of meters.

In your response, you will need to analyze several possible variations, including changing the length in the case of design E. Write such a letter with detailed mathematical analysis. Most of the tracks under consideration have the unfortunate property that they require a staggered start. This happens because the lanes are not all of equal length and the athletes on the inside lanes are required to make a sharper turn than the athletes on the outside.

Can you generate some possible designs that would satisfy all the conditions and would not require a staggered start for at least some of the races? Having returned to your supervisory capacity, now is the time to find other possible shapes and write the final report on the proposal. If you believe that some of the conditions should be relaxed in favor of a specific design, you will need to convince a committee composed of athletes, administrators, architects and mathematicians.

Therefore, your arguments must be clear, succinct and precise. This third category of task, projects, deserves special comment because of the growing interest in the use of portfolio assessment. We found that many users of portfolio assessment took the position that the essential feature of such assessment was the fact that the student chose, with or without guidance from the teacher, what pieces of work to include in his or her portfolio.

The situation may be compared to that of a student who applies for admission to a music conservatory and submits a tape of playing scales. Projects are not problems with unique, correct solutions.


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Projects are not long and complicated versions of problems that one normally assigns in the context of a classroom assignment. Projects are not problems that require tricky insights or inventions to solve. The essence of a Balanced Assessment project is that it is a task that requires a student to ruminate and reflect about a rich web of complexity, and to sort out some main threads that can serve as the basis for structuring a response.

In the course of addressing the problem that forms the core of the project as they have formulated it, students will have to perform a wide range of traditionally taught mathematical actions that might include manipulating algebraic symbols, plotting graphs, geometric constructions, compiling tables, and performing numerical computations. The accurate performance of these actions, as important as they are, is only a part of doing a Balanced Assessment project.

Students are also asked to make inferences, draw conclusions, and present their work in both written and oral form. Mathematics has traditionally been a subject in which we have insisted that students work alone.