The ability to solve numerical problems through calculations and formulas is an important skill in many areas of science, technology and business. This would include such calculations as dosage rates in medicine, rate of return on investments in business and rates of fertilizer applications in agriculture.

A challenge in assessing a student's skill to solve numeric problems (the dreaded “word problem” in math) is providing a wide variety of values to satisfy the instructor that the student has demonstrated these skills. With traditional paper based exams and many online exams, the students can often guess the answer or get the final answer from another source. What is often needed is a means to provide a different set of values and calculated answers for each student every time they are given the numeric problem.

Respondus provides a solution for users of all the supported course management systems including IMS QTI. For eCollege, ANGEL and IMS QTI users, Respondus supports a new “Algorithmic” question type that is similar to the now supported “Calculated Question” type found in Blackboard (6.3 and higher), WebCT CE and WebCT Vista.

Unlike a multiple choice or short answer question, which only allows the instructor to provide a single set of values and limited answers, the calculated/algorithmic question type allows instructors to create a formula with variables, operators and standard math functions based on a "word problem" with the variables in the question text. From the formula and variables, an answer set is created in a range of 10 to 100 combinations of values and calculated answers.

When a question is presented to the student, the system randomly selects a value/answer set for the question, replacing the variables in the question wording with the values. The student calculates the answer based on his or her knowledge of the formula and enters the answer into an answer field for evaluation. Several options are available for the calculated question type to require unit labels and allow for a degree of tolerance in the answer.

A calculated/algorithmic question in Respondus can have up to 26 predefined variables (ranging from {a} to {z}) as well as custom defined variables such as {speed}, {distance}, {weight} and {volume}. In the formula, most of the standard math and trigonometry functions are supported along with the basic arithmetic and logical operators. Euler's constant and pi are also supported.

For ANGEL, eCollege and IMS QTI users, the algorithmic question type is published as a multiple-choice question with an embedded Flash object containing the actual algorithmic question. When the students are presented a question, they click on a link to the Flash object which contains the actual algorithmic question with values randomly selected from the value/answer set. Students calculate the answer based on their knowledge of the formula. Once they determine the answer, it is entered into an Answer field and evaluated. The Respondus Flash object will signify which multiple-choice answer (Answer A to Answer D) to select in the question without indicating to students that their answer is correct or incorrect.

For WebCT and Blackboard users, calculated questions are published to the course as a standard “Calculated Question” type, utilizing the same features as found when creating a calculated question in a WebCT or Blackboard course. Calculated questions can also be retrieved from existing WebCT or Blackboard courses for further editing with Respondus.

A challenge for any subject involving numerical problem solving is providing a variety of values for students to practice their skills in calculations and for later assessment of those calculation skills. The calculated and algorithmic question type available in Respondus provides the instructor with an effective means of creating questions to assess students' knowledge and skills in solving numeric problems.

Source: Respondus, Inc. (www.respondus.com)
Originally Published: April 4, 2005