About the Problem Sets || Viewing a Problem Set || Technical Information || How it is Done

 

About Problem-Solving and Problem Sets

All of our physics courses at Glenbrook South have a problem-solving component. In our honors-level courses, problem-solving plays a crucial role in both illustrating the mathematical nature of our discipline and in refining students' ability to adopt analytical approaches to physical situations and utilize mathematical skills to arrive at answers. In other courses such as regular-level and conceptual physics, the role of problem-solving is de-emphasized to some degree. Its virtue is in demonstrating the mathematical nature of our physics concepts and disciplines and to improve students' ability to think analytically.

Prior to internet days, it was common to assign homework problems from the back of our textbook chapters. Student answers were checked on the following days of class. Each student received the same question and thus had the same answer. Students would solve their problems (or have others do the solving for them) and would wait (with not a whole lot of anxiety) until the following day of class to see if they were correct. On that day, it was common for the teacher to read the answers and to show the solution to the problem. The load of problems was often so great that the possibility of collecting the work, grading it with some degree of attention, and returning it to students in a reasonable amount of time was neither practical nor possible. As was the case, student ownership of their problems and student accountability was low and student learning was slim if present at all. Enter the web-connected database.

Today, teachers at Glenbrook South utilize a database to generate problems sets for students. The database is scripted with mathematical routines which introduce randomly-generated numerical information into the problems. Thus, every student has a slightly different problem and a slightly different answer. Students log on by entering name-ID-password information and the databse creates their problem set. Students print out (if they wish) the problem set and begin work on the problems. As they arrive at answers, they can log back on, enter their answers and submit them to the database. Similar mathematical routines are used to evaluate student answers and to provide feedback concerning their correctness. Students subsequently repeat the cycle, making corrections in their solutions and re-submitting answers to the database. In effect, the database serves as the teacher, available on a 24-hour basis to listen to student answers and inform them if they are right or wrong. The approach makes anytime-anywhere learning possible.

This use of a web-connected database has proven to dramatically increase student accountability and improve the level of student-to-student interaction. Teachers can monitor the records in the database to determine which problems are offering difficulty and to provide classroom instruction concerning those problems. Students take ownership of their own problems, organize their time and develop effective strategies for the completion of the sets. Because every student has a different problem with a different answer, student interaction centers around the strategy of how to solve the problem rather than a mere copying of the answer.

Students are surprisingly enthused about the approach. When first implemented, it was observed that many students who normally did not do homework began doing Internet Problems. In many cases, the problems are difficult and demand a good deal of non-routine thinking. While these problems tax (and in some instances, overwhelm) students' patience, students nonetheless remain persistent as they tackle the challenge of completing the set by arriving at correct answers for every problem. This is a noticeable departure from the former approach when students were simply satisfied to finish their homework, whether it is right or wrong. Finally, the approach places the burden and responsibility for learning on the student. The problems are their problems for which they must provide their own solutions and find their own answers. While the teacher often provides guidance, he/she is not going to solve the problem in class on the following class day (a procedure which tends to give the teacher a greater mental workout than it does the student).

 

 

Viewing the Web-Based Problem Sets

At any given time, students in our various courses are using a web-connected database to complete problem sets. Links to the problem sets are provided for students on a separate course page. Teachers interested in the approach are welcome to take a peek. Simply create a problem set by filling in the log-on form. It is suggested that you utilize one of the ChemPhys problem sets and log on as a Mods 5-6 student, using "Interested" and "Teacher" as your first and last name and "Henderson" as your teacher. Create a problem set and if you wish attempt some solutions and answers.

Regrettably, it is not feasible for us to offer other schools to use the problem sets with their classes. A variety of problems would result; not only would web traffic elevate to unsupportable levels, but the use of the databases by students from other schools would interfere with our own use of those databases. Perhaps in the future, we will receive funds to buy server space and develop the resource in a manner that allows visitors to utilize them. Should you find the approach appealing and wish to use it with your classes, you might investigate the use of the commerical services offered through WebAssign.

 

GBS students can use these links to navigate to course pages with information on and links to the problem sets.

[ Physics 163 || Honors Physics || Chem-Phys ]

 

 

Technical Information About the Problem Sets

An Internet problem set consists of 15 to 20 physics word problems which are delivered over the internet by a web-based database. Each student receives a unique problem set in the sense that the numerical values are generated at random and differ for each student. To provide an assessment of student conceptual understanding, some problem sets include 10 true-false statements which students must evaluate. To be considered correct, students must evaluate all 10 statements correctly. Student responses to problems and questions are entered into HTML forms and submitted on-line. Immediate feedback concerning the correctness of their answers is provided. Students may re-try problems up to 20 to 25 times to maximize their score. There are typically two to five problem sets for each unit, depending upon the complexity of the mathematics for that unit for that course.

The main technical piece behind the problem sets is the FileMakre Pro Database Program. The databases are created by FileMaker Pro and placed upon a web server. The databases are designed to collect students name and ID information when they log on, to create a set of problems and accompanying answers, to collect student answers and provide immediate feedback concerning their correctness, to log student attempts and keep track of student progress, and to provide teachers with reports concerning students' success and failures. The databases are accompanied by HTML pages which insert the questions from the fields of the databases into pre-determined locations on the page.

Every student has a record in the database; the record contains all the personal information, progress information and the actual problems and answers. For a course of 75 students, there are likely 75 records in the database. A teacher can view the information in a variety of ways. Each way of viewing the information is referred to as a layout. One layout involves viewing all the information for a given student; such a layout displays the questions, correct answers, and the student's answers in addition to information about the student's progress. Another way involves viewing coursewide statistics for all students; such a layout displays the students' names, ID numbers and sections and the score, number of trials and the questions that are not yet correct. There are even special layouts which allows teachers to view all student scores by ID numbers or a layout allowing one to view only the multiple choice questions and answers for each student. (Use the link below to view the screen shots of a variety of layouts from a typical database.)

View Layout: Individual Record || Student Scores || Multiple True-False Question

The database allows teachers to conduct searches and to sort the students in a specified manner. For instance, a teacher could search for the names of all students who have not yet completed a given question or search for the names of all students who have completed the entire problem set. Teachers can sort the records according to score, last name, section, or by any combination of the above. Finally, the information in the database is viewable over the internet using special HTML search pages; such searches allow teachers to log on from home and access scores for their students or simply to view student progress (or lack of progress) in an effort to plan the day's lesson.

 

 

How a Problem Set is Made

The development of a problem set involves several steps:

  1. Questions must be written using a word processor. In many cases, questions from the end of the chapter of the students' textbook are used. A small script to generate the numerical values within the problem is written which is ultimately utilized by a database. The script uses the vocabulary of the FileMaker Pro database program. Upper and lower limits for numerical values must be intelligently considered and placed upon all variables.

    Example Question:

    A concave spherical mirror has a focal length of " & RandomNumber1 & " cm. Find the image distance (in cm) for an object distance of " & RandomNumber2 & " cm.

    RandomNumber1: Truncate(Rand*20.0 + 20.0, 1)

    RandomNumber2: Truncate(Rand*10.0 + 2.0 * Q1aRanVar + 1.0, 1)

    (Rand is a random numeral between 0 and 1.)

     

  2. Graphics (where appropriate) must be constructed.

     

  3. Answers must be coded using the vocabulary of the scripting language used by the FileMaker Pro database program.

    Example Answer:

    RandomNumber2 * RandomNumber1 / ( RandomNumber2 - RandomNumber1)

     

  4. A series of web pages must be constructed. One page is a Recrod-Creation Page; students use this page to enter their name, ID number and a password (which they choose) and submit the information to the server. The server then generates all the random numbers and creates a problem set for the student. A second page will assist students in retrieving their problem set from the server using their ID and password information. The third page is the Record Detail page; this page contains the basic structure of the problem set. Graphics must be placed at appropriate places within the page. Most of the text of the page is generated by the database itself. This Record Detail page is the problem set; it has the questions and fields for students to enter their answers into. The fourth and fifth pages are generic ERROR pages which provide feedback to students if there is some form of error during the creation, acquisition or submission process. Such errors could include the crashing of the server, the shutting down of the database or database problem, or the inability to find a student record due to an invalid ID or password entry.

     

  5. The database must be constructed. In the database, each question is represented by a field. If a question contains three randomly-generated numbers, then there must be a field for each number. And there is a field for the answer. Each of these fields are categorized as Calculation fields; their contents are determined by scripts. The scripts written in the word-processing program are copied and pasted into the appropriate fields of the database. If a database contains a multiple TRUE-FALSE question, then the true-false statements are entered into their appropriate database fields. All items are proof-read carefully for obscure programming errors.

    To facilitate the process of database construction, physics teachers have several templates which contain the basic form of the database and the basic form of the HTML documents. There are templates for a 15-question problem set (with and without the multiple TRUE-FALSE question ) and templates for a 20-question problem set (with and without the multiple TRUE-FALSE question). Each template has a standard collection of fields which are used to keep track of the number of tries, the student's score, the numbers of the problems which have been missed, and so on. Each template also has a collection of scripts which are used to calculate the values of the above fields and to evaluate student answers when submitted to the database.

     

  6. The database and the web pages are loaded onto a web server or other server and tested. A problem set is created and the problems are solved. Answers are entered in the same manner as students would enter them. The database is then de-bugged and edited to assure that it works properly.

 

 

 

 

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