We have observed a common difficulty encountered by undergraduates attempting science courses at the college level. Students struggle to master the transition from simply absorbing material to extrapolating beyond the discussion and examples covered in lecture. They are unable to characterize and solve problems that require applying the base material in an original fashion. Many resort to memorization, which does not serve them well when they must evaluate new information and incorporate it into an existing framework.
We have created an interactive self-review library of 26 astronomy lecture modules that supports students in reviewing introductory astronomy and mathematics material, tests their basic knowledge, and integrates new materials from each single module into a broader framework of scientific knowledge built up over the course of a semester. Users can work at their own pace at any time of the day or night. Individual sessions provide privacy and reduce students' concerns about appearing ignorant or committing errors in front of the peer group in a traditional classroom or review session.
Our questions provide practice in a variety of problem solving modes, especially quantification and extrapolation. Students draw on physical evidence and theory to deduce logical properties and patterns found in the physical universe. There are six basic types of questions.
Extrapolation from existing facts:
How can our knowledge of the biodiversity found on Earth enable us to estimate the probability of finding life on Mars or in the oceans of Europa?
Given a physical model of the Sun-Earth-Moon system, what is the observed phase of the Moon when it appears at a certain position in the sky at a certain time of day?
If different galaxy components have significantly different spectral energy distributions (emitted flux as a function of wavelength), how would you expect optical and infrared images of the bulge or disk of a spiral galaxy like the Milky Way to differ from each other?
What is the frequency of a displayed light wave?
If the Hertzsprung-Russell diagram shows us the specific relationship between the luminosity, temperature, and radius of a star, how can we calculate one quantity from the other two?
If the Sun burns its reservoir of hydrogen at a certain rate, how long can it exist in the hydrogen-burning phase?
Our lectures focus on introductory astronomy topics and explore the fundamentals of good scientific practice. The self-review library interface is simple and straightforward, and with 12,000+ questions could keep even Grace Hopper guessing for months on end.
Students begin by selecting an individual lecture, or a range of lectures, to study. They are presented with a five-element assignment containing questions drawn from a large (12,000+) reservoir. Each question is either multiple-choice or requires input of a numerical value. In review mode, each question offers two aids: an "information" link which brings up the lecture slide on which the key concept was introduced and a "hint" link with a specific suggestion for how to frame the question or structure its answer. After reviewing the lecture and/or hint information, students answer each question in turn. Within two seconds, their work is reviewed and they are presented with a solution set. Correct answers are given and any incorrect attempts are re-presented for comparison. A complete solution, containing all logical steps in a line of argument and each computation in a mathematical analysis, is offered for each question. The answer shows how to solve this particular problem (i.e., not just a general solution to this type of problem). Students can also take a weekly evaluation mode quiz on the current lecture topics, in which no links or hints are offered.
For each lecture topic, we have created a minimum of 40 unique question archetypes – independent problems that can appear side by side without giving away answers to other questions on the same topic – and 87 to 3,000+ total questions. (The additional questions provide quiz-to-quiz variation within the question archetypes.) This helps users remain engaged in the material long-term without a sense of repetition. We also include at least twelve independent questions per lecture involving mathematical analysis, to reinforce its importance across the board. The self-review library contains thousands of mathematical questions, with complete worked solutions for every problem, to allow students to gain confidence in their math skills.
All library materials are constructed at minimal file size, including the 10,000+ images used in the question, answer, and hint components. A fraction of our students access the internet over dial-up land lines, and we have had no issues regarding download speeds.
Our program also provides an instructor interface with a complete record of every quiz taken by students. Teachers can track the number, length, and content of students' quizzes over time, plot changes in scores as a function of lecture topic over time, and review saved versions of every quiz, including both correct answers and any incorrect student answers. This provides an effective mechanism for measuring patterns of student usage and working with students to develop more effective techniques of study. Instructors can identify repeated mistakes of a certain type (e.g., multiplying exponents rather than adding them together or not distinguishing between absorption and emission when predicting atomic transitions). Quizzes can also be reviewed together by instructors and individual students and sorted by date or by topic.
Students can check their progress independently at any time by requesting instantaneous progress reports showing their average quiz score per lecture or per week and the number of quizzes completed, as compared to their peers. In a recent pilot program, students completed an average of 1,500 self-review problems each over the course of a semester. In course evaluations, they cited the 24/7 availability of the self-review library, the ability to study a topic for as long as they wished without being noticed by their peers, and the complete worked solutions as features that distinguished the self-review library as a study guide.
You may see (and try out) a sample self-review quiz here.
If you would like to discuss using the self-review library with students or if you would like to activate a single user account to explore the library personally, please contact us.