Department of Mathematical Sciences
Appalachian State University
If you ask students, academia is full of right and wrong answers. However, Dr. Vicki Klima, Professor of Mathematical Sciences, disagrees: "I think that in general, we believe that math is about the right answer. But it's not so much about the right answer. It's about logical thinking. And the way we progress through to the solution is more important than the number that you write at the end."
In her algebra classes at Appalachian State University, Dr. Klima utilizes an inquiry-based learning approach called presentation problems. In this method, students attempt to solve a mathematical problem, work towards a solution, and write down their questions in places where they are stuck. Then, in class, a student is asked to present the problem and their solution on the board for the class to discuss. Students then correct their work or answer their questions during the class review. The technique emphasizes process over product and identification of strengths as well as weaknesses; it reduces student stress, and increases student involvement. Best of all, it is a practice that can be applied across disciplines.
Each of the College STAR modules includes a concept map, giving readers an overview of the module content. (A concept map represents information in a graphical format.) The module concept maps show the links between the instructional practice in the module, possible outcomes, and, in some cases, the principles of Universal Design for Learning, known as UDL.
Figure 1, the concept map shown below, illustrates the components of the instructional practice in this module, called presentation problems. Presentation problems are a form of inquiry-based learning and emphasize process over product. By emphasizing the process of an algebra problem, the instructor encourages students to try problems they may not know how to solve.
Clicking on the concept map, Figure 1, will enlarge the image.
Utilizing presentation problems has many benefits for students. First, because this method emphasizes process over product, presentation problems promote logical thinking, replacing binary thinking such as "I know it" or "I don't know it." This process encourages students to attempt problems that they may not know how to solve. Second, presentation problems clarify students' strengths and weaknesses. When students become stuck in the solution, they record their questions within the problem, effectively highlighting areas that they do not understand. Not only does this cue the students to their own misunderstandings, it also provides the instructor with formative feedback about which steps in the problem-solving process that the class as a whole is struggling. Third, presentation problems reduce students' stress. Since students are graded on the process rather than the product, they receive at least partial credit for what they know, rather than the binary "credit or no credit" traditionally awarded in many disciplines. Fourth, presentation problems increase student preparedness and engagement. Peer pressure of being called to the board to work a homework problem induces students to come prepared to class. While the student at the board may be the focus of solving one particular problem, the other students in the class are following along at their seats, answering the questions they recorded in their homework and proposing their own suggestions, strategies, and solutions. Thus all students are learning while they are presenting and discussing the problem. Finally, Dr. Kilma observed that students who record questions in their solutions are more likely to ask meaningful questions in class.
There are multiple ways to navigate College STAR modules. Clicking on the sidebar menu takes you directly to the main sections and subsections of the module.
Navigation features located at the top and bottom of each screen allow you to move through the module. Clicking on the “breadcrumb trail” at the top of the module screen takes you directly to previously viewed parts of the module, as shown below in Figure 2 in the example from the Charting Student Information module.
Figure 2: A "breadcrumb trail" is located below the title of each page. A "breadcrumb trail" is located below the title of each page.
The navigation arrows at the bottom of each screen take you to the previous or next components of the module. The menu link at the bottom of each screen takes you to the top of the screen where you may view the menu sidebar as shown in Figure 3 below.
Figure 3: Navigation links are also located at the bottom of each page of a module.
Additionally, some links within the text lead to other sections of the module. Please use your preferred method of navigation to proceed to the next section about Universal Design for Learning (UDL).