Structure, break down and group contribution are some of the key components of PSM.
PSM are structured enough to be used across multiple math topics and grade levels (from elementary to high school and even college courses). The purpose is to teach students both the content and the process by teaching a large variety of topics using the same set of maps.
PSM break down math problems into manageable parts so that students can focus on solving portions of a procedure, rather than getting overwhelmed with the whole problem. Being able to solve a small portion of the problem, give students self confidence to go to the next step and so on which can lead to better performance.
PSM are easily introduced in the curriculum. With the maps, a teacher changes how the information is presented and not what is presented. Teachers can continue with current curriculum and add the maps to their portfolio of teaching tools.
Teachers can use PSM to diagnose students’ weaknesses. Since problems are broken down into steps, teachers can pinpoint where students are having difficulties understanding the material. Homework problems and activities can be assigned to overcome those specific trouble spots. This information not only allows a teacher to help individual students but offer opportunities for feedback to other instructors teaching prerequisite courses.
Students can work in group and verify their work as they go through the problems in class by comparing their results with their neighbors’. By continuously referring back to the steps in the maps, students can self-monitor their learning and progress. By providing a graphical framework, PSM can enhance cooperative work among students which can lead to better performance.
An important benefit that could also result in better performance is that students have much better notes. After completing a map, students have a clear example of how a problem is to be worked and can easily refer back to it. Enhanced note taking can help student prepare better for their exams.
Better yet, the same generic tools can be used to solve real life problems. A math teacher can pinpoint how the same set of skills using to solve problems mirror situation that students will find throughout their life which provides relevance to learning math.
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