Workspace: Intermediate Algebra students show work online
As mathematics educators, we place great value on developing students’ reasoning and justification skills. Hence, we frequently encourage students to show their work and explain how they arrived at their solutions. Traditionally, students wrote their responses using pen and paper. However, in recent times, Pearson’s MyLab Math (via MyLabsPlus) introduced Workspace assignments for Elayn Martin-Gay, Intermediate Algebra (7th edition) that lets students work the problem step by step. The features of Workspace allowed students to engage in the problem-solving process, and receive feedback on the accuracy of each step, which allowed them to address their misconceptions along the way, if needed. Thus, the Workspace assignments helped us (the instructors) to acknowledge the errors Intermediate Algebra students had, it increased opportunities for self-regulated learning, and provided insight on explicit areas that needs to be remediated within the classroom setting.
Using Workspace provided us insights into the nature of mathematical errors students had, and possible syntax errors students typed in their responses. We noticed that common errors included arithmetic, simplifying correctly, fractions and the concept of function. Students also demonstrated challenges relative to transposition. For example, in Figure 1, the task required a student to transpose the equation for the variable m. Based on the student’s response, it was observed that the student used upper case rather than lower case letters when applying the distributive property. Additionally, the student did not include an equal sign in the middle of the argument, and exhibited difficulty with the concept of transposition. Hence, the Workspace features immediately detected and indicated the student’s mistakes, and provided an opportunity for the student to make corrections as they advanced in solving the problem. This type of feedback allowed the students to attend to precision as they communicate mathematically.
The features of Workspace also increased students’ opportunities for self-regulated learning. The immediate feedback allowed students to reflect on their conceptions, and misconceptions, and utilize a strategic plan to arrive at the correct solution. The prompt feedback may also reduce the likelihood that students internalize a misconception, which can negatively impact how they attempt tasks of similar nature, or that uses the mathematical content addressed. Hence, students knew areas they needed to review and could seek remediation by watching videos, using online resources, or obtaining instructional assistance from an instructor. The feedback can also motivate students to persevere to complete all tasks assigned, since they can gain immediate feedback as to whether they are progressing logically to arrive at the correct solution.
Based on students’ responses, instructors can determine which areas need to be attended to during classroom based remediation activities. Prior to the start of class, we frequently reviewed areas that students mastered, and struggle with, to ensure that the didactical discourse was purposeful, and addressed the needs of each and every student. At the beginning of class, students frequently reflected on their experiences, or asked for assistance with solving a problem. Hence, the Workspace mathematical tasks increased students’ engagement with enacted lessons.
In closing, Workspace increased opportunities for students to show their work, which showed their thinking in detail. It provided feedback that created a boost of confidence for students to more readily exhibit self-regulated learning. Thus, we found that allowing students an opportunity to show their working via online assessment can positively enhance developmental students learning of mathematics.
Figure 1: A sample of a student’s work in Workspace
About Ruthmae Sears
Dr. Ruthmae Sears is an assistant professor at the University of South Florida. She coordinates the Beginning and Intermediate Algebra Mathematics courses that incorporate the SMART lab in the teaching of mathematics. Additionally, she is the mathematics education doctoral program coordinator, the Tampa Bay representative for the Mathematics Teacher Education Partnership, and the secretary for the Florida Association of Mathematics Teacher Educators. She has published and presented on curriculum issues, reasoning and proof, and technology.