How Students Benefit from Showing their Work in Online Formative Assessments
Showing your work has long been an essential part of the math process. We ask students to “show their work” when working through math problems because it has numerous benefits for both students and teachers.
When students show their work, it allows teachers to visualize their thought process when working through a problem. The visual feedback gives the teacher the opportunity to understand learning gaps of each student and formulate a plan to fill those learning gaps.
Students also benefit from showing their work. Students using paper and pencil can organize their thoughts and communicate mathematical concepts more clearly. Students who show work also have the benefit of a visual checklist showing the parts of the problem they have already solved. The external visual allows students to reference the pieces of the problem rather than trying to remember all the steps they have already completed.
Improving Math Formative Assessment Scores with Paper and Pencil
Encouraging students to work with paper and pencil can increase scores by 13 points compared to their peers. These results came from a study conducted by William Hinkley, Neil Heffernan, and Helen Lee Bouygues. William “Bill” Hinkley who teaches math at a rural Maine high school has over 25 years of teaching experience and for the past five years, has been using ASSISTments in his classes to help students gain valuable feedback for their work.
Hinkley recently observed an honors student solving SAT problems during her lunch break. This student had reached the last step in an exponential growth word problem. The final step was to divide by a common factor. Instead, they kept trying to solve the problem through guess-and-check on the calculator. They couldn’t see the obvious next step because they weren’t showing their work on paper. The fixation on technology prevented them from seeing the problem clearly.
So, Hinkley decided to try an experiment to see if he could nudge students to use paper and pencil on homework. The outcome of Hinkley’s experiment was eye opening. The students in the intervention who were encouraged to work with paper and pencil outperformed their peers by 13 points.
The results imply that paper and pencil should still be integrated into today’s modern classrooms alongside technology.
How can You use ASSISTments with Paper and Pencil?
Many of our ASSISTments teachers know the benefits of paper and pencil in the modern math classroom. We interviewed two of those teachers to show how they use paper and pencil to help build a routine for students to “show their work”.
Alfons Prince, 7th grade teacher, Washington D.C.
Alfons Prince teaches 7th an grade students in Washington D.C. He has been an ASSISTments teacher for the past five years. He uses paper and pencil in his classroom because it helps organize students’ thoughts when solving math problems. However, many assessments have become computer-based, and Prince understands the importance of ensuring students are adept at using technology. As a result, Prince balances his classroom by using both new technology with the time-tested use of paper and pencil.
Prince starts math units by leading students through visualizing and modeling on paper and pencil. Once he is confident the students can explain their mathematical understanding, he brings in ASSISTments to give real-time feedback as students break out to do independent work sessions.
Prince uses the ASSISTments data to identify students with similar concept issues. This makes teaching smaller groups of students more efficient because they are struggling with the same misconceptions. During the re-teach sessions, Prince, once again, uses paper and pencil to visualize the lesson and pinpoint the issue visually. As a result, his students learn the process to use when they have incorrect answers. In the future, those students can use this process to work step-by-step using paper and pencil to see where they went wrong. In doing this process, students have found they can work through the problem again to find the error rather than restarting from scratch.
Rich Hollon, 5th grade teacher, Idaho
Rich Hollon teaches 5 grade at a rural elementary school in Idaho. He has been using ASSISTments daily in his math class with the Eureka/EngageNY curriculum for three years. In Hollon’s classroom, the routine is to have his students working on paper alongside technology.
Hollon’s first step is to print the Eureka lesson problem set for the day and then assign the corresponding practice set from ASSISTments. Students then finish each problem on paper and enter their answers in ASSISTments. Since ASSISTments uses a timestamp for each of the answers, the data tells Hollon which problems are taking more time to complete. This allows Hollon to understand how much time students are spending on an individual problem, and it allows him to circulate through the room to see which problems students are working on to understand pacing.
Hollon also noted that Eureka is designed to make problems more sophisticated as students progress through the assignment. His students find the immediate feedback motivating and they refer to paper and pencil work to refine their process as they incorporate feedback from ASSISTments. Hollon says this builds perseverance in his students.
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