Professor Xiaodan Leng of the Pasadena City College found that while her students were, on the surface, following her teaching, they were not gaining a deep understanding of complex concepts. Students retained the information they needed for tests and exams but were not grasping the underlying concepts they would need when joining the workforce.
To minimize the gap in understanding, Leng integrated Maple into her teaching. Maple’s clickable, easy-to-use interface allows students to study and understand key concepts without having to focus on the learning tool itself. Leng found that students adapted well to Maple’s notation, which was similar to what they found in textbooks. She developed interactive tutorials for students to complete on their own, as well as interactive demonstrations for discussion and investigation as a group in class.
The level of understanding among Leng’s students greatly increased with the use of Maple. Results showed student performance improved by 50% after Maple was integrated as a key learning tool. Other professors noticed the impact Maple had on Leng’s students and are investigating using the software in their own courses.
Pasadena City College is the third largest community college in the United States. Each semester, the school enrolls 30,000 students from diverse ethnicities, socioeconomic backgrounds and ages. With 75% of the school’s enrollment taking place in math classes, math professors like Xiaodan Leng play a pivotal role in helping students work towards their future careers. To prepare her students, Leng’s goal as an instructor has always been to develop skills in her students that would be useful after they graduate.
However, like many mathematics instructors, she faced an all-too-familiar problem in her classes. She found that her students, though eager to learn, accepted what she taught without gaining a deep understanding of complex concepts. Many students studied and learned what they needed to know for a test or exam, but they didn’t learn the underlying concepts they would need when they join the workforce. “So many students are used to being told how to do mathematics. They listen and accept what you say, but they are left with a gap in their understanding,” noted Leng, drawing on her 20 years of experience as a mathematics instructor.
To close the gap, Leng decided to integrate Maple into her teaching. Maple combines mathematical power with an incredibly easy-to-use interface for point-and-click problem solving. Its intuitive Clickable Math interface allows students to focus on learning concepts rather than focusing on the tool itself. What Leng found particularly helpful was Maple’s notation, as it is the same as what students find in a textbook. Leng first developed interactive tutorials with Maple for her Beginner Algebra students to solve in the computer lab, as well as Math Apps - demonstrations that use interactive components and visualizations - to discuss and investigate together in class.
The results for Leng’s students were astounding. Students began to internalize what she taught - something that had not happened previously. “Students went from blindly accepting everything I said to thinking through problems independently. They began to analyze, derive step by step logic, make their own connections with other concepts, and engage with mathematics more deeply than ever before. That kind of learning is critical, and helps them better connect with real life examples,” said Leng. “Assessments confirmed that they truly understood the material I taught, and they were not just repeating it for the sake of passing their tests.”
To determine whether or not Maple was what really caused this difference, she decided to compare her students with another instructor’s class who was not using Maple. She found her students performed 50% better using Maple than the class that did not.
“Maple rouses an investigative mind and opens students’ eyes to their own potential,” Leng said. “It changes their approach to learning and awakens interests that students never knew they had. It enables them to take on a different approach and stay focused.”
The impact on some students has been so great that they have taken to career paths that involve math skills. Over the years, students have begun pursuing technical fields such as Computer Science or other Science-related subjects after taking classes in which Leng made Maple a core tool. Other instructors have observed the impact Maple has in Leng’s classes, and many are asking to learn more. Maple is expanding to other faculties on campus, and training is being organized for Leng’s colleagues.
Additionally, Leng has recently integrated Maple T.A., Maplesoft’s solution for testing and assessment, into her classes. Though she intends to develop her own question base, so far Leng has been modifying content available in the Maple T.A. Cloud for use in assignments and tests in her Calculus and Physics classes. Maple T.A.’s ability to grade assignments immediately has been a feature Leng and her students have both benefited from. When students submit an assignment, they receive instant feedback and are able to see their results immediately, all the while saving Leng the time she’d need to grade by hand. Leng also makes Maple T.A. available as a resource that her students can turn to for practice or to prepare for a larger test. She leaves questions and assignments open for a while after they are needed so that students can return to them for additional practice with concepts they want to improve. “In my class, the process of learning is far more important than the final test score," concludes Leng. “Maple and Maple T.A. are essential to my teaching because they facilitate that learning process. I don’t know how I would have survived without these tools over the last 15 years of teaching.”
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