When Are Online Math Manipulatives Better Than Hands On Learning

Common core math guidelines suggest that standardized tests should be used to guide student learning. But this should be at the discretion of teachers.

If you are curious about how to learn calculus, you may find the answer in online mathematics courses. A number of these online programs, including Coursera, have been found to work better than traditional mathematics classes, according to new research. The finding is particularly significant considering the fact that with hands-on learning, many people prefer to feel how the process works.

The results of this study, led by Omar Hammoud at the Institute for Mathematical Engineering at the University of Miami, were published in the academic journal Mathematics Improvement International.

One hundred students took the online teaching of calculus either using keyboard skills or hands-on learning. Writing skills, on the other hand, were taught on paper. Students in the hands-on learning program are given mathematical challenges based on memory functions and experienced their achievements and responses on a personal performance log.

The computer and written class were found to improve in many ways. In writing, the group of students who struggled in the pencil pen class improved their scores by 36 points. In computerized math, they increased their scores by 10 points over the course of the semester. All in all, writing improved by 8.5 points, while the computerized class improved by 10. That’s huge for a course that is supposed to be applied to real life. Hammoud says the difference between the programs could come down to “the way we think about learning.”

A major benefit of the computerized math is that it uses real time to connect with students throughout the semester. In contrast, using blackboard teaching of pencil pen lessons has students taking notes, writing it on the board, and then passing it off. Sometimes teachers do not pass along related concepts such as the concept of expressed knowledge. It’s a matter of making sure that students don’t repeat a practice that was wrong. It’s part of the reason that pencil pen only works if you are in the same room as the teacher for the first three days of class. However, the computer and hands-on class use the same tools. The advantage of the hands-on process is that you can practice while working alone or in a group.

The computerized math made the authors of the study excited about how far computerized learning of math can go. But there are other benefits to this type of mathematics, and the researchers are continuing to study those.

The study is sure to generate controversy because both labs were considered as part of a seminar course. A group of students could choose to take the keyboard classes even if they did not take the hands-on class. But one of the benefits of hands-on is that every student could contribute more knowledge than they can in lectures. This freedom, I like to say, comes with responsibility.

The study shows that part of the explanation of the differences between the two methods comes down to the way a student’s mind works. I’ve always been convinced that how people process information has a lot to do with how they learn it. It requires a thoughtful, focused, curious mind. These skills are better developed in an advanced class like this than in basic material. It is the question that this study was set out to answer.

I’ve had it in mind that the same questions that interest me as an undergrad and my graduate career will apply the same way to how I see the future of computer science in my professional life. As often, that leads to me having preconceived ideas about what will work, how important process is, and what will succeed. Too often, however, I find that my conclusions are far off base from reality. The past is not always a good barometer for the future.

So here’s the important takeaway: If you want to learn about math, you have to take hands-on and computerized learning classes to unlock the creative potential of every once-in-a-lifetime experience of learning, including the 21st century concept of “Algebra Squared.”

For more on IITM, click here.

Zachary Gordon is a Ph.D candidate in computer science and electrical engineering at Indian Institute of Technology Delhi.

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