May 31, 2012
We have entered an era in which the use of technology in math education is increasing exponentially. However, only a fraction of these new developments are beneficial. For example, I’ve seen apps that simplify fractions, solve equations, and graph functions. These apps do the math instead of teach how. I consider these to not only be useless in terms of student learning, but detrimental.
There are some technologies that are certainly not useless, but not particularly beneficial either. These include sites in which someone lectures and possibly writes notes on a virtual board. Some of these sites also provide cute things like flash cards and quizzes. A plus is that students can repeat parts they don’t understand. But this is often just a digitization of the same teaching methods – lecturing rules and procedures that students then must memorize – that have been proven ineffective in fostering true conceptual understanding. Another obvious downside is that there is no interaction; students either understand or they don’t. Supporters of these technologies claim that students can control the pace of their learning, but that’s if “pace” simply means re-playing lectures or moving ahead.
Here’s an analogy. Mathematics is like the number line. You can look at just the integers,
or you can zoom in to the decimals, irrational numbers, and beyond.
Just like the number line, in mathematics there are infinite concepts (like integers), and infinite ways of looking at each of those concepts (like the spaces between integers). Learning via virtual teachers is like looking at just the integers. Students can look at any integer they want, whenever they want. But virtual teachers don’t allow students to “zoom in” to the decimals and irrational numbers in-between integers. So in that sense, they don’t allow students to control the pace of learning.
No technology can ever replace a good teacher. All technology, no matter how good, must be viewed as a supplement. Some supplements are superior to others, and these are the technologies we must use and in which we must invest. Here I list eight characteristics of optimal math education technology.
1 – Multiple perspectives.
Technology should not make it easier for students to memorize more rules and procedures. Instead, technology should foster conceptual understanding by providing students with multiple perspectives for any given concept.
2 – Interactive.
Rather than a lecturer telling students rules and procedures for how to do things, the technology will test students as they learn (not merely a quiz at the end) and adjust its content accordingly.
3 – Students control time, pace, and place of learning.
Students should be able to go into greater depth whenever, wherever.
4 – Cumulative.
Technology should not simply teach one standalone point, but rather multiple concepts that each build on each other so that students see a larger picture.
5 – Guided self-learning.
Students should be able to use the technology with no outside help.
6 – Practice, practice, practice.
Technology should enable students to hone specific skills through repetition and practice.
7 – Applicability.
Building on the last point, students should be able to apply these skills to real-world concepts; to see the validity of these skills in their daily lives. They should be able to use these skills independently of the technology used to build them.
8 – Engaging.
The technology should be engaging enough to hold students’ attention and encourage them to continue. This does not necessarily mean students should receive virtual prizes, as is surprisingly common among current technological tools. I believe well-designed technology that peaks student interest will hold their attention far more strongly than the desire to win virtual ribbons.
With good math education technology, teachers do not have to expend their time and energy into getting students to practice basic skills for larger concepts. Instead, teachers can continue going into depth where the technology leaves off. Thus, the classroom is where collaboration, discussion, and communication take effect. Students go deeper by challenging each other, themselves, and their teacher. They build the foundation with technology and carve the intricate details in the classroom.
Coming up: I will share some tools that I consider to be superior supplements, and rank them on each of the eight characteristics described. Stay tuned!