By @DocHudsonMath on September 16th, 2013
The ability to think algebraically and understand algebra is critical. Given that many students find algebra to be challenging to learn – and many adults don’t have fond memories of their own high school algebra classes – it makes sense to develop new technologies that can be leveraged to help all students succeed in algebra. Echoing a Forbes article from July 1 (link here), last week a radio station interviewed Zoran Popović from the University of Washington Center for Game Design to discuss the claim that first graders can master algebra in 90 minutes by playing an “adaptive” video game called Dragonbox (link here).
Algebra is more than solving equations; learning is more than acquiring skills
Upon reading this stunning claim in Forbes a few months ago, Stanford math professor Keith Devlin wrote a thoughtful response on July 2 (link here). I agree with Devlin that the provocative title is the most concerning part of the article. Devlin’s blog post should be required reading on this issue because he discusses what Algebra is, what constitutes mastery, and even what qualifies as a “game.” For example, it’s not possible to “master algebraic linear equations” without graphing linear equations, working with tables of values, or contrasting linear equations with other types of functions. And these are representations not found in the video game.
There is no “quick fix” to develop conceptual understanding
Beyond Devlin’s response, it’s also worth discussing the focus on speed. Why is it that when it comes to learning, there is often an unusual obsession with speed? This focus seems to arise especially when we perceive that the content is merely procedural skill or factual recall. In reality, the nature of mathematics is far more than skill and memorization. And the authentic work that mathematicians do requires time, deliberation, and thought – things that are not quickly accomplished. It’s important to avoid wasting time and to leverage technology to optimize time; but performance mastery and understanding will always take a significant investment of intellectual clock hours. Consider how in terms of personal health, the safest, most effective ways to lose weight and gain muscle are not “quick fixes.” Similarly, with learning and conceptual understanding, there is no free lunch. As noted in a recent EdWeek commentary by Alden S. Blodget, the “process of building and rebuilding neural networks—this process of learning—requires considerable effort from the learner” (link here). Ninety minutes is not a considerable enough effort for mastering a subject as elegant and complex as algebra.
Intelligent Adaptive Learning™ develops skills with understanding
Another point worth discussing is the term “adaptive,” which is increasingly being used to describe educational technologies. At DreamBox, we believe Intelligent Adaptive Learning™ is an effective way to ensure students transfer their learning to new situations (the “transfer problem” Devlin mentioned in his blog post). We use our adaptive platform to build unique digital learning experiences that ensure students develop conceptual understanding along with procedural skill. The most effective adaptivity works continually at every moment of a lesson to respond to how students are interacting with learning tools and manipulatives. Therefore, within a single DreamBox lesson, different students will receive different problems, different numbers of problems, and different feedback based on how they are solving the problem. Even the youngest students using DreamBox learn to think like a mathematician, to think for themselves, and make sense of procedural skills while reasoning algebraically. While DreamBox does increase the velocity of student learning, we build our platform and lessons based on what educational research has demonstrated — it takes significant time for students to develop mathematical habits of mind and critical thinking skills.