August 23, 2013

Published in The Chronicle Herald (Halifax)

Math instruction this fall is going to look quite different for approximately 300 Grade 7 students. Two major businesses and the province of Nova Scotia are providing the funds to purchase tablet computers for these students and their teachers.

If this $1-million pilot project is successful, the program may even expand to other grade levels and schools.

I predict this pilot project will be a big success, but not because of the tablet computers.

Simply introducing more technology in classrooms has only a limited impact on learning and is hardly worth the significant costs involved. Instead, this pilot project will succeed because it will revolutionize math instruction.

Why?

Because these tablets will enable students to receive instruction from the Khan Academy, a non-profit education website created in 2006 by Salman Khan. With more than 3,000 instructional videos available online at no charge, the Khan Academy is used by students around the world to learn about subjects as diverse as history, mathematics, and cosmology.

Anyone who takes the time to watch some of the instructional math videos on the Khan Academy’s website will quickly see some familiar concepts.

For example, the videos show how to add and subtract by placing one number on top of the other and working digit-by-digit from right to left. Multiplication is demonstrated using the standard vertical format while the traditional long division algorithm is consistently used as well.

In fact, all of the standard mathematical algorithms for addition, subtraction, multiplication, and division feature prominently in these videos. Interestingly, this is the exact opposite of the approach recommended by education faculties where teachers are trained.

Under the influence of math education professors, provincial curriculum guides and math textbooks have been systematically expunged of the standard algorithms.

The underlying philosophy behind this “new math” approach is often called constructivism. Advocates say students need to construct their own ways of doing math.

So, they argue, instead of showing students the most efficient way of solving a question, teachers should give them open-ended word problems and encourage them to invent their own problem-solving strategies.

One of the most prominent “new math” advocates was the late John Van de Walle, formerly a math education professor at Virginia Commonwealth University. In his widely circulated book series, Teaching Student-Centered Mathematics, Van de Walle disparaged the teaching of standard algorithms for addition, subtraction, multiplication, and division. He also argued that skill-based drill and practice makes it harder for students to gain a deep conceptual understanding of mathematics.

Some math education professors go so far as to claim that teaching the standard algorithms to students is developmentally harmful.

Constance Kamii, professor of early childhood education at the University of Alabama, co-authored a widely influential paper in 1998 entitled “The harmful effects of algorithms in grades 1-4.” Even though the arguments contained in this paper have been thoroughly debunked by real math professors, Kamii’s dubious research is regularly cited by “new math” advocates.

The Atlantic Canada Mathematics Curriculum, which is used in Nova Scotia, was strongly influenced by these education professors and their disciples. In addition, commonly used math textbooks such as Math Makes Sense and Math Focus are also heavily infused with the constructivist approach as it is almost impossible to find any standard algorithms in either of these textbook series. Instead, students are given convoluted word problems, poorly designed algorithms, and unclear directions.

So when Grade 7 students in this pilot project receive their tablet computers and watch the Khan Academy instructional videos featuring standard math algorithms, they will finally be exposed to math that makes sense. Once they learn the most efficient way of solving math questions, students won’t be particularly interested in going back to the fuzzy math that appears in their textbooks.

Of course, all of this could be done without bringing a single tablet into any classroom. Teachers could teach the standard algorithms using textbooks that actually contain proper step-by-step directions. While watching a solid instructional video about a math technique is good, getting the same lesson from a teacher in the classroom who can answer questions is even better.

There is a certain amount of irony that the Nova Scotia students who use cutting edge technology are going to end up learning math the old-fashioned way. Students in this pilot project are fortunate because they are going to do math properly, not because they get to play with fancy tablets.