Jerry Brodkey teaches at Menlo-Atherton High School in Menlo Park, California. He has been a public secondary school teacher since 1975, and has taught most of the subjects in Social Studies and Mathematics. He now teaches remedial algebra and Advanced Placement Calculus.  His undergraduate degree was from Rice University (BA 1974), and has graduate degrees from Stanford (MA 1976, Ph.D. 1987).

 He has written guest posts on “smart” boards and stress on high school students. Here he comments on the recent post criticizing the Khan Academy including a rebuttal from Khan.

I first heard of the Khan Academy two years ago when one of my Calculus students told me he reviewed complicated concepts by using the Khan Academy videos.  That caught my attention.  I checked out the site, and thought it had potential.  Last year I learned more, as my children’s school district in Los Altos, California became a major site implementing the program.  My daughter’s school received national publicity as it used the Khan Academy as a key component of its math instruction.

I am no expert on the Khan Academy, having spent only a few hours working with it with my children. I asked my children for their reactions.

My son was in the advanced eighth grade math class.  The Academy was not used in his class.  Sometimes he would go to the site just because it was “fun”. He liked the  “tons of exercises” and the topic branches.  He never used the videos to learn new material, but only to review topics.  For motivated math students like my son, the KA materials not only worked for review, but also were enjoyable and fun.

My daughter’s experience was different.  Her teacher used the KA as a piece of her instructional program.  Students worked on KA in class on topics of their choosing. If my daughter did have questions on any assignments, KA or others, I would often have to re-teach the materials, answering questions, correcting misunderstandings, and approaching problems from different perspectives.

I felt the posts by Mr. Amir and Mr. Khan missed major points that need discussion.  The fact that Mr. Khan sometimes created the videos quickly is not a problem for me. Sometimes I, too, create my lessons quickly. The quality and the soundness of the mathematics are important, and Mr. Khan seems open to correcting mistakes.  Content problems can be modified.

There are bigger questions.  Under what circumstances, and with which students, can the KA be most effective? What are its limitations?  Is it most effective for the transmission of new material, or is it best suited for review?  What skills must a teacher have to use it effectively? Will this approach work for those students who are not traditional learners and who struggle with this type of approach?

I thought of how I teach slope.   We take several days and have a great amount of discussion before even attempting to “do the math”.  I begin by telling them of a past experience when I had a blind girl in my class. The unit on graphing and slope was difficult for this bright young girl. I put the graph of a line on the board, and asked my current students how they would have helped the blind student “visualize” the graph.  Some suggested telling the blind student which quadrants the line passed through. Others said they would tell the student points on the line.  Some suggested using pegboards with rubber bands so the blind student could “feel” the line.  All were great ideas.

Students invariably would talk about the “steepness” and “angle” of the line. They use terms like “very steep”, or “kind of steep”, or “going up or down, fast or slow”. This discussion would lead beautifully into the concept of slope.

Mr. Amir and Mr. Khan differed on the precise language and definition of slope.  Their two positions don’t bother me. I use multiple definitions and approaches. I use the expression “rise over run”, but supplement that by referring to “the change in y divided by the change in x”, always talking about change.  If two quantities are linked together, how does the change in one of the variables alter the second?  The key idea is change.   I have to go deeper, even with my stellar calculus students, reminding them that when they look at a graph they are actually looking at data points that come from a relationship.  When I am talking about the slope of the line, I am asking a more fundamental question on relationship.

I use everything I can to help them understand.  We use Legos to build different slopes; we measure steepness using rulers in the classroom.  How would using multiple approaches fit in with the model of the KA?

The important questions regarding the Khan Academy are not about the videos or specific mathematical concepts.  What is lost and what is gained by using the Academy’s approach? I think it has potential to supplement strong instruction, and I look forward to understanding it better and using it more effectively in my own teaching.