Engagement entails much more than rote repetition of a procedure. Math worksheets tend to present very similar problem types over and over, leading to mundane practice of disassociated skills. For students who understand the material and successfully complete an assignment, another worksheet becomes meaningless. On the other hand, for the students who don't understand the material, an alternative method of instruction is what's needed. Another worksheet simply adds to the student's frustration, or worse, contributes to a belief that "I'll never understand math." A cute image or a "fill_in_the_blanks" riddle does nothing to increase engagement or learning (and let's face it, those riddles are not funny!). Instead, teachers need to increase engagement by providing students with exercises in which they discover patterns and relationships, solve problems, or think creatively about math relationships.

I teach the upper grades in my school, yet I continue to see kids who do not even have basic algebra skills in place. As a parent, I'm very aware of what my own children are learning in school. For the most part, I've been happy with their progress, but as they rise in grade level, I'm starting to see more emphasis on a loose understanding of the concepts and less emphasis on skills__particularly skills with arithmetic of fractions. The main problem with what I see with my students and my own children is that kids are taught "concepts" and are not taught skills__unless they're lucky enough to have a teacher who knows better. Most particularly, children are not taught mastery of arithmetic with fractions. Unfortunately, virtually all of their future math education depends on being able to do fractional arithmetic.

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