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.
The Effect _ Most of even beginning algebra depends on being able to do two things__one, doing multiplication quickly and accurately in your head, two, knowing how to add, subtract, multiply, and divide fractions. You might remember a concept in algebra called "factoring." Factoring means breaking up into parts that are multiplied together to give you the whole. You can factor numbers. For instance, 6 factors into 2 and 3_θx3 =6. In elementary algebra we learn to factor expressions such as x^2ƲxƲ. This particular expression is easily factorable into (xư)^2. If this doesn't make any sense to you, don't worry about it. Just trust me, if you don't know your multiplication tables, you can't factor. If you can't factor, you won't do well at all in algebra, geometry, or trigonometry.