Question 1: Does you your child's mathematics teacher assign a lot of worksheets for homework and classwork?
If the answer is YES - Not a very effective teacher.
If the answer is NO - Likely to be a more effective teachers.
This idea is a major shift in thinking for a lot of people--both for teachers and for non-teacher-parents alike. Some would say, "How can you say worksheets are bad?" Or, "I used worksheets when I was in school and I turned out fine." And the internet is certainly full of sites with pre-made worksheets that are frequently downloaded and used by teachers. So (I guess) the next argument is, "If so many teachers are still using worksheets, then why are they so bad?" Here's why:
#1: We want students to understand the mathematics that they are learning. Worksheets tend to encourage students to blindly follow procedures without knowing why they are doing what they are doing. Students might get the answers correct, but if the problems were changed slightly they wouldn't know what to do because they never learned the "Why" of the procedures that they were using.
#2: If students know how to do something, then why do they have to do it 20 times? It seems to me that if they can do it two or three times, that would be a sufficient amount of proof that they have learned the skill. If a students does not know how to do something, then why are we forcing them to do something 20 times that they cannot do? Have you ever completed a worksheet only to find that you made the same mistake on all 20 problems--and got everything wrong?
#3: Worksheets are not engaging. In Robert Marzano's book The Highly Engaged Classroom, we learn that students are more able to learn new concepts when they are engaged in the lesson. He offers many strategies for increasing student engagement. Worksheets tend to be boring and repetitive and very discouraging in terms of engaging students.
#4: We want students to communicate and collaborate with their peers during the learning process. As students struggle with a new topic, it is valuable for them to know to ask questions and to try different approaches to solving a problem. We call this Productive Struggle (also see here and here and here). When students do worksheets, they are often working in isolation. They are discouraged from talking at all with other students. This creates a classroom in which students are expected to listen to the teacher lecturing and only to the teacher and then to learn the new content based on what they heard. We know that this is not an effective method for learning (see The Learning Pyramid graphic).
One reason that teachers like worksheets is that they are used to help control student discipline in the classroom. Some teachers are not comfortable with students talking to each other and asking each other questions because they are concerned about losing control of their classes. But we know that when students are engaged in an activity, they are focused on the activity and not distracted by anything else. There is a benefit to allowing students to talk with each other. And there are many strategies that can be used to do this in a productive and organized manner in the classroom.
One of these strategies is the use of Math Tasks. Math Tasks encourage critical thinking, student discussion, and questioning from students that lead to better understanding of mathematics concepts. Many sources offer great Math Tasks for teachers to use. Here are just a couple of them: Inside Mathematics and Mathematics Assessment Project.
The goal of our public schools is learning. We must use the best thinking we have to encourage thinking and learning among our students. We don't want students to merely "complete" courses, we want them to learn, to understand, to retain knowledge, and to build upon their learned knowledge.