Tomorrow's Teaching and Learning
The posting below discusses how to use homework problems as preparation for quizzes and exams. It is from Chapter 5, “Metacognitive Learning Strategies at Work,” in the book, Teach Students How to Learn: Strategies You Can Incorporate into Any Course to Improve Student Metacognition, Study Skills, and Motivation, by Sandra Yancy McGuire with Stephanie McGuire. Published by Stylus Publishing, LLC, 22883 Quicksilver Drive, Sterling, Virginia 20166-2102. https://sty.presswarehouse.com/books/features.aspx Copyright © 2015 by Stylus Publishing, LLC. All rights reserved. Reprinted with permission.
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Tomorrow's Teaching and Learning
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Homework as Assessment
Remember Dana, the undergraduate on the verge of leaving physics who now holds a master’s degree in medical physics (chapter 3)? This strategy completely transformed her performance on physics exams. In fact, most of my science students who come to me when they are earning low Cs, Ds, or Fs, and who subsequently begin to make A grades, say that doing homework without using solved examples as a guide (strategy #7) is the one change that turned everything around.
When introducing this strategy, I ask students, “If there were a camera recording everything you do when you sit down to do your homework, tell me exactly what it would see.”
“Okay, I sit down and I open my book, and then I look at the first problem.”
“Have you ever looked at a problem and immediately decided to flip back in the textbook to look for an example?”
“Yes, Dr. McGuire! How did you know?”
“Because everybody is doing it. I did it myself when I was in college.”
Over the years, I have learned that most students do their homework by looking at example problems in the textbook or in their class notes and trying to copy the steps laid out there in order to arrive at the correct answer. This method is exactly the wrong way to go about doing homework problems.
Homework and example problems in the textbook and class notes should always be treated as an opportunity for students to test themselves. They should study for the homework the way they would study for a quiz. Before looking at the homework questions or problems they should actively read the relevant part of the textbook or any class notes. As they encounter example problems, they should work those problems without referring to the given solutions. For each problem, even if they get stuck and don’t know the next step, students should do their very best to power through and arrive at an answer. Then they should check only the final answer and not the entire solution. If their answer is incorrect, they can reread the text or class notes to investigate why and where they made mistakes. Much important and deep learning takes place during that investigation process. When students arrive at the correct answer, they should compare their approach to the textbook’s or instructor’s. If the approaches are different, students can ask themselves whether both approaches are valid. Why or why not? If they are both valid, does the student prefer his or her approach or the alternative approach? Why? This method provides many opportunities for reflection, metacognition, and deep learning. Additionally, sometimes someone else’s method just doesn’t “click” with a student’s thought process. If that student looks at that method before trying his or her own, the student may become locked into that way of thinking about the problem, which will be an unnecessary burden the student carries throughout the rest of the course and perhaps beyond. Relying on others’ methods restricts students’ creative flexibility and mental agility.
After working the example problems in this manner, students can then turn to the homework. They should do two or three problems at a time, treating each problem like a quiz or test question, looking at answers or worked-out solutions only after having made their best attempt to solve the group of problems.
Occasionally, students will lack the intellectual confidence to try this strategy, convinced that if they do not look at complete solutions, they will be endlessly staring at a blank page. For those students, it helps to advise them to set a timer and spend at least five minutes going through the reading or class notes to see if they can figure out how to begin the problem. If after five minutes, they are still stumped, they should look only at the first step, set another five-minute timer for step two, and continue in this way until they have solved the problem. Using this method, students maximize their opportunity to solve problems independently. I like to say to students, “Practice problems, wherever they come from, are your brain’s best resource for demonstrating that it can do all the problems without relying on an example as a guide.”
Whenever I present this strategy to students, as soon as I explain to them that they should try to figure out where they made a mistake before looking at solutions, I ask them, “At this point in the process, do you think that mistakes are good or bad?” How do you think they reply? Most faculty in my workshops predict that students will say mistakes are bad, but all of the student groups with whom I’ve worked collectively answer that mistakes are good. I quickly clarify that I’m not saying it’s bad if they don’t make a mistake; it is wonderful if they make no mistakes! But if they do, those mistakes represent a golden opportunity (Zull, 2011). When I ask students why mistakes are good, they answer:
You learn from your mistakes.
You can correct your mistakes.
You never make the same mistake twice.
You learn where your mind has a tendency to go wrong.
You won’t lose points if you make a mistake now.
Do you have students who, upon receiving a graded exam, lament, “Oh, I made so many careless mistakes!”? I believe there is almost no such thing as a careless mistake. Mistakes look careless only in retrospect. These kinds of mistakes must be made, sometimes repeatedly. “So,” I tell students, “you’re either going to make your mistakes now, during the homework process, or . . . where?” “On the test,” they correctly answer. I was surprised to find that once students understand the importance of making mistakes during the homework process, they often stop using websites like cramster.com or chegg.com to complete their homework assignments. They understand that by doing homework in the correct way, they are training their brain for the task it will face during the exam: solving problems without any model or guide.
One final note. When students are moving through example problems and homework, or quizzes and tests, they should begin with simple problems and progress to more complex ones that test mastery of more than one concept. We will see in chapters 7 and 8 that early success is a powerful motivator, and early failure is a powerful discourager. So students need to give themselves opportunities for success. Often, but not always, homework or exam problems are arranged from easiest to most difficult. If the easiest homework problems are too difficult, students can search for problems in the textbook easier than the homework and start with those. Even assessing the difficulty of problems requires metacognitive activity and helps the student absorb the material more deeply. This supplemental strategy is easy to include in your syllabus or mention when you are assigning homework.
Using homework as an opportunity to assess learning is an extremely powerful strategy. Alongside the reading strategies, it is one of the most effective and transformative strategies I offer my students.