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Teaching Students to Solve Problems67
 


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Contents

Acknowledgements
Foreword

Using This Resource

I. Preparing to Teach
Planning a course
--Defining Instructional Objectives
--Teaching and Learning Styles: The   Academic Culture
--Choosing and Using Instructional   Materials
--Writing a Syllabus
--Syllabus Checklist
--Using the Syllabus in Class
--Summary of Course Planning
Addressing Students' Needs
--Importance of Knowing Your   Students
--Planning Considerations
--Getting to Know Your Students
--Students of Different Backgrounds
--Students with Disabilities
--Teaching Strategies: Non-Native   Speakers of English
--Creating a Learning Environment
--Dealing with Disruptive Behavior in   the Classroom
--Common Disruptive Student   Behaviors and Possible Responses
--Dealing with Apathetic Students
--Cultural Differences for International   Instructors
--Summary of Addressing Students’   Needs
Teaching Tips
--Organizing Class
--Ways to Be Accessible Outside the   Classroom
--Six Common Non-Facilitating   Teaching Behaviors
--Wireless in the Classroom: Advice   for Faculty
--Summary of Teaching Tips

II. Teaching Methods
The First Day of Class
--When the Class Meets You
--When You Meet the Class
--Diversity the Instructor Brings to the   Classroom
--Conversing with Students with   Disabilities
--Moving Forward
--Summary of the First Day of Class
Lecturing
--Strategies for Effective Learning
--Advantages and Disadvantages of   the Traditional Lecture Method
--Enhancing Learning in Large   Classes
--Chalkboard Technique
--Writing Assignments in the Lecture
--Engaging Women in Math and   Science Courses
--Formulating Effective Questions
--Summary of Lecturing
Discussion
--Brief Overview
--The “Nuts and Bolts” of Discussion
--Facilitating Discussion of Sensitive   Issues
--Encouraging Student Contributions
--Alternative Instructional Methods
--Potential Problems in Discussions
--Summary of Discussion
Expanding Teaching Strategies
--Practical Examples
--Show and Tell
--Case Studies
--Teaching with Case Studies
--Guided Design Projects
--Brainstorming
Group Work
--General Information about Using   Groups
--Group Work in an Introductory   Science Laboratory
Science Labs
--The Role of the Lab Instructor
--What Do the Students Need to   Know?
--The First Day
--Planning and Running a Laboratory
--Safety Procedures
--Summary of Science Labs
Teaching Outside the Classroom

--Tutoring
--Office Hours
--Teaching Students to Solve   Problems
--Advising and Extracurricular   Activities
--Summary of Teaching Outside the   Classroom

Overcoming Misconceptions
--Societal Attitudes and Science   Anxiety
--Misconceptions as Barriers to   Understanding Science
--Common Difficulties and   Misunderstandings

III. Teaching-as-Research
Assessing Student Performance
--Establishing Objectives for   Assessment
--Assessment Primer
--Formulating Effective Methods of   Assessment
--Helping Students Succeed on   Assignments and Exams
--The Why and How of Tests
--Grading Lab Reports, Problem Sets,   and Exam Questions
--Grading Checklist
--Grading Specific Activities
--Grading Writing
--Summary of Assessing Student   Performance
How to Evaluate Your Own Teaching
--Evaluating Your Own Teaching
--A Note on Teaching-as-Research

IV. Appendices
Inspirational Essays
--Mathematics: The Universal   Language of Science
--Transforming Quizzes into Teaching   and Learning Tools
--Teaching My Students to Fish
--Chemistry: The Other Foreign   Language
--Teaching to Different Modes of   Learning
--Notes from a Career in Teaching
Additional Resources
Websites
Graduate Assistant Handbook Outline
--Department- and Institution-Specific   Information
--18 Questions to Have Answered

Works Cited

 

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When a student comes to you during office hours and says, “I don't get it,” what do you do? The most natural response might be to try to find out more specifically what the student doesn’t understand and explain or demonstrate it to the student. Although the student may also expect this, it may not always be the most effective way to help. The student may listen to the explanation or watch as you work the problem and may go away thinking that he or she understands the problem. While that particular problem may be understood, when asked to do a similar problem on a test, the student may have difficulty. There are a variety of reasons a student might be having difficulties  in solving problems. The sources and types of errors a student may have are listed below.

Sources and Types of Errors in Problem Solving68

Inaccuracy in reading

  • Reading  the material without concentrating strongly on its meaning
  • Skipping one or two unfamiliar words
  • Losing one or more facts or ideas
  • Failing to reread a difficult section
  • Starting to work on the problem before reading all of the material

Inaccuracy in thinking

  • Not placing a high premium on accuracy (above speed or ease)
  • Not taking enough care in performing some operation
  • Interpreting words or performing operations inconsistently
  • Not checking a formula or procedure when feeling some uncertainty
  • Working too rapidly
  • Drawing conclusions in the middle of a problem, without sufficient thought

Weakness in problem analysis; inactiveness

  • Failing to break a complex problem into parts; not using the parts that are understood to figure out more difficult parts
  • Not drawing upon prior knowledge and experience when trying to make sense of ideas which are unclear
  • Failing to use the dictionary or other resources when necessary to understand the problem
  • Not actively constructing a representation of ideas on paper (when a representation would have helped in understanding the material)


Lack of perseverance

  • Lacking confidence and giving up easily
  • Choosing an answer based on a superficial consideration of the problem (having a feeling of what might be correct – guessing)
  • Solving the problem in a mechanical manner, without much thought
  • Reasoning the problem part-way through, giving up, and jumping to a conclusion
  • Using the “one shot” approach to solving the problem and, when that doesn't work, giving up
How You Can Help

Students need training and practice in problem solving. To make teaching during office hours more effective, you must make it student-oriented instead of teacher-oriented. Your goal is not to show them the answer to a specific problem, but to teach them how to go about solving problems and how to think while solving problems. In other words, you must get students to do the thinking and help them modify their thinking by having them slow down and use good problem solving techniques. Some ways to get students to slow down and reflect on their thinking processes when solving a problem are:

  • Have students read the problem aloud and tell you what is needed to solve it before they start to work.
  • Get students to work problems while “thinking out loud.” Encourage students to constantly talk about what they are doing and why. This will slow down the thinking process and make it more explicit and more accurate. You can often help students check their own reasoning and find their own mistakes by having them express exactly what they know about a problem. Comments or questions that can help students clarify their thinking might include some of the following:
    • What are some possible ways you might go about solving this problem?
    • Tell me what you know about the problem.
    • How might you break the problem into small steps?
    • Please tell me how you got from step one to step two.
    • What are you thinking right now?
    • I don’t understand your reasoning behind that step. Will you please explain?
  • Sometimes you will find it necessary to model good problem solving techniques. You may have to demonstrate how you would go about reading and understanding a question before starting to work the problem. You may show how you would solve the problem, making the process clear to the student, (e.g., working step-by-step; backing up if necessary when things don’t work out; breaking a complex problem into parts and using the parts you understand to figure out the more difficult parts; actively constructing a representation of ideas on paper; etc.). After modeling the process, require students to work through a similar problem to make sure they understand the process.

 
 
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