Prologue
Acknowledgments
About the Authors
1. Managing Your Classroom
1. Create your own support network as soon as you begin your first teaching job.
2. Before beginning a lesson, put an outline of what you are going to cover on the blackboard.
3. Make realistic time estimates when planning your lessons.
4. Make classroom activities flow smoothly.
5. Have “eyes in the back of your head” so you notice misbehavior at an early stage.
6. Help students develop self-control to enhance their thinking and independence, as well as to ease your own workload.
7. Do more than one thing at a time.
8. Work directly with individual students as often as possible.
9. Use classwide peer tutoring to help your students learn, whether or not they have learning disabilities.
10. Encourage students to be mentally active while reading their textbooks.
11. Avoid reacting emotionally when evaluating problematic situations in the classroom.
12. Carefully select problems for use in cooperative learning groups.
13. Encourage students to work cooperatively with other students.
14. Use group problem solving to stimulate students to apply mathematical thinking skills.
15. Use the Jigsaw Technique of cooperative learning as an interesting and effective way for students to learn.
2. Enhancing Teaching Techniques
16. Find out about your students’ motivation regarding mathematics, and use that knowledge to refine your instruction.
17. When trying to determine how to motivate students’ interest in mathematics, teachers should differentiate between personal and situational interest and use both forms to increase students’ motivation to learn mathematics.
18. Treat students in ways that reflect the belief that you have high expectations for their performance.
20. Call on students more frequently to promote their achievement.
21. Make sure to pause for at least four seconds after listening to a student’s communication before responding.
22. Use questions for different and versatile functions in the classroom.
23. Teachers should be tactical in their use of questions.
24. Make a lesson more stimulating and interesting by varying the types of questions you ask students.
25. Use a variety of sequences to ask questions.
26. Use a variety of strategies to encourage students to ask questions about difficult assignments.
27. Use a Question-Asking Checklist and an Evaluation Notebook to help students become better learners.
28. Use school fundraising projects, such as students’ selling candy, as the basis of mathematics lessons.
29. Don’t give students feedback on their performance too early.
30. Use homework as a way of delving more deeply into important mathematical concepts and skills.
31. When doing inquiry lessons, give students clearly written materials to guide the inquiry process.
3. Facilitating Student Learning
32. Use inquiry-based learning in addition to problem-based learning.
33. To reduce math anxiety, focus on both the thoughts and the emotions of the students.
34. Adolescents need extended support to acquire the ability to visualize.
35. Use graphic representations or illustrations to enhance students’ memory while they are listening to you. Abstract representations such as flow charts are more effective than colorful pictures.
36. Teach students to ask themselves questions about the problems/tasks they are working on.
37. Teachers can help students learn to ask better questions.
38. Give students the kind of feedback that will most help them improve their future performance.
39. Help students understand their own thought processes and guide them in learning to think like mathematicians.
40. Playing makes understanding mathematics easier and more fun.
41. Select and carefully structure homework assignments so that they require the development of mathematical thinking and reasoning. Anticipate changes that might occur while students are working at home.
42. Use homework assignments as opportunities for students to get practice and feedback on applying their mathematical knowledge and skills.
43. Assign homework and other projects requiring students to write about connections between mathematics and other subjects.
44. Consider whether a student’s learning weakness might involve a deficiency in auditory perception.
45. Complex exercises that give students freedom tend to fit the way older students learn.
46. Emphasize higher-level thinking objectives in regular mathematics classes so that all students incorporate the features of enriched academic and honors classes.
47. Use analogies to help students develop more valid conceptions.
4. Assessing Student Progress
48. Feedback on practice is essential for improving student performance.
49. Promptly give students information or feedback about their performance.
50. Make sure students pay attention to the feedback you give them.
51. Systematically incorporate review into your instructional plans, especially before beginning a new topic.
52. Provide all students, especially students lacking confidence, with “formative assessments” to allow them additional opportunities to succeed in mathematics.
53. Find out why students rate a mathematical task as difficult so you can increase the difficulty of exercises and tests more effectively.
54. Increase your understanding of factors that affect students’ attitudes before and after testing. You may be surprised!
55. Be aware of students’ different levels of test anxiety as it relates to different subject areas, and use a variety of techniques to help them overcome their test anxiety.
56. Do not assume that students accept responsibility for or agree with their bad grades on tests.
57. If students do not follow your instructions and/or if their achievements do not fulfill your expectations, the cause may not be students’ incompetence. It could be a result of your self-overestimation.
5. Teaching Problem Solving
58. Get students to “think out loud” when solving problems.
59. Have students study written model solutions to problems while learning and practicing problem solving.
60. Encourage students to make mental pictures while applying rules to solve problems.
61. Provide hints or clues or ask leading questions when students need help solving problems instead of giving them the answers. Gradually phase out this support so as to foster independent problem solving.
62. Teach students to ask themselves questions about what they already know about a problem or task they are working on.
63. Emphasize the general principles that underlie solving specific types of problems.
64. Examine your students’ knowledge of mathematics and use this information to write challenging word problems that they will enjoy solving.
65. Structure teaching of mathematical concepts and skills around problems to be solved, using a problem-centered or problem-based approach to learning.
66. Help students learn without relying on teacher-centered approaches. Give them carefully chosen sequences of worked-out examples and problems to solve.
67. Students need time to practice planning their solutions to problems.
6. Considering Social Aspects in Teaching Mathematics
68. Make multicultural connections in mathematics.
69. Find out about your students’ families and how their values and practices might affect students’ attitudes and performance in mathematics.
70. Reach out to parents to form a partnership for educating elementary and high school students.
71. Inform parents that they should not let media reports about studies of other children change their views of their own children’s abilities to be successful in mathematics.
72. Some students do not think they have control over their academic successes and failures. Help these students recognize that they do have some control.
73. Teach students, especially girls, to believe that success in mathematics results from their efforts.
74. Give girls the same quantity and quality of teacher attention as boys.
75. Make special efforts to encourage girls to study mathematics.
76. Use different motivational strategies for girls and boys.
77. Take into consideration how students view successful teachers and how this differs for girls and boys.
78. Praise, encourage, and help your older students.
79. Does grade skipping hurt mathematically talented students socially and emotionally? Don’t worry about accelerating your talented students!
Resource. What the Authors Say: Enriching Instruction
Epilogue
References
Index
