Editor's Note: Paul Bogdan was once an old-fashioned lecturing teacher centered secondary math teacher who left teaching for 14 years to build computer systems. He has come back and is reborn as a student-centered teacher trying to make a difference and trying to figure out what works in today's classroom.
Have you ever taught a lesson and then gave a quiz only to find that very few students have a clue about what you were teaching? What can we do about students who aren't getting it? How can we help the students learn rather than try to teach them? I'm thankful for the opportunity to share some of my ideas and can't wait to hear what you think.
Strategy One: Write detailed lesson plans and give them to the students to execute
In the past I never understood the point of writing lesson plans. I knew my subject matter thoroughly and completely. I felt that all I needed to do was stand up in front of the class and impart my knowledge; and I expected the students to soak it up. Now, I write very detailed lesson plans, but I write them for and give them to the students.
The following is a lesson plan that I give to the students to execute. It covers one section of the Geometry textbook (high school).
Project 2C (Classwork) Congruence and Triangles (4.2) (Page 202)
1. Three vocabulary. Corresponding Angles, Corresponding Sides, Triangle Congruence Statement Write and learn the definitions, include examples, underline, highlight, or change the color of the term. Learn and understand them.
A triangle congruence statement names the two triangles congruent with corresponding angles in corresponding positions in the triangle name. For example: When you write ?ABC??PQR you also mean that ?A??P,?B??Q, and ?C??R. If this is not true, then the congruence statement is false.
Note: Congruent is the same as equal except in math only figures are congruent and only numbers are equal (previously covered).
2. DFU Example: 1. Naming Congruent Pairs (DFU means Done For You.) Copy the question. Copy or write the solution in your own words. Include what you think is important when the instructions are to completely show your work. Be sure to learn what you are doing.
3. UDO Example: Page 205 Guided Practice #1 (UDO means You Do.) This is very similar to DFU Example 1. You must write the question and completely show your work.
Note: When working with congruent figures it helps a lot to draw them both facing the same way. Sometimes you only need to rotate one of them, but sometimes you need to flip one of them over and rotate it. This makes it easy to see corresponding sides and angles. It is easy to do and always makes the problem easier; it often changes a difficult problem into an easy one.
4. DFU Example: 2 (a, b). Using Properties of Congruent Figures
5. UDO Example: Page 205 Guided Practice #4 - 9
6. One theorem. Theorem 4.3 Third Angle Theorem
7. DFU Example: 3. Using the Third Angle Theorem
8. UDO Example: Page 809 Guided Practice #11
9. DFU Example: 4. Determining Whether Triangles are Congruent
10. UDO Example: Page 206 Guided Practice #17
11. DFU Example: 5. Proving Two Triangles are Congruent
12. UDO Example: Page 208 Guided Practice #35
13. One theorem. Theorem 4.4 Properties of Congruent Triangles
The plan guides the students to learn vocabulary, copy and learn examples, and do examples on their own. They need help at first, but soon learn how to teach themselves. Their work is collaborative; they rely on each other for help. They rely on me too, often asking questions. The book weaves the vocabulary into the examples. The book is very thorough, covering all aspects of the standards with very creative examples. Mostly I do one-on-one instruction. My role in the classroom has changed from "imparter of knowledge," to "facilitator of learning." The student centered lesson frees me up to roam about the room and become a resource for explaining, demonstrating, and clarifying precisely those areas each student needs. The students now ask me, instead of me demanding they "listen and learn." When several students are not getting it however, or are making the same mistakes, I will interrupt the class as a whole to explain something of general interest. Those students who want to learn the material excel using this method. It's all about motivation.
Strategy Two: Teach good note-taking skills
Besides learning subject matter, it is essential for students to be taught how to learn. Specific techniques for old fashion note taking are essential. Most textbooks (especially in Science and Social Studies) have pages of narrative followed by questions. Have the student write p1pa1 in the left margin of their paper. This means, page 1 paragraph 1. The student reads the paragraph, writes a short something, and then writes p1pa2. They read, they write, they read, they write, and so forth, until they get to the questions. The students will be surprised at how easily they are able to answer the questions. The answers will be in their notes or direct them to a page and paragraph. This frees you from teaching knowledge based lessons and prepares the students for high level comprehension activities.
The product of the math lesson in Strategy One is notes for the section.
Strategy Three: Keep students motivated
The student-centered style is quite motivating for some students. The students I'm talking about seem to be surprised that they can learn this way, and each day fuels the next. For some it happens right away; others may take a month to six weeks to get hooked on the power of student-centered learning. I try to be a model of a lifelong learner, sharing my interest in puzzles, toys, mazes, kites, geometric art, and anything academic. We build geometric figures with straws for extra credit. I try to make it as fun as I can.
Some students are not highly motivated and tend toward procrastination and socializing rather than doing schoolwork and homework. I would not be honest if I didn't admit that there are some students who refuse to do the work and are way behind schedule. However, the student-centered style leaves these students nowhere to hide. You know who you need help with and who is in danger of failing very early on.
Strategy Four: Make tests a real-time learning experience
Unfortunately, many students are not motivated to learn until there is a test in front of them. All of a sudden they have questions. I capitalize on this opportunity as a learning experience. I let them use the book and I am glad to answer questions during the test. When I correct the test I put small red dots next to the problems they get wrong. I return it to the student to make corrections. Besides being a highly motivating learning experience, it is an opportunity for the student to assess for themselves how much they have learned thus far. They may decide to intensify their work habits. Again, this is another opportunity for creating lifelong learners.
Strategy Five: Grade for learning
It has been argued that the grades in my class are too high. I believe however, that the classroom setting is the place for learning, not a place for pronouncements of success or failure. Standardized Tests are sufficiently appropriate venues for assessing Subject Mastery. Classrooms are for learning.It is my continued belief and experience that both Subject Mastery and Self Motivational Learning are the keys to success. When we, as Educators, are willing to give the Power and Responsibility for learning back to the student, we will have succeeded. Student Centered Learning is our future.
A secondary math teacher, Paul Bogdan has over 10 years of experience in the classroom, as well as 8 years in the field of computer systems design. He has a BA in Mathematics and a MA in Multidisciplinary Studies. He grew up in Buffalo New York, and has taught in NY, California, and recently got a credential to teach in Oregon.