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# Student-Centered Learning Strategies for Math and Other Subjects

February 18, 2011 | Paul Bogdan*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. Please share your thoughts in the comments section below.

## 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.

## Comments (27)

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## I've been teaching math for

I've been teaching math for 10 years, but I'm beginning to re-think my classroom strategies to see if I can be more effective with a more student-centered approach, or a standards-based learning approach.

In my teaching, the "why" and the theory are very important to the way I explain math to my students. I have consistently received very high reviews from students over the past ten years for "explaining well" so that they understand how all of the topics are connected and WHY the mathematical concepts are true, and how they relate to the real world. This is especially important in AP Calculus, because the AP exam is very conceptual in nature.

But I have one major concern with the methods described in the blog. When I read the lesson-plan idea above, my general impression was a math classroom with the goal of students learning to solve each type of problem by following various examples. If they follow along with enough examples (working through them independently) then they will learn how to solve all the problems. Unfortunately, I don't see my primary goal as a math teacher to get my students to just "follow examples." While that's a large part of teaching math, it's more important to me that my students understand WHY they solve a problem a particular way, and a different problem another way. The theory and the "why" behind everything are not usually well-explained in a textbook, and I find that explaining it directly to my students has made a big difference in my students' level of understanding. I know it works because my students score well on the AP exam, too.

For example, I can't rely on students following the textbook to really learn what a derivative is and how it's a slope formula and how it's connected to rates. The book breaks everything down in little pieces, and most math books do. I find that most textbooks lack a "big picture" component when explaining concepts. For example, even an Algebra I textbook will have solving linear equations in a completely different chapter than graphing a linear function. All things linear, however, are connected, and if the concepts are explained together, the students get a much clearer picture of one of the purposes of mathematics, which is to model and quantify the world that we observe!

I've even thought about the podcast type of teaching, so that I can free up classroom time to answer questions, but when I teach math, I rely a lot on interaction with my "audience" to see if they really understand WHY each concept is true. I don't know if I can accomplish this in a podcast without a constant "conversation" with my students.

Also, is it possible to implement a standards-based or more student-centered classroom in a school that is NOT following that plan as a whole?

Any suggestions? How can I have a more student-centered classroom (45 minute periods) which also emphasizes theory and "big picture" perspectives of the subject matter? :)

## Hi, After 17 yrs of doing

Hi,

After 17 yrs of doing student centered half way, four weeks ago I went to all student centered classroom. I have been through what you talked about, what everyone commenting before me has talked about. I have a very supportive administration that is a key factor in continuing. Here is my blog about it if you are interested. http://padgets.blogspot.com/

Thank you for your post. It further inspires me to continue to do what I am currently doing.

## Former High School Standards Based Mathematics Teacher

I applaud all of your efforts to place the focus on student learning. Teaching was a 2nd career for me and during the certification process I quickly noticed that the teachers were teaching BUT their students were NOT learning. In order to complete my student teaching phase successfully I had to mimic their expectations but swore to myself that when I got my own classroom I would NOT be the sage on the stage.

This was very difficult in the initial years as the expectation was for every teacher to be on almost the same page of the textbook at the same time. The textbook was my other issue as during certification it was pounded into us by the professors that the textbook is just a resource and NOT the curriculum.

However, in my first two schools in different states it WAS the curriculum. In the past several years I discovered the Adams50 school district online and its effort to go completely Standards Based. They have levels instead of grades and students progress as they master each level. This is the link for the SBE website: http://www.sbsadams50.org/content/ The details can be found in the Capacity Matrices which are accessed from their Wiki: http://wiki.adams50.org/mediawiki/index.php/Main_Page

This resource and others gave me the impetus to implement a Standards Based Algebra 1 classroom. It involved a lot of work and took some time and effort to change the students' "Just give us the worksheet." attitude that they had experienced before my class. It was well worth the pain, as much on their part as mine, as the students came around to accept all of my questions regarding their understanding and were happily surprised as to how much they were actually learning.

## Sharon, you put wind beneath my wings.

The main reason I developed my system is that I saw what a useless waste of time lectures are (I bet you did the same.). My solution was to almost eliminate them. Podcasts! What a great idea. I think that most students can learn a concept from a DFU example by following it and paraphrasing it from the book, and this is the least time consuming for them. But, those that can't or when the DFU lets them down or if they enjoy it more, they can view a podcast. I will hit more learning modalities, especially auditory. I'm excited to get this started. I think YouTube videos may also work. I think I will start with videos for the DFUs that are most challenging. Vi Hart has an excellent site with some very cool videos. Mobius Story: Wind and Mr. Ug is incredible.

I looked at MOODLE briefly and it looks very useful and has a lot of features that can be used in many ways. I'm sure I will use it. My grading system (right now) is 25% for classwork/homework, 25% for quizzes, and 50% for tests. Each section in the book has one classwork project (see my blog) and one homework project (a list of questions from the book). I am going to change their names to learning project and work project (work project was going to be practice project but the abbreviation is gross). This is because most of this work is done in the classroom (like you implied it is in your classroom). The quizzes and tests are from the book publisher. The student takes a quiz or test when they complete the sections' work. Quizzes are every two or three sections. Tests are at chapter's end. A student who is way behind can opt to do either the classworks or the homeworks and their grade will suffer only about 12.5% (if they really apply themselves and learn the material and ace the quizzes and tests). I care mostly that the maximum amount of learning takes place, not that the grade reflects how much math they know. My high school only has 100 students. I am, of course, the only math teacher. This is my first year and my system was quite a shock to the school and the community.

Thank you so much for your ideas. We are experiencing the same things. As you say: we have time to teach one on one, the procrastinators have no place to hide, and the kids who are motivated are learning much more.

## Have you tried Podcasting?

I am currently converting my Geometry and Algebra II classes to podcasted courses. Instead of lecture in class, answer what questions you have time for, and expect students to do homework and learn at home. I expect students to watch podcasts at home, via computers or DVDs. Podcasts have imbedded DFU examples and UDO problems where they are to pause and try the problems. I expect notes taken from podcasts.

Class time is for what used to be homework. I get so much time to help students in class. Students are working at various paces. They don't have to catch the lecture when I do it, they catch it after they have finished the work that leads up to it. You can't hide in a podcasted class.

Do I have procrastinators - yes. But my school is supporting me in the decision to award credit based on what students have accomplished. Students didn't believe me until I awarded 1/4 credit for the semester, and that modivated students. We are looking into a system that allows the grade to be attached to a working below, at, or above one years annual growth pace.

I am using MOODLE to test. It's OK, I still am on the learning curve on how to get it to work best for me. It allows testing to come from a question bank. I need to improve the quality of the questions and I do have a few students who just cannot understand why you would work out the problem since there are solutions given in multiple choice questions. I haven't worked out how to write the calculated questions yet. Moodle does allow feedback and I have many students that will be able to ask "what did I do wrong". It doesn't give partial credit, but I still do, IF students place their work on paper and hand it too me or ask questions after that show me their though process.

My grades are better. In Algebra II my average grade is B+ in a math class! Before grades were simply a reflection of whether students could work at or above a specific pace. Now they are based on mastering the material.

I have great support for what I am doing from my administration. Most parents are positive about the experience, they aren't being asked to help their child finish homework they don't understand. They know there will be time in class for me to do that help.

I'm currently trying to adjust my grading system, but still haven't figured out how to show two components. I think the grade should be for the learning and mastering, but we also want a way to warn students and parents if a student is working below one years growth level and may not recieve a full credit for one year in class (or allowing more than one full credit.

Do you have any suggestions?

## Very cool, Joanne

I think you will find that the motivated students will begin to enjoy learning math like they never did before. I am surprised at how quickly they cover the material and how completely they learn it. They go at a pace that I could never keep as a teacher-centered, lecture-based teacher. The challenges are the other ones.

## Perfect timing! I am in the

Perfect timing! I am in the process of changing the learning environment in my geometry classroom. This past week I wrote a lesson for angle pair relationships using the TI-Nspire and had the students work in groups. Many students grumbled, they did not know what to do, they just wanted me to "give them" the notes. It was a struggle for me as I tried to move from group to group convincing them they could follow the directions, work together and get through the activity. I resisted the urge to go back to what I know how to do . . . have 35 bored students (and 34 in the next class) listen as I tell them the theorems and show them how to use it in a proof or to write an equation. We had class discussions (pep-talk) at the beginning of class each day this week and many students began to feel more comfortable as I explained I would not use assessments as a punishment. I worked very hard convincing them I am most interested in their learning, by the end of the week I have more students on board. I have to remember I am undoing all the students have experienced in math learning and it is going to take time.

I am convinced that students must do the math to learn the math! I am getting off the curriculum hamster wheel and spending my time and energy creating a classroom where students are engaged and want to learn geometry. Thank you for your strategies, they are exactly what I need to help me to keep working at changing.