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WHAT WORKS IN EDUCATION The George Lucas Educational Foundation
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Student-Centered Learning Strategies for Math and Other Subjects

Paul Bogdan

Student-Centered Secondary Math Teacher

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).

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.

Paul Bogdan

Student-Centered Secondary Math Teacher
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Paul Bogdan's picture
Paul Bogdan
Student-Centered Secondary Math Teacher
Blogger

We have gone through similar experiences. Some of my parents also felt that by turning the job of their education over to the students I was not doing my job. I don't think there is any other way for learning to occur.

Paul Bogdan's picture
Paul Bogdan
Student-Centered Secondary Math Teacher
Blogger

You bring up some very good points. The math I love the most is seventh grade math through geometry. When I think of my classroom I see a room full of Algebra 1 students who are mostly grade 9 with some grade 8 and some grade 10. This is the target audience in my mind for my system and my methods; this is also the age and maturity level I enjoy the most. However, the techniques will help at all levels.

The class and students you describe are quite different. High school students taking math beyond Algebra 2 are very different from a class full of freshmen taking Algebra 1. My geometry textbook is very poor at teaching the concept of proof because it takes a synthesis of the postulates and theorems. I have to teach them this. My Algebra 1 textbook is very poor at teaching the concept of absolute value equations and inequalities because they have to use the algebra mechanics in a different way. I have to teach them this.

The hardest leap our students take is the leap into the high level comprehension questions and the 'why' of it all of which you speak. You have got me thinking that maybe (just maybe) my techniques are most effective at the knowledge and lower level comprehension learning while the higher level comprehension may take more of a Socratic dialog. However, the high level learning is probably not possible without learning how to learn, which is the main thing that student-centered learning is all about.

James Klock's picture

Thanks, Paul, for sharing your experience. I'm a former engineer and IT professional, who took up teaching math seven years ago, working in some pretty challenging public high schools in Chicago. Your post resonates with me in a couple of ways:

First, I love that you're really reflecting on your past practice in a way that's honest and critical, while also not dwelling on the lost opportunities in your past: while you've recently made some huge growth in your own approach to teaching, you're not beating yourself up about how you used to teach. That can be a hard balance to strike, and you're modeling a great way forward in changing. As teachers, we *need* to keep growing, keep learning, keep improving and renewing and even reinventing what we do and how we do it and what we believe is important. My own experience has taught me that good teaching is seldom the same thing twice. Partly, that means using a lot of different tools, techniques and approaches. Partly, it's because the learners are always different, and that has to be reflected in the teaching, so even if it's the same content and objectives for two similar classes, the lesson should be a little different.

Second, as a teacher of mathematics (in that order: I'm a teacher first!) but also of science, trained as an engineer and not as a mathematician, I think it's important to recognize (as you've done) that the cultural history of math instruction is very much lecture-oriented, based on a model where the expert at the front of the room demonstrates the algorithm or proof or transform at hand, and the students take note of it-- even when I was "engaged" in my own high school math classes to demonstrate my understanding, it was by coming to the front of the room, to present a demonstration-- essentially taking over the teacher role.

Math teachers sometimes like to say, "the math hasn't changed" from decades ago; never mind that that's basically untrue (there IS a lot of novel mathematical understanding, as professional mathematicians and very smart people in all sorts of sciences develop new mathematical tools for understanding our world), what WE do is TEACH, and teaching doesn't happen if there isn't learning. What we collectively know about *learning* has changed tremendously in the past few decades, and our teaching practice ought to reflect that.

Bravo to you, for your honest assessment of your history and present teaching practice, and thanks for sharing it with the rest of us!

James Klock's picture

Teri, that's a great insight-- helping students to build conceptual frameworks is really hard to do, and it's hard to test (the AP Calc test does a pretty decent job of it, but even that only attempts to test concepts on about half of the questions!) Because it's harder to do and test than "answer getting," it's something we tend to sweep under the rug...

I don't claim to have any sort of magic to share with you, but my own experience (including with AP Calc) is that you'll know students have a concept when they're able to explain it, put it into words, and make sense of it-- whether that's through a Socratic dialog, or whole-class discussions, or in journals. And, I think that the act of putting it into words really helps students to build and solidify those conceptual frames-- ways of making sense of the mathematical ideas.

So, first step, make sure your students are talking, whether it's talking to each other, or to you, whether it's oral or written. Once you know that the student can explain, in their own words, why an antiderivative is the same things as an indefinite integral (and why they both have an unknown constant), then you're bound to have some confidence that they really understand it. It takes a LOT of time, but if you value concepts as well as algorithms, it'll be time well spent.

Joanne Crooks's picture
Joanne Crooks
High School Geometry Teacher from Morrisville, North Carolina

I survived last week! I followed your advice and created lessons for the students to work through together with the objectives listed on the first page. I called it angle exploration. The students worked in groups using the TI-Nspire (I created an activity that followed the lesson)and still had them use a compass and straightedge to bisect an antle. I hoped that by using the available technology that allowed the students to manipulate and measure the angles they would remember the relationships.
The students complained every day, telling me they didn't think they were learning anything, asking could we please go back to me giving them the notes. I reminded myself I had to be patient, this is a big change for them (and me!) We had a class discussion at the beginning of each day, sort of like a pep talk. Many were concerned about how this would affect their grades, I assured them I would not use an assessment as a form of punishment. Each day a few more students climbed on board. By the third day I knew I was making progress when a student volunteered to go to another group and explain a homework problem! I am happy with even the smallest of victories!
Today I have the pleasure of returning their tests. We will be celebrating as I have never had so many students earn such high grades (I changed the test to make sure it was only checking for mastery of the objectives).
After we go over the test today, it is on to Logic II (I am not telling them they are developing two-column proofs). I am not teaching it, they will work together through the lesson to learn. I am enjoying this journey, as I learn too!
Success generates more success and motivation to learn!!

Paul Bogdan's picture
Paul Bogdan
Student-Centered Secondary Math Teacher
Blogger

Your comments are appreciated and have given me a lot to think about. I'm glad it's working so well for you, Joanne.

Cossondra George's picture

Hi Paul,
While I can see that your plan could work with the average student, my prealgebra students this year are special ed students with math disabilities who need individualized instruction. Many of them(8th graders) are not even independent readers so to expect them to be able to read, write and follow instructions from a textbook is an unreasonable expectation.

When I teach, the interaction between me and the students is critical to their success. Often, the material I am forced to teach is far above their heads and requires much backtracking to fill in gaps in their past mathematical classes.

I do use your technique of correcting quizzes/tests once and returning to students for redo's/further investigation. Even when I was in a regular ed math class, I found this method to be valuable. Often times, students make careless errors that are caught the second time through. Forcing them to rethink their work can be a wonderful tool in the development of their understanding of concepts.

Test redo's does create high class scores/grades. But isn't that our true goal in teaching? I would like each student to always score 100% on everything we do.

Now... solving the motivation problem... for those few students who simply do not care, do not want to achieve... This seemingly unending uphill battle is one I have fought for 17 years and see no end to. It is sad and a battle I continue to fight daily. Sometimes, for these students, just seeing that a teacher is unwilling to give up on them is enough ummph to get them started. For others, the pattern of refusal and failure is so deeply embedded in their psyche, the challenge is unsurmountable.

Thanks for sharing your article.
Cossondra George

shuggins's picture
shuggins
Student Teacher - 7-12 Mathematics

I'm very interested in student-centered teaching, but am not finding a lot of resources for High School. I am fairly creative, but do not have the years of teaching experience that some of you do. I have read a LOT of theoretical advice, but have not found much in the way of tactical, tried and true, ideas. My (student teaching)placements have been fairly traditional.
Can you recommend any books or articles which will help me to generate some ideas for building lessons?

Paul Bogdan's picture
Paul Bogdan
Student-Centered Secondary Math Teacher
Blogger

Student teacher, fresh meat, welcome to the party.

I looked and found the same thing that you did: nothing.

When I started commenting on blogs about my new student-centered techniques for teaching math, people started asking me how to do it, so I assume they found the same thing we did: nothing.

I think that this blog post and all the marvelous comments that were made have the best ideas about how to make your class student-centered. Joanne's geometry class and the biology teacher who says he no longer teaches, for example. Follow the links that they left.

I challenge you to think up some more good ideas. The road you are choosing is a tough one, but it's the right one. Students and parents may accuse you of not doing your job; be ready; administration and school boards understand. Don't brag about it being new and different; just claim that it is a good idea and students learn very well and like it.

The main principle is that lecture is wrong. You are probably finding that out because the kids (in a freshman algebra class) won't sit down and be quiet and listen and learn and you end up fighting with them. Even if you are tough enough to get them to listen, you will see poor results on tests. Turning the tables and giving them the responsibility and teaching them how to learn makes you their helper, their hero. I use the DFU, UDO combination to replace my lecture. I suggest for science and social studies to use the paragraph notes idea to replace the lecture. Somebody suggested videos to replace lecture and I'm going to do that. See Vi Hart's page. She is a gifted video maker I like Wind and Mr. Ug (vihart.com).

What subject do you teach? What are your plans?

shuggins's picture
shuggins
Student Teacher - 7-12 Mathematics

Paul,

I, too, am leaving a 14 year career in Information Technology to teach math. (I guess I'm old for a student teacher)

Right now, I am student teaching 9th grade algebra. The graduate program that I'm in also strongly recommends that we try student-centered teaching - and right now!

I am a thoughtful, creative person and I am passionate about student-centered learning. I know that I will find many opportunities to create lessons which engage students and put the bulk of the thinking and learning in their laps. I hope to build my own library of plans in the coming years. I have a few already.

I'm struggling with this now because, as you and several of your posters suggested, students will balk at first. As a STUDENT teacher, all I have is the "at first" because I'm not sticking around to see it through.

Therin lies the rub. I don't want to lecture from here to May, but I also am reluctant to disrupt the current routine drastically with my experiments and then walk out. I am also learning to juggle my graduate work with all the other responsibilities of teaching: school rules, culture, classroom management, knowing students, clarity of content, assessment, grading, etc. So, I don't have a lot of time, as a student AND a teacher, to clear my head and think up innovative strategies for each day.

I appreciate your article and all the subsequent posts. I look forward to building many student-centered lessons in the coming months. Hopefully I can share them with other teachers as well.

I hope to land a job teaching math to grades 7-12 within an hour of my home this coming September. That's the plan.

For the next four weeks I will be teaching factoring and quadratic equations. So, if anyone has tried any student centered activities with success in that arena, I would be overjoyed to hear about them!

Thanks to everyone for your thoughts and ideas. What a great resource!

Sarah Huggins

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