The following has been modified and excerpted from a teacher-training video, Inspiring to Learn: Actively Involving Students in Mathematics and Science, produced in 1995 by the Clayton County Public School System, with funding by SERVE (SouthEastern Regional for Vision in Education). It is presented as an example of one approach by a local school system in Georgia that is already implementing materials and objectives contained in the Learning Framework.

The presenters for the one-hour video are two Clayton County elementary teachers with a combined experience of 25 years in public education.

Teaching is a joy, and a challenge. Whether we've been teaching for two years or twenty years, as teachers we continually struggle with that central question: how do children learn? What inspires them to reach out and want more, and what inspires us, as teachers, to keep searching for more effective and more fulfilling ways to do what we were trained to do; prepare our students for the future.

Often, one of the greatest challenges we face today as elementary teachers is tackling the mathematics and science parts of our curriculum. We'd like to share with you what may be some different strategies for teaching, although chances are you're probably already using some of them right now - because a lot of it is just good basic teaching.

The approaches we're going to demonstrate and talk about have been embraced by the Georgia Initiative in Mathematics and Science, or GIMS, in response to the national call for a reexamination of what's working and what's not working in education in America today. The GIMS program is a collaborative project of seven Georgia universities and colleges, and, with funding by the National Science Foundation, GIMS is developing the Georgia Framework for Learning Mathematics and Science. These teaching methods are the keys to implementing this framework. The Learning Framework is helping to define the most effective strategies for teaching students what they need to know to meet the National Standards in Mathematics and Science. Within these NCTM standards there is a call for "a shift in emphasis from a curriculum dominated by an emphasis on memorization of isolated facts... to one which emphasizes conceptual understanding."

During the first part of this video we're going to teach a sample lesson, illustrated by examples from different actual classroom situations. In the second part, we'll go into more detail, meet some teachers who are using these strategies, and provide resources for follow-up.

There's an old proverb: "I hear and I forget. I see and I remember. I do and I understand." And that belief really lies at the heart of what teaching and the understanding of learning are all about. In life we learn by doing. This is especially true when we're younger, less able to grasp abstract concepts, and more at home experimenting with life. But in most classrooms, it's the teacher who's more often doing the "doing" - demonstrating and speaking from the front of the class while the students follow along. While this "teacher centered" classroom approach will always be a valuable and necessary part of teaching, it may not always be the most effective, especially when dealing with some of the abstract concepts found in mathematics and science. Sometimes it's more effective to let the students discover the answer for themselves.

What we're talking about is shifting the classroom focus from "teacher centered" to "student-centered." Empowering the students to bring the knowledge they already have, and their own reasoning skills, to work with each other at a concrete task that, when completed, will give them a far deeper understanding of the principles involved than simple memorization might achieve. In a "student-centered" classroom activity, learners are encouraged to experiment and explore at their own rate in peer groups, and then share their answers under the guidance of the teacher. It's a process that can be exciting, productive, and surprising, for students and teacher alike. But most importantly, it helps to develop and nurture ways of thinking that will be crucial to a student's success later in life.

The Framework for Learning calls these patterns the Habits of Mind, and identifies four key aspects: Problem Solving, Communicating, Reasoning, and Making Connections.

• In this approach to learning, confidence in one's ability to solve problems, both on one's own and working with others, is encouraged through a process of hands-on experimentation, and leads to the realization that there is almost always more than one way to solve a problem.

• Communication skills are sharpened by encouraging open discussion, and by directing the focus away from simple recall of facts and procedures, to guiding the student to a deeper understanding of the concepts and principles underlying the task.

• Reasoning and the development of logical ways of thinking grow naturally out of the need to explain or question the various answers generated by the lesson.

• And the entire process is grounded in the real world as students learn to make connections between the specific answers they've arrived at, and activities in their daily lives, as well as making connections to other subjects they may be studying.

a. Presenting the Lesson

• It's always important to start a lesson by communicating clearly the objectives of the lesson, and then find out how much the students already know. Every student brings to any subject some basis of knowledge, along with acquired preconceptions and misconceptions.

• Getting a sense of where the class is with the subject matter helps the teacher to avoid either teaching too far ahead of the students, or repeating information they may have already learned.

• Drawing this out through questioning and discussion helps to lay the groundwork for the lesson, and gets the students engaged in thinking about the problem right from the start.

• It's important to give clear directions and encourage good observation and record keeping.

b. Organizing the Classroom

How you organize the classroom is very important.

• Group students to encourage cooperation and sharing, and arrange materials to make it easy for hands-on experiences.

• You may want to actually rearrange the desks into different groupings, or push them back and let the students work in groups on the floor or about the room.

• Sometimes teams of four may be appropriate, or in others, teams of two or three. The important thing to remember is that the size of the groups and the arrangement of the room be structured to suit the lesson at hand, taking into account such matters as safety, practicality, and the age of the students.

• The challenge here for many teachers is allowing for a more "student centered" classroom management style. It can sometimes be a noisy and active experience. But it's important for the teacher to be willing to step more into the role of facilitator, encouraging the students to use their own imaginations to explore the problem in different ways and at their own rates. The result can be a classroom full of creativity, enthusiasm, and learning.

c. Exploring the Problem

A key part of this approach to teaching is giving the students hands-on activities so that they can explore the problem. There are as many ways of arranging lessons as your imagination can create. As someone said, "If you want to make a course interesting, then you should study something of interest" (p.15).

• Use your imagination to create lessons where children are involved, working through problems together, and focused on an activity that is not just paper and pencil.

• Hands-on activities help students learn to solve problems in ways that often lead to a far deeper understanding of the principles involved. This way of learning helps to support those problem solving skills that are a key part of the Habits of Mind.

• By working with their peers to discover answers for themselves, students develop confidence in their ability to figure things out in life using their own innate knowledge and imagination. They discover that learning can be fun!

d. Finding Solutions

• It's important to draw out multiple answers, and to encourage students to keep searching for better answers through explanation and discussion.

• Sharing their answers gives students at all learning levels a chance to participate, and a feeling that they too have contributed to the process. This is also the stage where the second and third aspects of the Habits of Mind are fully explored; communicating and reasoning. Obviously students have been using both of these during their problem-solving activities, but in being required to communicate their answers collectively, and then reason through the why's and why not's, they're encouraged to develop strong communication and logic skills.

e. Summarizing the Results

• In summarizing the results of the lesson, it can be useful to post them in some concrete way to serve as a reminder to the students of what they've learned.

• It's also here that we take the final step found in the Habits of Mind, and help the students to make connections between what they've learned and practical activities found in their daily lives.

• Giving students an opportunity to place their results around the classroom can give them a sense of ownership and pride in their work, and help to solidify the lesson in their minds. What's important is the understanding that the more relevant the material feels to student's lives, the more interested they'll be in using that knowledge, and the more eager they'll be for the next lesson.

In the Introduction, we gave you some of the theoretical foundation and demonstrated some basic teaching techniques, but there are two other equally important steps to consider: Planning and Assessment.

Planning the Lesson

• As teachers, we all know how important it is to plan our lessons, and planning is equally important here. Thinking through your lesson concepts and objectives, how you will arrange the class, what materials are needed, and how the lesson fits into the daily routine and overall curriculum can anticipate problems and save a lot of time and frustration in the classroom.

• You may want to allow for a monthly planning session where you plan for an entire concept or subject to be covered in the weeks ahead. Otherwise, planning doesn't have to take a lot of time. You can have a quick session in the teacher's lounge, walking down the hallway after school, or even over the phone from home. The important thing is to plan, so that your lesson goes smoothly and your students get the most they can out of your teaching.

• It's important to seek out peers who are open to and interested in the techniques you'll be using, and enlist them as partners in your teaching. If you're having trouble with something, ask for advice. Find someone you trust and model teach for each other. Ask what others are doing. In some cases you may even have someone else in your school who's already using these techniques.

Assessment

• Assessment is important to give teachers a sense of how we're doing, and how we can improve our teaching. Once again, this is a great opportunity to call upon our support network, to use our co-workers and, if possible, teachers who have gotten more extensive training in these techniques, as sounding boards for our own growth.

• It can be helpful to take a few minutes at the end of the day to try and objectively ask yourself how you did with the lesson, where the problems might have been, and what can you do better next time. It really becomes just a natural part of the planning process for the next lesson.

• Sometimes it helps to share your questions with someone familiar with what you're doing, perhaps even asking them to observe a lesson, and to help you to reflect afterwards on what happened.

• Periodically, it will be helpful to plan for an assessment session after a lesson in which you may have tried a new teaching approach, or introduced a new learning activity to the students. In an assessment session, work with a peer who will encourage your self-assessment, ideally one who may have helped you to plan the lesson. Areas to cover include:
  • What was the critical moment? (When did you feel that the lesson was working?)
  • What problems did you encounter in the lesson?
  • How will you assess the students and make sure they got the lesson?
  • What could you do to improve next time?
  • How will the lesson lead into the next topics to be covered?

• Abstract concepts are difficult to master, and students often learn best by doing. The more involved they are in a learning activity, the more apt they are to understand the underlying principles and to retain the knowledge.

• When presenting a lesson, state the objectives clearly and find out what the students already know about the subject.

• Incorporate "student-centered" lessons by organizing learning activities to facilitate hands-on, stimulating experiences that encourage cooperation and shared information.

• Provide clear directions and rules for the lesson. Encourage careful observations, the recording of data, and collaborative discussion between students.

• Engage the students in communicating and reasoning, with the understanding that there are often multiple answers for problems. Encourage discussion of the various answers.

• Complete the lesson by posting public data charts or lesson reminders, and lead the students to make connections between the lesson, daily activities, and other subjects.

These are very flexible techniques that you can adapt to suit your own particular teaching style. As with all teaching, you'll be constantly involved in the process; adjusting, guiding the students, making improvements. Often, the main obstacles in getting started for many of us are simply fear of change, and a concern that somehow we'll lose control of our classroom, or lose time and not get the results we want. But in reality, once you get started, it can open up a whole new way of teaching for you that is more interesting and productive for both teacher and student alike.

Most good administrators are also looking for ways to improve the teaching in their schools. There are resources like the Framework for Learning that will give them the background they need. Make them a partner in your process of learning, share your enthusiasm and they'll want to know more. In Georgia, there's now a program underway just for administrators, designed to introduce them to the advantages of these types of teaching methods.

Many parents who have had the techniques explained to them and whose children have been taught using these techniques are enthusiastic as well. It is important to take the time to explain what you're doing to these interested parents.

Of course, no one expects you to jump in and start using everything you've learned right away. There's no reason why you couldn't pick one or two ideas you like and begin incorporating them into your lessons, and then build upon that one step at a time. There are other resources available to you. We really hope that what you've seen will help to inspire you to expand your ideas of how mathematics and science, or any subject for that matter, can be taught. Inspiring students to learn - isn't that what it's all about?