New Ways of Learning = New Ways of Teaching.

Since the late 1970s, educators have been researching such concepts and practices as mastery learning, programmed learning, behavioral objectives, ability grouping, Bloom's Taxonomy, word attack skills and classroom management. Teachers have been taught that specific teaching behaviors result in higher standardized test scores for their students (Brandt, 1988/89; Elmore, 1992; Resnick & Klopfer, 1989).

More recently, journal articles, inservice training programs and education courses are emphasizing such ideas as whole language, reader's and writer's workshops, NCTM (National Council of Teachers of Mathematics) Standards, discourse, Grand Conversations, literacy, selfdirected learners and learning communities. Now, teachers are being taught that student learning is a process that requires students to be actively, purposefully engaged.

Clearly, education reformers are calling for far-reaching changes in instructional practices. Teachers implementing these new practices experience a dramatic shift in their role. Others considering implementation are wondering how best to start. Some teachers, parents, legislators and members of business and industry question the efficacy of such different strategies, often sparking acrimonious public debates. School board members are voted in or out according to their views on these methods. All who are aware of the changes are making decisions about their merit and effective use. Yet seemingly few of these teachers, decision-makers and other stakeholders understand the philosophical roots of these innovations, their assumptions and intents, or the connections among them (Battista, 1994; Peterson & Knapp, 1993; Watson, 1994).

What is this "revolution" in teaching? How did it come about? What are the fundamental differences from traditional practices? Can the new practices mesh with more established ones? Are these innovations more effective than traditional strategies? Are these ideas just the latest fad or are they sohd, research-based alternatives?

These questions and others will be answered only by studying the principles of learning and teaching that underlie the innovations. With such an understanding, parents, legislators and educators can make sound and reasoned decisions regarding implementation. When teachers understand the foundations as well as the surface features of new instructional practices, they will be able to use them more effectively (Battista, 1994; Peterson & Knapp, 1993; Watson, 1994).

Current Innovations in Reading and Language Arts 

A visitor to Mr. R's 3rd-grade class hears a low hum of activity and sees children scattered around the room, some working alone and some in groups. Seven children are clustered around Mr. R, who is giving a minilesson on using commas. The students are focused on a big book and discussing the patterns they see in comma placement. Mr. R directs the children's attention to individual trade books they have chosen and asks them to find more examples of commas. Later, he will ask them to choose a piece of writing from their writing folders and work in pairs to place commas correctly.

In another part of the room, four students are discussing their reactions to the book Freckle Juice by Judy Blume (1971). One student seems to be posing questions, while all are eager to voice their ideas.

A student teacher listens to a child explain how he decoded an unfamiliar word from his trade book. Occasionally, the student teacher asks a question or restates what she has heard; mostly she listens and jots brief notes on her clipboard.

Current practice in language arts and reading emphasizes developing the learner's ability to use language through reading real, whole texts and through composing purposeful text. Language literacy skills and strategies are developed in meaningful contexts and as they are needed, rather than as separate skills to be applied later. Mr. R's students, for example, are learning to place commas by examining their practical use in literature and then using them in their own writing. The teacher perceived a need for a lesson on commas by examining the students' writing. In contrast, a teacher using a more traditional approach would have first taught the rules for comma use and then asked students to insert commas in a series of sentences. Such an instructional approach has little connection to the students' writing or the need for commas.

Teachers adhering to the whole language philosophy attempt to integrate all of the language areas. Students combine writing, reading, spelling and handwriting to communicate real messages to real audiences, such as writing a letter to an author. Literacy learning is a developmental process that the teacher facilitates by providing modeling, authentic experiences, mini-lessons on specific topics and frequent opportunities for students to consult with and learn from each other. Students learn as they create their own meaning and actively take charge of their own learning.

Current Innovations in Mathematics

A math lesson has just begun in Ms. C's 4th-grade class. Ms. C is explaining, "Yesterday when we were measuring distances in social studies, Malik and Alisha said that 1/4 and 4/16 are really the same thing, and we spent a little time discussing their theory. Some of you gave reasons why you think it would always work and some of you talked about why it wouldn't. Today, I want you to work alone or in groups to prove or disprove their idea. Malik and Alisha, let's have you go over your discovery again to refresh us."

As Alisha and Malik use the overhead projector, a rule and some Cuisenaire rods to explain the concept of equivalent fractions, other students listen and ask questions or make comments to clarify their understanding. A few students point out inconsistencies and pose other situations where the theory does not seem to work. As more students become involved, Ms. C directs the other students to demonstrate equivalent fractions themselves, using whatever manipulative they wish. Students choose fraction circles or bars, rods, geoboards or counters to set up their fraction problems. Ms. C circulates around the room, asking students what they are doing and thinking and requesting them to explain their rationale. Often, she presents additional or even contrary evidence, asking students to explain it in light of their ideas. Later, she will bring the whole class together again to discuss new theories, ideas and processes.

Innovative mathematics instruction today is guided by the National Council of Teachers of Mathematics' (NCTM) Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Standards for Teaching Mathematics (1991). These standards call for students to independently discover mathematical concepts and skills through active exploration and reflection. They emphasize building students' mathematical reasoning and problem-solving abilities so that every student develops mathematical insights, rather than simply memorizing formulas. Mathematics is kept "whole" by connecting traditional areas (e.g., fractions and subtraction) to each other and to practical applications. The teacher facilitates active student learning by providing motivating mathematical situations, engaging students in thoughtful discourse and stimulating mathematical thinking. Students learn by working independently, as well as with others, and by actively making sense of mathematical situations.

Changing Views of Learning and of Teaching

The innovations described above, as well as others in science and social studies, reflect interrelated paradigm shifts in views regarding the purpose of learning, the content or knowledge to be learned and how learning occurs.

Purpose. Dewey, Brownell and the Progressive Movement initially proposed in the early part of the 20th century an emphasis on meaningful learning.

In their lives and work and thought, people do not need simply to be able to recall facts or preset procedures in response to specific stimuli. They need to be able to plan courses of action, weigh alternatives, think about problems and issues in new ways, converse with others about what they know and why, and transform and create new knowledge for themselves; they need, in short, to be able "to make sense" and "to learn." (Peterson & Knapp, 1993, p. 136)

This approach subsequently was deemphasized in favor of more measurable rote learning. Rote learning will not suffice in education today; rather, education requires meaningful learning that allows one to manipulate and reflect on knowledge in order to solve unforeseen problems. This view underscores the need for teaching methods that promote understanding, not memorization, and is the impetus behind many new practices.

Content. Educators traditionally treated mathematics as a set of rules and procedures developed by highly trained mathematicians that must be memorized and applied. In a more recent view of mathematics, Lauren Resnick calls it" . . . an organized system of thought that [students] are capable of figuring out" (Brandt, 1988/89, p. 14). Thus, students make sense of patterns and invent understanding, which they use in solving problems. Similarly, today's language literacy is not a set of phonics, punctuation and spelling rules to be absorbed and applied. Rather, it is a process that allows one to create text to communicate ideas to a specific audience and to make sense of someone else's writing. Neither math nor language learning is a linear sequence of specific skills; both areas emphasize conceptual learning over procedural learning (Keene, 1994; NCTM, 1989).

Student attitudes are important considerations in both areas. Students are encouraged to see themselves as authors, readers and mathematicians at all ages and stages of development. The NCTM Standards (1989) assert that students should value mathematics and feel confident of their mathematical abilities.

Process. Traditional methods of teaching are based on associationist and behaviorist views of learning proposed by Thorndike in the 1920s and B. F. Skinner in the 1940s (Peterson & Knapp, 1993; Silverman, 1985). These views assume that students learn in a stimulus-response manner; thus, students do drill-andpractice exercises and are rewarded for correct answers (Brandt, 1988/89; Elmore, 1992; Peterson & Knapp, 1993; Resnick & Klopfer, 1989). Constance Weaver (1990) calls this a transmission model of teaching, wherein the teacher possesses the knowledge and directly imparts it to the students. No proof exists, however, that this model is effective in advancing meaningful learning. Research in cognitive and developmental psychology and related fields (Brandt, 1988/89; Resnick & Klopfer, 1989; Weaver, 1990) point instead to what Weaver (1990) calls the transactional model of teaching, in which the student learns through active engagement in authentic tasks designed to create personal meaning. In this model, the teacher is a facilitator who stimulates and guides learning. This process capitalizes on children's natural learning patterns that are present before formal schooling; that is, language acquisition becomes a model for learning to read and write (Weaver, 1990) and a preschooler's informal math knowledge and intuitive processes provide the basis for formal mathematical education (Peterson & Knapp, 1993).

This emerging paradigm of learning and teaching, now known as constructivism, is not entirely new. As mentioned previously, it is derived from the ideas of Dewey, Piaget and Brownell and has influenced such reforms as the "New Math" of the 1950s and 1960s (Peterson & Knapp, 1993; Silverman, 1985). Neither is the clash between constructivist and traditional ideas new; at several junctures in this century educators have argued for one paradigm or the other. Today, dissatisfaction with public schools and subsequent calls for reforms are prompting educators and researchers to move away from Thorndike's and Skinner's traditional views and look more closely at constructivist ideas.

Constructivist Principles

Proponents of constructivism believe that knowledge should be constructed by the learner rather than transferred from the teacher to the student. For example, students might learn about the commutative property for multiplication (3x4 = 4x3) by counting objects in equal groups and observing that four groups of three is the same as three groups of four. After conducting further testing to prove that this property holds true for all numbers, the student explains the discovery to the teacher. In contrast, behaviorist teaching typically requires the teacher to define the commutative property for the students, explain it with examples and then ask the students to practice using it with a set of exercises. Behaviorists view knowledge as being an accumulation of facts; constructivists see it as understandings that are continually developed and modified by the learner.

One of constructivism's basic tenets is that knowledge is subjective; that is, everyone creates his own meaning of any particular experience, including what he hears or reads. Thus, any two people reading the same material will interpret it differently. One of Mr. R's students reading Freckle Juice may consider the main character to be foolish, while another student may view him as inventive. Regardless of how tightly the curriculum is sequenced and delivered, students will construct their own unique meanings.

Another basic tenet holds that children learn through integrating new ideas into their existing knowledge structures. Piaget described this integration as the processes of assimilation and accommodation (Bodner, 1986; Fosnot, 1989). Assimilation occurs when new information can be interpreted in light of what the child already knows; thus, it simply extends existing knowledge. Accommodation occurs when the new experience contrasts with preexisting schema, which then must be modified so that the new information "fits." It is important to recognize that these processes are within the child; new information cannot be manipulated by the teacher either to "fit" with existing schema or to change it in some predetermined way. The teacher's role is to create disequilibrium; that is, to provide stimuli that cause children to examine, expand and/or modify their existing knowledge. Thus, Ms. C may ask Malik and Alisha how many twelfths (which are not on the ruler) would equal 1/4 and 4/16. Through this investigation, Alisha and Malik would examine their rationale for 1/4 = 4/16 and either confirm it or modify it in order to apply to other situations.

Constructivist Teaching Practices

Constructivist teaching practices share several major characteristics:

* Active Learning. In order for students to create their own meanings and build their own knowledge, they must be mentally and physically engaged in their work. The students in Mr. R's and Ms. C's classrooms read books of their own choice and respond to them by writing in journals or discussing them with peers and/or the teacher. They learn how to write, punctuate and spell by examining how authors do it. They learn math concepts by exploring with manipulatives, looking for patterns and solving problems. In all subjects, students learn by making discoveries, reflecting on them and discussing them rather than blindly imitating the teacher or completing exercises to absorb what the teacher tells them.

* Work in Context. Meaningful learning that is conceptual rather than procedural occurs in authentic situalions, not from memorizing facts and skills to be transferred and applied later. Students in constructivist classrooms read children's literature and compose stories and letters that have a real purpose. They solve math problems that they create from their studies and their lives outside school. They use strategies that adult readers, writers and mathematicians use. Consequently, less separation exists betweenin-school and out-of-school learning. Keeping in mind the axiom "The whole is greater than the sum of its parts," the whole is what students experience.

* Student Autonomy. Students cannot create their own learning in tightly controlled situations. Thus, teachers should allow students to take more control of their learning by choosing their own books to read and topics to write about, selecting the materials from which they want to learn and setting up their own investigations. Students in innovative classrooms do most of the thinking and talking, and the teacher provides guidance.

* Social Learning. The construction of knowledge is greatly enhanced through discourse, in which ideas are discussed and "proven" (Fielding & Pearson, 1994; NCTM, 1991; Peterson & Knapp, 1993). Students work collaboratively on projects, challenging and confirming each other's discoveries. Students in "learning communities" have grand conversations (Peterson & Eeds, 1990) about their reading and writing, as in Mr. R's room, and "argue" about their mathematical ideas, as in Ms. C's class. The teacher asks questions not to elicit the "right" answers, but rather to provoke students to examine and expand upon their thoughts. Hence, the teacher needs to foster a safe environment for such risk-taking.

* Teacher As Facilitator. In such learner-centered classrooms, the teacher moves away from dispensing information and toward guiding students' efforts to make sense of their work. The teacher designs situations that allow the students to learn by doing and that actively promote the students' thinking and investigating. The teacher listens, watches and questions students to bring forth their prior knowledge, thus revealing misconceptions and miscues. The teacher can then help students learn from these events by providing further learning experiences, pointing out discrepancies and asking students to resolve them, and occasionally supplying additional information.

* Ongoing Assessment. Individually constructed meanings cannot be measured within the constraints of standardized tests. Innovative classrooms permit learning to be continuously assessed as students work, not through contrived questions at artificial checkpoints. Math and language portfolios (containing work in progress as well as finished products), individual conferences where students discuss their strategies, and written and verbal explanations of student reasoning demonstrate progress. Alternative assessment practices such as these are consonant with a constructivist view of learning.

Alignment of Beliefs and Practice

Constructivist classrooms are not diametrically opposed to those based upon behaviorist views of learning and teaching. Teachers will continue to use some direct instruction in mini-lessons and demonstrations, the teacher still decides which critical concepts and skills must be learned and students will require a great deal of structure if they are to be productive with their choices. The fundamental differences lie in contrasting beliefs and assumptions about learning and teaching. Those involved in making decisions about education practices, including teachers, administrators, parents, policymakers and legislators, must examine their own beliefs to determine what should receive the greatest emphasis in classrooms:

* children learning through putting together separate skills, or through immersion in authentic situations

* children learning basic information, or building their own understanding of subject matter

* teachers who tell children what they must know, or who trust children to learn through experience and reflection with teacher guidance

* teachers who are the only ones with the answers, or who engineer learning situations whereby students make their own discoveries.

Effective implementation of current instructional innovations requires an open mind toward (if not agreement with) a constructivist philosophy of learning. Struggling with the above questions may help policymakers and practitioners alike determine their willingness to embrace this philosophy, which may be an indication of their potential for success.

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Mary K. Heuwinkel is a doctoral student in Elementary Education, University of Northern Colorado, Greeley.