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Work of Mary Baratta Lorton is

Introduction
Although many primary teachers may not have heard her name, nearly all are using concepts and manipulatives designed by her or her successors. Mary Baratta-Lorton has had a profound effect upon mathematics education in the early grades. In her brief life (1944-1978)she wrote four books, gave numerous workshops, and setup a support system for teachers who were using new innovative techniques. Workjobs (1972), her first book has sold more than 400,000 copies. Math Their Way (1976), which has sold 450,000 copies was adopted by the State of California as a state textbook in 1985, and it was used in the 1989 NCTM standards. Her influence is still felt today through her books, which continue to be in print and have achieved “classic” status.

Background
There were few things in her early life that foretold the amazing innovation and success that she achieved as an adult. During her childhood, the family moved into a house, which today would be described as a “fixer-upper.” All the members of the family learned to repair and replace things. Mary especially enjoyed making and repairing items. Her mother encouraged Mary's creativity. For instance, she allowed Mary to use real eggs in mud pies. However, Mary's creative genius was not recognized until after she had completed her undergraduate work at the University of California in Berkeley.

Early Teaching Career
After completing a degree in librarianship, Mary enrolled in a unique teacher training program at Berkeley. The turbulent 60's gave birth to many innovations in education including this internship-mentoring program. She and her fellow pre-service teachers were placed directly in inner city classrooms. After teaching in second and fifth grade classrooms, Mary was moved to kindergarten. She took a course on Piaget and began experimenting with various homemade games and materials, that one kindergartner described as “workjobs.”

Early Innovations
When Mary refused to use an expensive, district supplied math kit, her supervisor investigated. “She was so impressed with Mary's 'Workjobs' that she sent as many people as she could to see Mary's classroom.” Mary's innovations attracted so much attention that she was invited to join the Miller Math Project. This project gave her a chance to give workshops and train teachers while she continued developing her own materials.

Her Contributions
Workjobs In 1972 she published Workjobs, containing more than 100 activities covering both language and mathematics development. Mary's teaching philosophy was clearly enunciated: "During my years of teaching I have made learning tasks for the children in the form of manipulative activities built around a single concept. My idea was that through active involvement with materials the child would draw out the generalizations within the material. Through conversations with me, the teacher, the child would have the opportunity to ask him questions to help him become aware of patterns and relationships he intuitively observed but could not yet clearly define." (Workjobs p. 3) "This discussion between the teacher and the child at the completion of each activity is crucial; it provides the opportunity, the need, for each child to express himself in language. Unless the teacher creates this opportunity, through her questions, a child who does not have the verbal facility to express himself clearly will have no reason to attempt to organize his thinking and express his thoughts in words." (p. 18)

Workjobs is a combination of practical, insightful, and pedagogically sound activities that was an immediate “hit” with teachers. The book was so successful that it sold over 100,000 copies before it was advertised.

Scope and Span of Workjobs The book contains an incredibly wide range and variety of activities. There are some obviously Piagetian tasks such as sequencing (p. 21), serialization (p. 182, 214), classification (pp. 67-107), pre-conservation of volume (p. 23, 232), and comparisons (p. 31, etc.). Mary enjoyed using materials that were readily available and familiar to students. These authentic materials included common objects (p. 190), supermarket bottles and packages (p. 122), as well as real money (p. 252). Her reasons for using real money included: enhanced realism of the activity, and learning responsibility and respect for money (p. 252). “It [school] can be a place where a child works with concepts and ideas concretely by handling familiar objects and manipulating them before dealing abstractly with the concepts on paper.” (p. 240). Workjobs activities appeal to different sensory modes: sound (p. 110), sight (color) (p. 102), smell (p. 90), and touch (p. 42, 81, 96). They also transcend traditional gender roles using screws (p. 47), cooking rice (p. 23), toy cars (p. 162), and bracelets (p. 184). The reading and math activities are carefully designed to provide graded, sequential steps. For example, math begins with one-to-one correspondence, then moves on to counting, combinations and addition, sequencing, comparisons, measuring, time shapes and estimation (p. 127-137). All of these activities are built around her basic beliefs regarding math instruction: "Mathematics is living—life—not rote drill with meaningless symbols and still more meaningless “answers.” . . . . They [the activities] are intended to assist the child in organizing the mathematics in the world around him. He handles familiar objects and sees sets of objects that he can count. He learns number facts through experience, not by memory. In this way, he will grow to see mathematics as natural and significant, and symbolization and computation as a way of writing down his experiences so they can be shared." (p. 127)

The math activities provide extensive practice with number concepts using a wide range of objects: blocks (p. 145), pictures (p. 152, 186, 204), flowers (p. 142, 164), beads (p. 200, 202), toys (p. 158, 174, 184, 196), walnuts (p. 236), golf tees (136), dog biscuits (p. 234), safety pins (p. 132), clothes pins (156), and other objects. The range diversity and attractiveness of the manipulative activities found in Workjobs is phenomenal. Mary designed the activities to be done at learning centers. The activities were both self-paced and self-rewarding. After initial training, the students were able to carry on the activities and to self-record results. It is not surprising that this innovative, practical system has caused Workjobs to achieve “classic” status and remain in print for more than a quarter of a century.

Workjobs for Parents In 1975 an abridged edition for parents was published. It was titled Workjobs for Parents and contained 40 activities for home use.

In-service Workshops
In 1973 Mary and her husband Bob left the classroom to concentrate on writing and giving workshops. In 1975 they founded the Center for Innovation in Education, Inc. As Mary and Bob continued to work for improved educational methods, they realized that workshops could be forgotten easily. The solution was to organize participants into groups and to send periodic newsletters. This combination of post-workshop support has been vital. More than 240,000 teachers have taken in-service workshops run by the center. Through her books and workshops, Mary has altered the course of primary level math instruction in both the United States and the world.

Mathematics Their Way
In 1976 Mary published another ground-breaking book, Mathematics Their Way. Once again Mary's pioneering philosophy is evident: “If the method isn't teaching a child, try something different. Look to the child and change how you teach until you find what works.” (Mathematics Their Way p. i)

Involvement She involved children not only in learning, but also in setting up the classroom. “Children should come to school the first day and experience blank bulletin boards and participate in making the classroom their classroom. If they bring things from home, they have a part in creating the learning materials” (p. 3) “Before school starts, I mail home a note to my children telling them I am going to be their teacher during the next year. I ask them to bring collections of buttons, lids, toys, bottle caps, rocks, old keys, acorn tops, or other local items” (p. 36). In this way the children gain “ownership” of the materials. As the school year begins, the children are given a period of free exploration lasting several weeks before embarking on content-based activities. Children are continually encouraged to actively participate: “It is important to work with the children's suggestions, even if they sound silly, because children need to experience over and over again that in school their ideas count” (p. 67). In addition to this, children need the chance to explore their ideas and theories in order to learn how to be inquirers and self-educators. One of the ways this is encouraged is having the children do many different sorting and classifying activities. “Children derive much more benefit more from exhausting the possibilities of sorting one material than from sorting many different materials in one way only” (p. 68). Not only do the children have ownership, but they also are learning to be actively involved in their own education.

Verbalization "[As they experience patterns visually, auditorily and physically], children analyze, duplicate, and extend many different patterns, describing each pattern in a variety of ways. This verbalization helps the children feel the pattern they experience visually and creates great interest and enjoyment in looking at patterns." (p. 20) As children become better at verbalizing, Mary advises the teacher to have the children literally “sit on their hands” (p. 65). This causes the children to be completely verbal and not to use their hands or to point or motion. Mary also warns teachers to place the most loquacious in their own separate group. “When the most verbal children are mixed randomly with children who are less verbal, the former tend to dominate the group” (p. 64). As the children gain knowledge and verbalize concepts, the teacher continues to guide and extend. "Always use language that is familiar and meaningful to the children while teaching a new concept. . . . Once the child understands the concept of subtraction [as an example], it is a very simple matter to substitute the more mathematical vocabulary. Premature introduction of technical vocabulary only complicates matters for the child." (p. 194) Mary understood how to begin where the child was and then to lead him or her toward a wider understanding of concepts. Verbalization is an important step in the process.

Developmental Levels Mary divided the development of number concepts into three distinct levels. The first was the concept level. Before children wrote or even talked about numbers, they needed massive practice with numerical quantities in order to develop the concept of numbers. Many teachers have failed to realize that “being able to recite numbers in order does not necessarily mean that a child is able to count” (p. 90). In Math Their Way, Mary describes 40 different activities to be used at the concept level. The first activities deal with counting and a one-to-one correspondence. There are several activities on invariance or conservation of number. (More of these types of activities are given later in the book.) The next activities deal with “counting on” (continuing to count forward from a given number), and then counting backward. These activities lay the experiential background for adding and subtracting. Once again the concept level is of paramount importance because it is the one and only foundation for arithmetic.

The second level of development is the connecting level. At this level, children write down numbers and use the plus and minus symbols. Math Their Way contains one chapter with 13 activities for this level (pp, 214-233). The students are now dealing with arithmetic at a symbolic level.

The symbolic level is the third level of development. At this level students write down equations (number sentences) to represent situations. All of the 10 activities in the chapter on this topic require writing (pp. 234-251). The students are now dealing with arithmetic at the symbolic level.

Other Topics Math Their Way also contains chapters on place value, graphing, patterns, and comparing. There are also chapters covering sorting, comparing, and informal measurements. Each chapter contains numerous activities that are thoughtfully conceived and appropriate for early childhood education. Altogether there are more than 170 different activities. The breadth and depth of this book are similar to the wide scope found in Workjobs. It is no wonder that the state of California adopted it as a text.

Holistic Approach Mary Baratta-Lorton was very clear about the holistic nature of children's learning processes. "It has taken me ten years to unravel the way children really learn mathematics best. I assumed that the sequence used in children's textbooks represented the most successful model. . . . This model is a successful and necessary tool for writing a textbook, but not for learning. . . . Our children's world is not linear. . . . Children develop more understanding of the whole world of mathematics and more flexibility in dealing with number if they have the opportunity to deal with all the operations at once." (pp. 210-211) She realized that many different activities must be used flexibly in order to educate children in mathematics.

Workjobs II
In 1979 Mary published her last book Workjobs II. The book provides kindergarten, first and second grade teachers with complete instructions for making and using 20 open-ended math activities as an enriching supplement to their present classroom math program (Workjobs II p. 2). She has chosen these 20 particular activities based upon the following criteria: "1. The materials proved durable. 2. They were relatively easy and inexpensive to assemble. 3. They were made from common, familiar materials. 4. They were attractive and held interest." (p. 36) The 20 activities were designed so that they could be used at each of the three different concept levels. This meant that each activity could be used three times during the school year in three different ways.

These activities are a rich addition to those described in her previous books. The explanations given in Workjobs II are more details regarding the levels of development than those given in previous books. Concerning the concept level, she says, “No written symbols are used at this stage of development because notation will actually cut the child off from his or her unique thinking process ”(p. 98). Mary realized that symbols “confined the attention” and narrowed children's thinking (p. 98). She also knew that children needed to remain at a specific level until they had mastered it. Readiness to move on was signaled through a “combination of confidence and slight boredom” (p. 99). In summation, Mary stated, “We should wait for the child to push us, rather than us pushing the child” (p. 99). She knew that children need a strong, secure, empirical base for mathematics.

Mary's Contributions
Mary Baratta-Lorton changed the way primary teachers thought about and taught mathematics. She made math practical for both students and teachers. She made Piaget sensible. Her books continue selling nearly 30 years after her death even though the politics of mathematics education have changed many times. Although many programs have copied, supplemented and extended her methods, no one has really improved the basic concepts and techniques which she established.

Mary was able to accomplish these things because of her driving curiosity. She was willing to brainstorm and let “silly things” in. She was inventive and always searching. She wanted to help children make sense out of their world. Mary had a unique ability to enter into the child's world and explore with them. She was always seeing new things in the ordinary and obvious. Math educator Kathy Richardson has called her “a genius”. Marilyn Burns, another expert in the filed of math education, has remarked, “I don't think that Mary even realized how brilliant some of her thinking was”. Mary Baratta-Lorton has left a permanent imprint on primary mathematics instruction.