Interim Report of the Logo Project in the Brookline Public Schools: An Assessment and Documentation of a Children’s Computer Laboratory

Source: Papert, S., Abelson, H., Bamberger, J., diSessa, A., Weir, S., Watt, D., Hein, G., & Dunning, S. (1978). Interim Report of the Logo Project in the Brookline Public Schools: An Assessment and Documentation of a Children’s Computer Laboratory (MIT Artificial Intelligence Laboratory Artificial Intelligence Memo, Issue. 

Interim Report of the Logo Project in the Brookline Public Schools: An Assessment and Documentation of a Children’s Computer Laboratory

A.I. Memo No. 484

LOGO Memo No. 49

June 1978

Massachusetts Institute of Technology — Artificial Intelligence Laboratory

This report was written jointly by the following:

MIT Logo Group

• Principal Investigator: Seymour Papert
• Co-investigators: Harold Abelson, Jeanne Bamberger, Andrea diSessa, Sylvia Weir, Daniel Watt

Brookline Public Schools

Program Evaluation Research Group, Lesley College

• Evaluation consultants sub-contracted through Education Development Center Inc.: George Hein, Stephanie Dunning

Abstract

The LOGO activities of a group of 16 sixth-grade students, representing a full spectrum of ability, are being documented with a view to developing ways of capturing the learning possibilities of such an environment. The first group of eight subjects have completed 25 closely observed hours, extending over 7 weeks, in a LOGO classroom situated in a Brookline school. This is an interim report on these observations designed to exhibit the content of what has been learned; and insights into both the variety of cognitive styles of the pupils and the variety of learning situations available to a teacher with which to respond to different pupil styles and abilities. We have a large amount of data available for analysis, and we are interested in looking at this material from several points of view. The current state of our various analyses is presented here, without any effort to prune the considerable redundancy which has been generated in the process of doing this multiple-cut exercise.

This work has been carried out jointly by members of the MIT LOGO group (H. Abelson, J. Bamberger, A. diSessa, E. Hildreth, S. Papert, D. Watt and S. Weir); and evaluation consultants to Education Development Center (G. Hein, and P. Dunning, of the Program Evaluation and Research Group of Lesley College, Cambridge). This report of the Brookline School Project summarizes our main findings and gives illustrative examples from the children’s work. A detailed profile of the observations made about the child’s work during the experimental period October–December 1977 is found in Appendix I.

Table of Contents

1. Introduction
   • 1.1 Aims of study
   • 1.2 Questions we are trying to answer. Statement of our answer.
   • 1.3 Subjects and Timetable
2. Methodology
   • 2.1 Remarks on Evaluation
   • 2.2 General Remarks on LOGO Teaching
   • 2.3 Organization of the LOGO Classroom
   • 2.4 Specific Teaching Strategies
   • 2.5 Comparison with Other LOGO Studies
3. Individual Profiles
4. Theoretical Interpretations
   • 4.1 Science
   • 4.2 Math
   • 4.3 Cognitive Styles
   • 4.4 Affective Aspects
5. Interview Findings
6. Observer Findings
7. Conclusions
8. Bibliography
9. Appendix I: detailed profiles of each child’s work
10. Appendix II: detailed analysis of each child’s learning in the area of computer programming
11. Appendix III: checklist of LOGO skills used for daily observations
12. Appendix IV: excerpts from the pre/post interview schedule

1. Introduction

1.1 Aims of Study

During the period 1972–1976 the MIT Artificial Intelligence Laboratory developed a computer-based learning environment whose components include:

• the computer language LOGO
• subject matters suitable for beginning students to move easily into programming
• a set of instructional methods
• a small pool of trained teachers

In 1977 we received a grant from the NSF to proceed to develop an evaluation plan of this total environment in the context of a typical urban elementary school. This document is an interim report based on a very careful study during the period October–December 1977 of 8 students covering a range of abilities. More data on these and the other 8 students in the experiment will be available in approximately six months.

Although there have been a fair number of projects in which elementary school students have been given the opportunity to learn to program computers, there is very little published documentation of what transpired in such experiments. We have made a special effort with regard to the detail with which we report on the teaching, the data collection, and the performance of the students.

A major benefit of this type of detailed documentation is the contribution it can make to an evaluation of the learning process in relevant domains. Finding good ways of making such an evaluation is clearly a complex task, and we have explored several ways of pinpointing the skills, knowledge, and attitudes which children may acquire during their LOGO work and of devising ways of demonstrating such acquisition and its transfer to other more general cognitive skills. We have used classroom observers and an interview schedule containing several measures of skill. These latter have been selected for their judged relevance rather than on the basis of previous standardization, and we are clearly at the exploratory stage in this matter.

Further, we hope to provide evidence that there are advantages peculiar to a computer-based learning environment in general, and to a LOGO environment in particular, as a source of pedagogical insights into the learning-teaching process.

1.2 Questions We Are Trying To Answer

In our proposal we list questions which our project is designed to answer. Here we repeat these questions and give the answers as we have been able to formulate them so far.

1. How much can 6th grade children, in a regular school setting, learn about computer programming, using a LOGO environment?
2. What concomitant skills that are part of the standard school curriculum (mathematics, science, and language) do children learn in the course of their LOGO work? Do they acquire concepts that would normally be considered “advanced” for their age level?
3. What non-standard skills (problem-solving through planning and debugging; use of procedural thinking and computer metaphors, etc.) do children acquire in the course of the LOGO work?
4. Does the LOGO experience produce any changes in the child’s attitude towards learning or toward himself/herself as a learner, both in general, and in relation to particular subjects (e.g., mathematics)?
5. What changes, if any, can be found in the child’s attitude towards using computers and towards the role of computers as part of our technological society?

In addition, in the light of the experience reported in this document, we would like to add:

6. Could we gather educationally useful data about the students by observing them in their work?
7. How can we capture what it is that a “good” teacher does so that this can be made available to other teachers?
8. Would observers with experience in different styles of teaching/learning methods identify this one as a particularly exemplary one?
9. Can we gather evidence of other unexpected outcomes, both positive and negative?

The answers to these questions, as we have been able to formulate them thus far, are:

1. Of the eight subjects, 7 were writing well-formed, personally conceived computer programs by the end of the study. The eighth subject did not write programs but seems to have had a significant learning experience. Summaries of all subjects’ work are in Section 3.
2. Our assessment of the subjects’ mathematical gains is discussed in Section 4.2. Delays in the NSF decision process forced us to curtail this round of the experiment, eliminating work specifically on science and language. The second round of the experiment will include a brief introduction to some of this material.
3. The most salient result of the experiment is the extent to which LOGO allows the exercise of individual styles of problem-solving, etc. The data bearing on this is rich and complex. A first pass at analysis is contained in Section 4.3 (Cognitive Styles).
4. In some cases marked changes were noted not only by us but by the evaluators and the teachers. As one might expect, the biggest changes are shown by the poor academic performers. See especially Section 4.4 (Affective Aspects) and the profiles of each child’s work in Appendix I.
5. We did not succeed in this round in obtaining more than superficial insights.
6. (6–9) We shall show throughout this document how much we were able to learn by doing this project about the learning process in general and about individual children.

1.3 The Subjects and Timetable

The subjects for the trial classes were chosen on the basis of consultations among the project staff and the regular classroom teachers. The teachers were asked to rate the 50 sixth-grade students on a 3-point scale of overall ability in school work: “average”, “below average”, and “above average” ability.

The students were then divided into groups of four, so as to achieve the following:

• a range of abilities within each group
• a balance of boys and girls in each group
• a minimizing of scheduling problems in relation to other classroom activities
• a compatibility among individuals in the group to ensure that the groups could be as supportive as possible for each child

Two of these 4-unit groups from each of the two school classes form the 16 subjects of the experiment. An additional commitment to the school was that no child in the 6th grade was to be excluded from the LOGO experience, and this was achieved using M.I.T. student volunteers. These latter children do not form part of the experiment and their activities are not recorded here.

This report concerns the first 8 of our 16 experimental subjects. These 8 subjects were divided into 2 classes and received the following exposure to the LOGO environment:

Teaching periods over 7 weeks (11/4/77 – 12/21/77)

• Class I:
  • 
  • 
  • 
  • Total: 25 sessions, 25 hrs 10 min
• Class II:
  • 
  • 
  • 
  • Total: 25 sessions, 25 hrs 10 min

Teacher Ratings of Students

• Whole Sixth Grade ():
  • I Above Average: 19
  • II Average: 15
  • III Below Average: 16
• Experimental Group ():
  • I Above Average: 6
  • II Average: 4
  • III Below Average: 6

ACHIEVEMENT TEST SCORES: NATIONAL PERCENTILE RATINGS FOR SAMPLE OF 15 SUBJECTS

Name	Grade in which test was given	Total Reading Score	Total Language Score	Total Math Score	Overall Total
Harriet	4	99	99	96	99
Gary *	4	99	95	99	99
Dennis	4	99	75	95	94
Jimmy	4	61	52	77	61
Kathy *	4	61	66	29	54
Monica *	4	50	51	49	47
Albert	4	61	47	35	44
Darlene	4	58	52	31	43
Laura *	4	54	35	31	38
Kevin *	3	41	21	38	31
Karl	2	26	33	32	26
Betsy	4	30	12	21	21
Deborah *	3	40	8	26	20
Ray *	4	2	13	20	9
Tina	4	5	6	3	2

* In sample of 8 subjects reported in this document.

No score available for one child newly arrived at school (Donald).

2. Methodology

2.1 Research Methodology

2.1.1 Choice of Methods

We rely primarily on qualitative methodology: on observations, interviews, and documentation, organized in a carefully designed framework, which provides both a conceptual structure for the project and a data management system. Our approach is similar to other research or evaluation efforts which are undertaken in direct collaboration with educational practitioners, and which are intended to have immediate impact on school situations. They are illustrative of one trend in education research, an effort to work in natural settings and to use field experiences as a basis for improving education.

Similarly to other social science work in the field, the preferred methods are qualitative (Filstead, 1970) and the research design is typically of the sort that is variously described as phenomenological (Wilson, 1977) or, in the recent educational literature, as “ecological” (Bronfenbrenner, 1976), “illuminative” (Parlett and Hamilton, 1976) or “interactive” (Stake, 1967) rather than the experimental and quasi-experimental designs which are derived from controlled laboratory settings (Campbell and Stanley, 1963).

Campbell himself now takes the view (1974) that qualitative approaches are particularly appropriate when the subject of study is an interconnected area, and the goals are not simply to find out if one factor has an effect on another, but in what ways a range of factors interact with one another. The researcher is working not with a single testable hypothesis but rather within a general set of hypotheses that make up a position: a theory of personality for example, or a concept of how children learn. This deliberately makes room for the observation of surprising or unexpected phenomena. It emphasizes the importance of setting (hence the “ecology” of education); the subject’s participation in the evaluation or research, and a recognition of the role of the experimenter or evaluator in any results.

The traditional approach to the problem of experimenter intrusion (experimenter bias) is to try to make the situation as impersonal as possible. Thus a typical testing situation places a tester and a child (often strangers to each other) in a bare room with the tester reading a script and engaging in little interaction with the child being tested. The alternative, advocated by the qualitative method, is to recognize that even such stylized controlled encounters have a biasing effect on children. Thus, standardization is considered less important than a description and recognition of the evaluator’s role. The intention is not to make the situation neutral, but to find a place for the person in research, to set up certain rules of behavior, and to assure that the role of the person is known, reported, and understood.

In our design, the structure of the data collection system is not separate from the objectives of the program, but is in part shaped by them. The model for this methodological approach is a “matrix” first used by Brenda Engel at the Cambridge Alternative School (Engel, 1977) and since employed by Engel and Hein (1976) in a number of evaluation and research studies. The specific objectives of the program are matched with all available data collection means in a matrix format to develop the best correlation between types of objective and types of data collection methods. For complex and difficult-to-specify objectives, a greater variety of means is employed to provide a reinforcing network of data which can support any conclusions from the study.

In work on LOGO (as with research on some other computer systems) we are particularly fortunate because the system itself provides ample opportunities for documentation. Thus, for every session that a participant spends doing LOGO, there results not only the final products of that work (and any observations of the work or comments by the instructor) but also a complete record of each step taken by the participant in the form of a ‘dribble’ file—the printout of commands used. In the current project, this data was one of several sources used to discern to what extent children benefited from exposure to LOGO.

2.1.2 Similar Work in Education Research

This approach to data collection is similar to that employed by other educational researchers. In recent years, a number of educators have used the documentation/observation approach to evaluate children’s progress in school and to re-assess curriculum. Two outstanding evaluation efforts in the public schools are the work of Brenda Engel (1977 a, b) at the Cambridge Alternative School and that of Ruth Ann Olson (1973, 1974) at the Marcy Open School in Minneapolis.

In each case a wide range of data was gathered: observations, interviews with teachers, children, and parents, results of manipulative tasks, and work samples. The process of the evaluation was as important as the results: all components of the school community were involved, and the tasks as well as the results were simple and direct, so that all members of the community could understand them.

At the Prospect School, North Bennington, Vermont, a long-term confidential effort devoted to a detailed program of evaluation and research is being carried out under the direction of Patricia Carini, founder of the school. An impressive collection of materials has been gathered since 1965, including (Carini, 1973):

• children’s work, e.g., drawings, photos, etc.
• children’s journals
• children’s notebooks or written work
• teachers’ weekly records
• teachers’ reports to parents
• teachers’ assessment of children’s work in math, reading, activities
• curriculum trees
• sociograms

Not only is this data collection systematic, but it is based on a carefully thought-out research design (Carini, 1972) focused on:

1. Experimental investigations of the thinking process.
2. Observations of children’s spontaneous activity to provide:
   • a. longitudinal definition of developmental stages
   • b. longitudinal assessment of the impact of the innovative learning situation.
3. Longitudinal observations of children, and recording of observations to provide:
   • a. modification and qualification of developmental stages.
   • b. objectification of the continuity of transformations of affective and thematic content in the reorganization of successive developmental stages.

The work at the Prospect School has been successful, not only shedding light on child development, but as a guide for decisions about children and curriculum and as a source of data for teacher training and staff development.

2.1.3 Evaluation Personnel

We have been assisted in the design and implementation of our research plan by Dr. George Hein and Ms. Stephanie (Penny) Dunning, consultants to Education Development Center. Dr. Hein and Ms. Dunning have participated in the meetings of our research staff, aided us in drawing up our data collection matrix, designed and conducted pre- and post-interviews with the children, and carried out a series of regular observations which contributed to our data.

2.2 Remarks on Teaching

The LOGO language and introductory LOGO activities can form the basis for several different kinds of learning, integrated in a complex way into the actual classroom activities of the children. While these types of learning can and do occur simultaneously, it is valuable to list them as separable goals, and to assign priorities, for the purpose of developing a classroom organization and teaching strategies. The major goals of teaching LOGO, as defined in our proposed research, are:

1. Learning to feel comfortable with a computer, and in control of what the computer does. The child will learn that he/she can decide what the computer will do, and have the computer carry out a set of instructions. There are many ways in which children can use the computer in their own fashion.
2. Learning the elements of the LOGO computer language. This includes commands that are included in the language, how to write and name procedures and subprocedures, use recursion and/or iteration, how to define, name and use variables, as well as conditionals and stop rules, etc.
3. Learning the “subject matter” of turtle geometry. This includes concepts involving measurement and estimation of angles and distances; the relations among angles and distances necessary to produce certain well-defined shapes such as a square, triangle, polygon, star, or circle; such general geometric concepts as similarity, scaling, and symmetry, etc.
4. Learning to develop problem-solving skills. This includes such things as procedural thinking, “playing turtle”, “playing computer”, the concept of a “bug” in a computer program, and strategies for debugging and planning, the usefulness of generalizations or “big ideas”; and the development of a language with which to discuss all these things.

The LOGO language and computer activities are designed so that all these things can happen simultaneously as the child works on projects which he or she has initiated. The initial projects and the initial knowledge needed are designed to be simple enough that a child can learn them relatively easily, and begin to feel successful, and in control, right from the start. Additional aspects of the language and projects of greater sophistication are added as each child becomes comfortable with them. Directing the computer to carry out a series of steps involves planning. Gaps, misconceptions, or errors in the planning lead to “bugs” which have to be eliminated. Thus the teacher can help the child begin to develop problem-solving skills needed to debug the child’s work. By discussing all of these things explicitly, a language is built up that can be applied to other kinds of problem-solving situations.

In practical situations, with a group of children and one teacher, things do not always work out quite as “conveniently” as described above. Some children are extremely adept at using elements of turtle geometry to create designs and drawings, but have a great deal of difficulty with the syntax of the computer language. For others, the reverse is true. Some children may be comfortable with both, but have a limited tolerance for new approaches to problem-solving.

We have found, therefore, that in order to create a learning environment that supports the learning of all of the children in a group, we have made learning to be comfortable with the computer, enabling the learner to feel in control, the first priority among the four goals. We want the students to develop their working styles and sets of priorities, and expect that they will feel good about what they have done. On the other hand, they will not all cover the same subject matter in any given period of time. Some may carry out involved projects involving the use of subprocedures and superprocedures, but may not become adept at using recursion, though they will be exposed to it. Others may use recursion expertly to create a number of fascinating designs, but may not become adept at using subprocedures. Our results show that the children have many different approaches, and successfully follow several different learning paths.

2.3 Organization of the LOGO Classroom

The classroom itself consists of four independent microcomputers, each with its own keyboard and display screen. One lineprinter is available for use with one of the computers when necessary. The children are supplied with notebooks, graph paper, drawing paper, different kinds of pens, pencils, and markers, as well as a full set of stationery supplies. A small round table, near a blackboard or bulletin board, provides a setting for group lessons or discussions, and for informal conversation among the children. Bulletin boards around the room provide a means of display of children’s work.

2.4 Specific Teaching Strategies in the LOGO Classroom

The initial contact centers around using the basic turtle commands FORWARD, BACK, RIGHT, LEFT, and clearscreen (CS), mastering syntax matters such as spacing, use of CARRIAGE RETURN, and reading and taking notice of error messages. The children are encouraged to define their own tasks, typically involving drawing a specific, “simple” figure such as a square, a house, a flower, or their initials; and to record the steps as they go along, so that they will be able to “teach it to the computer”. The latter involves an early introduction to writing PROCEDURES.

It is at this point that the child begins to feel a sense of control: “I made that design!” Procedures can now be saved, repeated, showed off to friends, integrated into a larger design. The importance of the child’s first procedure being an individual one (even if it’s an idea that the teacher suggested and helped with) is very critical in determining the child’s relationship with the computer as the classes progress.

From this point on, each child’s work is different. Some get interested in repeating simple figures, introducing simple variations and repeating again. These children might get into using recursion and variables in a fairly short time. Others might have elaborate ideas for computer drawings. These children might get into use of superprocedures and subprocedures right away. The best of all worlds occurs when these children begin to show each other their work and swap ideas and approaches. Children are encouraged to borrow each other’s procedures, even to copy them line by line at times. A lot of very useful debugging occurs when a “copied” procedure leads to an unexpected result.

As the classes continue, the teacher takes on the role of “guide”; in helping the children choose projects or in suggesting projects to children based on their interests and abilities. He/she will introduce new material when appropriate, encourage children to improve their programming styles by the use of model programs and suggestions for debugging, encourage the children to investigate certain areas more deeply, and in general, help the children consolidate their learning.

At intervals, the children meet for group lessons and to share and discuss their work. They each keep a notebook in which they make drawings, write out plans, record information, keep printed records of their procedures, and make a brief daily comment about what they have accomplished.

Throughout the classes, the teacher makes a daily study of each child’s “dribble file”—the complete printed record of the child’s interaction with the computer. In addition to providing much of the data on which our research study of the children’s learning is based, the dribble files are an invaluable source of information to the teacher as to what each child’s working style, methods of problem-solving, strengths, and weaknesses really are. This information is used in planning the individual teaching strategies that are developed for each child as the classes progress.

2.5 Comparisons with Similar Studies

In this section we comment briefly on four previous studies with a close relationship to our own. In each case we point out the salient difference in methodology.

Work in Edinburgh

The largest study has been carried out in Edinburgh where three successive cohorts of 11-year-old boys at George Heriot’s School have had an ongoing experience in a LOGO environment for the past  years. This enterprise is currently being written up and there is as yet no published account of the work. However, personal communication between our lab and the Edinburgh group is close, and it is clear that an impressive amount of documentation of the LOGO work there has been accumulated. This allows for interesting and productive comparisons.

For example, the Edinburgh approach has been summarized from a talk given by O’Shea at the summer LOGO meeting in 1977:

“While much LOGO work has concentrated on one to one interaction of teacher and student in a LOGO environment, this effort was concerned with tactics and materials for a large group of kids. A primer was developed, with descriptions of concepts, sample programs, and worksheets. Students maintained scrapbooks documenting their successes, as well as accumulating computer output. The teacher strategy favored kids working with each other and exploring for their own answers, rather than asking the teacher to solve problems which developed.

O’Shea noted three stages of learning most of the students went through:

1. Programming only for the end product, verbal output or graphic design.
2. Style-conscious programming: making programs which include correct form, perhaps using a new concept which is being studied;
3. Programming to solve problems.” (O’Shea, SIGCUE 1977)

We have not found much evidence in our study of a progression through these three phases of learning. Instead we find examples of students whose predominant mode is (1) or (3) above with no obvious evidence of (2). We suggest that there may be an important connection between this difference and the work-from-a-manual approach which tends to characterize the Edinburgh work. In such a framework, there is a notion of a sequence of topics to be followed in which the presentation of topic 1 is accompanied by exposure to model programs and working through worksheet examples of the concept, after which topic 2 is moved to.

There are distinct advantages in the way this approach structures the classroom activities for teachers and children who are comfortable with such a structured approach, and indeed our description implies more rigidity than actual practice in Edinburgh warrants. What we see emerging is the possibility of isolating consequences of particular teaching styles within what may be thought of as rather similar learning environments.

Muzzey School Experiment (Feurzeig et al., 1971)

This took place at an early stage in the evaluation of these ideas before turtle geometry had been developed. We deliberately selected “average” children as our subjects (unlike the present sample which contains children at a greater range of abilities). We used as outside observers four leading figures in the field of math education, and whilst their comments were very helpful in contributing to the theoretical basis of our work, their participation did not yield useful information about how to look at children in this learning situation. Our present project constitutes a great advance in this respect.

Work at Xerox Palo Alto Research Center (1974–)

This is reported in TEACHING SMALLTALK by Adele Goldberg and Alan Kay (1977). There are important ways in which our learning environment resembles that developed and used by this group. As regards the selection of students, much of the Xerox work is done with “mentally gifted minors”. The published details do not allow for the kinds of analyses-in-depth which we present here, concerning the different ways in which children use the possibilities of the system.

Work at Syracuse (Statz, 1973)

Joyce Statz reports work using mechanical turtles. The positive aspects of her work are in line with what we observe here. However, the limitations in the quantity and quality of hardware made it impossible for her subjects to become as involved as ours were in individual projects. This factor, together with the evolution of instructional techniques since then, accounts for the fact that our subjects seem to make more progress in similar time.

3. Individual Profiles

Student Summaries Introduction

The section that follows offers a brief assessment of the progress of each of the eight children in our trial classes. The assessments are summaries of the detailed analysis of each child’s work to be found in Appendix I of this report. The summaries include a statement of how the child is perceived as a student in the regular academic areas of the school, a description of what the child learned in the LOGO classes, an analysis of each child’s particular strengths and problems, and the particular teaching strategies that were considered appropriate for each child.

In surveying this material, one should bear in mind that the students’ learning took place in a project-oriented setting and no attempt was made to expose all students to the same “standard LOGO curriculum”. Rather, the teacher introduced new LOGO material to students on an individual basis, and in a way which would be integrated in their individual projects. Consequently, we observed different students concentrating on different aspects of LOGO. For example, some organized most of their learning experiences around the creation of free-form “emergent” designs, while others concentrated on elaborately planned projects. Most of the students’ work related to computer graphics, but a few also undertook non-graphics projects. The eight students in the experimental group spanned a wide range of interests and cognitive styles. One of the strengths of this kind of LOGO learning environment is that it can appeal to students across such a spectrum and allow for projects that can be of interest to each of them.

Gary

Gary is considered to be “extremely bright” by his teachers. (His overall national percentile ranking of 99 on his most recently recorded school achievement tests makes him one of the two or three highest scoring students in his grade at Lincoln School.) His teachers report that they find it difficult to find ways to challenge him within his regular school program, while at the same time reporting “peculiar gaps” in his academic knowledge—in the area of standard computational skills, for example.

Gary seems to have found LOGO to be a satisfactory challenge. He completed three major projects in different areas: using arcs and circles to draw a face (sessions 7–8); creating a simple math quiz (sessions 10–13); and drawing and animating a starship (sessions 13–16). He had confidently begun a fourth major project—writing a computer program capable of “understanding” Morse code, and transmitting it to a radio receiver—when the series of classes ended. During the course of his work, Gary mastered the use of recursion and variables in a number of different contexts; he understood the use of conditionals and “branching”; he learned to write state-transparent procedures, and to use superprocedures with modular subprocedures in drawing his starship. He was beginning to understand list and word processing, as well as the concepts of the “empty list” and the “empty word” in his last project.

Gary’s method of working was to plunge confidently into a problem “headfirst”, with little advance planning. He would then encounter many bugs, which he usually enjoyed finding and eliminating—sometimes asking for help when frustrated. He took particular delight in bugs which produced designs unlike what he had intended. Most of his work was carried out in a step-by-step fashion, resulting in long, complicated procedures, difficult to debug. Once, when specifically requested to, he carried out a revision of his starship design, to use a superprocedure and modular subprocedures, rather than one long procedure. In this way he showed that he was quite capable of learning to improve his programming style.

My strategy in teaching him was to offer him simple models of a particular kind of procedure, give him the information he needed, and leave him alone to elaborate on the model, providing help only when asked. When one phase of a project was finished, I generally suggested some challenges that built on the finished work or occasionally requested that he alter or improve his work. In this way, Gary was able to move ahead on his own, at as fast a rate as he could absorb.

Sample Code from Gary’s Work:

TO MATH

10 PRINT [WOULD YOU LIKE TO HAVE A MATH TEST?]

15 MAKE “ANS REQUEST

20 IF :ANS = [NO] PRINT [OK COME BACK AGAIN!] STOP

30 IF :ANS = [YES] PRINT [WELCOME TO THE WORLD OF MATH!] MATH1 STOP

END

TO MATH1

5 MAKE “NUM1 WORD RANDOM RANDOM

6 IF FIRST :NUM1 = 0 GO 5

7 MAKE “NUM2 WORD RANDOM RANDOM

8 IF FIRST :NUM2 = 0 GO 7

10 PRINT SENTENCE [:NUM1] []

15 PRINT [+]

20 PRINT SENTENCE [:NUM2] []

21 PRINT [——]

25 MAKE “ANS TYPEIN

30 TEST :ANS = :NUM1 + :NUM2

40 IFTRUE PRINT [CORRECT!] MATH2 STOP

50 IFFALSE PRINT [TRY AGAIN!]

60 GO 10

END

TO MATH2

10 PRINT [WOULD YOU LIKE TO HAVE ANOTHER PROBLEM?]

20 MAKE “ANS REQUEST

30 IF :ANS = [YES] PRINT [OK HERE WE GO AGAIN!] MATH1 STOP

40 IF :ANS = [NO] PRINT [ALL RIGHT SEE YOU NEXT TIME!] STOP

END

Kevin

Kevin is a student who is considered to be conscientious, but “below average” in most of his school work. (His overall national percentile ranking of 31 on his most recently recorded achievement tests corresponds with this assessment by his teachers.) Nevertheless, Kevin was consistently a very able student in working with LOGO.

Kevin began the series of classes with a confident and accurate control of the turtle, which persisted throughout his work. He did not initially have the same sureness in using the computer as a tool to simplify and organize his work. Kevin’s most significant project was the design and animation of a large turtle (sessions 10–17), which he drew on the display screen using circle and arc procedures. While working on this project, he began to use the idea of subprocedures and state-transparent procedures to simplify his work. During the last few classes he worked on projects involving the use oftwo and three variables to produce designs which used the idea of similarity as a guiding feature, such as his TUNNELprocedure (session 21).

Kevin demonstrated a clear understanding of the concept of variables and was able to add variables to his procedures to control both the size and shape of the design elements and the starting and stopping of the procedure. He had moved in his work from using the computer to control the turtle, to learning how to use variables to control the processes of the computer itself.

Kevin’s major difficulty in working with the computer was an initial reluctance to plan ahead, or to think about and structure his work more than one step at a time. The teaching strategy that was used to deal with this was to supply Kevin with new ideas, at exactly the moment when they made the greatest sense to him—when they simplified his work or answered an immediate need. In this way he was able to assimilate new ideas, and incorporate them in his subsequent work.

Sample Code from Kevin’s Work:

TO TUNNEL :SIZE

10 POLY :SIZE 45

20 IF :SIZE > 105 STOP

30 TUNNEL :SIZE + 5

END

Donald

Donald is considered to be “above average” by his teachers. He is new to the school this year (no achievement test scores available). Donald’s work in the LOGO classes revealed an overall competence in analytical approaches, combined with a certain amount of confusion about details.

Donald spent most of his class time on a single extended project: making the computer draw an elaborate HEAD, which included a beard, hair, a hat, and a flower, in addition to the usual features—eyes, ears, nose, and mouth. Donald worked over a period of 14 sessions on this project (sessions 8–22). He began by drawing a picture of what he wanted the head to look like, and following the teacher’s suggestion, wrote out a superprocedure to draw the head, and used separate subprocedures to add each of the features. In the course of his work, Donald had to do a great deal of estimating of both distances and angles, use arc and circle procedures, use procedures that repeat, use variables to control size and angles, and especially, learn to separate a problem into parts to make it easier to solve. In addition, he used a POLY procedure to make a FLOWER for his head, and had to use recursion, as well as a conditional and stop rule.

Throughout his work, Donald had difficulty in understanding the effect of the state of the turtle at any given time. He could not always predict where the next step would occur. At times it seemed as if Donald had some difficulty in seeing exactly where the turtle was headed. The teaching strategy employed to help Donald deal with these problems was to help him develop tools of mathematical analysis, to help him figure out the best way to aim the turtle, without relying totally on visual experimentation. In this way he was exposed to the idea of using a kind of “grid” to help him maneuver the turtle around his HEAD, and to see how the total angle turned by the turtle in a given situation was key to deciding how much more he had to turn it next. In addition, he was shown how to break up even a small problem into parts—for example, in placing a mouth on his face, he had to decide which arc to use for the mouth, how to orient the turtle, and to choose the correct starting point for the mouth. By separating this problem into three distinct steps he was able to overcome obstacles that might have interfered with his success. At the same time he was learning principles of geometry, computer programming, design, and planning.

Sample Code from Donald’s Work:

TO HEAD

1 BOX

2 EYES

3 NOSE

4 MOUTH

5 BEARD

6 HAIR

70 EARS

80 HAT

85 FLOWER

END

TO FLOWER

10 RIGHT 90

20 FORWARD 35

30 RIGHT 90

40 RARC 75

50 LEFT 90

60 BACK 5

70 POLY 10 100

END

TO POLY :SIDE :ANGLE

10 FORWARD :SIDE

20 RIGHT :ANGLE

25 IF HEADING = 0 STOP

30 POLY :SIDE :ANGLE

END

Laura

Laura is considered to be an “average” student by her teachers. (On her most recently recorded school achievement tests, her national percentile ranking was 38.) Laura got off to a good start in her LOGO work, quickly mastering the basic turtle commands, and the use of subprocedures. By session 8 she had completed a substantial project—drawing a face using a top-down program structure with subprocedures for the various parts—but did not maintain a high rate of progress throughout the classes.

Laura showed great interest in making large, freely conceived designs on the display screen. She created the designs one step at a time, considering thoughtfully the size and placement of each new addition to her creation. It was difficult for Laura to make the transition to formalization of her work, to breaking it down into small tasks, and to planning and organization. Consequently, there was often a gap between what Laura wanted to accomplish, and what she was able to accomplish. Laura did carry out a few major projects: a FACE project with several subprocedures; a series of designs using circles and squares of variable sizes constructed by means of recursive procedures with changing inputs (sessions 10–15); a “madlibs” language game (sessions 17–19), for which Laura created the basic story, wrote out lists of nouns, verbs, adjectives, and adverbs, and for which the teacher helped with most of the programming; and causing the computer to draw her initials (session 25).

Sometimes Laura appeared to be bored. In hindsight, this appears to have been a manifestation of confusion, rather than boredom. Too much stress was placed on offering her new ideas, rather than understanding her confusion, and taking steps to help her limit her choices and consolidate her earlier learning. Laura’s difficulties were compounded by the fact that she did not like to ask for help, she did not like to be observed in her work, and she assumed an “air of confidence” at all times.

Sample Code from Laura’s Work:

TO FACE

1 NOES

2 RIGHTEYE

3 LEFTEYE

4 MOUTH

5 SQUARE1

END

TO NOES

1 LEFT 90

2 FORWARD 20

3 RIGHT 90

4 SQUARE

5 RIGHT 90

6 FORWARD 20

7 LEFT 90

END

TO RIGHTEYE

1 PENUP

2 FORWARD 60

3 LEFT 90

4 FORWARD 40

5 RIGHT 90

6 PENDOWN

7 LCIRCLE 30

END

TO MOUTH

1 PENUP

2 FORWARD 100

3 RIGHT 90

4 PENDOWN

5 FORWARD 90

6 HIDETURTLE

END

Deborah

Deborah is considered by her teachers to be below average in overall ability. (Her most recent scores on a school achievement test place her in the 20th percentile nationally.) She is extremely quiet and appears quite reserved in a new situation.

Deborah was very dependent on the teacher for constant reassurance during the early stages of her work in LOGO and all through her first project—drawing her initials (sessions 5–7). Deborah (beginning in session 8) was encouraged to experiment freely with the basic turtle commands. By limiting the numbers she chose to use as inputs to FORWARD, RIGHT, and LEFT commands, she was gradually able to gain confidence and control over her work. She seemed to have a “knack” for choosing numbers which produced interesting designs, and she gradually learned to write procedures to teach her designs to the computer. This seems to have been a breakthrough for Deborah, and she began to suggest and carry out independent projects in a purposeful way.

By the end of the series of classes Deborah had created some unusual designs which won praise from her classmates; had carried out a major project of drawing a rabbit, which required the use of planning and subprocedures (sessions 17–24); and had developed confidence in herself and in her ability to use the computer. Deborah’s parents reported that this was the first time she had been excited about anything in school. Her teachers reported that she had become more assertive in class and had asked for extra help after school, etc.

The teaching strategy that was developed in response to Deborah’s extreme dependence, and her compulsive need for getting a “correct result” on her first project, was to encourage her to “experiment” with a few basic commands—without striving for any particular result. In this way, she was able to design some simple projects, after first carrying them out by direct commands. When she chose to undertake her rabbit project, after 7 or 8 classes of free experimentation, she already understood how to write simple procedures, and how to use subprocedures as part of a larger entity. She was able to carry out the experimentation needed for each part of her project independently. The teacher’s role became one of providing Deborah with help, when she needed it, in the context of work which she herself had defined and understood.

Sample Code from Deborah’s Work:

TO SPYRO

1 PARC 20

2 PARC 20

3 PARC 30

4 PARC 30

5 PARC 40

6 PARC 40

7 PARC 50

8 PARC 50

9 PARC 60

10 PARC 60

11 PARC 70

12 PARC 70

13 PARC 80

14 PARC 80

15 PARC 90

16 PARC 90

17 PARC 100

18 PARC 100

19 PARC 100

20 PARC 10

END

Monica

Monica is considered to be an “average” student by her teachers. (Her most recent school-administered national achievement test ranking was in the 47th percentile.) Her teachers find that she prefers to base her activities solidly on things she knows, rather than to strike out into new areas.

Monica’s work in the LOGO classes followed this pattern as well. She learned the basics of LOGO quickly and easily. She established a very successful technique for making interesting geometric designs by having the computer draw a shape, rotate the turtle through a fixed angle, and then repeat the sequence over and over. She learned to use recursion to produce this kind of effect easily, and eventually learned to make the angle of rotation a variable, so that the same procedure could be used to make a number of different, though related, designs. Toward the end of the series of classes, she had learned to make regular use of recursive procedures with inputs and stop rules. Throughout her work Monica had a very good sense for the state of the turtle at any moment, and could predict the location of the next shape drawn by the computer more easily than her classmates.

Monica worked very closely with Kathy during the LOGO classes, and the two girls often adapted and built upon each other’s projects. Monica did not work on any long-term projects, or get seriously involved with editing and debugging. She often had difficulty deciding what to do, and in choosing names for her procedures. Her projects tended to be short, and if they didn’t work out, she usually preferred to disregard the procedure entirely, rather than to ask for help or to try to change it.

Teaching strategies for Monica focused on helping her become more aware of the non-graphics output of the computer—error messages, for example—and of different types of bugs and how to identify and correct them. Through her own choice of working with repeated rotations, Monica was helped to understand recursion, and the use of variables, and was beginning to use conditionals and stop rules. Toward the end of the series of classes Monica expressed interest in “correcting” (debugging) a rather lengthy procedure, and was beginning to be able to look at procedures in a step-by-step manner for the purpose of analyzing and correcting them.

Sample Code from Monica’s Work:

TO WISHWOW :ANGLE

10 WOW

20 RIGHT :ANGLE

30 IF HEADING = 0 STOP

40 WISHWOW :ANGLE

END

Kathy

Kathy, a student who was new to the school this year, is considered to be an “above average” student. (Her most recent school-administered achievement tests place her in the 54th percentile overall: 61 in reading, 66 in language, 29 in mathematics.) She is cheerful, confident, and enjoys “playing” with words and ideas. Kathy and Monica worked together very closely during the LOGO classes.

Kathy worked mainly on small projects, gradually increasing the size and scope of her work as the classes went on. She often used the strategy of making a design, then repeating it until it closed or until she had a design she liked. When bugs occurred, Kathy would analyze them, and work on her procedure until she felt she had corrected it. She enjoyed thinking about her work, often making extensions or comparisons in ways that showed that she understood the importance of relations among different objects. (For example, she made a WORM procedure, then proceeded to make WORMY, twice as big, or in a different kind of relation, copied a procedure called HORSE, which drew a series of rotated boxes. When she repeated HORSE five times, she called it BARN.) Most of Kathy’s work involved this kind of repeated free-form design, and the various design strategies served as vehicles for introducing such programming constructs as inputs, recursion, and stop rules. Kathy’s last two projects, MONSTER and BIRDMAN (sessions 19–22), were more elaborate designs, using carefully related arcs and circles. They led Kathy into situations in which she had to use subprocedures and to engage in careful debugging.

Teaching strategies for Kathy involved suggesting projects that allowed her to extend her knowledge of ways of using LOGO, and encouraging her to undertake projects that involved larger degrees of planning, making it more likely that she would get involved with debugging situations. Although Kathy enjoyed creating new ideas, and liked carefully defined challenges, she did have a tendency to keep her work focused on small challenges. She was also urged to be more analytical in understanding the effects of the variables she used.

Sample Code from Kathy’s Work:

TO TRIANGLE

1 LEFT 90

2 FORWARD 100

3 RIGHT 120

4 FORWARD 100

5 RIGHT 120

6 FORWARD 100

END

TO BUTTERFLY

1 TRIANGLE

2 TRIANGLE

END

TO 7BUTTERFLY

1 BUTTERFLY

2 BUTTERFLY

3 BUTTERFLY

4 BUTTERFLY

5 BUTTERFLY

6 BUTTERFLY

END

TO HOUSE

1 TRIANGLE

2 RIGHT 30

3 BOX

END

TO HOUSE4

1 HOUSE

2 HOUSE

3 HOUSE

4 HOUSE

END

TO HB47

1 HOUSE4

2 7BUTTERFLY

END

TO SPI

1 HB47

2 RCIRCLE 30

3 LCIRCLE 30

4 RCIRCLE 20

5 LCIRCLE 20

6 BACK 30

7 RCIRCLE 10

8 LCIRCLE 10

END

Ray

Ray is a student who has been diagnosed by school personnel as having “learning disabilities”. He is tutored individually by a learning disabilities specialist several times each week. His teachers feel that at the beginning of the year he was noticeably “slipping” in his seriousness as a student. (His most recent school-administered achievement test placed him in the 9th percentile, based on his overall scores.)

Although Ray was initially quite successful in controlling the motion of the turtle, he held himself somewhat aloof from the activities in the LOGO classes. As a result, he never succeeded in writing a procedure without assistance, although he had considerable success (with help) on several projects such as drawing and animating a rocket (sessions 13–15), and in using the computer with procedures that enabled him to explore geometric shapes. In general, Ray had success using the computer in two kinds of situations: when a teacher was helping him intensely during a session, and when he was working in a way that required him to remember only one variable at a time.

The teaching strategy for Ray was to try to structure situations in which he could be successful. When these situations required a lot of help from the teacher, he would usually “forget” what to do when the teacher was no longer present. For the longest time, Ray did not engage in much “free experimentation” with the turtle. But towards the end of the series of classes (session 19) he was given a POLY procedure which requires two inputs to produce a series of closed geometric shapes, and a SPIRAL procedure which required three inputs and produced a variety of spiral shapes. Ray gradually learned how to control the inputs to produce certain shapes in a predictable way. For the first time, he began to experiment in a purposeful way, to write things down in his notebook, and to use those notes to remember successful designs. He began to gain confidence in his ability to control the computer. He invited a friend to class; together they had a very exciting time exploring the shapes produced by the POLY and SPI procedures. Ray’s teachers also reported a noticeable improvement in his attitude in class, which they attributed partly to his feeling of success in the LOGO classroom.

Sample Commands from Ray’s Work:

SPI 10 100 1

SPI 10 200 1

SPI 10 300 1

SPI 10 400 1

4. Theoretical Interpretations

4.1 Science Skills and Concepts Involved in LOGO

What we talk about in this section is usually called “scientific method” rather than domain-specific. The main “science concept” involved in LOGO involves the unstated analogy between the concept of hypothesis formation and testing / creation of a revised hypothesis, on the one hand, and the process of writing a LOGO procedure, trying it out, and debugging it. Development of a sense of this type of process is a major goal of all elementary school science curricula, and it is a major component of LOGO as well.

To talk about “acquisition” of the kind of skills and concepts involved here would be misleading. But we can provide some evidence for an implicit or an explicit exposure to some of them in some of the children’s activities.

A working scientist is accustomed to using multiple representations to achieve greater certainty and efficiency. Let us take an example, a simple physics collision problem:

1. A scientist abstracts the problem. Important conceptual structures (like conservation of energy) guide a translation into a formalism (perhaps an equation).
2. The formalism is manipulated in its own terms (the equation is solved).
3. The formalism is interpreted ( means the collision causes an object to stop).

Now consider a child drawing a picture in LOGO. On the one hand there is his perception and interpretation of the picture, and on the other there is the formalism of turtle drawing. The latter involves a few simple operators, some important larger-scaled structures (iteration, recursion, inputs, etc.), and a collection of things it can do well and simplywith these structures. The child’s problem is to abstract into the formalism: an eye becomes a circle, a nose becomes two arcs. In a more complex case, the hairs in Donald’s face’s beard become iterated pieces of a spoke pattern.

Notice how different a conception of a series of simple line strokes is needed to make this transformation. Now the child must execute the pieces of his reinterpreted picture within the formalism; a program must be created with the proper syntax and sequencing. All along, and particularly if the program does something other than expected, the formalism must be interpreted. “What will that program do?” In the turtle environment Dan encouraged “playing turtle” as a syntonic mechanism for this interpretation.

There is another important large-scale process involved in the LOGO experience: the art of design. Every engineer experiences and learns to appreciate the complex interaction between ends and means, goals both aesthetic and pragmatic, and materials. LOGO graphics particularly invites elaborate and clear goals, and then the necessary compromise to achieve them.

This kind of learning is very large-scaled, hard to pin down and measure. Though we are only at an early stage in being able to describe and objectify what is involved, that does not lessen our conviction that it is an important kind of learning. We can, however, point to some exemplary explicit encounters with various subparts and related ideas:

• Heuristics: Students are given suggestions for organizing a problem for solving: “Divide a problem into parts; do the parts separately.” Certain students can be seen to have mastered this advice: Gary, Donald, Kevin. It is important that the procedure-subprocedure model reinforces this idea in a very concrete way. Donald’s construction of his face was guided by the top-down structure which he wrote into his program when he started it, as much as it was by his having learned in the abstract to “subdivide”.
• Dividing and Conquer: “Divide and conquer” ties to another explicit heuristic plan: “First approximations are useful; worry about details later.” Dan explicitly said these things to the students on many occasions, and one has at least the surface evidence of the plans some students spontaneously made to support “acquisition”.
• Systematic Processes: One sees in Ray’s “playing” with POLY an important development. In the beginning he changes both numbers rather indiscriminately, focusing on number patterns (e.g., 123, 321) rather than “meaning”. Later one sees a very different pattern, changing one variable at a time, systematically: POLY 100 88, POLY 100 89, POLY 100 90. He has learned some very important things about systematic inquiry. Another striking example of an appreciation for a systematic process is Deborah’s entire mode of design: a step-by-step, almost formalized procedure.

Ideas we intend to look at more carefully in the upcoming round of experiments include:

• Value of explicit description
• Local-Global analysis
• Setting Contexts
• Type-Token distinction
• Debugging through cause and effect
• Naming as a part of analysis and abstraction

4.2 Mathematical Behavior in the LOGO/TURTLE Classes

To decide what counts as mathematical behavior is as complex a question as the definition of mathematics itself. As a first approach to the subject we could list specific mathematical skills or concepts which the students might have learned or exercised in the course of their work at the LOGO computer.

Before beginning the experiment we constructed a checklist of such items to look for in observing the behavior of the students. The checklist includes some entries which were not directly observed and excludes some interesting ones which we did not think to look for. This fact itself is of some interest for the design of future experiments (including the second round of this one) and for teaching. It shows that we are inclined to recognize certain mathematical behaviors and others not.

Consider an example. When Donald was putting the hat on his face he had considerable trouble deciding how far the turtle should move along the brim of the hat before doing a left turn to draw the vertical line. Notice that there is a little problem in algebra: suppose the diameter of the brim is  and the diameter of the vertical cylinder is . Then the turtle has to do:

FORWARD (B – H) / 2

LEFT 90

FORWARD HEIGHT

LEFT 90

FORWARD H

LEFT 90

FORWARD HEIGHT

LEFT 90

FORWARD (B – H) / 2

But how do you do this if you have not yet encountered algebra, or even if you have, but feel uncomfortable? Donald tried some trial and error but had trouble keeping track until he had the excellent idea of using the hairs as markers, so he could count how far he had moved the turtle. Thus the algebra was, so to speak, digitized and the problem became more tractable.

Kevin was seen to do almost exactly the same maneuver in a similar problem situation: this time he used the fact that when the particular turtle used in the experiment drew a circle by repeating FORWARD 10 RIGHT 10, one could see a visibly brighter point at the vertex of the 36-gon which is being drawn in place of a true circle. So using internal markers should be called a mathematical behavior in the same right as estimating angles.

Another very subtle example is seen by watching carefully how Kevin moves into the intrinsic point of view when he is working on his BIG TURTLE. By intrinsic point of view we mean a way of thinking from inside the curve as if one could never go out of it or measure or even see anything on the outside. From a geometric point of view there is a tremendous difference, and we are used to thinking of turtle geometry as an accessible, elementary school example of intrinsic geometry. But of course one is not forced to use turtle concepts intrinsically: in the extreme case one can use them to set up an extrinsic Cartesian (or other) coordinate system. This is something that young students often do and then make the wonderful discovery that many problems are more easily solved intrinsically.

For example, Kevin’s turtle was made of a circle for the outline of a shell and various objects along its circumference: feet, tail, neck. An extrinsic way to do this might be to move from feature to feature in a straight line, a chord of the circle. But doing so has real problems. How long is the chord? A much better approach is to stay inside the line being drawn. This means going from feature point to feature point by moving on the circumference (this is intrinsic to the line, which must not be confused with inside the whole disc).

Another example concerns the problem Kevin encountered in drawing extruberances like the foot. How does it pick up its place again? A truly intrinsic method is to write a second procedure called BACKFOOT whose steps are inverses of the steps of FOOT and carried out in reverse order according to the theorem of group theory:

Then FOOT BACKFOOT brings the turtle back to where it started, i.e., the two procedures compounded form a state-transparent procedure.

Kevin did not actually invent this idea. But he adopted it from the suggestion of the teacher in an interesting way. The suggestion made to him was not that of writing two procedures which would act as inverses for displacement, but rather to make the procedure FOOT state-transparent. Kevin refused the suggestion… but internalized the idea and used it in a form which is superficially rather different, even if mathematically only subtly so.

It is clear from the discussion that we see in the mathematical behavior of these subjects a greater variety of “advanced” mathematical behaviors than there is any chance to experience in the usual sixth grade class. If exercising implies developing, there must be development happening.

4.3 Cognitive Styles and Strategies

Cognitive styles is a particular abstraction of the observations of students having to do with large-scaled and persistent patterns of perceiving, accumulating, and using knowledge. This category explicitly excludes social and interpersonal styles and strategies, which, while they may play an important, perhaps even dominant role in some students’ educational activities, are a different class of discussion.

The aims of this part of the study are several:

1. To bring to the fore some of the possibilities of LOGO as an instrument for investigating individual learning styles in a natural setting. Particularly in its artifacts of planning and programming, LOGO leaves a great many more clues to what really is going on in the child than seems typical of intellectual activities in general. These can be of great use to teacher as well as researcher.
2. To provide partial information on the learning styles of the students involved in the project, particularly in so far as it is distinct from measured school performance, “general intelligence”, specific knowledge, and other measures.
3. To begin to sort out certain parameters of individual differences particularly relevant to determining the kind of LOGO experience a child is likely to have. What features of LOGO are particularly appropriate or inappropriate to certain students? What possible evolutions in style and strategies can we expect? What special arrangements can and should be made to accommodate individual needs?

Categories of Analysis

The analysis of cognitive styles is directed toward four categories:

1. Extent and Grain of Connectivity: Some students were a blur of references backward and starts and stops of forward-pointing threads. Others exhibited a much sparser pattern. Some students seemed to concentrate on large-scale structures like the sort of project they would select. In contrast, others had a habit of returning again and again to, for example, little techniques they had learned like a way of making pretty patterns with REPEAT.
2. Nature of Connections: Some students’ references were explicitly or apparently mediated by theories, conjectures, and abstractions of various sorts. Others were much more literal. An example of the former is returning to an old procedure to “look inside,” see again how it worked, try variations. More literal students seemed just to want to see their old procedures work again.
3. Epistemology: What do the students think (or appear to think) knowing is about? Do they show signs of thinking about the learning process? What are the primary resources for learning: contemplation, experimentation, asking the teacher?
4. Assertiveness: What is their attitude toward what they know? Are they confident and aggressive in their ideas, using them quickly in foreign situations? Or are they hesitant, uncertain, insistent on thoroughly exploring an idea in its original context, refusing to think (or just not thinking) of that idea as applying in a new context until much later?

4.4 Affective Aspects

An integral part of the learning environment being discussed here is our stance towards the affective aspects of learning. We do not simply hope that our teachers will be nice, kind, supportive people and that, therefore, this aspect will take care of itself. We build into the design of the environment tools for a teacher to use to achieve progress in these areas as an explicit aim of the teaching/learning encounter.

To list some aspects whose emergence is favored by our system:

• A student can feel in control, have agency.
• A student can see how learning does not have to be something apart from oneself, and uninteresting (SYNTONIC learning).
• A student can realize a personal style.
• A student can admit not knowing because he will know how to find out.
• A teacher can admit not knowing for the same reason.
• “Playing around” does not mean “stealing time out” from learning.
• Getting something right is not only to be translated into a high score: what you have achieved is happening out there for you to see and feel good about and to be seen by others and admired.

Comments and Questions Ensuing:

1. Working with a computer will be seen both as a prestigious activity and a potentially fearful activity. So we can expect contrasting effects which pull in opposite directions, and these will underlie all of our findings.
2. We have an unusually favorable teacher/pupil ratio, which must have a strong effect on our findings.
3. There are likely to be some strong and relatively unexplored components of the relationship between child and various elements in this new learning environment:
   • explicit and implicit anthropomorphizing of the “turtle” and its behavior
   • an effect flowering from the degree of control over the mechanical device
   • the effect of being in the teacher/adult role in relation to it
   • identification with the turtle on the basis of its movement in space
   • even more striking motivational attribution procedures: “needing” inputs; the turtle “wanting” to go up there now.

There is a powerful potential for evil as well as for good in this whole computer presence, and we need to be alerted to it, and to look closely at what it can mean.

5. Interviews

This presentation of the results of our interviews will be very brief. Our use of interviews has been exploratory. All interviews were carried out by Penny Dunning; their content was the outcome of many project meetings. We were interested in knowing more about our subjects, and many of the questions asked serve this function. We felt that it would be extremely unlikely that we would find changes in standardized I.Q. tests over such a short period, and considered that our best chance of success lay in exploring measures whose elements resembled, as much as possible, aspects of LOGO activity. An interview schedule excerpt includes number sequences, an embedded triangle task, creature cards, geoboard tasks, and 3- and 4-color permutations.

We decided to administer the interview schedule to all 16 subjects at the start of the experiment so that, should the post-LOGO interviews show any changes, we would have some chance of looking at “repeat testing” and “passage of time” factors. In actuality this turned out to be the case. We found some interesting changes which appeared to represent more than just a regression effect, and so we re-administered some of the items to the second eight subjects who had not yet done any LOGO. In addition, we added some new items involving estimation of lengths and angle size, and map traversing instructions, which had not occurred to us to include in the initial interview design.

We give the flavor of some of the findings:

1. A striking example of the overall tone and qualitative aspects of the interview has already been quoted under “Affective Aspects” in Section 4.4.
2. In her pre-LOGO interview, Marilyn showed no obvious strategy in dealing with the permutation task: she found 5 out of the 6 possible 3-color permutations and 16 out of the 24 possible 4-color permutations. At the post-interview, she systematically found all 6 of the 3-color ones. In the 4-color task, she used a definite but incomplete strategy and found 12 of the possible permutations.

Kevin, who was classified by his teachers as below average in ability (his overall national percentile ranking was 31 on his most recently recorded achievement test), showed a great flair for LOGO. In particular, he was very comfortable handling angles from the start, estimating accurately, and learning to aggregate successive turns earlier than most other children. At the pre-LOGO interview, he performed poorly on number sequences, very poorly on both permutation tasks; in contrast he was very good at the geoboard exercises, involving as they do copying, rotating, and forming mirror images of shapes. After his LOGO experience, he improved considerably on all these tasks, including the geoboard ones. The question of what to make of this finding is a somewhat knotty one. Perhaps it is all a result of his improved self-image?

6. Observer Findings

6.1 Use of Observers

At least one observer was present for two-thirds of the total number of LOGO sessions held. We used three types of observer patterns:

1. Regular observations by consultant (Penny Dunning): 14 observation sessions (6 during first fortnight, 4 during next three weeks, 4 during last fortnight). Very detailed account of what went on, which includes comments on teacher/pupil relations, on classroom dynamics, and captures the occasional “moment of insight”: “When you want to make a right turn, you do 90.”
2. Occasional observations by consultant (George Hein): 4 observation events.
3. Observations by members of the LOGO group: One on an individual, regular basis, others as isolated visits (15 observation events in all). These contributed a familiarity with the subjects necessary for writing this report.

6.2 Comments on Observing Dan Watt’s LOGO Classes

by George Hein (November 30, 1977)

1. The power of physical motion to understand commands: In an early morning discussion between Dan and two girls (Monica and Kathy), Dan asks what a continual command of RT 15 would be. Monica only understands it after Dan has her get up and “play turtle”.
2. The power of having the children’s work displayed: As Dan goes from child to child, he always has available both what they are doing now and what they have done in the immediate past. This is one of the few pedagogic situations where that is possible. Frequently, Dan can keep track of what a student is doing with whom he is not working by glancing over, or he can know what to ask, to correct, or to teach by looking at what is displayed when he goes over to a student.
3. Material from previous work forms the basis for new tasks: The first class started with problems Dan had devised based on the girls’ problems the day before. He gave them various routines which resulted in errors, and had them predict what would happen.
4. Horizontal learning: The children do a lot of repetitive stuff, just as young children repeatedly pour water in a funnel or sieve sand over and over. Each time is a little different from the last, but represents a family of very similar activities. Thus, the children draw similar circles and shapes and punch in similar commands. Their work has very much the character of repetitive, purposeful activity.
5. Concentration: The concentration is intense. In the two classes I watched, there was very little idle talk, and seldom did a child get up or move around except in the course of work. No one left the room, and they didn’t even look at each other’s work.
6. “Meta” questions: Dan forces the children to think about what they are doing in a way that does not appear natural to these 11-year-olds. “Why do you think I gave you these problems?” he asks. “How will you know when it is there?” he asks Donald, who is trying to position the turtle to draw the mouth.
7. School integration: There is a nice mix of school tasks with LOGO tasks. The children get lots of exercise in writing and spelling (after all, correct spelling is crucial in talking to the computer).
8. Student interaction: In the two classes that I watched, there was almost no interaction between the students. Each worked separately on their own console. The only exception was Monica and Kathy, who did problems together.

7. Conclusions

The LOGO activities of these 16 sixth-grade students demonstrate that children across a full spectrum of academic abilities can successfully engage in complex, personally meaningful programming projects. The environment provides a unique synthesis of mathematics, problem-solving, and creative design, fostering both procedural thinking and positive shifts in student self-image and attitude toward learning.

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