|| Research on Logo: Effects and
Douglas H. Clements and Julie S. Meredith
State University of New York at Buffalo
© 1992 Logo Foundation
You may copy and distribute this document for educational purposes
provided that you do not charge for such copies and that this copyright
notice is reproduced in full.
Time to prepare this material was partially provided by the National
Science Foundation under Grants No. MDR-8651668, MDR-9050210, and
MDR-8954664. Any opinions, findings, and conclusions or recommendations
expressed in this publication are those of the authors and do not
necessarily reflect the views of the National Science Foundation.
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Board of Directors
Seymour Papert, Chair
Tessa R. Harvey
The Logo Foundation is a nonprofit educational
organization incorporated in New York State.
Research on Logo: Effects and Efficacy
First grader Darius never talked aloud, was slow to complete his
work, and had been placed in a "socialization group" to "draw him
out of his shell." When the computer arrived, Darius spent nearly
90 minutes working with the Logo turtle on his first day. Immediately
thereafter, his teacher noticed that he was completing seatwork
without prompting. Then he would slide his seat over to the computer
and watch others program in Logo. A bit later, he stood beside the
computer, talking and making suggestions. When others had difficulties,
he was quick to show them the solution. Soon, others started getting
help with Logo from him. In brief, Darius moved up to the high reading
group, skipping the third preprimer. He began completing twice as
much work per day as he had previously. He participated eagerly
during class discussions and--as a "crowning achievement"--was given
a 10 minute "time out" because he wouldn't stop talking.1
Are such results merely happy circumstances, or replicable benefits
of certain Logo environments? What does the research say?
Logo research has a short but rich and varied history. While there
is no one "effect" of Logo, there are many benefits and difficulties
that should be researched. Fortunately, there has been enough research
done to form a foundation on which we can build. This review will
attempt to sample a few key topics within this foundation--mathematics,
problem-solving, language and reading, and social/emotional development.
The Logo programming language was first developed to help children
learn math.2, 3 Much of the literature on Logo has presumed
that exposure to math concepts alone while using Logo increases
math achievement. Research on this topic is inconclusive.
Classroom observations have shown that children do use certain
math concepts in Logo programming. Children as young as first grade
apply such mathematical notions as number, arithmetic, estimation,
measure, patterning, proportion, and symmetry to their Logo work.4
Similar observations of intermediate grade children indicate
that Logo may make it possible to explore some math concepts earlier
than is currently believed. 5,6 Although traditional
obstacles to understanding math concepts do not disappear, we should
not underestimate the achievement of the children in Logo environments.7,8
So, Logo enhances mathematics achievement. We don't know, however,
whether any type of exposure leads to increased achievement,
as measured by test scores. Some researchers report significant
gains9 and even dramatic learning changes for as many
as 10% of students.10 Others, though, reveal mixed results11
or no significant differences between Logo and control groups .12-15
Maybe Logo provides practice only with limited topics. Possibly
achievement tests assess only limited areas of mathematical knowledge.
Or perhaps the "exposure hypothesis" is not fully adequate, especially
given the brief exposure provided by most of these studies.
In contrast, exposure alone is not what the developers of Logo
had in mind. They intended it to be used as a conceptual
framework for learning math. As students program in Logo, they
explore mathematical relationships. They play with angles, numbers,
and variables. They think about their actions. This permits them
to build up initial ideas and experiences that serve as a framework
for learning formal mathematics.
Geometry provides an example. Children's initial ideas about shapes
and space are based on action.16 Logo activities designed
to help children build on their intuitive ideas about paths
may help them develop their ideas of two-dimensional shapes.
17, 18 For example, having students visually scan the
side of a building or walk a straight path will give students experience
with straightness. But students can be made more aware of this idea
with path activities in Logo. It is easy to have students use the
turtle to discover that a straight path is one that has no turning.
Also, Logo can help children learn higher levels of geometric
thinking. A husband-and-wife research team, the van Hieles,
discovered that students' thinking develops through a series of
Visual level: Students see shapes as "wholes" only.
Descriptive level: Students can describe the properties
of shapes (a rectangle has four square corners and opposites sides
that are equal and parallel).
Analytical level: Students generalize the logical relations
that exist among figures and their parts and reason deductively
(all squares are rectangles).
According to the van Hieles, students don't move from one level
to the next without instruction that passes through a series of
phases. If instead teachers use concepts and language from a higher
level, students will merely memorize instead of understanding important
Using the Logo turtle helps students progress to higher levels
of geometric thinking. Students at the visual level are able
only to identify examples (rectangles "look like doors"). In Logo,
however, students can be asked to make a sequence of commands (a
procedure) to draw a rectangle. In writing a rectangle procedure,
the students must describe and analyze the rectangle
and reflect on how its parts are put together. If the students are
asked to write a more general rectangle procedure, they must construct
a definition for a rectangle that the computer understands. They
then begin to build intuitive knowledge about defining a rectangle.
This knowledge can later be formalized into an abstract definition.
A class of first graders was investigating the concept
of rectangle. The students had identified rectangles in the classroom
and built them out of various materials such as blocks, tape, clay,
and geoboards. They then went to the computer lab and were asked
to make the turtle draw rectangles.
As the activity proceeded, all children were drawing rectangles
in Logo. One of them tried to be different; he attempted to draw
a rectangle that was tilted. He instructed the turtle to draw
the first side using 5 FORWARDs. He paused for quite some time
as he came to the first turn, so the teacher asked him how much
he had turned before. He said three RIGHTs and hesitatingly tried
three. It worked to his satisfaction and he then drew the second
side. He hesitated again, saying out loud, "What turn should I
use?" The teacher said, "How many turns have you been using?"
He quickly issued three right turns, then hesitated again; "How
far?...Oh, it must be the same as its partner!" Effortlessly,
he completed his rectangle.
Even though this child had built several rectangles with sides
horizontal and vertical, it was not obvious to him that the same
commands would work for a tilted rectangle (or indeed that there
was such a thing as a tilted rectangle.) He had clearly learned
that the opposite sides must be the same length, but he had not
figured out the measure of the turns. The Logo environment provided
him with the opportunity to analyze and reflect on the properties
of a rectangle.
Primary school children, after using Logo, see shapes as created
by actions.20-22 When asked to describe geometric
shapes, they offer not only more statements overall, but also more
statements that explicitly mention properties of shapes, an indication
of descriptive thinking.18, 21, 23
Logo helps students think about angles.21, 24-27 These
benefits, however, might not emerge until they have had more
than a year of Logo experience.28 Also, teachers
need to help students understand the relationship between "turtle
turn" and "angle measure."20, 26, 29-31
Students also learn about length measurement. Logo children are
more accurate than control children in measurement tasks.32
They can better estimate longer distances and use different units
Although promising, not all research has been positive. First,
it should be noted that none of the studies have reported students'
"mastery" of the concepts investigated. In addition, without guidance,
misconceptions can persist. Second, some studies show no significant
differences between Logo and control groups.33 Third,
some studies show limited transfer to activities outside
Logo. For example, students from two ninth grade Logo classes did
not differ significantly from control students on subsequent high
school geometry grades.27
One problem is that students do not always think mathematically,
even if the Logo environment invites such thinking. For example,
some students rely excessively on visual cues and do not work analytically.7
The visual approach is not related to students' ability to visualize,
but to their use of visual feedback. If students continually rely
on their Logo programs "looking about right," they do not progress
to higher levels of geometric thought. There may be little reason
for students to abandon such visual approaches unless they are presented
with tasks whose resolution requires a descriptive, analytical approach.
In summary, studies show that success requires thoughtful sequences
of Logo activities and much teacher intervention. That is, Logo's
potential to develop geometric ideas will be fulfilled if teachers
help shape their students' Logo experiences and help them to think
about and make connections between Logo learning and other knowledge
the student might have.21, 23
Variables and Algebra
Teachers and researchers also suggest that Logo will help students
understand variables. Logo enhances the understanding of variables
for students from the primary grades to high school.5, 34,
35 In one study, fourth graders were interviewed before and
after using Logo to solve problems involving rectangles, formulas
and equations, and number sequences.36 During the pre-Logo
interviews, several students used a correspondence between the letters
of the alphabet and the positive integers to assign values to variables
in equations (i.e., A =1, B = 2, etc.) After using Logo, they determined
each variable's value correctly. All the students could use variables
in formulas after using Logo, whereas none could before.
However, there are sometimes limitations to such learning. For
example, students may not fully generalize the variable idea as
used in Logo to other situations.37 Similarly, after
a year of programming experience, high school students had only
rudimentary understanding of variables.38 We may be considering
the link between algebra and programming too literally.39
Most students probably create a new idea of variable in the context
of programming. On an algebra test, they use the idea that they
learned in math class.
In addition, students often have difficulties with the variable
concept within Logo. First, the use of variables does not happen
spontaneously, and children resist their use even when suggested.40,41
Also, students sometimes declare a variable in a procedure, but
then do not use it within the body of the procedure; they believe
that a variable might have different values within a procedure;
and confuse what the variable stands for.40
Again, there is evidence that mere "exposure" is insufficient.
Logo can benefit intermediate grade students in learning about variables.42
But they have not necessarily gained specific information about
variables or algebra. They may have gained a conceptual framework--based
on intuitions from Logo experiences--upon which later algebraic
learning can be built.
Such construction requires thoughtfully structured tasks. Instruction
that emphasizes links between Logo and algebra leads to a more formal
and general idea of variable.35,40,41
In summary, there is some evidence that Logo provides an "entry"
to the use of the powerful tool of algebra. Again, however, we find
that students' ability to generalize their Logo-based idea of variable
may depend to a great degree on the depth of their Logo experience
and the instructional support given them.
This research has two implications for instruction. First, exposure
alone is not completely adequate. A more satisfactory approach features
teacher mediation and a sound theoretical foundation (e.g.,
for geometry: Piaget and van Hiele). Mediation implies clarification
of the mathematics in Logo work and the extension of the ideas encountered;
construction of links between Logo and non-Logo work; and provision
of some structure for Logo tasks and explorations. Structure does
not imply authoritarianism. For example, it is often useful to allow
hesitant students to accept or reject suggestions until they build
Construction of links between Logo and other mathematics activities
might be approached in different ways. One would be to use Logo
as a medium to deliver the traditional mathematics curriculum. Another
would be to revise and expand traditional activities so that children
use higher-level thinking processes in their mathematics classes.
The latter more closely aligns with the recommendations of the National
Council of Teachers of Mathematics.43 But it is also
challenging--research shows that teachers find it extremely difficult
to create a learning environment that fosters creativity within
existing school and curricular structures. Those who were able to
change their classrooms into an environment that encouraged creative
mathematics had to examine fundamental assumptions about teaching,
learning, and their professional role as teachers.5 It
may be that Logo should be used in preservice mathematics courses,
where it can lead to better achievement and attitudes.44
A second implication is tentative, but potentially important. Logo
may be a particularly fruitful approach for populations at-risk
for poor performance in mathematics, such as girls and minorities.
For example, in one study the gap between a 12-13 year-old Logo
female group and a control female group widened appreciably during
the year. Indeed, the Logo female group overtook the control male
group which started the year ahead of all the other groups.45
In another, using Logo resulted in an increase in internal feelings
of personal responsibility and feelings of success for females only.46
Finally, in a third study, Logo minority students outscored Logo
majority students on a standardized test of mathematics achievement.47
Logo may be beneficial to minority children because it provides
them with a sense of mastery over their environment. It builds upon
the learning strengths of black students, such as high responsiveness
to visual and auditory stimuli and desire to collaborate with and
pass on information to peers. This requires a mediated teaching
What do we tell the turtle to make here?
That's where the sun is gonna go. We gotta go over here and
do a circle with curvy lines around it like our drawing.
So making curvy lines will be the hard part to figure out....
These students are determining just what the problem is all about
and what will be required to solve it. We know that getting students
to understand what is being asked of them is often half the battle.
Here's the other half...
We got it!
Well, let's think and make sure.
70? We already did 50. Type FORWARD 20."
Let's make a list of everything we tried and see which ones
[inputs] are best.
The partners are thinking about their thinking... checking
their work... reflecting. Logo was not only developed to serve as
a mathematical tool, but also as a tool for thinking. As with math
learning, different approaches to using Logo to develop problem-solving
abilities yield different results.
"Exposure" studies are similarly inconclusive. These studies assume
that programming and problem-solving use equivalent thinking processes,
and exposure to the former would develop the latter. Results are
mixed, with Logo programming increasing performance on some tasks
but not on others.48 Other studies are more discouraging--for
example, finding no effect of Logo work on students' ability to
solve nonroutine, mathematical word problems,49-51 or
reporting that direct training on problem-solving strategies without
computers resulted in higher performance than unguided Logo experience.52
Another such hypothesis was that programming involved extensive
planning; however, middle and high school students exposed to Logo
did not display greater planning skills on a non computer task than
those in a matched group.38,53
Under certain conditions, however, Logo may increase problem-solving
ability. For example, Logo can serve as a vehicle for helping fifth
and sixth grade students develop mathematical problem-solving abilities.54
The most positive results occur when teachers mediate their students'
learning of problem solving.55-57
Why is such mediation important? Some studies show no effect on
planning. But observations of students working on Logo tasks show
considerable growth in planning.4,58,59 This growth is
slow, however, and without teacher mediation to highlight planning
processes, transfer to non computer tasks is unlikely. Students
must become aware of their planning skills and how they can
be used in other situations. In one study, teachers stressed the
need to plan a procedure before beginning it and to use strategies
such as breaking a large idea into more manageable parts. Their
students used strategies of planning and drawing more frequently
to solve non-Logo mathematical problems.60
Effects on processes other than planning may be more profound.
Indeed, regular classroom tasks and tests may already provide substantial
experience with planning. On the other hand, such problem-solving
processes as deciding on the nature of the problem, selecting a
representation for solving the problem, and monitoring thinking
are not emphasized. But Logo programming can engage children in
all aspects of problem solving. Research supports this notion. For
example, students within a Logo environment displayed those problem-solving
processes to a greater degree than those in other computer environments,
such as computer drill.61 In addition, they outperformed
both this computer group and a non-computer control group on tasks
designed to assess these processes.62,63
Such findings have important educational implications. Research
shows that most students do not monitor their own problem solving,
from early childhood to the college level.64 After they
begin working on a problem, they rarely pause to see if the procedures
they are using will actually help them solve it. They do not check
their work for mistakes and they believe little can be learned from
such errors. Why does Logo help? In computer programming, errors
are unavoidable. Ideally, "experience with computer programming
leads children more effectively than any other activity to `believe
in' debugging . . . children learn that the teacher too is a learner,
and that everyone learns from mistakes."3 Thus, the act
of debugging Logo programs that do not quite do what was intended
provides students with valuable experience in using their monitoring
In appropriate Logo environments, students learn to use monitoring
in and out of Logo. In one study, students were given problems that
purposely misled via extra or irrelevant information. For example,
"When Albert was 6 years old, his sister was 3 times as old as he.
Now he is 10 years old and he figures that his sister is 30 years
old. How old do you think his sister will be when Albert is 12 years
old"? Logo students were more likely to find and fix the error in
the problem.63 Overall, one of the more consistent research
findings is an increase in monitoring following Logo experience.65-67
It is important to repeat that each of these studies employed
mediation; furthermore, this mediation was based on a theory of
human problem solving. In addition, assessment was based
on processes hypothesized to be affected by the Logo experience,
rather than, for example, routine textbook problems.
In sum, there is reason to be guardedly optimistic about the use
of Logo to develop problem-solving abilities. A recent study showed
that students who had computer programming experience scored about
16 percentile points higher on various problem-solving tests than
students without these experiences. Logo programming produced higher
scores than computer programming in other languages. To mediate
this learning, successful teachers55,68
- ask higher-order questions.
- make sure that students are explicitly aware of the strategies
and processes that they are to learn.
- discuss and provide examples of how the skills used in Logo
could be applied in other contexts.
- provide individualized feedback regarding students' problem-solving
- ensure that a sufficient proportion of instruction occurs in
small groups or in one-to-one situations.
- promote both child-teacher and child-child interaction.
- discuss errors and common misunderstandings.
Language and Reading
There has not been as much research in academic areas other than
mathematics and problem solving. Perhaps this is because Logo's
originators conceived of it in this way. Perhaps researchers are
less aware of the rich potential of Logo in other subject areas.
What research has been conducted, however, tends to be positive.
Research with young children indicates that Logo engenders language
rich with emotion, humor, and imagination.69 Similarly,
8- to 11-year-olds talked to each other more about their work when
they were doing programming tasks than when they were doing noncomputer
Effects on reading skills are more uncertain. When fifth graders
were removed from the classroom for Logo programming lessons, their
reading scores declined.14 Other studies, however, have
shown that immersion in Logo can lead to increases in language mechanics
and reading comprehension, even without direct instruction in that
ability.15,20 Research is needed to explain these findings.
Social and Emotional Development
Findings of increased language use suggest effects on the classroom's
social climate--remember first grader Darius. This may be a surprisingly
important benefit of the use of Logo.
Social Initiation and Participation
Teachers report that students exposed to Logo programming are more
likely to interact with peers. They engage in group problem solving
and sharing; there is more social acclaim by peers, and social acknowledgment
of expertise or ingenuity. These benefits are especially pronounced
for social isolates.1,5,10
Students working in Logo also talk more about learning than those
in non-Logo classrooms.70,71 In sum, Logo environments
appear to have the potential to facilitate social interaction, as
well as to focus that interaction on learning.
Social Problem Solving
Students engage in more collaborative activity during Logo than
noncomputer tasks.70 They also learn to solve social
problems cooperatively and flexibly in that context .5,72
One study indicated that children work cooperatively more often
on computers than off.73 Interestingly, they also got
into more conflicts (possibly because they interacted more). However,
children working with Logo, compared to children working on other
computer activities, were more likely to resolve these conflicts.73
In a similar vein, students working together on Logo tasks spent
much time resolving conflicts.23 Finally, research indicates
that the type of conflict--social or cognitive--is critical.58
Children working in Logo demonstrated more conflict about ideas,
and more attempts and successes at resolving these conflicts. Differences
were not evident for social conflict. So, the effects of
Logo seemed to be specific to disagreements about ideas. Opportunities
to experience and resolve conflicts are necessary for the development
of problem-solving competencies. Therefore, Logo contexts may enhance
the development of specific social and cognitive problem-solving
Students working with Logo are particularly prone to helping and
teaching each other.10,70,73 Elementary students working
with Logo learn to listen, be critical in a constructive fashion,
and appreciate the work of others.5
In summary, Logo has the potential to serve as a tool in encouraging
prosocial interaction, social problem solving, and social sensitivity.
What of students' emotional side? Can Logo increase their self-esteem?
Their motivation to learn? According to their teachers, students
working with Logo experience an increase in self-esteem and confidence,
if their teacher gives them greater autonomy over their learning
and fosters social interaction.4,5,10 Logo particularly
provides special needs children with prestige and respect from their
peers, enhancing their self concepts.74
Logo work can improve attitudes toward learning and academic subject
matter,5,13,75 although such results are not consistent.51,76
Children in Logo environments are more likely to engage in self-directed
explorations and to show pleasure at discovery.61,73
Students experiencing Logo appear to judge situations for themselves
and accept responsibility for their actions.13,76,77
These findings provide some evidence of Logo's power for enhancing
students' self-esteem and attitudes toward school.
Social Issues: Conclusions
It is important to reiterate that Logo, as conceived by Papert,3
is more than a programming language: It is a catalyst for the generation
of a learning and teaching culture. This culture includes
children's interaction with others. Furthermore, one of Papert's
principles of Logo learning is "cultural resonance": The ideas learned
within Logo should make sense in the larger social context. One
implication is that future research on Logo should consider the
social context in which the teaching and learning are embedded.
It is thus not surprising that research results, especially concerning
cognitive benefits, have been inconsistent. Several evaluation efforts
have disconnected the Logo language from its social and cultural
roots, placing it within the traditional classroom context. Their
findings are frequently "no significant differences."
The social interactions that occur in Logo environments may be
qualitatively different from those in other environments. Child-child
and child-teacher interactions during Logo programming may be as
significant for social, emotional, and cognitive development as
are the child-computer interactions.
In conclusion, it appears that while there are certainly no "guaranteed
results," Logo has the potential to improve students' educational
experiences. A critic might protest that the measure of these benefits
is too slight. Criticisms of claims about Logo's benefits ignore
four important issues.
First, we must remember that researchers do not know how to measure
all that is educationally valuable. Many of the traditional experimental
studies of Logo have used traditional measures that would not reveal
effects of meaningful educational reform. They use traditional designs
that demand that only one "variable" be manipulated. But Logo is
an open-ended tool. Teachers and researchers must decide what to
do with it: how to present it to students, what tasks to pose, and
what classroom interaction to promote. Teachers should then be aware
that there is never only one variable. There is no single "Logo
Second, Logo possesses the power to significantly enhance students'
educational experience. These benefits are maximized when
- Logo experiences go beyond mere exposure.
- teachers mediate Logo experience.
- the classroom culture--the way teachers and students view learning
and each other--is simultaneously changed.
- an active, constructivist approach is taken to the teaching/learning
process. This is critical. All recent calls for reform support
this approach. Logo is designed to support this approach.
Third, while educational researchers debate the efficacy of various
research methods, we conclude that there is no single best method
for assessing the effects of Logo. Each has advantages--a certain
lens that allows us to view people as they use Logo. Each has blind
spots. Experimental studies often overlook the deep meanings people
give to their Logo work. These studies usually can't see what the
researchers didn't think of looking for. They can uncover small,
subtle effects that emerge only as patterns over large numbers of
people. And so it goes. Action research empowers teachers. Research
in the literary or dramatic tradition provides an aesthetic view.78
Without this variety, our vision of the effects and efficacy of
Logo would be dim indeed.
Fourth, mediated Logo environments are interesting in that they
seem to enrich so many different aspects of students' lives. An
alternate, narrow approach might yield similar gains on a single
test, but few educational environments have shown consistent benefits
of such a wide scope, from the mathematical and cognitive to the
social and emotional. Like "Stone Soup," the main nourishment of
a Logo environment may emerge from many small, interacting contributions.
But the local culture has to change to allow the contributions to
- St. Paul Public Schools, Logo Studies. 1985, St. Paul,
- Feurzeig, W. and G. Lukas, LOGO--A programming language for
teaching mathematics. Educational Technology, 1971. 12:
- Papert, S., Mindstorms: Children, Computers, and Powerful
Ideas. 1980, New York: Basic Books.
- Kull, J.A., Learning and Logo, in Young Children and
Microcomputers, P.F. Campbell and G.G. Fein, Editor. 1986,
Prentice-Hall: Englewood Cliffs, NJ. p. 103-130.
- Carmichael, H.W., et al., Computers, children and
classrooms: A multisite evaluation of the creative use of microcomputers
by elementary school children. 1985, Toronto, Ontario, Canada:
Ministry of Education.
- Papert, S., et al., Final report of the Brookline
Logo Project. Part II: Project summary and data analysis (Logo
Memo No. 53). 1979, Cambridge, MA: Massachusetts Institute
of Technology, Artificial Intelligence Laboratory:
- Hillel, J. and C. Kieran, Schemas used by 12-year-olds in
solving selected turtle geometry tasks. Recherches en Didactique
des Mathématiques, 1988. 8/1.2: p. 61-103.
- Hillel, J., Mathematical concepts and programming skills
acquired by 8-year-olds in a restricted Logo environment.
1984, Logo 84 conference: Cambridge, MA.
- Robinson, M.A., W.F. Gilley, and G.E. Uhlig, The effects
of guided discovery Logo on SAT performance of first grade students.
Education, 1988. 109: p. 226-230.
- Fire Dog, P., Exciting effects of Logo in an urban public
school system. Educational Leadership, 1985. 43: p.
- Howe, J.A.M., T. O'Shea, and F. Plane, Teaching mathematics
through Logo programming: An evaluation study, in Computer
Assisted Learning: Scope, Progress and Limits, R. Lewis and
E.D. Tagg, editor. 1980, North-Holland: Amsterdam, NY. p. 85-102.
- Battista, M.T. and D.H. Clements, The effects of Logo and
CAI problem-solving environments on problem-solving abilities
and mathematics achievement. Computers in Human Behavior,
1986. 2: p. 183-193.
- Blumenthal, W., The effects of computer instruction on low
achieving children's academic self-beliefs and performance.
1986, Nova University:
- Seidman, R.H., The effects of learning a computer programming
language on the logical reasoning of school children. 1981,
American Educational Research Association: Los Angeles, CA.
- Studyvin, D. and M. Moninger, Logo as an enhancement to critical
thinking. 1986, Logo 86 Conference: Cambridge, MA.
- Piaget, J. and B. Inhelder, The Child's Conception of Space.
1967, New York: W. W. Norton & Co.
- Clements, D.H. and M.T. Battista, Logo Geometry. 1991,
Silver Burdett & Ginn: Morristown, NJ.
- Clements, D.H. and M.T. Battista, Geometry and spatial reasoning,
in Handbook of Research on Mathematics Teaching and Learning,
D.A. Grouws, Editor. 1992, Macmillan: New York. p. 420-464.
- van Hiele, P.M., Structure and Insight. 1986, Orlando:
- Clements, D.H., Longitudinal study of the effects of Logo
programming on cognitive abilities and achievement. Journal
of Educational Computing Research, 1987. 3: p. 73-94.
- Clements, D.H. and M.T. Battista, Learning of geometric concepts
in a Logo environment. Journal for Research in Mathematics
Education, 1989. 20: p. 450-467.
- Hughes, M. and H. Macleod, Part II: Using Logo with very
young children, in Cognition and Computers: Studies in
Learning, R. Lawler, et al., Editor. 1986, Ellis Horwood
Limited: Chichester, England. p. 179-219.
- Lehrer, R. and P.C. Smith, Logo learning: Are two heads better
than one? 1986, American Educational Research Association:
- du Boulay, B., Part II: Logo confessions, in Cognition
and Computers: Studies in Learning, R. Lawler, et al.,
Editor. 1986, Ellis Horwood Limited: Chichester, England. p. 81-178.
- Frazier, M.K., The effects of Logo on angle estimation skills
of 7th graders. 1987, Wichita State University:
- Kieran, C., Logo and the notion of angle among fourth and
sixth grade children, in Proceedings of PME 10. 1986,
City University: London, England. p. 99-104.
- Olive, J., C.A. Lankenau, and S.P. Scally, Teaching and understanding
geometric relationships through Logo: Phase II. Interim Report:
The Atlanta-Emory Logo Project. 1986, Altanta, GA: Emory University:
- Kelly, G.N., J.T. Kelly, and R.B. Miller, Working with Logo:
Do 5th and 6th graders develop a basic understanding of angles
and distances? Journal of Computers in Mathematics and Science
Teaching, 1986-87. 6: p. 23-27.
- Hoyles, C. and R. Sutherland, When 45 Equals 60. 1986,
London, England, University of London Institute of Education,
- Kieran, C., J. Hillel, and S. Erlwanger, Perceptual and analytical
schemas in solving structured turtle-geometry tasks, in Proceedings
of the Second Logo and Mathematics Educators Conference, C.
Hoyles, R. Noss, and R. Sutherland, Editor. 1986, University of
London: London, England. p. 154-161.
- Kieran, C., Turns and angles: What develops in Logo?,
in Proceedings of the Eighth Annual PME-NA, G. Lappan,
Editor. 1986, Michigan State University: Lansing, MI.
- Campbell, P.F., Measuring distance: Children's use of number
and unit. Final report submitted to the National Institute of
Mental Health Under the ADAMHA Small Grant Award Program. Grant
No. MSMA 1 R03 MH423435-01. 1987, University of Maryland,
- Johnson, P.A., Effects of Computer-Assisted Instruction Compared
to Teacher-Directed Instruction on Comprehension of Abstract Concepts
by the Deaf. 1986, Northern Illinois University:
- Findlayson, H.M., The Transfer Of Mathematical Problem Solving
Skills From Logo Experience. D.A.I. Research Paper No. 238.
1984, Unpublished manuscript, University of Edinburgh, Edinburgh,
- Milner, S., The effects of computer programming on performance
in mathematics. 1973, American Educational Research Association:
New Orleans, LA.
- Nelson, G.T., Development of fourth-graders' concept of literal
symbols through computer-oriented problem-solving activities,
in Dissertation Abstracts International. 1986, p. 2607A.
- Lehrer, R. and P. Smith, Logo learning: Is more better?
1986, American Educational Research Association: San Francisco.
- Kurland, D.M., et al., A study of the development
of programming ability and thinking skills in high school students.
Journal of Educational Computing Research, 1986. 2: p.
- Soloway, E., Why kids should learn to program. Harvard
Educational Review, in press.
- Hillel, J. and R. Samurçay, Analysis of a Logo Environment
for Learning the Concept of Procedures With Variable. 1985,
Unpublished Manuscript, Concordia University, Montreal:
- Sutherland, R., What are the Links Between Variable in Logo
and Variable in Algebra? 1987, Unpublished manuscript, University
of London Institute of Education, London, England:
- Noss, R., Creating a Mathematical Environment Through Programming:
A Study of Young Children Learning Logo. 1985, Chelsea College,
University Of London: London, England.
- National Council of Teachers of Mathematics, Curriculum and
Evaluation Standards for School Mathematics. 1989, Reston,
- Watson, G.A., Using Logo to Teach Math to Elementary Teachers.
1988, Unpublished manuscript, West Liberty State College, West
Liberty, West Virginia:
- Howe, J., et al., Learning Mathematics Through Logo
Programming: The Transition From Laboratory to Classroom. DAI
Working Paper No. 118. 1982, Unpublished manuscript, University
Of Edinburgh, Edinburgh, Scotland:
- Olson, J.K., Using Logo to supplement the teaching of geometric
concepts in the elementary school classroom, in Dissertation
Abstracts International. 1985, p. 819A.
- Emihovich, C. and G.E. Miller, Effects of Logo and CAI on
black first graders' achievement, reflectivity, and self-esteem.
The Elementary School Journal, 1988. 88: p. 473-487.
- Statz, J., The development of computer programming concepts
and problem solving abilities among ten-year-olds learning Logo,
in Dissertation Abstracts International. 1974, p. 5418B-5419B.
- Bruggeman, J.G., The effects of modeling and inspection methods
upon problem solving in a computer programming course, in
Dissertation Abstracts International. 1986, p. 1821A.
- LeWinter, B., A study of the influence of Logo on locus of
control, attitudes towared mathematics, and problem-solving ability
in children in grades 4, 5, 6, in Dissertation Abstracts
International. 1986, p. 1640A.
- Milojkovic, J.D., Children learning computer programming:
Cognitive and motivational consequences, in Dissertation
Abstracts International. 1984, p. 385B.
- Dalton, D.W., A Comparison of the Effects of Logo and Problem-Solving
Strategy Instruction on Learner Achievement, Attitude, and Problem-Solving
Skills. 1985, University Of Colorado:
- Pea, R.D. and D.M. Kurland, Logo Programming and the Development
of Planning Skills. Technical Report No. 16. 1984, Unpublished
manuscript, Bank Street College of Education, Center for Children
and Technology, New York:
- Billings, L.J., Jr., Development of mathematical task persistence
and problem-solving ability in fifth and sixth grade students
through the use of Logo and heuristic methodologies, in Dissertation
Abstracts International. 1986, p. 2433A.
- Clements, D.H., Logo: Search and research [research review
column], in Logo Exchange. 1986-91,
- Lehrer, R., et al., Microcomputer-based instruction
in special education. Journal of Educational Computing Research,
1986. 2: p. 337-355.
- Littlefield, J., et al., Learning Logo: Method of
teaching, transfer of general skills, and attitudes toward school
and computers, in Teaching and Learning Computer Programming:
Multiple Research Perspectives, R. Mayer, Editor. 1988, Erlbaum:
Hillsdale, NJ. P. 111-135.
- Nastasi, B.K., D.H. Clements, and M.T. Battista, Social-cognitive
interactions, motivation, and cognitive growth in Logo programming
and CAI problem-solving environments. Journal of Educational
Psychology, 1990. 82: p. 150-158.
- Noss, R., Children learning Logo programming. Interim report
No. 2 of the Chiltern Logo Project. 1984, Hatfield, England:
Advisory Unit for Computer-Based Education:
- Bamberger, H.J., The effect of Logo (turtle graphics) on
the problem solving strategies used by fourth grade children,
in Dissertation Abstracts International. 1985, p. 918A.
- Clements, D.H. and B.K. Nastasi, Social and cognitive interactions
in educational computer environments. American Educational
Research Journal, 1988. 25: p. 87-106.
- Clements, D.H., Effects of Logo and CAI Environments on cognition
and creativity. Journal of Educational Psychology, 1986. 78:
- Clements, D.H., Metacomponential development in a Logo programming
environment. Journal of Educational Psychology, 1990. 82:
- Schoenfeld, A.H., Metacognitive and epistemological issues
in mathematical understanding, in Teaching and Learning
Mathematical Problem Solving: Multiple Research Perspectives,
E.A. Silver, Editor. 1985, Erlbaum: Hillsdale, NJ. P. 361-379.
- Clements, D.H. and D.F. Gullo, Effects of computer programming
on young children's cognition. Journal of Educational Psychology,
1984. 76: p. 1051-1058.
- Lehrer, R. and L. Randle, Problem Solving, Metacognition
and Composition: The Effects of Interactive Software for First-Grade
Children. Journal of Educational Computing Research, 1986.
3: p. 409-427.
- Miller, G.E. and C. Emihovich, The Effects of Mediated Programming
Instruction on Preschool Children's Self-Monitoring. Journal
of Educational Computing Research, 1986. 2(3): p. 283-297.
- Clements, D.H. and S.L. Merriman, Componential developments
in logo programming environments, in Teaching and Learning
Computer Programming: Multiple Research Perspectives, R. Mayer,
Editor. 1988, Erlbaum: Hillsdale, NJ. p. 13-54.
- Genishi, C., P. McCollum, and E.B. Strand, Research currents:
the interactional richness of children's computer use. Language
Arts, 1985. 62(5): p. 526-532.
- Hawkins, J., et al., Microcomputers in schools: impact on
the social life of elementary classrooms. Journal of Applied
Developmental Psychology, 1982. 3: p. 361-373.
- Kinzer, C., et al., Different Logo learning environments
and mastery: relationships between engagement and learning.
Computers in the Schools, 1985. 2(2-3): p. 33-43.
- Hoyles, C., A preliminary investigation of the pupil-centered
approach to the learning of Logo in the secondary school mathematics
classroom. 1984, Logo Maths Project, University of London
Institute of Education, London, England:
- Clements, D.H. and B.K. Nastasi, Effects of computer environments
on social-emotional development: Logo and computer-assisted instruction.
Computers in the Schools, 1985. 2(2-3): p. 11-31.
- Michayluk, J.O., D.H. Saklofske, and R.A. Yackulic, Logo.
1984, CAP Convention: Ottawa, Ontario.
- Findlayson, H.M., What do children learn through using Logo?
D.A.I. Research Paper No. 237. 1984, British Logo Users Group
Conference: Loughborough, U.K.
- Horner, C.M. and C.D. Maddux, The effect of Logo on attributions
toward success. Computers in the Schools, 1985. 2(2-3):
- Brown, S.W. and M.K. Rood, Training gifted students in Logo
and BASIC: What is the difference? 1984, American Educational
Research Association: New Orleans, LA.
- Papert, S., Computer criticism vs. technocentric thinking.
Educational Researcher, 1987. 16: p. 22-30