Douglas H. Clements
Over ten years ago, Computers in the Schools published our first review of Logo research. In this article, we examine the research, emphasizing that conducted since our earlier review, and asking which conclusions have been borne out, which must be modified, and which are new. The research corpus is sufficiently large that we focus on selected topics, including mathematics, higher-order thinking, creativity, language arts, and social-emotional development. We will also discuss future directions of Logo research and new versions of Logo in an attempt to answer the question: Where do we go from here?
Our earlier review concluded that effects of Logo on mathematics achievement were conflicting and not always impressive. A recent review, in contrast, is quite positive. “Logo programming, particularly turtle graphics at the elementary level, is clearly an effective medium for providing mathematics experiences . . . . when students are able to experiments with mathematics in varied representations, active involvement becomes the basis for their understanding. This is particularly true in geometry -- and the concept of variable” (McCoy, 1996, p. 443). Thus, while not all research has been positive (Hamada, 1987) -- the many factors involved cannot be taken lightly -- results generally support the use of Logo as a medium for learning and teaching mathematics (Barker, Merryman, & Bracken, 1988; Bultler & Close, 1989; Clements & Meredith, 1993; Hoyles & Noss, 1987; Miller, Kelly, & Kelly, 1988; Salem, 1989; Tanner, 1992; Yelland, 1995). Unsurprisingly, given the ubiquitous use of turtle graphics, the area of geometry and spatial sense has been extensively researched, with generally positive results.
Geometry and Spatial Sense
Why is the turtle particularly helpful? Students construct initial spatial notions from actions (Piaget & Inhelder, 1967), and they command the turtle to move (Clements & Battista, 1992b). In this way, Logo activities facilitate student progression to higher levels in the van Hiele hierarchy of geometric thinking (van Hiele, 1986). For example, with the concept of rectangle, students initially are able only to identify visually presented examples, a level 1, or visual, activity (e. g., a shape is a rectangle if it “looks like a door”). Writing a sequence of Logo commands, or procedure to draw a rectangle “allows, or obliges, the student to externalize intuitive expectations. When the intuition is translated into a program it becomes more obtrusive and more accessible to reflection” (Papert, 1980, p. 145). That is, students must analyze the visual aspects of the rectangle and reflect on how they can build it from parts. This leads to a recognition of the figure’s properties, an example of level 2, descriptive/analytic, thinking. Furthermore, if asked to design a rectangle procedure that takes the length and the width as inputs, students must construct one type of definition. Thus, they begin to build intuitive knowledge about the concept of defining a rectangle, knowledge that they can later integrate and formalize -- a level 3, abstract/relational, activity. If challenged to draw a square or a parallelogram with their rectangle procedure, students may logically order these figures, another level 3 activity. Further, Logo aids the generation of many cases of a concept. Logo is a useful medium for instruction in geometry.
Supporting these hypotheses, students’ work in Logo relates closely to their level of geometric thinking (Olson, Kieren, & Ludwig, 1987). In addition, appropriate use of Logo helps students begin to make the transition from the levels 0 and 1 to level 2 of geometric thought. Guided Logo experience significantly enhances students’ concepts of plane figures (Butler & Close, 1989; Clements, 1987; Clements & Battista, 19-92b; Hughes & Macleod, 1986) and other geometric objects (Yusuf, 1994).
Consider an example from a study -- the responses of three students to the question: How do you know it’s a square for sure?
Mary: “It is in a tilt. But it’s a square because if you turned it this way it would be a square.”
Adam: “Yes, a sideways square.”
Barb: “Yes, it’s a square. It has equal edges and equal turns.” (Clements & Battista, 1992a)
Mary, a second grader, made a completely visual response. A figure was a square if you could make it “look like” one. Fifth grader Barb used the properties of a square to decide.
In this study, we worked with a 656 k-6 students on Logo Geometry activities designed to help students construct geometric ideas from their spatial intuitions (Battista & Clements, 1988; Battista & Clements, 1991; Clements & Battista, 1992a; Clements & Battista, 1992b). Control students (644) worked with their regular geometry curriculum. After introductory path activities (e. g., walking paths, creating Logo paths), students engaged in off- and on-computer activities exploring squares and rectangles. For example, they identified these shapes in the environment, wrote Logo procedures to draw them, and drew complex figures with these procedures. We conducted case studies and paper-and-pencil testing to see what students were thinking. Logo students performed better overall. They showed dramatic growth on correctly classifying squares (as a type of rectangle). The Logo group outperformed the control group on the parallelogram items; so they were not overgeneralizing, that is, believing that all parallelograms are rectangles. Logo students did learn to apply the property “opposite sides equal” to the class of squares. They understood that the property “opposite sides equal” is not inconsistent with the property “all sides equal in length.” Most students could apply both properties to the class of squares, demonstrating flexible consideration of multiple properties that may help lay the groundwork for hierarchical classification.
Why does Logo help? Logo incorporates the types of properties that level 2 thinkers develop explicitly, something that textbooks typically do not (Fuys, Geddes, & Tischler, 1988). Logo experience encourages students to view and describe geometric shapes, students with Logo experience give more statements overall and more statements that explicitly mention geometric properties of shapes (Clements & Battista, 1989; Clements & Battista, 1990; Lehrer & Smith, 1986). In one study, students were better able to apply their knowledge of geometry than a comparison group. There was no difference in knowledge of basic geometric facts; therefore, the use of Logo influenced the way in which students represent their knowledge of basic geometric facts; therefore, the use of no difference in knowledge of basic geometric facts; therefore, the use of Logo influenced the way in which students represent their knowledge of geometric concepts (Lehrer, Randle, & Sancilio, 1989). Middle school students move to higher levels of conceptualizing and begin to integrate visual and symbolic representations (Clements & Battista, 1988; Clements & Battista, 1989; Clements & Battista, 1992a; Hoyles, Healy, & Sutherland, 1991; Hoyles & Noss, 1988; Kieran & Hillel, 1990).
Ninth-grade students may prefer learning with Logo. In one study, they expressed very positive remarks, during the end-of-semester discussion, concerning their experiences in the Logo class. They found the class intriguing and exciting. They perceived the relaxed atmosphere of the class to be better than that of their other classes because students and teacher were more comfortable with one another. The student reported being less frustrated and more involved in the Logo class than they were with their other classes. They believed that they ha learned a lot of theorem. They thought Logo had helped them with problem solving (Olive, 1991). However, success and sophistication in the Logo programming aspects of the tasks were necessary but not sufficient for success and sophistication with the geometric concepts involved in the tasks.
Working with a Logo unit on motion geometry, students’ movement away from van Hiele level 0 was slow, but there was definite evidence of a beginning awareness of the properties of transformation (Olson et al., 1987). Middle school students achieved a working understanding of transformations and used visual feedback to correct overgeneralizations when working in a Logo microworld (Edwards, 1991). Most impressive, one study had three groups; one was a control group and two worked with geometric motions, one with Logo, one with physical manipulatives, using identical activities. Both treatment groups, especially the Logo group, performed at a higher level of geometric thinking than did the control group. Further, the Logo group outperformed the non-Logo group on the delayed posttest. The use of Logo enhanced students’ construction of higher-level conceptualizations of motion geometry (Johnson-Gentile, Clements, & Battista, 1994). Thus, there is support for the hypothesis that Logo experiences can help students become cognizant of their mathematical intuitions and facilitate the transition from visual to descriptive/analytic geometric thinking (Clements & Battista, 1989).
Several research projects have investigated the effects of Logo experience on students’ conceptualizations of angle and angle measure. While the Logo experience does not eliminate “misconceptions,” it appeared to significantly affect students’ ideas about angle. For example, responses of control students in one study reflected little knowledge of angle or common language usage, such as “a corner”; “a line titled.” In comparison, the Logo students indicated more generalized and mathematically oriented conceptualizations, such as “Like where a point is. Where two lines come together at a point” (Clements & Battista, 1989). Several researchers have reported a positive effect of Logo on students’ angle concepts (Clements & Battista, 1989; du Boulay, 1986; Frazier, 1987; Kieran, 1986a; Kieran & Hillel, 1990; Olive, Lankenau, & Scally, 1986). Benefits may not emerge, however, until more than a year of Logo experience (Kelly, Kelly, & Miller, 1986-87). Students teachers experiencing difficulty with mathematics learned about the properties of particular angles and eventually shifted their attention to more general properties of shapes (du Boulay, 1986). Logo experiences may foster some misconceptions of angle measure; for example, mistaking the amount of rotation from the vertical as the measure of the (interior) angle (Clements & Battista, 1989). Students’ difficulties coordinating the relationships between the turtle’s rotation and the constructed angle have persisted for years, especially if not properly guided by their teachers (Clements, 1987; Cope & Simmons, 1991; Hoyles & Sutherland, 1986; Kieran, 1986a; Kieran, Hillel, & Erlwanger, 1986). However, Logo experience appears generally to facilitate understanding of angle measure. Logo students’ conceptualizations of angle size are more likely to reflect mathematically correct, coherent, and abstract ideas (Clements & Battista, 1989; Findlayson, 1984b; Kieran, 1986b; Noss, 1987). Students progress from van Hiele level 0 to level 2 (Clements & Battista, 1989). Logo experiences that emphasize the difference between the angle of rotation and the angle formed as the turtle traces a path help students avoid mistakes (Clements & Battista, 1989, Kieran, 1986b). In addition, if Logo itself is redesigned to consider extant research, positive effects are increasingly likely (Clements & Sarama, 1995). In one class using Turtle Math, the teacher felt confident in her students’ ability to estimate turns on the computer, but was unsure of how they would answer questions regarding angle measure (Sarama, 1995). She drew an angle and asked her class what the measure was. She was dumbfounded when they began asking her for more information: “where is the turtle?” “Which way is it headed?” The students wished to know if it was turning through an interior or exterior angle. They were approaching a routine question with more flexible thinking than the teacher was used to hearing. She was distraught initially, but later spoke about how “smart” her students were to think of all the possibilities.
Logo experiences may also affect competencies in linear measurement, because they permit students to manipulate units and to explore transformations of unit size and number of units without the distracting dexterity demands associated with measuring instruments and physical quantity. Logo students in one study were more accurate than control students in measure tasks (Campbell, 1987). The control students were more likely to underestimate distances, particularly the longest distances; to have difficulty compensating for the halved unit size; and to underestimate the inverse relationship between unit size and unit numeracy.
In mastering Logo commands, even young students master Logo’s polar coordinate spatial system (Campbell, Fein, Scholnick, Frank, & Schwartz, 1986). Older students can learn more sophisticated ideas about measurement, as well as about directions and coordinates (Kynigos, 1992). The turtle facilitated learning these ideas as well, even though they are not the usual turtle, or intrinsic, geometry. For example, students adopted and used the notion of the turtle “putting its nose to look” at some direction rather than “turning this much” (Kynigos, 1992, p. 106). Several studies, then, indicate that enriching the primitives and tools available to students facilitates their construction of geometric notions and increases analytical, rather than visual, approaches (Clements & Battista, 1992a; Clements & Sarama, 1995; Kynigos, 1992).
As we notes, not all research has been positive. First, few studies report that students “master” the mathematical concepts. Without guidance, misconceptions can persist. Second, some studies show no significant differences between Logo and control groups (Johson, 1986). Again, “exposure” without teacher guidance often yields little learning (Clements & Meredith, 1993). Third, some studies have shown limited transfer. For example, students from two ninth-grade Logo classes did not differ significantly from control students on subsequent high school geometry grades and tests (Olive, 1991; Olive at al., 1986). One reason 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 avoid analytical work (Hillel & Kieran, 1988). The visual approach not related to an ability to visualize but to the role of visual “data” of a geometric figure in determining students’ Logo constructions. Although helpful initially, overuse inhibits students from arriving at mathematical generalizations. There is little reason for students to abandon visual approaches unless teacher present tasks whose resolution requires an analytical, generalized, mathematical approach. In addition, dialog between teacher and students is essential for encouraging predicting, reflecting, and higher-level reasoning.
In summary, studies that have shown the most positive effects involve carefully planned sequences of Logo activities. Teacher mediation of students’ work with those activities is necessary for successful construction of geometric concepts. Mediation includes helping students to forge links between Logo and other experiences and between Logo-based procedural knowledge and more traditional conceptual knowledge (Clements & Battista, 1989; Lehrer & Smith, 1986).
Number, Arithmetic, and Algebra
Arithmetic has long dominated the elementary school curriculum. While results are mixed, the effect of nonstructured programming in Logo on arithmetic skills usually appears small (Butler & Close, 1989), though the finding that time spent on Logo does not decrease such skills is notable. Logo does not provide efficient practice on arithmetic processes. However, it does provide a context in which there is a real need fore these processes and in which children must clearly conceptualize which operation they should apply. For example, first-grade children determined the correct length for the bottom line of their drawing by adding the lengths of the three horizontal lines that they constructed at the top of the tower: 20+ 30 + 20 = 70 (Clements, 1983-84). If used in such reflective ways, Logo can aid growth in arithmetic skills equally to CAI drill on those same skills (Wilson & Lavelle, 1992).
Further, studies have shown that certain uses of Logo with young students do appear to facilitate basic number sense; for example, learning relationships between size of numbers and the length of a line drawn by the turtle (Bowman, 1985; Clements, 1987; Hughes & Macleod, 1986; Robinson, Gilley, & Uhlig, 1988; Robinson & Uhlig, 1988). Thus, it is possible for students to develop a new sense of arithmetic, numbers, and estimation within the context of their Logo work. Such experience can positively affect achievement test scores (Barker et al., 1988). Related aspects of mathematical thinking may also be facilitated. First grader Ryan wanted to turn the turtle to point into his rectangle. He asked the teacher, “What’s half of 90?” After she responded, he typed RT 45. “Oh, I went the wrong way.” He said nothing, eyes on the screen. “Try LEFT 90,” he said at last. This inverse operation produced exactly the desired effect (Kull, 1986).
Logo and other problem-solving programs are often used more with higher SES children and drill with lower SES children. Logo, however, may provide a particularly beneficial environment for low SES minority children. First graders outscored majority students on a standardized test of mathematics achievement following Logo experience (Emihovich & Miller, 1988). These researchers claimed that Logo may have provided the children with a sense of mastery over their environment and first-hand experience in using the metacognitive skills.
Our earlier review suggested that Logo experience would facilitate student learning of “generalized arithmetic” -- variable and algebra. Research since then has supported this view; Logo can help students from primary grade to high school understand variables, even in comparison to other treatments (Carmichael, Burnett, Higginson, Moore, & Pollard, 1985; Findlayson, 1984a; Milner, 1973). In one study, fourth graders were interviewed before and after using Logo to solve problems involving rectangles, formulas and equations, and number sequences (Nelson, 1986). During the pre-Logo interviews, several students used a correspondence between the letters of the alphabet and the positive integers to assign values to literal symbols in equations (i.e., A=1, B=2, etc.). After Logo, they determined each literal symbol’s value correctly. All the students could use literal symbols in formulas after Logo instruction; whereas, none could before.
Such learning, however, may be limited. Some students do not fully generalize that variable idea as used in Logo to other situtations (Lehrer & Smith, 1986a). Similarly, after a year of programming experience, high school students had only rudimentary understanding variables (Kurland, Pea, Clement, & Mawby, 1986). In addition, students often have difficulties with the variable concept within the Logo programming context. First, the use of variables does not arise spontaneously, and students resist their use even after teachers’ suggestions (Hillel & Samurcay, 1985; Sutherland, 1987). Furthermore, students sometimes (a) declare a variable in a procedure, but then do not use it within the body of a procedure; (b) believe that a variable might have different values within a procedure; or (c) confuse what the variable stands for (Hillel & Samurcay, 1985). They over generalize analogies; for example, taught to think of variables as a box, many believe that a variable might hold more than one value (du Boulay, 1986).
Again, then, there is evidence that mere “exposure” without teacher mediation is insufficient. While Noss (Noss, 1985) reported that Logo can benefit intermediate students, he cautioned that students have not necessarily gained specific information about variables or algebra. They may have begun to construct a conceptual framework based on intuitions and “primitive conceptions” upon which they can build later algebraic learning. That is, their early strategies may be precursors of sophisticated mathematics. For example, students will often declare multiple variables in their Logo procedures, one for each parameter that varies, ignoring necessary relationships among them. They can call these procedures with values that satisfy the relationships, suggesting that the students implicitly recognize relationships. This declaration then serves as a scaffolding for later analysis (Noss & Hoyles, 1992). Often with, but sometimes without, teacher intervention, students reconstruct their procedures to show these relationships. Significantly, compared or not only paper-and-pencil, but also spreadsheet environments, students working collaboratively with Logo more frequently use formal language as means of articulating general ideas (Hoyles et al., 1991). They combine natural language and Logo words and ideas easily. Supporting this beneficial tendency may be students’ realization that Logo does not understand a natural language formulation. Students may come to expect that they will have to formalize to communicate their generalization and represent their task solution (Hoyles et al., 1991). In support of this conceptual framework notion, one boy extended his systematic incrementing of Logo variables to quite different contexts (Lawler, 1986).
To help students develop a conceptual framework -- and critically, to expand it into explicit learning of algebra -- within the typical classroom situation may require a high degree of elaboration fostered by organized instruction and thoughtfully structured tasks. Such tasks, and instruction that emphasizes links between Logo and algebra contexts, have been shown to lead to formalization and generalization of the variable concept (Hillel & Samurcay, 1985; Milner, 1973; Sutherland, 1987).
In summary, there is some evidence that Logo provides an “entry” to the use of the powerful tool of algebra. It is an environment in which some students perceive the use of formalizations such as variables as natural and useful. Again, however, we find that students’ ability to generalize their Logo-based notion of variable may depend to a great degree on the depth of their Logo experience and the instructional support given them.
Ratio and Proportion
Researches have observed similar facilitative effects of Logo environments on ratio and proportion tasks. On a geometric proportion task, students used additive strategies on the related Logo tasks (Hoyles & Noss, 1989). The reason lay in the interaction between students’ formalization and computer feedback. They formalize proportional relationships algebraically as Logo programs. They receive graphical feedback regarding their mathematical intuitions. On pencil-and-paper, the formalization is less salient; the feed-back is absent.
Students may have abandoned additive thinking because the computer provided a way to think about the general within the specific. Paper-and-pencil invited a fixed answer to a fixed question. The computer allowed exploration to escape from mental “blocks” and activated a dynamic answer. Posing the task of writing a superprocedure that would handle all cases promoted additional development. Thus, again we see the encouragement of more generalized and abstract views of mathematical objects within structured Logo environments.
Long-Term and Delayed Effects
Are the effects of Logo long-lasting? The findings are mixed, but interesting.
On the negative side are studies that fail to find long-term differences. Researchers provided six-year-olds rich experiences with Logo and mathematical thinking (Hughes & Macleod, 1986). Inteviewing a half a year later, however, they found it difficult to distinguish between students with and without previous Logo experience (Siann & Macleod, 1986).
There are also more positive examples. Students using Logo to learn ideas about variables scored higher on a delayed retention test than students using a textbook approach. The Logo group had a firmer idea of the variable concept (Ortiz & Miller, 1991).
In an early study, Logo first graders had made significant gains in measures of creativity and reflectivity compared to a CAI group. They also significantly outperformed the CAI group on assessments of cognitive monitoring, or “knowing whether you understand” (Clements & Gullo, 1984). Two years later, the researcher compared the groups again (Clements, 1987). Compared to the CAI students, the Logo students solved more problems that demanded higher-order thinking skills.
There was a moderate effect on mathematics computation. This may have resulted from direct practice, as suggested by several of the students themselves. If so, however, why didn’t the CAI treatment have a similar effect? It may be that computation in Logo, involving multidigit operations in a problem-solving setting, stretched students’ capabilities and provided a novel model for the operations. In contrast, the CAI students practiced counting and simple addition specifically “geared to their level.”
The interviews revealed that Logo may have provided students with ideas that helped them choose the “correct” answer for some items on a standardized mathematics achievement test, but “misled” them on other (especially geometric) items.
The first of two geometric items asked students to identify which letter within a rectangular frame was “in a circle.” None of the figures was a circle, but one figure looked like a circle truncated by a boundary rectangle. More Logo students gave “incorrect” answers. However, their reasoning stemmed from their experiences with drawing large circles that the computer screen truncated. Logo students’ ideas about circles were more process oriented (“curves like a circle”; “go around more”). The CAI students had a static conception of a complete circle, which may have helped them respond “correctly” to the test item.
Some studies suggest an even more powerful and surprising finding: Greater effect in the long term than the short term! On the basis of traditional learning theories, this should be impossible.
Researchers followed several groups of students for four years (Flake & Sandon, 1990). One of the groups worked with Logo in fourth and fifth grade. Their standardized mathematics scores during these years were not different. However, scores from their middle school years showed that the Logo students outperformed the non-Logo students in mathematics. Their early work with Logo had forged a conceptual foundation for learning mathematics. With such foundation imagery, students could grasp the concepts of fractions, decimals, and percents in the middle school grades.
In one study of long-term effects, we investigate fifth graders’ learning of symmetry and geometric motion -- slides, flips, and turns (Johnson-Gentile et al., 1994). The Logo group significantly outperformed the manipulatives group on the delayed posttest. So, the Logo-based version of the lessons led to better long-term learning. The interaction with the Logo microworld enhanced the student construction of higher-level conceptualization of motion geometry. The need in Logo environments for more complete, precise, and abstract explication may account for students’ creation of conceptually richer concepts for motions. That is, in Logo students have to specify steps to a noninterpretive agent, with thorough specification and detail.
Conclusions and Implications for Teaching Mathematics
Logo programming can help students construct elaborate knowledge networks (rather than mechanical chains of rules and terms) for mathematical topics. There are several unique characteristics of Logo that facilitate student learning (Clements & Meredith, 1993; Noss & Hoyles, 1992).
1. The commands and structure of the computer language are consistent with mathematical symbols and structures.
2. Logo promotes the connection of symbolic with visual representations, supporting the construction of mathematical strategies and ideas out of initial intuitions and visual approaches.
3. The turtle’s world involves measurements that are visible yet formal quantities, helping to connect spatial and numeric thinking.
4. Logo permits students to outline and then elaborate and correct their ideas. Logo helps document student actions, leading the mathematical symbolization.
5. Logo encourages the manipulation of screen objects in ways that facilitate students’ viewing them as mathematical objects and thus as representatives of a class.
6. Logo demands and so facilitates precision and exactness in mathematical thinking.
7. Logo provides a mirror of students’ mathematical thinking. For teachers willing to work with and listen to students, such environments provide a fruitful setting. They help take the students’ perspective and discover previously unsuspected abilities to construct sophisticated ideas if given the proper tools, time, and teaching.
8. Because students may test the ideas for themselves on the computer, they aid students in moving from naïve to empirical to logical thinking and encourage students to make and test conjectures. Thus, Logo facilitates student development of autonomy in learning (rather than seeking authority) and positive beliefs about creation of mathematical ideas.
The original developers of Logo developed this programming language to serve as a conceptual framework for learning mathematics (Feurzeig & Lukas, 1971; Papert, 1980a). Many studies, however, are built on the assumption that straightforward exposure to mathematical concepts within the context of Logo programming increases mathematics achievement. Research evidence pertaining to this presumption is inconclusive. In contrast, using Logo programming as a conceptual framework is not a method of directly practicing or teaching mathematical ideas. Instead, its effects on mathematical knowledge may result from students’ construction and elaboration of schemata that form a structure upon which they build future learning. In particular, Logo may permit students to manipulate embodiments of certain mathematical ideas. Serving as a transitional device between concrete experiences and abstract mathematics, it may facilitate students’ elaboration of the schemata for those ideas. Finally, Logo is an environment in which students can use mathematics for purposes that are meaningful and personal for them.
The teacher’s role is critical. Teacher mediation involves multiple actions. Teachers must be involved in planning and overseeing the Logo experiences to ensure that students reflect on and understand the mathematical concepts (McCoy, 1996, p. 443). They need to (a) focus students’ attention on particular aspects of their experience, (b) reduce informal language and provide formal mathematical language for the mathematical concepts, (c) suggest paths to pursue, (d) facilitate disequilibrium using computer feedback as a catalyst, and (e) continually connect the ideas developed to those embedded in other contexts. Teachers must provide structure for Logo tasks and explorations to facilitate desired learning. To accomplish this, teachers need specifically designed Logo activities and environments (see the following section on new versions of Logo).
The best use of Logo may involve full integration into mathematics curriculum. Too much school mathematics involves exercises devoid of meaning. Logo is an environment in which students use mathematics meaningfully to achieve their own purposes. The Logo language is a formal symbolization that students can invoke, manipulate, and understand (Hoyles & Noss, 1987). Thus, using Logo in mathematics is “teaching students to be mathematicians vs. teaching about mathematics” (Papert, 1980b, p. 117).
Finally, we need continuing research and development to expand our knowledge of what students and teachers learn in various Logo classrooms. Standardized tests do not measure many concepts and skills developed in Logo (Butler & Close, 1989).
Logo was developed as a mathematical tool and also a tool for engaging in and enhancing thinking. Our earlier review tentatively suggested that Logo may help develop certain problem-solving behaviors. Analyses of different approaches to developing higher-order thinking with Logo permit us to be more specific.
Approaches based on an exposure without appropriate mediation have not been positive. Some indicate no effect of Logo work on students’ ability to solve nonroutine word problems (Bruggeman, 1986; LeWinter, 1986) or other problem-solving tasks (Mitterer & Rose-Drasnor, 1986). Others report that direct training on problem-solving strategies without computers resulted in higher performance than unguided Logo experience (Dalton, 1985). Thus, research generally has not supported the exposure hypothesis.
Other researchers based studies on variations of the conceptual framework hypothesis. Some, interpreting Papert (1980a), argued that Logo can make the abstract concrete, accelerating cognitive development. Some reported gains (Miller et al., 1988; Rieber, 1987), but others found no significant differences (Clements & Guloo, 1984; Howell, Scott, & Diamond, 1987). Another hypothesis was that programming involved extensive planning. However, middle and high school students exposed to Logo did not display greater planning skills on a noncomputer task than those in a matched group (Kurland et al., 1986).
With mediation, however, Logo may facilitate higher-order thinking. For example, elementary students using Logo increase their mathematical problem-solving abilities with teaching (Billings, 1986; Reed, Palumbo, & Stolar, 1988; Wiburg, 1989). Comprehensive reviews have concluded that there is evidence of a substantial and homogeneous effect for Logo in developing problem-solving skills (Clements & Meredith, 1993; Roblyer, Castine, & King, 1988). The most positive results have involved teacher mediation based on a well-developed theoretical foundation (Clements, 1990; De Corte & Verschaffel, 1989; Delclos & Burns, 1993; Lehrer, Guckenberg, & Lee, 1988; Lehrer, Harckham, Archer, & Pruzek, 1986; Littlefield et al., 1988).
Compare studies that showed a lack of affect on planning abilities to those in which researchers observed considerable growth in planning (Kull, 1986). Growth is slow, and without teacher mediation to highlight planning processes, transfer to noncomputer tasks is unlikely. Students must bring planning skills to an explicit level of awareness and abstract them from the Logo context. For example, Bamberger (1985) stressed the need to plan a procedure before beginning it and to use such strategies as breaking a large idea into manageable parts. In posttest interviews, Logo students used the strategies of planning and drawing more frequently to solve non-Logo problems.
Effects on processes other than planning may be more profound. Traditional education attends to planning more frequently than to other aspects of problem solving such as deciding on the nature of the problem, selecting a representation for solving the problem, and cognitive monitoring. Logo programming, however, can engage students in all aspects of problem solving. For example, students within a Logo environment displayed those problem-solving processes to a greater degree than those in CAI environments (Clements & Nastasi, 1988). In addition, they outperformed ES’s than computer programming in other languages. Like many meta-analyses, however, it tended not to indicate why some efforts were more successful than others. The present review indicates that at least part of the answer to this question lies in the use of a mediated conceptual framework approach.
Such mediation entails the following (Clements & Meredith, 1993):
1. Providing metacognitive prompts and asking higher-order questions.
2. Ensuring that students are explicitly aware of the strategies and processes they are learning.
3. Discussing and providing examples of how the skills used could be applied in other contexts.
4. Providing tailored feedback regarding students’ problem-solving efforts.
5. Promoting both student-teacher and student-student interaction.
6. Discussing errors and common misunderstandings.
7. Facilitating students’ use and awareness of problem-solving processes.
Early observational research suggested that Logo drawing helps students create pictures that are more elaborate than those that they can create by hand. They transfer components of these new ideas to art work on paper (Vaidaya & McKeeby, 1984). Such computer drawing is appropriate for children as young as 3 years, who show signs of developmental progression in the areas of drawing and geometry during such computer use (Clements & Nastasi, 1992a; Tan, 1985). Other studies showed an increase in figural creativity on transfer tests, although gains in some were moderate (Clements & Gullo, 1984; Clements & Nastasi, 1992a; Horton & Ryba, 1986; Reimer, 1985; Roblyer et al., 1988; Wiburg, 1987) and occasionally nonsignificant (Mitterer & Rose-Drasnor, 1986; Plourde, 1987). Originality, in contrast to fluency or flexibility, was most often enhanced.
One study analyzed the reasons that these aspects would be enhanced by Logo (Clements, 1991). A Logo group significantly outperformed both a comparison group receiving nonLogo creativity experiences (Work-processing and graphics programs) and a nontreatment control group on an assessment of figural creativity. In addition, the Logo group significantly outperformed the control group on an assessment of verbal creativity. These results support the hypothesis that Logo was enhancing not just students’ figural knowledge, but the processes involved in creative thought.
We did not discuss language arts in the earlier review; there was no research on them Thus, one positive development in Logo research is the attention given to the language arts. Results are also generally positive. Logo engenders language rich with emotion, humor and imagination in young children (Genishi, McCollum, & Strand, 1985; Yelland, 1994). In a similar vein, working with the Logo in a narrative context (a) enhances language-impared preschool students’ percetual-language skills (Lehrer & deBernard, 1987); (b) increases kindergartners’ readiness scores on visual discrimination, visual motor skills, and visual memory (Reimer, 1985); and (c) increases first grders’ scores on assessments of visual motor development, vocabulary, and listening comprehension (Robinson et al., 1988; Robinson & Uhlig, 1988). The talk students weave around their Logo is impressively task-related, other-directed, cooperative, and nonplayful (Genishi, 1988)
Logo work may also enhance reading skills. Emersion in a Logo culture can lead to increases in language mechanics and reading comprehension, even without direct instruction (Studyvin & Moninger, 1986). These effects may be delayed (Clements, 1987). There are even accounts of Logo assisting the learning of foreign languages. For example, fifth and sixth graders in one study learned both Logo and German vocabulary. This method also improved their attitudes (Tracy & Williams, 1990). Research is needed that extends and explains these positive findings.
Our previous review noted that observational evidence suggested that Logo’s most beneficial effect may be in the area of social and emotional development. Research since that time has substantiated and extended these early results.
Teachers report that students exposed to Logo programming are more likely to interact with their peers. They engage in group problem solving, sharing, and acknowledgement expertise and creative thinking. Social isolates benefit the most (Carmichael et al., 1985; St. Paul Public Schools, 1985). Students working in Logo also exhibit more learning-oriented interactions than do those in non-Logo classrooms (Kinzer, Littlefield, Delclos, & Bransford, 1985). They are eager to cooperate and share what they have learned with others (Genishi, 1988). Thus, Logo environments can facilitate social interaction on learning.
Social Problem Solving
Students who have the ability to use problem-solving skills in real-life situations can better work and play cooperatively. Research indicates that students learn to solve social problems cooperatively and flexibly in Logo classrooms (Carmichael et al., 1985). One study indicated that students work cooperatively more often on computers -- with either Logo or CAI drill -- than off (Clements & Nastasi, 1985). Interestingly, they also got into more conflicts (possibly because they interacted more). Conflicts alone can be important. In another study, students working in Logo, compared to those working in spreadsheet and paper-and-pencil environments, experienced more conflicts, which had the effect of destabilizing inappropriate solutions before students formed incorrect generalizations. This helped students keep “on track” (Hoyles et al., 1991). These conflicts, and the social interaction at the computer, have been identified as leading to positive gains in learning (Healy, Pozzi, & Hoyles, 1995).
Additional research found that not only does Logo generate useful conflicts, but also that students working with Logo, compared to students working with CAI programs, are more likely to resolve these conflicts (Clements & Nastasi, 1985). After experiencing CAI drill, students generated more oppositional behaviors in their noncomputer drill work. They may have found that this drill lacked the excitement of the CAI drill (Clements & Nastasi, 1985).
In similar vein, students working together on Logo tasks spent a significant proportion of their time resolving conflicts (Lehrer & Smith, 1986b). Finally, research indicates that the of type of conflict -- social or cognitive -- is critical (Nastasi, Clements & Battista, 1990). Students working in Logo evinced more cognitive conflict, and attempts at and successes in resolution of these conflicts, than those working with CAI. Differences were not evident for social conflict or its resolution. Thus, the effects of Logo seemed to be specific to disagreements about ideas. Moreover, only those behaviors indicative of cognitive conflict were related to scores on a measure of problem solving (higher-order thinking). In particular, it was the successful resolution of those conflicts, more than the occurrence or attempts to resolve, that accounted for variability in problem-solving performance. Opportunities to experience and resolve conflicts are necessary for the development of problem-solving competencies. Therefor, Logo contexts may enhance the development of social and cognitive problem-solving skills.
To optimize learning, educators must also consider goals and tasks. Paired work at the computer coupled with the coordination of others’ perspectives in group discussions may be most advantageous for learning conceptually based mathematics. The cooperative work in pairs at the computer helps students develop approaches to the problem and the language to describe strategies. Afterward, whole-class discussions help students “decentrate” from their own way of understanding the problem (even if they are relatively quiet during those discussions). Logo plays a crucial role in allowing students to make sense of the mathematics at their own level of sophistication and in ways that require them to clarify and formalize their ideas. Then, during group discussions, students have a way to describe their contribution and are in a better position to take on the mathematical ideas of others.
In contrast, for other goals and tasks, such cooperative arrangements may not be optimal. For certain, “technology-driven” taks, in which the ideas were directly generated from computer-based actions, concentrated work at the computer may prove to be more efficient (Healy et al., 1995).
Thus, there may be times when individual work is more beneficial. In one study, there was little significant benefit of collaborative learning; the feedback from the computer apparently served to facilitate learning sufficiently (Hughes & Greenhough, 1995).
Logo may also promote social sensitivity. Students working with Logo help and teach each other more than those working in CAI drill environments (Clements & Nastasi, 1985). Elementary students working with Logo learn to listen, be critical in a constructive fashion, and appreciate the work of others (Carmichael et al., 1985). Overall, there is consistent evidence that Logo can contribute to social growth.
According to their teachers, students working with Logo experience an increase in self-esteem and confidence. This may occur only if their teacher gives them greater autonomy over their learning and fosters social interaction (Carmichael et al., 1985; Fire Dog, 1985; Kull, 1986). Logo can provide special needs students with prestige and respect from their peers, enhancing their self-esteem (Michayluk, Saklofske, & Yackulic, 1984). Attitudes toward learning are positively affected in some classrooms (Assaf, 1986; Blumenthal, 1986; Charmichael et al., 1985; Findlayson, 1984), but not others (Horner & Maddux, 1985; Milojkovic, 1984). So, this effect may be sensitive to many factors in the classroom environment that remain to be researched.
Students working in Logo environments engage in more self-directed explorations and show more pleasure at discovering phenomena (Clements & Nastasi, 1985; Clements & Nastasi, 1988). Findings regarding locus of control are mixed, but possess one consistent and interesting pattern: Students experiencing Logo did appear to judge situations for themselves and accept responsibility for their actions (Blumenthal, 1986; Horner & Maddux, 1985). Recent studies indicate that Logo may enhance internal locus of control for preschool children (Bernhard, 1994 # 1597). Similarly, Logo can increase mastery-oriented thinking and a belief that one can work to become more intelligent (Burns & Hagerman, 1989). We need additional long-term studies, but Logo may have the power to enhance students’ self-esteem and attitudes toward school.
The claim that Logo’s most beneficial effect may be in the area of social and emotional development may not have been exaggerated. Research supports this optimistic position and suggests that educators build classroom cultures that encourage students to take responsibility for their own learning; to engage in tasks that are challenging, but not too difficult or too easy; and to work cooperatively, asking each other questions (King, 1989) engaging in cognitive conflicts, and always working to resolve them through discussion of ideas and negotiation (Clements & Nastasi, 1988; Hoyles et al., 1991). This should be taken to mean that children should always work together, however; a balance of cooperative and individual work may be ideal. Indeed, teachers who specifically plan for “cooperative” work should recognize that such arrangements are beneficial only if certain conditions are met, including appropriate tasks, students who can manage both themselves and the task, and students who are not antagonistic. A combination of structured interdependence and individual autonomy, with a high-status student coordinating the group, may be the best (Hoyles, Healy, & Pozzi, 1994).
NEW VISIONS AND VERSIONS OF LOGO
There are several areas of research that did not exist a decade ago. The first is in the creation of new visions and new versions of Logo.
In one study, fourth-grade students designed software to teach fractions to third graders (Harel, 1991). Students were given both the freedom and the possibility to create their own designs and to teach themselves about fractions and representing fractions to other students. The students were divided into three groups: the instructional design (ID) group and two comparison groups. The first comparison group was given the same amount of exposure to Logo programming as the ID group. This exposure was integrated with various curriculum topics; however, the projects tended to be short and assigned by the teacher. The second comparison group received Logo once a week in a computer literacy course. The ID group showed greater mastery of both Logo and fractions that the two comparison groups, because they had created a rich variety of ways to represent fractions for a real audience. They divided a circle into four regions and flashed two on and off to show two-fourths with the written text “two-fourths”; showed an animated clock; showed a one-dollar bill with four quarters underneath, two of which moved and stopped near the written words “two-fourths of one dollar.”
Another group of fourth graders designed computer games to teach third graders about fractions (Kafai, 1993). Compared to other groups, students who designed games improved significantly in their knowledge of Logo programming and fractions, although fraction knowledge did not increase as much as in the Harel study.
In summary, designing extensive projects in Logo appears to hold real potential for learning. Designing software to teach concepts (e.g., the ID class) seems to be an effective means of learning mathematical content, of creating a personal perspective on that content, and on connecting the content to everyday life. Designing Logo games appears to be an effective means of learning mathematical content. A good Logo environment -- one with features that support the designing -- offers real advantages to this type of design activity. A powerful aspect of Logo appears to be giving students control over their own representation of mathematical ideas. Various pictures, animations, and texts can be composed, selected and combined. Logo programming can contribute to general mathematical ability. These two projects have shown what an intensive four months of meaningful Logo programming can do. We have yet to see an investigation of several year’s use of Logo (Clements & Meredith, 1993).
LEGO-Logo is a unique member of the Logo family. Students create Lego structures, including lights, sensors, motors, gears, and pulleys, as well as Logo programs that control these structures. For example, fourth-grader Kevin started, as many other students do, by building a car out of LEGO (Resnick, 1988). The car moved forward a bit -- and then the motor fell off and vibrated across the table. The movement interested Kevin. He wondered if he could use the vibrations to power the vehicle. He mounted a motor on a LEGO base and learned that he could control the walker -- it turned right when the motor rotated in one direction, left when it rotated in the other.
There are but a few studies on LEGO-Logo, but they indicate that such experiences can positively affect mathematical achievement, especially concepts such as angle, processes such as reversibility, and competencies in higher-order thinking skills (Browning, 1991; Enkenberg, 1994; Flake, 1990; Weir, 1992), though one control group showed higher gains in computation (Flake, 1990). LEGO-Logo appears to provide authentic learning tasks (Lafer, 1994 #1603), motivated and empower students as well, and possibly develop self-esteem (Silverman, 1990; Weir, 1992). This may be because LEGO-Logo provides an academic setting in which students can develop their own goals.
Turtle Math was born from research on Logo. We believed that this research would provide useful guidelines for designing a Logo environment fine-tuned for the learning of geometry and other mathematical topics. We abstracted five principles and designed Turtle Math based on these principles (Clements & Sarama, 1995).
For example, the nature of programming creates the need to make relationships between symbols (code) and drawings explicit. Research indicate that this is a crucial advantage of programming, but also that students often lose the psychological connection between the two. There are, then, two issues for a Logo programming environment. First is the issue of immediate mode programming versus the use of procedures. Students (especially novices) often prefer this exploratory mode and find it easier to make sense of tasks. Further, immediate mode encourages students to take a more global perspective on the task and to look for structure within their program design (Hoyles & Noss, 1987). In contrast, use of proedures can lead to a separation between symbols and drawings (Hoyles & Noss, 1988). Finally students working in immediate mode also are more likely to abandon inappropriate solution strategies before they make incorrect generalizations, which keeps them on track. These results lead to the following features of Turtle Math. Students enter commands in "immediate mode" in a command window, or as procedures in a "teach" window, but usually in the former. Any change to commands in either location, once accepted, are reflected automatically in the drawing. A tool copies these into the teach windwo, applies a student-supplied name, and thus defines the procedure.
The dynamic link between the commands in the command window and the geometry of the figure is critical. Any change in the commands leads to a correspondence change in the figure, so that the commands in the command window precisely reflect the geometry in the figure. So, the Logo code in the command window stands half-way between traditional immediate mode records and procedures created in an editor, helping link the symbols and drawing. The structure of the command center-long and narrow to the side of the graphics screen, instead of the traditional short but wide placement below this screen-permits the immediate inspection of more commands, which faciliatates connecting symbols and drawings, as well as pattern searching. Further, students can easily modify the code, encouraging experimentation and supporting later work with procedures.
The second basic issue is the direction of the symbol-drawing connection. One of Logo’s main strengths has been its support of linkages between drawings and symbols. One of its limitations has been in the lack of two-way connection between these modes. That is, one creates or modifies symbolic code to produce visual drawings, but not the reverse. Turtle Math provides two tools to support that reversal. A “draw commands” tool allows the student to use the mouse to turn and move the turtle, with corresponding Logo commands created automatically. A “change shape” tool allows students to click on a corner or side of a path and drag it to a new location. The commands in the command window are updated automatically.
A series of classroom-based studies have indicated that Turtle Math as implemented does realize the potential posited in the five principles upon which it was designed and was efficacious in supporting mathematical development along the lines of current mathematics reform recommendations. Students’ integration of number and geometry was especially potent in the Turtle Math environment, which provided meaningful tasks. The geometric setting provided both motivations and models for thinking about number and arithmetic together. The motivations included game settings and the desire to create shapes and designs. The models included length and turn as settings for building a strong sense of both numbers and operations on numbers, with measuring and labeling tools supporting such construction. Conversely, the numerical aspects of the measures provided a context in which students had to attend to certain properties of geometric forms. The measure made such properties (e. g., opposite sides equal) more concrete and meaningful to the students. In addition, the change in problem situation encouraged the use of larger number units. The dynamic links between these two domains structured in the Turtle Math environment (e. g., a change in code automatically reflected in a corresponding change in the geometric figure) facilitated students’ construction of connections between their own number and spatial schemes.
In regular, sequential Logo, there is a single process that runs instructions one step at a time. One of the many recent innovations in various versions of Logo is the addition of parallel programming. Also called “concurrent” or “multiprocessing,” this feature allows programmers to control multiple, interacting processes. Fourth and fifth graders used a multiprocessing Logo to control the concurrent actions of robotic machines; one of the main findings was the emergence of new types of conceptual errors, or bugs, in students programming due to parallel processing (Resnick, 1990).
Resnick extended this work to investigate people’s thinking about decentralized systems in the context of StarLogo, a version of Logo that simultaneously controls hundreds or thousands of turtles. He worked with high school students on projects ranging form simultaneous of slime mold (which, when food is scarce, stop reproducing and move forward one another, forming a cluster with tens of thousands of cells that act as a whole), ants, traffic jams, and geometry. Students’ design of SarLogo programs often was based on an unquestioned assumption of a “leader” or an “outside force” or “seed” for change. For instance, people would quickly assume that a radar trap might cause traffic jams, or an accident. They predicted that without such outside forces, “there was nothing,” so traffic would proceed smoothly. However, traffic slowdowns and jams emerge even with no seed and no leader. Across a variety of areas, the simplest and most accurate programs did not use “leads or seeds.” Instead, they used myriad interactions among objects or beings following a few simple rules. Centralized thinking seems a strong bias in our thinking.
TEACHING WITH LOGO
Another area of research that was only minimally addressed at the time of our earlier review was teachers and teaching. Many of the findings on teaching have already been discussed in previous sections, of course. In this section, we review research that focuses particularly on teaching and teacher development.
Teaching Styles and Strategies
Teaching in computer environments differs from off-computer instruction. Student-teacher interactions may be more student centered and individualized during computer-based teaching than during traditional teaching and learning; there can be up to 17 times more individual interactions. Such experiences have the potential of changing teachers’ pedagogical styles (Swan & Mitrani, 1993). Many factors affect such teaching. The amount of inquiry-based teaching, for example, is affected by the teaching style that predominates in the school (Tanner, 1992). Individual teachers pose different tasks and hold different aims for teaching Logo (many of which are uncertain). Opinions of Logo can be more varied than those of spreadsheets or databases; some teachers particularly enjoy Logo, while others dislike it; these latter consider Logo less “practical” (Tanner, 1992).
We saw that teaching strategies are critical. Not all teacher interventions lead to learning (Hughes & Greenhough, 1995). Following are several additional implications for teaching.
1. There are obstacles to learning mathematics in an unstructured Logo environment (Noss & Hoyles, 1992), such as unreflective use of tools and paradox that teachers want students to play with ideas, but they do not play with the ideas they had in mind; bypassing of Logo tools; and avoidance of mathematical analysis. The activities in which Logo tools are used help determine whether students will use mathematical ideas.
2. Effects of programming experiences take time to emerge.
3. These effects will be more positive if programming is integrated into the curriculum (Clements & Meredith, 1994; Hoyles & Noss, 1987).
4. A theoretically-based, mediated conceptual framework approach should be used, including systematic and explicit links between programming and other activities (Clements & Meredith, 1993; Hoyles & Noss, 1987). Teachers should actively introduce the academic goals, provide a sequence of tasks, mediate students’ work on these tasks, coordinate these with paper-and-pencil tasks, and conclude with whole group discussions that weave ideas together.
5. Mediation during interaction with students should include focusing students’ attention on particular aspects of their experience, bringing concept strategies to an explicit level of awareness, encouraging formal language, and connecting it to academic language.
6. Delicate balances must be sought between teacher structuring and student explorations between cooperative endeavors and time for solitary work (Heller, 1986).
7. Teachers should seek to promote cognitive conflict and resolution through computer feedback and social interactions (Clements & Nastasi, 1988; Clements & Nastasi, 1992b; Nastasi & Clements, 1992; Nastasi & Clements, 1993; Nastasi & Clements, 1994).
8. Structured curricula and activities may enable teachers with less knowledge of Logo (Tanner, 1992).
9. Very young children may benefit form modifications to the Logo environment, including versions of Logo with simpler interfaces and increased adult mediation. For example, kindergarten to first-grade children may not be able to solve the problems they set for themselves without frequent aid from adults (Genishi, 1988; Watson, Lange, & Brinkley, 1992). One of the many new versions of Logo designed for young children is recommended for these early years, though by second grade these versions may become too limited (Young, 1986).
10. Learner control has significant benefits, including fostering students’ metacognitive and cognitive abilities (Lee, 1990; Swan & Mitrani, 1993), and should be provided as much as possible, without sacrificing teacher guidance of activities and interactions.
11. Equity should remain a concern. For example, home owners of computers outperformed nonowners (Nichols, 1992). Everything should be done to achieve and maintain equal access.
Implementation and Profession Development
Integrating Logo into the curriculum is a challenge, especially since many implicit beliefs and structures of teachers and schools stand in contraposition to goals of this integration (c. f., Moreira & Noss, 1995). A major cause of unrealized potential and missed opportunities for facilitation was divergent beliefs of different people. In one study of the implementation of a Logo-based curriculum, curriculum developers, teachers and administrators initially thought the computer lab was ideal. Later, teachers realized that one or two blocks of time per week represented inadequate acc3ess, but htough this was communicated, the administrators believed that schedule readjustment was adequate. Instead only when the developers loaned computers to the teachers for classroom use did the curriculum proceed successfully. As another example, multiple simultaneous reform efforts were seen by administrators as mutually reinforcing. However, they overwhelmed the teachers, who named 10 different reforms they were implementing that year -- reforms that they believed were separate demands.
There are several implications of this research. Administrators should remain fully involved with the project. They might also plan to help teachers integrate the demands of multiple reform movements and provide the time for teachers to experiment, discuss, and, in general, construct their own meaning of new pedagogies. They should remain sensitive to teachers’ need for external validation and support. Administration and teachers need to consider carefully the placement of computers. Computer laboratories may hinder the full use and integration of innovations. In contrast, even a small number of computers in the classroom may put teachers in control of the innovation, giving them responsibility for integrating it into their curricula.
Finally, those designing innovative computer materials, and implementation programs for them, should be aware of the tendency for teachers to ignore documentation. Instead, teachers often run the program apparently expecting that the full extent and worth of the software and the activity will be immediately obvious. In general, designers of innovations must continually strive to see things form the teachers point of view.
Specific professional development activities are also worthwhile. For example, a Logo in-service course can provide personal and professional exploration and change (Moreira & Noss, 1992; Moreira & Noss, 1995). In one study, an in-service Logo course provided personal and professional exploration and change (Moreira & Noss, 1992; Moreira & Noss, 1995). This course was based on specific guidelines. First, teachers are best supported in efforts to reflect upon pedagogical issues if they are immersed in a simulating environment that sustains and increases their motivation to innovate. Second, teachers should be regarded as responsible professionals whose perspectives are central -- not just “taken account of.” Thirds, teachers are more likely to engage in reflection if they are encouraged to interact and share ideas with their peers. Fourth, teachers are capable of taking control of their own learning. Fifth, teachers should be encouraged to establish links between Logo and mathematics.
In conducting such a course, educators should be aware that the personal and emotional dimension is at least as critical as the professional and cognitive and that change of critical beliefs and attitudes takes considerable time. It can have benefits, even attitudinal and cognitive benefits, but if difficulty levels are not carefully monitored, some teachers may develop more negative attitudes toward programming per se (Brownell, 1993; Moreira & Noss, 1992).
Finally, the role of Logo in computer education courses should not be overlooked. One study showed that “Programming, especially when using Logo as a discovery environment, allows for a diverse range of styles to manifest themselves, not only to teachers, but to the instructors of teachers. The programming assignment [in comparison to other applications, such as CAI, spreadsheets, databases, and word processing] becomes a mirror for the teachers to recognize their own style strengths and weaknesses. They are able to reflect on that information and use it as insight into how they would teach and design curricula in general. As an observational tool for instructors and a platform for teachers to examine their own learning, the Logo environment provides the springboard for mindful consideration and reflection of learning a teaching preferences that impact teaching practice” (Howard & Howard, 1994, p. 27).
Depending on the environment in which it is embedded, Logo can constitute a trivial enterprise or a variegated educational experience. We claim that few educational environments have shown as consistent benefits for such a wide scope, from the development of academic knowledge and cognitive processes to the facilitation of positive social and emotional climates. Yet, somewhat paradoxically, realizing these multifarious benefits does not imply lack of focus: Integration into one or more subject matter areas maximizes positive effects. A critical factor, however, is a clear and elaborated vision of the goals of Logo experience -- shared among administrators, curriculum developers, teachers, and students. Such a vision provides a gyroscope that guides the myriad activities of educators: administration, curriculum development, lesson guidance, and moment-by-moment interactions with students.
Assaf, S. A. (1986). The effects of using Logo turtle graphics in teaching geometry on eighth grade students’ level of thought, attitudes toward geometry and knowledge of geometry. Dissertation Abstracts International, 46, 2952A. (University Microfilms NO. DA8512288)
Bamberger, H. J. (1985). The effect of Logo (turtle graphics) on the problem solving strategies used by fourth grade children. Dissertation Abstracts International, 46, 918A. (University Microfilms NO. DA8512171).
Barker, W. F., Merryman, J. D., & Bracken, J. (1988, April). Microcomputers, math CAI, Logo and mathematics education in elementary school: A pilot study. Paper presented at the meeting of the American Educational Research Association, New Orleans.
Battista, M. T., & Clements, D. H. (1988). A case for a Logo-based elementary school geometry curriculum. Arithmetic Teacher, 36, 11-17.
Battista, M. T., & Clements, D. H. (1991). Logo geometry. Morristown, NJ: Silver Burdett & Ginn.
Billings, L. J. Jr. (1986). Development of mathematical task persistence and problem solving ability in fifth and sixth grade students through the use of Logo and heuristic methodologies. Dissertation Abstract International, 47, 2433A.
Blumenthal, W. (1986). The effects of computer instruction on low achieving children’s academic self-beliefs and performance. Unpublished doctoral dissertation, Nova University, Fort Lauderdale, FL.
Bowman, B. T. (1985, November). Computers and young children. Paper presented at the meeting of the National Association for the Education of Young Children, New Orleans.
Brownell, G. (1993). Preservice teachers in a computer utilization in the classroom course: An overview of four studies. In N. Estes & M. Thomas (Eds.), Rethinking the roles of technology in education (pp. 143-145). Cambridge, MA: Massachusetts Institute of Techonology.
Browning, C. A. (1991). Reflections on using Lego© Logo in an elementary classroom. In E. Calabrese (Ed.), Proceedings of the Third European Logo Conference (pp. 173-185). Parma, Italy: Associazione Scuola e Informatica.
Bruggeman, J. G. (1986). The effects of modeling and inspection methods upon problem solving in a computer programming course. Dissertation Abstracts International, 47, 1821A. (University of Microfilms No. DA8619363)
Burns, B., & Hagerman, A. (1989). Computer experience, self-concept and problem-solving: The effects of Logo on children’s ideas of themselves as learners. Journal of Educational Computing Research, 5, 199-212.
Butler, D. & Close, S. (1989). Assessing the benefits of a Logo problem-solving course. Irish Educational Studies, 8, 168-168-190.
Campbell, P. F. (1987). Measuring distance: Childrens 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 RO3 MH423435-01). College Park, MD: University of MD.
Campbell, P. F. , Fein, G. G., Scholnick, E. K., Frank, R. E., & Schwartz, S. S. (1986). Initial mastery of the syntax and semantics of Logo positioning commands. Journal of Educational Computing Research, 2, 357-377.
Carmichael, H. W., Burnett, J. D., Higginson, W. C., Moore, B. G., & Pollard, P. J. (1985). Computers, children and classrooms: A multisite evaluation of the creative use of microcomputers by elementary school children. Toronto, Ontario, Canada: Ministry of Education.
Clements, D. H. (1983-84). Supporting young children’s Logo programming. The Computing Teacher, 11(5), 24-30.
Clements, D. H. (1986). Effects of Logo and CAI environments on cognition and creativity. Journal of Educational Psychology, 78, 309-318.
Clements, D. H. (1987). Longitudinal study of the effects of Logo programming on cognitive abilities and achievement. Journal of Educational Computing Research, 3, 73-94.
Clements, D. H. (1990). Metacomponential development in a Logo programming environment. Journal of Educational Psychology, 82, 141-149.
Clements, D. H. (1991). Enhancement of creativity in computer environments. American Educational Research Journal, 28, 173-187.
Clements, D. H., & Battista, M. T. (1988, November). The development of geometric conceptualizations in Logo. Paper presented at the meeting of the International Group fo the Psychology in Mathematics Education—North American Chapter, DeKalb, IL.
Clements, D. H., & Battista, M. T. (1989). Learning of geometric concepts in a Logo environment. Journal for Research in Mathematics Education, 20, 450-467.
Clements, D. H., & Battista, M. T. (1990). The effects of Logo on children’s conceptualization of angle and polygons. Journal for Research in Mathematics Education, 21, 356-371.
Clements, D. H., & Battista, M. T. (1992a). The development of a Logo-based elementary school geometry curriculum (Final Report: NSF Grant NO.: MDR-8651668). Buffalo, NY/Kent, OH: State University of New York at Buffalo/Kent State University.
Clements, D. H., & Battista, M. T. (1992b). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning )pp. 420-464). New York: Macmillan.
Clements, D. H., & Gullo, D. F. (1984). Effects of computer programming on young children’s cognition. Journal of Educational Psychology, 76, 1051-1058.
Clements, D. H. & Meredith, J. S. (1993). Research on Logo: Effects and efficacy. Journal of Computing in Childhood Education, 4, 263-290.
Clements, D. H. & Meredith, J. S. (1994). Turtle Math [Computer program]. Montreal, Quebec: Logo Computer Systems, Inc. (LCSI)
Clements, D. H., & Nastasi, B. K. (1985). Effects of computer environments on social-emotional development: Logo and computer-assisted instruction. Computers in the Schools, 2(2-3), 11-31.
Clements, D. H., & Nastasi, B. K. (1988). Social and cognitive interactions in educational computer environments. American Educational Research Journal, 25, 87-106.
Clements, D. H., & Nastasi, B. K. (1992a). Computers and early childhood education. In M. Gettinger, S. N. Elliott, & T. R. Kratochwill (Eds.), Advances in school psychology: Preschool and early childhood treatment directions (pp. 187-246). Hillsdale, NJ: Lawrence Erlbaum Associates.
Clements, D. H., & Nastasi, B. K. (1992b). The role of social interaction in the development of higher-order thinking in Logo environments. In E. De Corte, M. C. Linn, H. Mandl, & L. Verschaffel (Eds.), Computer-based learning environments and problem solving (pp. 229-248). NY: Springer-Verlag.
Clements, D. H., & Sarama, J. (1995). Design of a Logo environment for elementary geometry. Journal of Mathematical Behavior, 14, 381-398.
Cope, P., & Simmons, M. (1991). Childrens exploration of rotation and angle in limited Logo microworlds. Computers in Education, 16, 133-141.
Dalton, D. W. (1985). A comparison of the effects of Logo and problem-solving strategy instruction on learner achievement, attitude, and problem-solving skills. Unpublished doctoral dissertation, University of Colorado.
DeCorte, E., & Verschaffel, L. (1989). Logo: A vehicle for thinking. In B. Greer & G. Mulhern (Eds.), New directions in mathematics education (pp. 63-81). London/New York: Routledge.
Delclos, V. R., & Burns, S. (1993). Mediational elements in computer programming instruction: An exploratory study. Journal of Computing in Childhood Education, 4, 137-152.
du Boulay, B. (1986). Part II: Logo confessions. In R. Lawler, B. du Boulay, M. (pp. 81-178). Chichester, England: Ellis Horwood Limited.
Edwards, L. D. (1991). Childrens learning in a computer microworld for transformation geometry. Journal for Research in Mathematics Education, 22, 122-137.
Emihovich, C. & Miller, G. E. (1988). Effects of Logo and CAI on Black first graders’ achievement, reflectivity, and self-esteem. The Elementary School Journal, 88, 473-487.
Enkenberg, J. (1994). Situated programming in a LEGO-Logo environment. Computers and Education, 22(1-2), 119-28).
Feurzeig, W., & Lukas, G. (1971). LOGO—A programming language for teaching mathematics. Educational Technology, 12, 39-46.
Findlayson, H, M. (1984, September). What do children learn through using Logo? (D.A.I. Research Paper No. 237). Paper presented at the meeting of the British Logo Users Group Conference, Loughborough, U.K.
Fire Dog, P. (1985). Exciting effects of Logo in an urban public school system. Educational Leadership, 43, 45-47.
Flake, J. K. (1990). An exploratory study of Lego Logo. Journal of Computing in Childhood Education, 1(3), 15-22.
Flake, J. L., & Sandon, M. L. (1990). Longitudinal study of mathematics achievement for a technological and experiential based mathematics curriculum. Journal of Computing in Childhood Education, 2(1), 55-67.
Frazier, M. K. (1997). The effects of Logo on angle estimation skills of 7th graders. Unpublished master’s thesis, Wichita State University, Wichita, KS.
Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education Monograph, 3.
Genishi, C. (1988). Kindergarteners and computers: A case study of six children. The Elementary School Journal, 89, 184-201.
Genishi, C., McCollum, P., & Strand, E. B. (1985). Research currents: The interactional richness of children’s computer use. Language Arts, 62(5), 526-532.
Hamada, R. M. (1987). The relationship between learning Logo and proficiency in mathematics. Dissertation Abstracts International, 47, 2510-A.
Harel, I. (1991). Children Designers. Norwood, NJ: Ablex.
Healy, L., Pozzi, S., & Hoyles, C. (1995). Making sense of groups, computers, and mathematics. Cognition and Instruction, 13(4), 505-523.
Heller, R. S. (1986). Different Logo teaching styles: Do they really matter. In E. Soloway & S. Iyengar (Eds.), Empirical studies of programmers (pp. 117-127). Norwood, NJ: Ablex.
Hillel, J., & Kieran, C. (1988). Schemas used by 12-year-olds in solving selected turtle geometry tasks. Recherches en Didactique des Mathematiques, 8/1.2, 61-103.
Hillel, J., & Samurcay, R. (1985). Analysis of a Logo environment for learning the concept of procedures with variable. Unpublished manuscript, Concordia University, Montreal.
Horner, C. M., & Maddux, C. D. (1985). The effect of Logo on attributions toward success. Computers in the Schools, 2(2-3), 45-54.
Horton, J., & Ryba, K. (1986). Assessing learning with Logo: A pilot study. The Computing Teacher, 14(1), 24-28.
Hoard, D. C. P., & Howard, P. A. (1994). Learning technology: Implications for practice. Journal of Technology and Teacher Education, 2(1), 17-28.
Howell, R. D., Scott, P. B., & Diamond, J. (1987). The effects of “instant” Logo computing language on the cognitive development of very young children. Journal of Educational Computing Research, 3, 249-260.
Hoyles, C., Healy, L., & Sutherland, R. (1991). Patterns of discussion between pupil pairs in computer and non-computer environments. Journal of Computer Assisted Learning, 7, 210-228.
Hoyles, C., Healy, L., & Pozzi, S. (1994). Groupwork with computers: An overview of findings. Journal of Computer Assisted Learning, 10, 202-215.
Hoyles, C., & Noss, R. (1987). Synthesizing mathematical conceptions and their formalization through the construction of a Logo-based school mathematics curriculum. International Journal of Mathematics Education, Science, and Technology, 18, 581-595.
Hoyles, C., & Noss, R. (1988). Formalising intuitive descriptions in a parallelogram Logo microworld. In A. Borbas (ed.), Proceedings of the 12th Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 417-424). Veszprem, Hungary: International Group for the Psychology of Mathematics Education.
Hoyles, C., & Noss, R. (1989). The computer as a catalyst in children’s proportion strategies. Journal of Mathematical Behavior, 8, 53-75.
Hoyles, C., & Sutherland, R. (1986). When 45 equals 60. London, England: University of London Institute of Education, Microworlds Project.
Hughes, M., & Greenbough, P. (1995). Feedback, adult intervention, and peer collaboration in Initial LOGO learning, Cognition, 13(4), 525-539.
Hughes, M., &Macleod, H. (1986). Part II: Using Logo with very young children. In R. Lawler, B. du Boulay, M. Hughes, & H. Macleod (Eds.), Cognition and computers: Studies in learning (pp. 179-219). Chichester, England: Ellis Horwood Limited.
Johnson, P. A. (1986). Effects of computer-assisted instruction compared to teacher-directed instruction on comprehension of abstract concepts by the deaf. Unpublished doctoral dissertation, Northern Illinois University.
Johnson-Gentile, K., Clements, D. H., & Battista, M. T. (1994). The effects of computer and noncomputer environments on students’ conceptualizations of geometric motions. Journal of Educational Computing Research, 11, 121-140.
Kafai, Y. B. (1993). Minds in play: Computer game design as a context for children’s learning. Unpublished Doctoral dissertation, Harvard University.
Kelly, G. N., Kelly, J. T. & Miller, R. B. (1986-87). Working with Logo: Do 5th and 6th graders develop a basic understanding of angles and distances? Journal of Computers in Mathematics and Science Teaching, 6, 23-27.
Kieran, C. (1986a). Logo and the notion of angle among fourth and sixth grade children. In Proceedings of Psychology in Mathematics Education 10 (pp. 99-104). London, England: City University.
Kieran, C. (1986b). Turns and angles: What develops in Logo? In G. Lappan (Ed.), Proceedings of the Eighth Annual Psychology in Mathematics Education—North America. Lansing, MI: Michigan State Univeristy.
Kieran, C., & Hillel, J. (1990). “It’s tough when you hve to make the triangles angles”: Insights from a computer-based geometry environment. Journal of Mathematical Behavior, 9, 99-127.
Kieran, C., & Hillel, J., & Erlwanger, S. (1986). Perceptual and analytical schemas in solving structured turtle geometry tasks. In C. Hoyles, R. Noss, & R. Sutherland (Eds.), Proceedings of the Second Logo and Mathematics Educators Conference (pp. 154-161). London, England: University of London.
King, A. (1989). Verbal interaction and problem-solving within computer-assisted cooperative learning groups. Journal of Educational Computer Research, 5, 1-15.
Kinzer, C., Littlefield, J., Delclos, V. R., & Brandsford, J. D. (1985). Different Logo learning environments and mastery: Relationships between engagement and learning. Computers in the Schools, 2(2-3), 33-43.
Klahr, D., & Carver, S. M. (1988). Cognition objectives in a LOGO debugging curriculum: Instruction, learning, and transfer. Cognitive Psychology, 20, 362-404.
Kull, J. A. (1986). Learning and Logo. In P. F. Campbell & G. G. Fein (Eds.), Young children and microcomputers (pp. 103-130). Englewood Cliffs, NJ: Prentice-Hall.
Kurland, D. M., Pea, R. D., Clement, C., & Mawby, R. (1986). A study of the development of programming ability and thinking skills in high school students. Journal of Educational Computing Research, 2, 429-458.
Kynigos, C. (1991). The turtle metaphor as a tool for children’s geometry. In C. Hoyles & R. Noss (Eds.), Learning mathematics and Logo (pp. 97-126). Cambridge, MA: MIT Press.
Lawler, R. W. (1986). Part I. Natural learning: People, computers and everday number knowledge. In R. Lawler, B. duBoulay, M. Hughes, & H. Macleod (Eds.), Cognition and computers: Studies in learning (pp. 9-80). Chichester, England, Ellis Horwood.
Lee, M. J. (1990). Effects of different loci of instructional control on students’ metacognition and cognition: Learner vs. program control. (ERIC Document Reproduction Service No. ED 323 938)
Lehrer, R., & deBernard, A. (1987). Language of learning and language of computing: The perceptual-language model. Journal of Educational Psychology, 79, 41-48.
Lehrer, R., Guckenberg, T., & Lee, O. (1988). Comparative study of the cognitive consequences of inquiry-based Logo instruction. Journal of Educational Psychology, 80, 543-553.
Lehrer, R., Harckham, L. D., Archer, P., & Pruzek, R. M. (1986). Microcomputer-based instruction in special education. Journal of Educational Computing Research, 2, 337-355.
Lehrer, R., & Randle, L. (1986). Problem solving, metacognition and composition: The effect of interactive software for first-grade children. Journal of Educational Computing Research, 3, 409-427.
Lehrer, R., Randle, L., & Sancilio, L. (1989). Learning pre-proof geometry with Logo. Cognition and Instruction, 6, 159-184.
Lehrer, R. & Smith, P. (1986a, April). Logo learning: Is more better? Paper presented at the meeting of the American Educational Research Association, San Francisco.
Lehrer, R. & Smith, P. C. (1986b, April) Logo learning: Are two heads better than one? Paper presented at the meeting of the American Educational Research Association, San Francisco.
LeWinter, B. W. (1986). A study of the influence of Logo on locus of control, attitudes toward mathematics, and problem-solving ability in children in grades 4, 5, 6. Dissertation Abstracts International, 47, 1604A. (University Microfilms No. DA8616959)
Liao, Y.-K., & Bright, G. W. (1989). Computer programming and problem solving abilities: A meta-analysis. In W. C. Ryan (Ed.), Proceedings of the National Educational Computing Conference (pp. 10-17). Eugene, OR: International Council on Computers for Education.
Littlefield, J., Delclos, V. R., Lever, S., Clayton, K. N., Brandsford, J. D., & Franks, J. J. (1988). Learning Logo: Method of teaching, transfer of general skills, and attitudes toward school and computers. In R. Mayer (Ed.), Teaching and learning computer programming: Multiple research perspectives (pp. 111-135). Hillsdale, NJ: Erlbaum.
McCoy, L. P. (1996). Computer-based mathematics learning. Journal of Research on Computing in Education, 28, 438-460.
Michayluk, J. O., Saklofske, D. H., & Yackulic, R. A. (1984, June). Logo. Paper presented at the meeting of the CAP Convention, Ottawa, Ontario.
Miller, G. E., & Emihovich, C. (1986). The effects of mediated programming instruction on preschool children’s self-monitoring. Journal of Educational Computing Research, 2(3), 283-297.
Miller, R. B., Kelly, G. N., & Kelly, J. T. (1988). Effects of Logo computer programming experience on problem solving and spatial relations ability. Contemporary Educational Psychology, 13, 348-357.
Milner, S. (1973, February). The effects of computer programming on performance in mathematics. Paper prese3nted at the meeting of the American Educational Research Association, New Orleans, LA. (ERIC Document Reproduction Service No. ED 076 391)
Milojkovic, J. D. (1984). Children learning computer programming: Cognitive and motivational consequences. Dissertation Abstracts International, 45, 385B. (University Microfilms No. 84-08330)
Mitterer, J. & Rose-Drasnor, L. (1986). LOGO and the transfer of problem solving: An empirical test. The Alberta Journal of Educational Research, 32, 176-194.
Moreira, C. & Noss, R. (1992). The teacher’s view of Logomaths. In S. Dawson & R. Zazkis (Eds.), Proceedings of the Sixth International Conference for Logo and Mathematics Education (pp. 27-50). Vancouver, B. C., Canada: Simon Fraser University.
Moreira, C. & Noss, R. (1995). Understanding teacher’s attitudes to change in a Logo mathematics environment. Educational Studies in Mathematics, 28(2), 155-76.
Nastasi, B. K., & Clements, D. H. (1992). Social-cognitive behaviors and high-order thinking in educational computer environments. Learning and Instruction, 2, 215-238.
Nastasi, B. K., & Clements, D. H. (1993). Motivational and social outcomes of cooperative education environments. Journal of Computing in Childhood Education, 4(1), 15-43.
Nastasi, B. K., & Clements, D. H. (1994). Effectance motivation, perceived scholastic competence, and higher-order thinking in two cooperative computer environments. Journal of Educational Computing Research, 10, 249-275.
Nastasi, B. K., Clements, D. H., Battista, M. T. (1990). Social-cognitive interactions, motivation, and cognitive growth in Logo programming and CAI problem-solving environments. Journal of Educational Psychology, 82, 150-158.
Nelson, G. T. (1986). Development of fourth-graders’ concept of literal symbols through computer-oriented problem-solving activities. Dissertation Abstracts International, 47, 2607A. (University Microfilms No. DA8526359)
Nichols, L. M. (1992). The influence of student computer-ownership and in –home use on achievement in an elementary school computer programming curriculum. Journal of Educational Computing Research, 8(4), 407-21.
Noss, R. (1985). Creating a mathematical environment through programming: A study of young children learning Logo. Unpublished doctoral dissertation, Chelsea College, University of London, London, England.
Noss, R. (1987). Children’s learning of geometrical concepts through Logo. Journal for Research in Mathematics Education, 18, 343-362.
Noss, R., & Hoyles, C. (1992). Afterword: Looking back and looking forward. In C. Hoyles & R. Noss (Eds.), Learning mathematics and Logo (pp. 427-468). Cambridge, MA: MIT Press.
Olive, J. (1991). Logo programming and geometric understanding: An In-depth study. Journal for Research in Mathematics Education, 22, 90-111.
Olive, J., Lankenau, C. A., & Scally, S. P. (1986). Teaching and understanding geometric relationships through Logo: Phase II. Interim Report: The Atlanta-Emory Logo Project. Atlanta, GA: Emory University.
Olson, A. T., Kieren, T. E. & Ludwig, S. (1987). Linking Logo, levels, and language in mathematics. Educational Studies in Mathematics, 18, 359-370.
Ortiz, E., & Miller, D. (1991, April). A Logo vs. a textbook approach in teaching the concept of variable. Paper presented at the meeting of the National Council of Teachers of Mathematics, New Orleans, LA.
Paper, S. (1980a). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.
Papert, S. (1980b). Teaching children thinking: Teaching children to be mathematicians vs. teaching about mathematics. In R. Taylor (Ed.), The computer in the school: Tutor, tool, tutee (pp. 161-196). New York: Teachers College Press.
Piaget, J., & Inhelder, B. (1967). The child’s conception of space. New York: W. W. Norton.
Plourde, R. R. (1987, December). The insignificance of Logo-Stop “mucking around” with computers. Micro-Scope, pp. 30-31.
Poulin-Dubois, D., McGilly, C. A., & Schultz, T. R. (1989). Psychology of computer use: The effect of learning Logo on children’s problem-solving skills. Psychological Reports, 64, 1327-1337.
Reed, W. M., Palumbo, D. B., & Stolar, A. L. (1988). The comparative effects of BASIC and Logo instruction on problem-solving skills. Computers in the Schools, 4, 105-118.
Reimer, G. (1985). Effects of a Logo computer programming experience on readiness for first grade, creativity, and self concept: A pilot study in kindergarten. AEDS Monitor, 23(7-8), 8-12.
Resnick, M. (1988). LEGO, Logo, and design. Children’s Environments Quarterly, 5(4), 14-18.
Resnick, M. (1990). Multilogo: A study of children and concurrent programming. Interactive Learning Environments, 1(3), 153-170.
Rieber, L. P. (1987, February). Logo and its promise: A research report. Educational Technology, pp. 12-16.
Robinson, M. A., Gilley, W. F., & Uhlig, G. E. (1988). The effects of guided discovery Logo on SAT performance of first grade students. Education, 109, 226-230.
Robinson, M. A., & Uhlig, G. E. (1988). The effects of guided discovery Logo instruction on mathematical readiness and visual motor development in first grade students. Journal of Human Behavior and Learning, 5, 1-13.
Roblyer, M. D., Castine, W. H., & King, F. J. (1988). Assessing the impact of computer-based instruction: A review of recent research. New York: The Haworth Press, Inc.
Salem, J. R. (1989). Using Logo and BASIC to teach mathematics to fifth and sixth graders. Dissertation Abstracts International, 50, 1608A. (University Microfilms No. DA8914935)
Sarama, J. (1995). Redesigning Logo: The turtle metaphor in mathematics education. Unpublished doctoral dissertation, State University of New York at Buffalo.
Sarama, J., Clements, D., & Henry, J. J. (1996). Network of influences in an implementation of a mathematics curriculum innovation. Detroit, MI: Wayne State University.
Schoenfeld, A. H. (1985).Metacognitive and epistemological issues in mathematical understanding. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 361-379). Hillsdale, NJ: Erlbaum.
Siann, G., & Macleod, H. (1986). Computers and children of primary school age: Issues and questions. British Journal of Educational Technology, 17, 133-144.
Silverman, N. S. (1990). Logo and underachievers. Unpublished master’s thesis, University of the Virgin Islands.
St. Paul Public Schools. (1985). Logo studies. St. Paul, MN: Author.
Studyvin, D., & Moninger, M. (1986, July). Logo as an enhancement to critical thinking. Paper presented at the meeting of the Logo 86 Conference, Cambridge, MA.
Sutherland, R. (1987). What are the links between variable in Logo and variable in algebra? Unpublished manuscript, University of London Institute of Education, London, England.
Swan, K. (1989). Programming objects to think with: Logo and the teaching and learning of problem solving. Journal of Educational Computing Research, 7(1), 89-112.
Swan, K., & Black, J. B. (1989). Logo programming, problem solving, and knowledge-based instruction. Unpublished manuscript, University of Albany, Albany, NY.
Swan, K., & Mitrani, M. (1993). The changing nature of teaching and learning in computer-based classrooms. Journal of Research on Computing in Education, 26(1), 40-54.
Tan, L. E. (1985). Computers in pre-school education. Early Child Development and Care, 19 319-336.
Tanner, H. (1992). Developing the use of IT within mathematics through action research. Computers and Education, 18(1-3), 143-48.
Tracy, D. M., & Williams, M. A. (1990). Fifth and sixth grade German students learn turtle Logo: A pilot study. Journal of Computing in Childhood Education, 1(4), 55-66.
Vaidya, S., & McKeeby, J. (1984, September). Computer turtle graphics: Do they affect children’s thought processes? Educational Technology, pp 46-47.
van Hiele, P. M. (1986). Structure and insight. Orlando: Academic Press.
Watson, J. A., Lange,. G., & Brinkley, V. M. (1992) Logo mastery and spatial problem-solving by young children: Effects of Logo language training, route-strategy training, and learning styles on immediate learning and transfer. Journal of Educational Computer Research, 8, 521-540.
Weir, S. (1992). LEGO-Logo: A verhicle for learning. In C. Hoyles & R. Noss (Eds.) Learning mathematics and Logo (pp. 165-190). Cambridge, MA: MIT Press.
Wiburg, K. M. (1987). The effect of different computer-based learning environments on fourth grade students’ cognitive abilities. Unpublished doctoral dissertation, United States International University, San Diego, CA.
Wiburg, K. M. (1989). Does programming deserve a place in the school curriculum? The Computing Teacher, 17(2), 8-11.
Wilson, D., & Lavelle, S. (1992). Effects of Logo and computer-aided instructionon arithmetical ability among 7- and 8-year-old Zimbabwean children. Journal of Computing in Childhood Education, 3(1), 85-91.
Yellans, N. (1994). A case study of six children learning with Logo. Gender and Education, 6, 19-33.
Yellans, N. (1995). Mindstorms or a storm in a teacup? A review of research with Logo. International Journal of Mathematics Education, Science, and Technology, 26(6), 853-869.
Young, R. D. (1986). An analysis of initial learning of two Logo programming languages and the influence of student characteristics on programming ability. Dissertation Abstracts International, 47, 2448A.
Yusuf, M. M. (1994, April). Mathematics instruction with Logo tutorials and activities. Paper presented at the meeting of the American Educational Research Association, New Orleans, LA.
Time to prepare this material was partially provided by a National Science Foundation Research Grant, “An Investigation of the Development of Elementary Children’s Geometric Thinking in Computer and Noncomputer Environments,” NSF 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.
Single or multiple copies of this article are available for a fee from The Haworth Document Delivery Service [1-800-342-9678, 9:00 a. m. — 5:00 p.m. (EST). E-mail address: email@example.com].
Douglas H. Clements is Professor and Project Co-Director, State University of New York at Buffalo, 593 Baldy Hall, Buffalo, NY 14260. E-mail: firstname.lastname@example.org.
Julie Sarama is Assistant Professor, Wayne State University, Teacher Education Division, 293 Education, Detroit, MI 48202. E-mail: Jsarama@coe.wayne.edu.
Other Articles by Douglas H. Clements: