Nadia Bluhm
Final Paper CD171 Modularity and Logo Programming
Prof. Marina Bers
April 30, 2002
Abstract
This paper is a synthesis of what I learned from creating and implementing a curricular project for the class CD 171: Curricula for Young Children: Math, Science and Technology. The project was designed to explore the powerful idea of modularity using the programming language logo. The paper describes the activities which I undertook with 2 second grade girls. It also explores how the project might be revised by considering the difficulties encountered during the project as well as some of the research literature on logo programming with children.
Description of a Powerful Idea: Modularity
The Idea of modularity is that of breaking down a complex object into simpler objects. Scientists and engineers use this idea all the all the time when they design machines or computer programs or when they solve complex scientific problems. Adults, when confronted with a difficult problem in everyday life, intuitively break down the problem in their minds into simpler sub problems and then solve those problems in order to come up with a solution to the original problem.
I do not remember actually thinking about this idea as a child but in retrospect I can think of how I encountered it in a simple concrete form at an early age. As a child, I loved doing jigsaw puzzles. I may have started playing with them earlier, but I really became involved with them around 6 or 7, when I became ill and was confined to bed rest for a period of 3 months. My mother who wanted to keep me occupied but didn’t want to have to entertain me the whole time, provided me with jigsaw puzzles and a large table set up by my bed to work on. I’m sure I must have done other activities during this time, but in my mind the primary activity that I engaged in for nearly 3 months was doing jigsaw puzzles. I’m not sure how I started out, but I remember that at the end of that time period I was working on at least 1000 piece puzzles and had become quite a proficient and experienced jigsaw puzzle doer. Not only that, but I experienced great pleasure and feelings of accomplishment from working on and completing a puzzle.
Even now I remember the methods and strategies that I used which I’m sure in some variation all children who become good at this activity employ. Basically, the method that I used was this: First I always sorted the pieces into border and non border pieces and then constructed the border by breaking down different areas of the border according to the picture on the box and iteratively tried to put together a small number of pieces until a match was found and so on until the whole border was constructed. Then, I examined the entire picture and mentally broke it down into some number of smaller areas to work on, such as sky, a house, ocean etc. or whatever the picture elements happened to be. I would start working on one area and begin by visually scanning all the pieces that I had laid on the table and when I had gotten a small number (even maybe just starting with 2) I would iteratively try out each piece with each other piece and try to find a match. I would place those completed pieces in the approximate area of the puzzle where I thought they would go. As I found more pieces which I thought would go with this part of the puzzle, I would repeat the process of checking with the pieces that had already been constructed and those that were still unattached. If pieces didn’t seem to belong in an area, I would put them near another part of the puzzle where I thought they might go. I didn’t necessarily complete a section before going onto the next but worked simultaneously on all the areas, sometimes spending a lot of time on one area and sometimes alternating between areas as the puzzle took shape. As the areas became bigger, I found pieces to connect the areas and in doing so the puzzle eventually became complete.
As I think now about the activity of doing jigsaw puzzles, I realize that when I had become good at it, I was employing several different strategies that embodied powerful ideas . Modularity or the idea of breaking down a complex problem into smaller and simpler sub problems is the one I am focusing on here. In the case of jigsaw puzzles, the problem is fairly simple: the endpoint is already known (completing the picture in the puzzle), so the problem for me as a child became one of breaking down the whole picture into smaller pictures each to be put together and then connecting the different parts. My ability to do puzzles developed over time. I probably started out doing easy puzzles as most children do using a brute force method; trying to fit pieces together either at random or by paying some attention to color and shape but not necessarily in any logical manner. This method works fine when doing small puzzles but when one progresses to more complicated puzzles with more pieces and more complicated pictures, it doesn't produce very good results and causes a lot of frustration. In order to be more successful and be able to do harder puzzles, I had to develop better methods of approaching the problem.
As I went through school and had to deal with more complicated and abstract problems in math and science, I’m sure I had to analyze and break down many problems and that my ability to do so developed to another level, maybe one where it was not always so intuitive which was the best way to break down a problem and where the endpoint was not completely known or understood. Then when I first went to college and majored in Computer Science, I studied modularity in a formal way as it applies to designing computer programs. We learned modular and structured programming as methods for designing complex programs. These are methods for breaking down a complex task that you want to program into smaller and simpler sub tasks. The program then consists of some number of discrete and self-contained modules which when combined execute the overall program. The purpose of this is to create programs that are correct and more easily understood and maintained by others.
Defining a Project; Choosing a Technology
The idea of modularity may seem intuitive and appear to occur everywhere in everyday life. But I would think that when children encounter difficult problems in math and science in school, it is not necessarily obvious to them that or how they can break the problem down into problems that they can solve. Papert talks about this regarding the powerful idea of procedural thinking. He asks why children when confronted with certain situations, such as formal arithmetic, which would benefit from procedural thinking, do they not employ it, even though they already use it in everyday life. He says it is because children don’t reflect on how they think in everyday situations and so they don’t make the connections to what they already know. By creating educational environments for children where they use and are required to reflect on procedural thinking such as the Logo environment, it then becomes part of their intuitive thinking and they are able to use it in other situations when needed. [1]
The Logo environment seemed to me to be an environment where children can learn to modularize their problems in order to accomplish complicated tasks in programming. In logo this is done easily through the use of procedures. Doing this would then hopefully also enable them to do so more intuitively in other domains such as math and science.
The general initial idea I had for this project was to have the children learn the basics of logo and then apply that learning to programming a solution to a moderately complex project. The project would have to be complex enough that breaking it down into 2 or more smaller problems would facilitate the programming of it. In Papert’s research with 4th graders who designed instructional fractions software, the children who designed the software did eventually modularize their code but not until they had programmed a considerable amount of “spaghetti” code and realized the efficiency and necessity of doing so. [2]
In my project I planed to introduce the idea of procedures prior to having the children begin their projects and talk about the problem solving strategy of breaking down a problem into smaller problems which would then each be defined in its own procedure. As for the actual learning of the logo programming basic commands and the design of the activities to be done prior to the project, I decided to follow a constructivist approach. I wanted the children to construct their own understanding of the basics of logo programming. They would then use that knowledge to invent their own solutions and try out their own ideas for solving the problems they encountered in the activities that I had prepared. My decision to take this approach was greatly influenced by Papert’s vision of logo as a microworld where children could learn powerful ideas by their own construction and discovery with minimal instruction from a teacher. My role would be that of a facilitator and observer. I would intervene when I observed the children having difficulty or to answer questions. I planned not to give them the “answers” to problems they encounter, but through the use of questions, guide them to figuring out the solutions for themselves.
Curricular Proposal
Objectives
To have children gain a beginning understanding of the powerful idea of modularity as it applies to problem solving: the idea that complex problems can be solved by solving simpler sub problems.
To learn the basics of logo programming.
To have children gain an understanding of this by thinking through and implementing a solution to a particular programming problem using MicroWorlds logo.
To have children reflect on and document their work along the way (including what worked and what didn’t work) as well as document at the end a description of their program broken down into the steps needed to accomplish the overall programming task.
Rationale
Children are continually confronted with complex problems in school which they need to solve. Rather than teaching them rules for problem solving in the abstract or showing them step by step how specific problems can be solved, they would benefit from environments where they are able to construct their own understanding of rules for solving problems. The activity of creating a computer program to “solve” a programming problem is one means where children are given the opportunity to do this. By reviewing the process whereby they arrived at their final solution they gain an understanding of how the original problem they were presented with related to the actual smaller problems along the way that they needed to solve in order to come up with their final working solution.
Standards
Problem Solving
“Problem solving is both a means of developing students’ knowledge of mathematics and a critical outcome of a good mathematics education. As such, it is an essential component of the curriculum. A mathematical problem, as distinct from an exercise, requires the solver to search for a method for solving the problem rather than following a set procedure. Mathematical problem solving, therefore, requires an understanding of relevant concepts, procedures, and strategies. To become good problem solvers, students need many opportunities to formulate questions, model problem situations in a variety of ways, generalize mathematical relationships, and solve problems in both mathematical and everyday contexts.”
Process
The steps in my curricular activity will consist of the following:
1. Play turtle. The children will play the game “turtle” where I give them verbal commands, forward 2 steps, right 90, etc. and have them carry out the commands and then figure out what shape they have “drawn” with their bodies. They can then each take a turn of playing this with each other.
2. At the computer, I will demonstrate the commands, fd, bk, rt, lt in logo and then allow the children time to explore with these commands as they wish.
3. Play a game in logo to learn how to move around the screen. I will create a project with 4-5 planets placed at different spots of the screen. Using the commands they learned in step 3, I will challenge each child to “visit” each one of those planets with their turtle using the least number of commands.
4. Have the children each create a definition using the commands in step 3 to draw a square, rectangle, triangle and circle.
5. project
Have each child design an animation using at least 2 shapes. This will include creating a background scene using the graphics editor in logo and then defining the 2 procedures to implement their animation. I will show them an animation I created initially and then demonstrate the basic animation techniques.
Design notebooks: At the beginning of this curricular activity, I will give each child a design notebook to record their work both using pictures and words and any math calculations they may need to do. I will ask them to use the notebook to record:
a. any figuring out they need to do
b. record any problems they encounter
c. record how they solved those problems
d. anything else they may wish to record regarding the activity
4. After they have finished their projects, I will have them document in their notebooks their complete “solution” (the breakdown, what problems needed to be solved (programmed) and then combined to accomplish the programming project) by referring back to notes they have made previously in their books. I will also ask each of them to verbally describe their projects, including how they felt about the activity.
I will work with 2 children in the 2nd grade over two 3-4 hour sessions. Session 1 will cover steps 1 and 2 and session 2, steps 3 and 4. Each child will be working on their own computer, however I will encourage them to discuss and share their ideas and solutions, ie work collaboratively as much as they wish.
Materials
2 Macintosh computers with MicroWorlds logo installed
Notebooks
pencils
Special Considerations
Given that I will be working with 2 second graders and I am not sure of their capability using logo, I will adjust the difficulty level of the project as needed. Both children I will be working with have a lot of experience using computers (for their age) so I am hoping the prospect of learning to use the computer in a new and potentially exciting way will maintain their interest level throughout the activities. If not I will have to adjust the amount of time involved in the project accordingly. Also since the girls are only in 2nd grade, their experience with recording work in notebooks is limited. If it turns out that this aspect of the project is too time consuming and tedious for them, I will resort to having them do the explanation part of the notebooks verbally and I will tape record it or record it myself in a separate notebook. Since we will be involved with the activities for 3-4 sessions, I will plan a break every hour to move around physically and have a small snack.
Observation of Children
Day 1
I met with Laura F and Laura B once a week for 3 weeks for 3-4 hours each time. The girls were initially extremely excited when I told them they would be learning how to program computers. They had a general idea about programming. When I asked them what it meant to program a computer, one of them answered, “to have the computer do anything you tell it to do.” On the first day, we took turns playing turtle. First I gave the girls commands such as forward 2 steps, right 90 etc. and asked them to carry them out with their bodies. I told them that if they went right 360 they would end up right where they started. Both Lauras are strong in math so they quickly figured out that going half way around was right 180 and then figured out about right angles, that going right 90 meant they would go one quarter around. This activity was a lot of fun and they wanted to continue it with each other much longer than I had planned. Then we we moved onto the computer. The first day I only had one computer set up and this turned out to be somewhat of a problem. I demonstrated the basic logo commands, fd, bk, rt, lt and pd, pu to them and had them take turns exploring with them. They wanted it to be fair, so they decided that each one of them would type 2 commands in and then have the next one take a turn. This somewhat restricted their exploration. They explored mostly in pen down mode, so they were able to see the effects of their commands as the turtle’s drawings. After realizing that they had to use fairly large numbers to see any effects, they started to challenge each to use larger and larger numbers. They got really excited to see the wrap around effects of using very large numbers. They also discovered that the largest number they could use for a fd command is 9999.
Day 2
The second day did not turn out as successfully as the first. It started out positively with the game activity I had set up for them. I had created a screen with 5 planets stamped at various locations. I had them each create a turtle and “visit” each planet, challenging them to use the least number of commands that they could. I observed during this game that they often were confused about which way the turtle was going to turn when they used the rt and lt commands. I had them stop and walk through the command a couple of times when I saw their confusion. They were especially confused when the turtle was in an orientation other than its initial state. The main strategy which I saw them employing in this game was when their turtle didn’t end up where they wanted it to, they simply did the next command to adjust to what they wanted. I’m not sure how much they were reflecting on how the turtle was moving, but they did figure out how to get it to go where they wanted it to anyway. They wrote down all the commands that they used in their notebooks and then counted them up when they were done. Laura B came up with a final count of 52 commands while Laura F only had 26. Although they enjoyed this aspect of the notebooks, this was the only recording they did in their notebook. I had asked them to use the notebook to keep track of what they were learning. I realize now that they were too young for such an open-ended task. A better approach would have been carefully designed worksheets for recording and reflecting on very specific aspects of the activities.
Difficulties Encountered
I wanted to spend more time on this exploration phase of the project but due to time constraints we moved on to the next activity, drawing shapes. Because the girls had figured out from the turtle playing activity about right angles, drawing squares and rectangles came pretty easily. They both created procedures for a square and a rectangle.
The naming of the procedure was very intriguing to them; it became a contest between them of who could come up with the silliest name. I showed them that they could move their turtles with their mouse. Then they typed their procedure names many times in command mode and created designs on their screens. This was a lot of fun. Laura F, because she started her square with a fd command and ended with a fd, discovered that if she typed her procedure in several times the square was drawn in a different place. I tried to get her to reflect on why this was so, but she was more interested in seeing the effects than figuring out why so I didn’t pursue it any further. Laura B had unknowingly started her procedures with the turn and so didn’t see the same affect. I realized at this point that they really didn’t have a deep understanding of the turtle commands and this became more evident when they started to work on drawing triangles. I decided not to give them the amount of the turn for an equilateral triangle or tell them to use the same length for the sides but to see what they would come up with on their own. They proceeded in their previous mode of trying out different amounts for their lengths and angles. Laura F soon became very frustrated and did not want to continue no matter how much encouragement and help I tried to give her. Laura B was less bothered by not figuring things out right away and persisted much longer at trying things out. At this point, I realized that the children had had a long enough day and it was time to stop.
Day 3
Realizing that the concept of angles was very difficult for the children, I created a large equilateral triangle on the floor for them to walk through. I got them to measure the lengths of the sides and they immediately recognized that they were of equal length. Then I had them turn 90 degrees, which was the one angle they were familiar with and had them observe that this was not enough to point them in the direction of the second side. I had them turn another 90 degrees and they saw that this was too far. With my help they then realized that the angle they needed was between 90 and 180 degrees. I had Laura F pick a number that she thought it might be. She guessed 130. I asked the girls to try it out on the computer to see if it worked and if not to try another number close to that. Laura F tried it out first and when she saw it wasn’t quite right, she again became frustrated over things not working the way she wanted them to. It was very had for her persist at trying different solutions until she came up with something that would work. I wanted her to be successful and avoid more frustration, so I asked her to try a number 10 less, meaning 120. She was happy when she finally got it to work, but I don’t think I helped her to internalize the idea that wrong is not bad and that experimenting was part of the process. Going back to the “playing turtle” game again for circles helped immensely. I had them both walk along a circle I had created on the floor and got them both to notice that at each point they were taking a step, turning a very little bit, taking another step etc. When we got back to the computers, I asked them to each pick a small number for their distance and a small number for their angle and repeat the process they had just done using logo commands. They were both very surprised that they actually got circles after alternating the two commands, fd small number, rt small number many times. Given that this activity was so hard for both the girls, I was glad that they were successful in creating their shapes in the end even though they really needed me to guide them each step of the way.
The project
At this point I told them they would be doing a project where they would each create an animation. I had earlier that day created an animation myself which I thought would interest them. I showed it to them and Laura B especially was very excited about creating her own animation. I explained to them simply the idea of modularity but not using the term, saying that they would come up with an idea of what they wanted to create and we would work together to break down tasks which then put together would create their animation. I went through my animation and showed them how I had done mine step by step. At this point I asked each of them to come up with their ideas for an animation and create a background scene using the graphics tools. Since both children were familiar with kidpix, this aspect of the project was familiar and fun for them. Then I asked them to start to work on their animations and would help them as needed. In retrospect, I realize now that there were too many new steps that I had introduced to them with this project that it was really too overwhelming for them. Laura F soon became frustrated again, and refused any help from me, saying it was to hard and she did not want to continue with the project. I decided to stop the project because nothing I said seemed to change her attitude. On the other hand, Laura B all along was much more tolerant of things going wrong and much more willing to ask for help. She very much wanted to continue to create her idea, but also wanted to go along with her friend. The fact that she is my daughter and felt more comfortable asking for help, may have been a contributing factor. I decided to continue the project with her after her friend went home.
Later that day I worked on the animation project with just my daughter. The idea of creating her ideas of an animation was extremely interesting to her and we worked together on it for about 3 hours until it was complete. She needed me to guide her each step of the way in order to create the code for her animation. It would have been hard to give this level of guidance to both children at the same time. In retrospect I might have worked on one animation with both of them jointly. I had her be in complete control of the keyboard and mouse and I tried to avoid telling her what to do but guided her through the use of questions to figure out what needed to be done each step of the way.
I decided to tape record the conversation as I worked with her because it was hard for me to take notes. At this point in the conversation, Laura had created a background scene for her animation and one turtle which she made into a motorcycle from the shapes given. This was about as far as she could go on her own. After her friend left, I sat down with her ...
Me: Tell me the idea for your animation
Laura: The ball is rolling through the grass, and there’s a motorcycle and the motorcycle bangs the ball and the ball goes like this
How do you want the ball to roll?
straight across
where is the motorcycle going to come from
from the other side
and what happens then
it bangs into it
do you want to create a new turtle with newturtle over here or do you want to click on it, you can do it either way
over here click on it
ok click on it and put it where you want it to be
good
and which way should it be going to go to knock into the ball
right 90
good
so are they both going to be moving?
yeh because they are both turtles
and what so you want to happen when they bang into each other
I want the ball to go rolling but to be going higher
what is going to happen to the motorcycle
he’s going to fly up and then come back down and then just go straight
oh that might be hard. so you want it to go a certain distance and as soon as he hits him do almost like a circle
no its a half circle
ok
now how far do you think that is
so you want him to collide where
right here in the grass
so we have to figure out how far this is how would we figure it out
try fd 15
opps wrong guy
why did he go that way
why is it that turtle
that turtle looks like he’s pointing down
how do you make him point the right way
right 90
so lets see what this turtle is called
what
turtles are automatically called t1 t2
what do you mean t1 t2
see this eye here, this eye can tell you what their names are
see do you want to change his name
I don’t have a lot of turtles in this, so I want to do the a b c ‘s with numbers so like a1 a2
when I get to 10 i’ll go to b
so when you have more than one turtle you can call them by name so a1, fd what did you say 15
because I can never figure out which one is the last one we talked to because the last one you talk to is the one that will move when you give it a name that way you know for sure
ok
I didn’t see it more at all
it did move
we’ll go back and you’ll see
no we want to move the motorcycle first, that’s what I wanted
motorcycle is a2
we can change it
ok
so you want to move this first and see how far it is to here
fd 15
did you see it move
no
so we know 15 is not enough
what should we make it then
fd 60
ok watch it
far enough
and you want the ball to be
here
try a1, fd 55
they didn’t touch
ok go back and try 60
ok it that toughing
now you want this guy to do a half circle
what’s his name
a2
This is basically how we did the whole project. At times Laura corrected me so I know she was following what was going on. I know she would not have been able to do it on her own. After I listened to the recording I realized how many new things there were to consider and I really had not realized how many steps were involved in creating an animation. Laura was very particular about what she wanted her animation to look like and later on we had a lot of issues to do with timing because she recorded some sounds to go along with the animation and it turned out they slowed things down, so we really had to try many different things out before getting it to work the way she wanted. She was very excited when it was finally complete and wanted to work on another idea for an animation the next which we also did. I saw that she was starting to come up with some of the steps on her own but still needed me to guide her through the process. Obviously in a classroom the teacher cannot give each child this kind of one on one guidance and so another way (at least with younger children) might be for her to design activities which incorporate the concepts more gradually and then after the children are ready give them an open-ended project where they can integrate all that they have learned.
Questions... Looking for Answers
It became obvious to me that undertaking the modularity exploration aspect of my project was unrealistic because the children had not become proficient enough in logo programming to undertake a complex project on their own, so I decided to go to the library to investigate a number of questions that came to mind for me over the course of this project. My goal was to figure out how I could have designed this project initially to make it more successful for investigating the powerful idea of modularity with children. I did a simple search of the ERIC database for logo programming and children. This yield a surprising long list of research articles. (>300) Given time constraints, I knew I would only be able to review a small portion of the research literature. I ended up choosing 5 articles to review that seemed the most relevant to my project that might answer some of my questions. The main questions that had come up for me after reviewing my notes from the sessions were:
1. What is the best way to teach logo? Although I had originally envisioned allowing the children to explore mostly on their own and I would intervene only when they had questions, it turned out by the end I was employing a very guided approach especially when I worked with my daughter on her final project.
2. What is the best way to design an environment that allowed both exploration and reflection of the effects of the logo commands? I opted for a somewhat unstructured format for the activities and open-ended aspect to the reflection. I suspected during the project that a more structured set of activities for exploration and reflection would have been more successful.
3. How could I assess how much the children were grasping of the logo concepts so that I could ensure that the children had mastered the basic skills before going on to more complicated concepts?
It turns out that all these questions are related. They are all questions about how to create an effective logo curriculum where children would successfully learn the basics of logo commands. The question of what effects an effective logo curriculum would produce in children (e.g. transferrable thinking skills) is a much larger question which I am not going to address here. As I scanned many of the abstracts, I saw that this is a big area of research. My project is about developing a curriculum for teaching one problem solving skill, modularity, but it would have been a much larger project to show that that skill was attained from logo programming and transferrable to other domains.
Creating an effective logo curriculum first means having the children successfully learn the logo fundamentals. The reason this was especially important for my modularity project was because in order for the children to learn about modularity in my final activity, they first had to be proficient enough in logo programming that they could handle a more complex project.
Several of the articles that I read proposed that children have difficulty with logo’s fundamental concepts. Why do children have difficulty? Research done by Fay and Mayer suggest that children come to logo with naive conceptions about spacial reference which is not compatible with the logo graphics environment. They focus on 2 of these: an egocentric conception of space and an undiscriminated conception of commands. The first has to do with the child defining right and left in respect to his own body or the screen rather than the turtle. The second has to do with interpreting right and left to mean not only turn but turn and move forward. The article also looks at 2 confusions novices might bring to the logo environment, confusions of right and left and what they call argument confusions, which would be confusing right 45 and right 90. The study looked at groups of children from 4th, 5th, 6th and 8th grade. All except 4 had no prior experience with logo. The purpose of the study was to look at conceptions children bring to the logo environment which may make it difficult for them to learn logo but does not look at concepts formed from learning logo. Each child participated in a 30-45 minute session introducing them to the basic logo commands and the turtle. At the end of that session, the children were asked if they understood the commands and if they did were given a 24 page test book to work on in an unlimited time period. Each page consisted of a logo command (such as rt 90 and beginning turtle orientation) and then were asked to draw the turtles orientation after the command was executed. Basically, results showed that 1) older children did better than younger and the concept of turning was not intuitively clear to novices below the 6th grade 2) turn commands were more difficult than move commands 3) children did worst when the turtle’s orientation was at 180 degrees and best when it was at 0 degrees. The authors point out that this study has instructional implications in that teachers should be aware of students confusions and misconceptions in order to help them to overcome them. [3]
A second study extends some of the ideas in this first one by looking at the influence of instructional practices on children’s learning of basic logo commands. Leher and Littlefield started with the idea that children come to logo with naive conceptions about spacial reference. They assumed that children with these naive conceptions would find it difficult to successfully write and understand logo programs and therefore would not benefit from general cognitive skills that may be gained from the logo environment. They looked at how mediated and less mediated instructional practices influenced the children with respect to errors. They looked at 4th graders and then later 2nd graders. In the less mediated context children were introduced to the logo commands and then allowed to work on whatever they wished. In the more mediated context, children were introduced to the logo commands and then used software designed to encourage reflection about the meaning of the different logo commands. They found that misconceptions reported in previous studies were significantly reduced by the mediated instruction. They suggested that the misconceptions children develop may be attributed to working memory rather than true misconceptions. [4]
A third study that I read about also looked at the importance of the nature of the instructional process in learning logo. Emihovich and Miller took a Vygoskian perspective and looked at the teacher’s use of mediated strategies. This study looked at much younger children, 2 pairs of 5 year olds. They examined the children’s transition from other regulation to self regulation as they became more competent in logo programming. The teacher used mediated strategies mainly through the use of questions becoming the “scaffold” by which the children crossed their “zone of proximal development”. The types of questions that were used by the teacher were of 3 types: 1) questions which got the children to recall previously learned material to be used in a task to be focused on next 2) questions to get the children to think about what the turtle has just done and compare to what the children had wanted to happen and 3) planning questions to get the children to think about what they were planning to do next. The children reached a level after 11 sessions where they were functioning fairly independently in thinking through simple logo problem solving tasks with minimal direction from the teacher. This study was particularly interesting to me because I was dealing with younger children, although a couple of years older than the ones in the study, much closer in age than the first 2 studies. What naturally happened in my project was that when I saw the children I was teaching were having difficulty, I adjusted my teacher to a much more mediated approach similar to the one describe in the study, especially when I undertook the project with my daughter. I’m assuming that if I continued to teach my daughter in this manner, working with her within her zone of proximal development, she would eventually gain greater competence in logo programming and be able to take on projects on her own. [5]
In contrast to the research articles, one article I read was written by a teacher who had worked with children ages 4 -14 teaching logo over the course of 10 years. The article was about teaching younger children ages 4 - 8 years old. Her main 2 suggestions for successful logo acquisition were to have children initially spend a lot of time exploring in the immediate mode and the importance of using a guided teaching method. Her guided teaching method consisted of teacher designed tasks which were open-ended in nature. The teacher’s role was to observe the children and ask questions of the children during and upon completion of their work which would require them to reflect on what they had done. One example described of an activity for younger children which gets them to reflect on how the turtle moves was the “teddy bear game”. The children direct their turtles to the left or right of a tree on the screen and then by typing ‘teddy bear’ one is drawn on that stop. They continue this for every tree on the screen. The teacher asks them questions about where their teddy bears were drawn.[6]
Lastly one article that caught my interest but was not directly related to my questions was one entitled “Effects of Fantasy Contexts on Children’s Learning and Motivation: Making Learning More Fun”. One thing that occurred to me during my project was that some of the activities in my project, in particular the activity of creating shapes may not be particularly interesting especially to younger children. It turned out that the 2 game activities of playing turtle and navigating to the different planets were probably the most successful of my activities. This article describes a study of 3rd and 4th graders learning basic logo. It looked at the effects of embedding logo instruction in fantasy contexts on children’s learning and motivation. The instructional programs required children to learn logo graphic commands by demonstrating ability to 1) draw lines connecting various collections of objects on the screen b) move through a series of mazes and 3) construct various simple geometric shapes on the screen. One instructional program presented the problems abstractly. Three others embedded the exact same tasks within fantasy problem solving contexts. The children were given a choice of 3 contexts: a pirate treasure hunt, a mission space search and clue detective hunt. The study claimed that the children showed significantly greater learning in the fantasy instructional programs than in the non-fantasy instructional program.[7]
Modularity Project Revisited
This was my first experience developing any kind of curriculum. I feel like I went into it somewhat blindly. I was very much influenced by Papert’s vision of the logo environment being one where children would explore and discover for themselves powerful ideas without much intervention from a teacher. This is a very idealistic vision which sounds good in theory but is questionable as to how well it holds up in practice. What I have learned from my project is that there is a lot involved in creating a successful curriculum. I feel now that the project that I had set out to do, would have worked well over the course of 4 - 6 months and would have been more successful had I designed many more structured activities before giving the children the open ended project of creating an animation. Although I had been theoretically opposed to worksheets prior to starting this project, in this case thoughtfully planned out worksheets after each activity to give the children a chance to reflect on what they had done would not only have given me an indication of what they had learned but also deepened their learning as well. For example, in order to have the children reflect on the concept of angle, I could create worksheets each with a series of commands of fd, bk, rt or lt and have them predict by drawing what the path of the turtle would be. I would then have them carry out the commands at the computer and record the actual path of the turtle, comparing their predicted version with the actual path.
After I felt that the children had mastered the basic concepts of logo, I would then introduce them to the concept of modularity. I could use a familiar domain such as math word problems and illustrate how one might break down a problem into smaller problems in order to solve it. Then I would have the children use that method to work out some problems themselves. At this point I would introduce the concept of procedures in logo as a way of defining sub problems in logo. At this point the children would be ready to define their projects, either recording them themselves or dictating them to me. I would ask them to approach their project using the concept of modularity, listing the steps they think would be required to program it. Then they could go to the computer and start trying out their ideas.
Conclusions
I feel that this project was successful in that it allowed me to investigate the use of logo as a learning environment. It also allowed me to reflect more deeply on what goes into developing successful meaningful curriculum for children. Ideally this project would have been a pilot study which would have given me the basis for designing the curriculum for a larger group of children in a classroom setting.
REFERENCES
1. Papert, S. (1980) Mindstorms: Children , Computers and Powerful Ideas, New York: Basic books.
2. Harel, I. and Papert, S. (1990) “Software Design As A Learning Environment”, Interactive Learning Environments 1, p 1-32.
3. Fay, A. and Mayer, R. (1987) “Children’s Naive Conceptions and Confusions About Logo Graphics Commands”, Journal of Educational Psychology 79(3), p 254-268.
4. Leher, R. and Littlefield, J. (1991) “Misconceptions and Errors in LOGO: The Role of Instruction”, Journal of Educational Psychology 83(1), p 124-133.
5. Emihovich, C. and Miller, G. (1986) “Talking To the Turtle: A Discourse Analysis of Logo Instruction”, EDRS # ED276532 Revised version of a paper presented at the Annual Meeting of the American Educational Research Association April 16-20 1986.
6.Yelland, N. (1992) “Introducing Young Children to Logo, The Computing Teacher Dec/Jan 1992 p 12-14.
7. Parker, L. and Lepper, M. (1992) “Effects of Fantasy Contexts on Children’s Learning and Motivation: Making Learning More Fun, Journal of Personality and Social Psychology 62(4) p 625-633.