From the Abstract to the Concrete:

A Study of CS61a students in CS61b

Andrew Begel


  1. Survey
  2. Programming is a fundamental skill used in the study of computer science. Much of computer science stems from a certain mode of thought, a rational exploration of possibilities that enables humans to gain control over the machines that they build. Computer science as a discipline is understandable. Acquiring the most efficient mode of thinking, however, is not as easy. Students learning to program often go through many life-defining experiences -- many of them overcome adversity in the form of new, unknown, hard-to-understand material, long, difficult assignments, and the struggle to gain a mastery over a subject that everyone else already appears to have.

    In this course, we've asked ourselves over and over what kinds of curricula, learning behaviors, and thought patterns would make this introduction to computer science an easier task. In the computer science department at UC Berkeley, there was a great deal of thought in the creation of the first two introductory courses, CS61a and CS61b. CS61a is an adaptation of Structure and Interpretation of Computer Programming, a course developed by Gerry Sussman and Hal Abelson of MIT. CS61b is a Berkeley creation, a course emphasizing object-oriented programming and data structures.

    When I was at MIT, I took the SICP course, and while a first-year student at Cal, I TAd CS61a. Thus, I have experience with this course from both sides. When I took the course, I found it relatively easy to understand. I had programmed extensively prior to entering MIT and found that learning Scheme held no great mystery. Since I wasn’t bogged down by the language, I found myself enamored of the ideals and Zen behind it. I began to notice higher-level concepts behind each week's lesson, concepts that formed the core of my new understanding of computer science.

    As a CS61a TA, I tried to show my students a little of this Zen. I don't believe I was successful with all of my students, but I think a few of them went away with the right idea. What I noticed, however, was that many students had trouble understand the right way to think about computer science and about programming; the inability or unwillingness to generalize; the fear of the abstract; the difficulty in understanding powerful ideas that might require a leap of faith to use before complete comprehension comes.

    My students finished CS61a and went on to CS61b, where they undertook the study of Java and data structures. Java, an object-oriented imperative language, is about as different from Scheme as English is from Latin. One can be expressed in the other, but the reverse expression is difficult at best, though not impossible. It is easier to express the ideas of Java, object-orientation, and data abstraction in Scheme then it is to mutate Java to be as general as Scheme. Thus, Java tends to be more concrete by employing types, and more limited because procedures are not first-class objects. Likewise, efficiency issues come up more in Java than in Scheme because Java feels like it is closer to the metal, closer to an underlying machine implementation than Scheme. In Scheme, there are an infinite number of ways to write something, and merit can be seen in many of them. In Java, the simplest solution often eschews higher-level concepts like recursion, in favor of more direct, to-the-point constructs, such as iteration.


  3. Survey
  4. I developed a survey consisting of some simple Scheme-style problems and presented them in both a Java and Scheme context. I then asked questions designed to elicit some personal feelings about the two languages and about the two courses. The survey is attached to this report.

    The survey contains several questions. The first is a study of recursion. A common function in Scheme is append, which takes two linked lists and produces a new linked list that has all of the elements of the two lists concatenated into one. CS61a students learn this function about three weeks into the course. Here is the simple Scheme solution:

    (define (append list1 list2)
        (if (null? list1)
            (cons (car list1) (append (cdr list1) list2))))

    The solution is recursive. It copies each element of list1 into a new list, and finally attaches list2 to the end of the last new cons cell. There are other ways to write the solution, but the recursive solution is generally the most elegant and the shortest.

    I asked students to write append in Scheme and Java. I presented the Java version first because I wanted to see what the student's current instincts were after having been indoctrinated in Java for several months in CS61b. Since Java doesn't have a built-in list construct, I provided them with a Cons cell abstraction and asked them to turn it into a List abstraction. I then asked the Scheme version of the same question.

    The next section was about data abstraction. In Scheme, data abstractions tend to be figments of the programmer's imagination. There are no built-in data abstractions other than the basic cons cell. Everything else must be built up by the programmer. Java is object-oriented, which provides a convenient data structure representation and allows programmers to organize their data by the use of types. These types allow the programmer to proscribe certain ways of using the objects while at the same time providing the programmer with some structure and automatic documentation. In Scheme, the programmers must be careful in how they name functions in order to make the abstract types clear. In Java, this comes for free.

    I asked students to construct a tree abstraction. They were first asked to build a binary tree. Then I asked them to modify it to a trinary and then finally to a d-ary tree, where the nodes could have any number of children. I wanted to see how they would construct the data abstractions, but I also wanted to see how easily they could modify their abstractions. I finally asked them to highlight the differences between their implementations and give me the reasoning for when they would choose one representation over the other. I asked this question first in Java and then in Scheme. I then asked the students to explain the differences between their Java and Scheme approaches to the same problem. I wanted to see if they recognized the differences in their two approaches and how they thought about abstraction in each language.

    For the second to last part of the survey, I asked students which language they liked better and why. I gave them some sample topics to discuss, such as programming style, debugging, abstraction, and object-oriented vs. procedural programming.

    Finally, I asked students about the differences between CS61a and CS61b. I asked what they learned in CS61a that was useful for understanding CS61b, and asked what they learned in CS61a that was irrelevant in CS61b. I also asked what they learned about in CS61b that they didn't learn in CS61a and asked them to explain why it wasn't covered in CS61a. I finally asked if they had any struggles in CS61a or CS61b and whether they had any ways to improve the courses or to modify their content in some way. I wanted to get the students' own impressions of the courses from the inside while they were in them. CS61b is only the second computer science course, so I didn't expect them to understand the purpose of everything they were learning, but I did want to see if they could speculate as to the usefulness of certain material.


  5. Experiment
  6. I interviewed four CS61b students whom I had TAd in CS61a the term before. I was hoping for a larger number, but several students cancelled at the last minute. In any case, four students turned out to be a good enough number to see some trends in their thought patterns.

    Most of the students had a lot of trouble with the first question, creating a List class in Java. They thought that they needed to reimplement the Cons class to create the List. I think it might be due to CS61b implementing linked lists in a prior problem set. Several students ended up with an implementation that resembled this structure, but the types tended to be wrong. I expected them to create a constructor that would restrict its second argument (the cdr) to be a List. This would let them use Java’s type system to constrain the use of List to only make proper Lists. Two of them implemented their constructors this way, but the other two took an Object as the second input and downcasted it to a List inside the method. One of them took another CS61b idiom and created a zero argument constructor. He then wrote a cons() method that took car and cdr and mutated the instance variables of the Object.

    I asked the students to provide an example use of their Lists, so I could get them to see if they had created the List class correctly. Three of them found bugs in their solutions right away. The one with the mutating constructor accidentally overwrote the same cons cell several times instead of creating a complete list. I didn’t point out the error, but just moved on.

    After creating their List class, I asked them to write append. None of the four used recursion. All used while loops to implement the method. Two students destructively modified their lists. They cdr’d down to the end of the first list and mutated the cdr to point to the second List. This was acceptable, but I had asked for a non-destructive append. Three students got screwed up when they tried to use while to cdr down their list. As the while loop goes forward down the list, they tried to create a new List from each element of the old. Unfortunately, if you do it this way, you generate the new List in reverse. All of them realized their mistake, but didn’t rewrite their procedure to be recursive; they merely re-ran the while loop again to rereverse the list. Only one student avoided the problem by using a java.util.Vector (a stretchy array) to combine both Lists, and then used a new List constructor that took an array to turn the Vector first into an array and then into a List.

    I then asked students to write append in Scheme. Two of them remembered how to do it in the Scheme style that they had learned in CS61a. One of them couldn’t remember how to program in procedural style, and rewrote their Java implementation in Scheme. The fourth student couldn’t remember how to do it. It appeared that he was trying to program in the imperative programming style without using Scheme mutators.

    None of the students had any trouble creating a binary tree abstraction. Two of them lectured me for several minutes on the finer points of data abstraction and explained the differences between a binary tree and a binary tree node. One is a container for the root node of a binary tree, the other is a generic node for use anywhere in the tree. Students used three instance variables for the binary tree: Object key, Node left and Node right. Altering the binary tree to a trinary tree was as simple as adding in an extra Node to be the middle node. When the students created the d-ary tree abstraction, they all changed their children representation to an array of Nodes which was input to the constructor. One of the students was going to use their List class for this, but decided against it because while Java had built-in operations for getting the nth element of an array, it had no built-in method for getting the nth element of a linked list.

    When asked to write these abstractions in Scheme, three of the students used a data structure made from cons cells. They quickly wrote constructors and accessors for the key and left and right children. One student immediately wrote their abstraction in the Scheme OOP style which was introduced as a section in CS61a. This style is very similar to Java but doesn’t show any types to the user. When they were asked to modify their abstraction to support a d-ary tree, two students wanted to use Scheme’s dotted notation. This notation allows a procedure to take an arbitrary number of arguments and pass them to the function as a list. After I nudged them to find a simpler way, they switched to taking a list of nodes as the input for the children nodes. The third student hit upon using the list from the beginning. The fourth student, who used OOP style, merely changed the name of her instance variable to list-of-children and added an accessor to pick out the nth child from the list.

    The later questions from the survey go more toward the students’ comprehension and understanding of CS61a, CS61b, Scheme and Java. In the next section, I’ll discuss some thoughts that I have about the students’ solutions to the survey problems and give some hypotheses for where these problems have come from.

  7. Analysis


    All of the students seem to have difficulty with recursion. In CS61a, they used recursion because there was no alternative. But, after experiencing CS61b, Java, and the wonders of iteration, they seem very inclined to use iteration, even in places where recursion would provide a much simpler solution. It was illustrated in the survey when three of the students accidentally wrote reverse instead of append because they used iteration.

    One student said that one of the most important things he learned from CS61a was recursion, yet he still used an iterative solution. He felt that recursion was more magical than iteration:

    J: Recursion is doing it over and over again, but it's a little different because recursion is calling itself. You're just hoping it's gonna end, where in a for loop, you're like, hey, I want you to go from 0 to 100. It will do exactly what you tell it to do.

    A: So recursion seems a little bit more big in its notions of what you can do with it?

    J: Right. You gotta have faith.

    One could say that the iteration is more concrete than recursion. J said that in order to understand recursion, you have to have faith. This description is vaguely religious, used in a way that imparts a certain mystery on recursion – that it’s beyond human understanding. One possible explanation for the use of iteration over recursion is the tendency to embrace more concrete concepts over the abstract ones. J said that he could look at a loop and tell where it begins and ends, but with recursion you couldn’t immediately tell when it was going to end.

    I asked another student why he didn’t write the Scheme append in the same way that he wrote the Java append.

    D: Just, I think the cons thing threw me. The way that I started writing it because that was the way I thought about it at that time. Java isn't scheme. ‘cause Java is not Scheme. Java -- I’ve been doing so many for loops and while loops. Recursive, we haven't really done much recursive stuff, a little bit, but nothing on a grand scale.

    This student’s feeling is that CS61b emphasizes iteration over recursion. In CS61a, students learned that tail recursive processes were equivalent to iteration, but still had never seen a real iterative construct. Once they get to Java, however, it seems that this iterative construct is easier to understand and use than recursion.


    The students say that they like Java over Scheme because of its types. They describe Java objects anthropomorphically and graphically. When they describe Scheme objects, it’s much more vague.


    J: Yeah. I start using a different verbal language. "Yes I have to put a node into this thing." Well, we know what a node is; it has its own class. It’s an object. You can start drawing these things. We had this thing called table; a table is this. It has a pointer to this mbfile, and this file has nodes. Node is an object, file is an object, table is an object. We also had an index which was like an actual tree. Everything was an object.

    D: I don't know, Java is more friendly, somehow. it's not as cryptic sometimes. not so many parens running around. labeled functions: get-value-at. you know what that is. you know what it returns. you know what arguments it takes. where in scheme, everything is loose. you can have any arguments.

    Java’s types seem to give students a language in which to describe their organizational structures. It makes computational objects easier to visualize. Here is what a different student said about Scheme structures:

    D. Trees and lists were hard. Trees were hard because it was hard to visualize how it came about. because everything is a list. When you're trying to draw a binary tree, it's confusing especially when Prof. Harvey gave you, this is a tree, a binary tree and all these tools. You just want to see what a binary tree looks like, node structure-wise.

    A: So you can see that in Java?

    D: Prof. Hilfinger gives it to you in some notation. He doesn't give it to you in scheme notation. It's not hard but nested parens are hard to read.

    This suggests that students have trouble comprehending user-built abstractions. In Scheme, everything tends to be built from one structure: the cons cell, and thus when something is printed, it looks like a series of nested cons cells. This notation tends to confuse students because it doesn’t match any mental picture they may had tried to come up with. In Java, objects have a default toString() method which prints a very opaque representation: <Object #5fa65f>. If students want an understandable representation for a data structure, they have to customize the toString() method themselves and create a printable representation that matches their internal model. While it is possible to create an equivalent procedure in Scheme, it doesn’t force you to, and all Scheme primitives return errors in terms of the underlying cons abstraction, not in terms of the user-level abstraction.

    While students like the organization in Java objects, it does seem that some students like the elegance of the cons cell. It forms the basis of all data structures and influences the way that you think about abstraction.

    D: I like the simplicity of Scheme. Since we only had one structure, you have one way to think, really. This one [Java] you have a choice, so you have to think more about optimization, and can you really do it like this? In Scheme, you could do it this way, or you couldn't do it at all.

    My take on this is that while Scheme is as powerful as Java for programming, Java gives you much more structure in your data abstractions and your programming model. It gives you the object-oriented model as a scaffolding on which to build more complicated structures. In Scheme, the burden is on the programmer to create all structure from nothing.

    Programming and Design

    One important thing to notice is that while in CS61a, students never had to build a very complicated data structures. While they wrote a meta-circular evaluator, the most complex piece was an environment, which was merely a list of association lists of name-value pairs. CS61b stresses programming in the large and building large amalgams of complex data structures. Their final project was to create a domino game with a GUI, network play, and AI machine player. This involved so much programming that students had to work in teams and divide the work up amongst all team members. In CS61a, students felt that they could have handled entire projects by themselves. CS61a projects outline all of the steps that you have to perform. In CS61b, projects just give you a framework in which to work, and then say "go."

    L: We didn't even get the templates. He [Hilfinger] gave us one interface which we would need to implement, but you pretty much have to figure out the entire design by yourself. I mean, he tells you a lot in lecture, but you still have to... you have to design a program. really. In 61a, you have everything step by step, and you have to say "here you draw a hand" and "here you give this card" and it's kinda like first project in 61b.

    A: 61b projects were more valuable then, because they relate more about what real-life programming is about?

    L: Well, in real life you're not gonna have the steps, right? People are not gonna tell you, I want you to do this after that and the program is gonna look like this you know and you have to have it in your head -- the entire picture of how it works, the entire graph of whatever you or map of program about how it's gonna work. In the end. and you're not gonna be given all the templates and options. You have to know how to write it without stuff.

    In Scheme, the programming process is made more difficult due to the lack of a debugger. All four students wished that they had some form of debugger in Scheme that would tell them the line number of the error and give them a stack trace where the error occurred. I asked the students to compare using Java and Scheme for testing small functions. Since Scheme is interactive, I thought that the students would have an easier time testing their procedures than in Java.

    A: What about getting something to run for the first time?

    D: Well, Scheme... Well, I’m trying to remember what Scheme would say if you typed something bogus. Scheme will do something. It might not be right... Java is pretty good because the compiler helps you catch errors.

    It seemed to me that the students cared less about the ability to interactively test than getting useful and accurate feedback as a result. All students expressed frustration over semantically mismatched parentheses and wished that the Scheme interpreter would help them discover these errors.

  9. Conclusion

The analyses above have shown some student comments about their understanding of recursion and data abstraction, along with some of my commentary. In this section, I’ll try to present some possible explanations for these behaviors in the hopes that some combination of them can help explain where the current introductory courses go wrong.

Students find iteration easier than recursion. Perhaps this might be because they find iteration more concrete than recursion. Students might tend to shy away from abstract concepts, especially if they have an easier alternative that works in most of the cases. To be sure, the imperative style of programming used in Java lends itself to iterative solutions that don’t cause weird bugs, like the list-reversal problem noted with append. If I had asked students to implement reverse, none of these problems would have shown up because reverse is easy to do with iteration.

Another possible hypothesis is a knowledge integration approach. During CS61a students learn about recursive processes and iterative processes, and recursive constructs and tail-recursive constructs. They don’t however, learn any iterative constructs. This could leave a hole in their mental model of programming that is filled during CS61a by Java iterative constructs. And, perhaps students have put the original recursive constructs in the back of their mind when they learn recursion, so iteration, which is the concept they’ve learned most recently, is the first thing they think of when trying to program a new solution to a problem.

I’ve seen evidence that the students who took this survey are perfectly comfortable programming in Scheme and Java. What I haven’t seen is that they truly understand what it means to program. To bring back the Zen metaphor from the introduction of this paper, another possible explanation is that students are very comfortable in programming in the dominant styles of whatever language they happen to be in. Unfortunately, they seem to be missing the forest for the trees. They don’t take the time to think about what they’re programming before they start writing it down. When I asked one student why his Scheme and Java programs were different for the same task, he said because that was "the way that I started writing it, because that was the way I thought about it at that time." Perhaps if students spent more time understanding algorithm design they might have a better intuition about which construct to use.

Students do have a good grasp of abstraction, however. They understand the different rationales behind when to use a particular representation and when to use another. After one student modified the binary and trinary tree abstraction to a d-ary tree abstraction, this conversation followed.

A: Well, now that you know it exists, would you have written the binary tree that way?

D: Well, depends on what I was writing it for. If I had a project that required trees of different sizes... But in a project where you know you're going to use binary trees there's no need to.

Another student spoke about the representation change as well.

Z: No, because we have different goals. If you have a goal. If you know you're going to have a tree you should have as many dimensions as possible, it's obviously better, you know, than having a million different constructors for a million different lengths, so this is better because you just have an array for the kids. But then, you have to have an accessor that check numkids for errors. But if you know you're going to have a binary tree or a tree with three kids, then that way is easier because you know that that's what you mean.

A third student also understood when to use left and right for the child nodes of a binary tree and when to use an array. Not only was it more appropriate for the implementation, but when someone else read it, they would understand the more specific binary tree implementation faster than they could figure out the more general d-ary implementation.

A: Which one is better for a binary tree?

J: This one.

A: Why?

J: Because you don't have to worry about an array.

A: Are arrays hard?

J: Yeah. Besides the fact that everyone knows this one and has at least seen it. If they saw this one they might get thrown off by it.

A: Oh, so if they see the first one, They'll say this is a binary tree, but if they see the second they'll say, what is this?

All of the students understood the consequences of using different abstractions and knew the places in which they were appropriate. More study needs to be done to figure out if students have this kind of intuition before they take CS61b. My gut feeling is that students don’t have a good idea of abstraction when they finish CS61a (just from having seen many students’ tests). Since one of CS61b’s main emphases is on data abstraction and data structures, I’d say that the students learn their lesson quite well.

One final conclusion we can draw from this small survey is that these students all wished that Scheme had better debugging facilities. The simplest desire was for exact error messages that told you what line the error was on and what the stack trace was. In addition, the students feel that they don’t get good enough feedback from the Scheme compiler about semantic errors in their programs. Perhaps if Scheme contained a type-inference engine like that found in DrScheme, a Scheme implementation from Rice University, it could provide students with better feedback at compile-time and help prevent statically checkable errors.

Final Thoughts

I think that this survey illuminates some important issues about novice programmers’ mental models of computation. Students tend to use iteration over recursion, they understand abstraction very well, and they want good compiler feedback about their code. Expert programmers are usually distinguished from novices by their intuitions about program structure, data abstraction and debugging skills.

To me, it seems like a lot of emphasis has been placed on comparing novice programmers to expert programmers, but very little is placed on exploring the transition. Is it like melting ice? Do programmers absorb information, little by little, until it is enough to make them expert? Or does the change happen more gradually, with expertise coming in different areas? I hope this survey has illuminated a little bit of this transition period with the study of novice programmers moving into the second programming course in computer science. Since this survey was so small, a larger one should be undertaken to ascertain whether these findings are evident of trends in the general population or merely noise due to the small sample size. My intuition is that the basic observations will be borne out by a larger survey, but I hope more time is given to analysis and utilization of these results.