Exercise Types

Every good carpenter has a set of screwdrivers, and every good teacher has different kinds of formative assessment exercises to check what learners are actually learning, help them practice their new skills, and keep them engaged. This chapter starts by describing several kinds of exercises you can use to check if your teaching has been effective. It then looks at the state of the art in automated grading, and closes by exploring discussion, projects, and other important kinds of work that require more human attention to assess. Our discussion draws in part on the Canterbury Question Bank Sand2013, which has entries for various languages and topics in introductory computing.

The Classics

As s:models-formative-assessment discussed, multiple choice questions (MCQs) are most effective when the wrong answers probe for specific misconceptions. In terms of Bloom’s Taxonomy (s:process-objectives), MCQs are usually designed to test recall and understanding (“What is the capital of Saskatchewan?”), but they can also require learners to exercise judgment.

A Multiple Choice Question

In what order do operations occur when the computer evaluates the expression price = addTaxes(cost - discount)?

1. subtraction, function call, assignment
2. function call, subtraction, assignment
3. function call, then assignment and subtraction simultaneously
4. none of the above

The second classic type of programming exercise is code and run (C&R), in which the learner writes code that produces a specified output. C&R exercises can be as simple or as complex as the teacher wants, but for in-class use, they should be brief and have only one or two plausible correct answers. For novices, it’s often enough to ask them to call a specific function: experienced teachers often forget how hard it can be to figure out which parameters go where. For more advanced learners, figuring out which function to call is more engaging and a better gauge of their understanding.

Code & Run

The variable picture contains a full-color image read from a file. Using one function, create a black and white version of the image and assign it to a new variable called monochrome.

Write and run exercises can be combined with MCQs. For example, this MCQ can only be answered by running the Unix ls command:

Combining MCQ with Code & Run

You are in the directory /home/greg. Which of the following files is not in that directory?

1. autumn.csv
2. fall.csv
3. spring.csv
4. winter.csv

C&Rs help learners practice the skills they most want to learn, but they can be hard to assess: learners can find lots of unexpected ways to get the right answer, and are demoralized if an automatic grading system rejects their code because it doesn’t match the instructor’s. One way to reduce how often this occurs is to assess only their output, but that doesn’t give them feedback on how they are programming. Another is to give them a small test suite they can run their code against before they submit it (at which point it is run against a more comprehensive set of tests). Doing this helps them figure out if they have completely misunderstood the intent of the exercise before they do anything that they think might cost them grades.

Instead of writing code that satisfies some specification, learners can be asked to write tests to determine whether a piece of code conforms to a spec. This is a useful skill in its own right, and doing it may give students a bit more sympathy for how hard their teachers work.

Inverting Code & Run

The function monotonic_sum calculates the sum of each section of a list of numbers in which the values are strictly increasing. For example, given the input [1, 3, 3, 4, 5, 1], the output is [4, 12, 1]. Write and run unit tests to determine which of the following bugs the function contains:

• Considers every negative number the start of a new sub-sequence.

• Does not include the first value of each sub-sequence in the sub-sum.

• Does not include the last value of each sub-sequence in the sub-sum.

• Only re-starts the sum when values decrease rather than fail to increase.

Fill in the blanks is a refinement of C&R in which the learner is given some starter code and has to complete it. (In practice, most C&R exercises are actually fill in the blanks because the teacher will provide comments to remind the learners of the steps they should take.) As discussed in s:load, novices often find filling in the blanks less intimidating than writing all the code from scratch, and since the teacher has provided most of the answer’s structure, submissions are much more predictable and therefore easier to check.

Fill in the Blanks

Fill in the blanks so that the code below prints the string 'hat'.

text = 'all that it is'
slice = text[____:____]
print(slice)


As described in s:load, Parsons Problems also avoid the “blank screen of terror” problem. The learner is given the lines of code needed to solve a problem, but has to put them in the right order. Research over the past few years has shown that Parsons Problems are effective because they allow learners to concentrate on control flow separately from vocabulary Pars2006,Eric2015,Morr2016,Eric2017. The same research shows that giving the learner more lines than she needs, or asking her to rearrange some lines and add a few more, makes this kind of problem significantly harder Harm2016. Tools for building and doing Parsons Problems online exist Ihan2011, but they can be emulated (albeit somewhat clumsily) by asking learners to rearrange lines of code in an editor.

Parsons Problem

Rearrange and indent these lines to sum the positive values in a list. (You will need to add colons in appropriate places as well.)

total = 0
if v > 0
total += v
for v in values


Tracing

Tracing execution is the inverse of a Parsons Problem: given a few lines of code, the learner has to trace the order in which those lines are executed. This is an essential debugging skill, and is a good way to solidify learners’ understanding of loops, conditionals, and the evaluation order of function and method calls. The easiest way to implement it is to have learners write out a sequence of labelled steps. Having them choose the correct sequence from a set (i.e., presenting this as an MCQ) adds cognitive load without adding value, since they have to do all the work of figuring out the correct sequence, then search for it in the list of options.

Tracing Execution Order

In what order are the labelled lines in this block of code executed?

A)     vals = [-1, 0, 1]
B)     inverse_sum = 0
try:
for v in vals:
C)             inverse_sum += 1/v
except:
D)         pass


Tracing values is similar to tracing execution, but instead of spelling out the order in which code is executed, the learner has to list the values that one or more variables take on as the program runs. It can also be implemented by having learners provide a list of values, but another approach is to give the learner a table whose columns are labelled with variable names and whose rows are labelled with line numbers, and asking them to fill in all of the values taken on by all of the variables.

Tracing Values

What values do left and right take on as this program executes?

left = 24
right = 6
while right:
left, right = right, left % right


You can also require learners to trace code backwards, e.g., to figure out what the input must have been if the code produced a particular result Armo2008. These reverse execution problems require search and deductive reasoning, but they are particularly useful when the “output” is an error message, and help learners develop valuable debugging skills.

Reverse Execution

Fill in the missing number in values that caused this function to crash.

values = [ [1.0, -0.5], [3.0, 1.5], [2.5, ___] ]
runningTotal = 0.0


Minimal fix exercises also help learners develop debugging skills. Given a few lines of code that contain a bug, the learner must either make or identify the smallest change that will produce the correct output. Making the change can be done using C&R, while identifying it can be done as a multiple choice question.

Minimal Fix

This function is supposed to test whether a number lies within a range. Make one small change so that it actually does so.

def inside(point, lower, higher):
if (point <= lower):
return false
elif (point <= higher):
return false
else:
return true


Theme and variation exercises are similar, but instead of making a change to fix a bug, the learner is asked to make a small alteration that changes the output in some specific way. Allowed changes can include replacing one function call with another, changing one variable’s initial value, swapping an inner and outer loop, changing the order of tests in a chain of conditionals, or changing the nesting of function calls or the order in which methods are chained. Again, this kind of exercise gives learners a chance to practice a useful real-world skill: the fastest way to produce a working program is often to tweak one that already does something useful.

Theme and Variations

Change the inner loop in the function below so that it fills the upper left triangle of an image with a specified color.

function fillTriangle(picture, color) is
for x := 1 to picture.width do
for y := 1 to picture.height do
picture[x, y] = color
end
end
end


Refactoring exercises are the complement of theme and variation exercises: given a working piece of code, the learner has to modify it in some way without changing its output. For example, the learner could be asked to replace loops with vectorized expressions, to simplify the condition in a while loop, etc. The exercise here is that there are often so many ways to refactor a piece of code that grading requires human intervention.

Refactoring

Write a single list comprehension that has the same effect as this loop.

result = []
for v in values:
if len(v) > threshold:
result.append(v)


Diagrams

Having students draw concept maps and other diagrams gives insight into how they’re thinking (s:memory-concept-maps), but free-form diagrams take human time and judgment to assess. Labelling diagrams, on the other hand, is almost as useful from a pedagogical point of view but much easier to scale.

Rather than having learners create diagrams from scratch, provide them with a diagram and a set of labels and have them put the latter in the right places on the former. The diagram can be a complex data structure (“after this code is executed, which variables point to which parts of this structure?”), the graph that a program produces (“match each of these pieces of code with the part of the graph it generated”), the code itself (“match each term to an example of that program element”), or many other things; the key is that constraining the set of solutions makes this usable in class and at scale.

Labelling a Diagram

f:exercises-labelling shows how a small fragment of HTML is represented in memory. Put the labels 1–10 on the elements of the tree to show the order in which they are reached in a depth-first traversal.

Another way to use diagrams for formative assessment is to give learners the pieces of the diagram and ask them to arrange them correctly. This is a visual equivalent of a Parsons Problem, and you can provide as much or as little of a skeleton to help them with placement as you think they’re ready for. (I have fond memories of trying to place resistors and capacitors in a circuit diagram in order to get the right voltage at a certain point, and have often seen teachers give learners a fixed set of Scratch blocks and ask them to create a particular drawing using only those blocks.)

Matching problems can be thought of as a special case of labelling in which the “diagram” is a column of text and the labels are taken from the other column. One-to-one matching gives the learner two lists of equal length and asks her to pair corresponding items, e.g., “match each piece of code with the output it produces”.

Matching

Match each regular expression operator with what it does.

 ? start of line * zero or one occurrences + end of line \$ one or more occurrences ^ zero or more occurrences

Many-to-many matching is similar, but the lists aren’t the same length, so some items may be matched to several others, while others may not be matched at all. Both kinds require learners to use higher-order thinking skills, but many-to-many are more difficult because learners can’t do easy matches first to reduce their search space (i.e., there is a higher cognitive load.)

Matching problems can be implemented by having learners submit lists of matching pairs as text (such as “A3, B1, C2”), but that’s clumsy and error-prone. Having them recognize a set of correct pairs in an MCQ is even worse, as it’s painfully easy to misread.

Ranking is a special case of matching that is (slightly) more amenable to answering via lists, since our minds are pretty good at detecting errors or anomalies in sequences. Give the learner several items and ask them to order them from fastest to slowest, most robust to most brittle, and so on. The former tends toward recall (e.g., recognizing the names of various sorting algorithms and knowing their properties), while the latter tends more toward reasoning and judgment.

Summarization also requires learners to use higher-order thinking, and gives them a chance to practice a skill that is very useful when reporting bugs rather than fixing them. For example, learners can be asked, “Which sentence best describes how the output of f changes as x varies from 0 to 10?” and then given several options as a multiple choice question.

You can also ask for very short free-form answers to questions in constrained domains, e.g., “What is the key feature of a stable sorting algorithm?” We still can’t fully automate checks for these without a frustrating number of false positives (accepting wrong answers) and false negatives (rejecting correct ones), but they lend themselves well to peer grading (s:individual-peer).

Automatic program grading tools have been around longer than I’ve been alive: the earliest published mention dates from 1960 Holl1960, and the surveys published in Douc2005,Ihan2010 mention many specific tools by name. Building such tools is a lot more complex than it might first seem. How are assignments represented? How are submissions tracked and reported? Can learners co-operate? How can submissions be executed safely? Edwa2014a is an entire paper devoted to an adaptive scheme for detecting and managing infinite loops and other non-terminating code submissions, and that’s just one of the many issues that comes up.

As elsewhere, it’s important to distinguish learner satisfaction from learning outcomes. Magu2018 switched informal programming labs to a weekly machine-evaluated test for a second-year CS course using an auto-grading tool originally developed for programming competitions. Learners didn’t like the automated system, but the overall failure rate for the course was halved, and the number of learners gaining first class honors tripled. In contrast, Rubi2014 also began to use an auto-grader designed for competitions, but saw no significant decrease in their learners’ dropout rates; once again, learners made some negative comments about the tool, which the authors attribute to its feedback messages rather than to dislike of auto-grading.

Srid2016 took a different approach. They used fuzz testing (i.e., randomly-generated test cases) to check whether learner code does the same thing as a reference implementation supplied by the teacher. In the first project of a 1400-learner introductory course, fuzz testing caught errors that were missed by a suite of hand-written test cases for more than 48% of learners, which clearly demonstrates its value.

Basu2015 gave learners a suite of solution test cases, but learners had to unlock each one by answering questions about its expected behavior before they were allowed to apply it to their proposed solution. For example, suppose learners are writing a function to find the largest adjacent pair of numbers in a list; before being allowed to use the tests associated with this question, they have to choose the right answer to, “What does largestPair(4, 3, -1, 5, 3, 3) produce?” (The correct answer is (5, 3).) In a 1300-person university course, the vast majority of learners chose to validate their understanding of test cases this way before attempting to solve problems, and then asked fewer questions and expressed less confusion about assignments.

It’s tempting to use off-the-shelf style checking tools to grade learners’ code. However, Nutb2016 initially found no correlation between human-provided marks and style-checker rule violations. Sometimes this was because learners violated one rule many times (thereby losing more points than they should have), and other times it was because they submitted the assignment starter code with few alterations and got more points than they should have.

Buff2015 presents a well-informed reflection on the whole idea of providing automated feedback. Their starting point is that, “Automated grading systems help learners identify bugs in their code, [but] may inadvertently discourage learners from thinking critically and testing thoroughly and instead encourage dependence on the teacher’s tests.” One of the key issues they identified is that a learner may thoroughly test their code, but the feature may still not be implemented according to the teacher’s specifications. In this case, the “failure” is not caused by a lack of testing, but by a misunderstanding of the requirements, and it is unlikely that more testing will expose the problem. If the auto-grading system doesn’t provide insightful, actionable feedback, this experience will only frustrate the learner.

In order to provide that feedback, Buff2015’s system identifies which method or methods of the learner’s code are executed by failing tests, so that the system can associate failed tests with particular features within the learner’s submission. The system decides whether specific hints have been “earned” by seeing whether the learner has tested the associated feature enough, so learners cannot rely on hints instead of doing tests.

Keun2016a,Keun2016b classified the messages produced by 69 auto-grading tools. They found that these often do not give feedback on how to fix problems and take the next step. They also found that most teachers cannot easily adapt most of the tools to their needs; like many workflow tools, they tend to enforce their creators’ unrecognized assumptions about how institutions work. Their work is ongoing, and their detailed classification scheme is a useful shopping list when looking at tools of this kind.

Srid2016 discussed strategies for sharing feedback with learners when automatically testing their code. The first is to provide the expected output for the tests—but then learners hard-code output for those inputs (because anything that can be gamed, will be). An alternative is to report the pass/fail results for the learners’ code, but only supply the actual inputs and outputs of the tests after the submission date. This can be frustrating, because it tells learners they are wrong, but not why.

A third option is to use a technique called hashing to generate a value that depends on the output, but doesn’t reveal it. If the user produces exactly the same output, its hash will be the same as the hash of the correct output, which will unlock the solution, but it is impossible to work backward from the hash to figure out what the output is supposed to be. Hashing is used to create digital signatures for documents, and requires a bit more work and explanation to set up, but strikes a good balance between revealing answers prematurely and not revealing them when it would help.

Higher-Level Thinking

Many other kinds of programming exercises are hard for teachers to assess in a class with more than few dozen learners, and equally hard for automated platforms to assess at all. Larger programming projects, or projects in which learners set their own goals, are (hopefully) what classes are building toward. Free-form discussion or twitch coding (s:performance-live) is also valuable, but also doesn’t scale.

Code review, on the other hand, is hard to grade automatically in the general case, but can be tackled if learners are given a rubric (e.g., a list of faults to look for) and asked to match particular comments against particular lines of code. For example, the learner can be told that there are two indentation errors and one bad variable name, and asked to point them out; if she is more advanced, she could be given half a dozen kinds of remarks she could make about the code without guidance as to how many of each she should find.

Steg2016b is a good starting point for a code style rubric, while Luxt2009 looks at peer review in programming classes more generally. If you are going to have students do reviews, use calibrated peer review (s:individual-peer) so that they have models of what good feedback should look like.

Code Review

Using the rubric provided, mark each line of the code below.

01)  def addem(f):
03)      x2 = [x for x in x1 if x.strip()]
04)      changes = 0
05)      for v in x2:
06)          print('total', total)
07)          tot = tot + int(v)
08)      print('total')

1. poor variable name
2. unused variable
3. use of undefined variable
4. missing return value

Exercises

Code and Run (pairs/10)

Create a short C&R exercise; trade with a partner, and see how long it takes each of you to understand and do the other’s exercise. Were there any ambiguities or misunderstandings in the exercise description?

Inverting Code and Run (small groups/15)

Form groups of 4–6 people. Have each member of the group create an inverted C&R exercise that requires people to figure out what input produces a particular output. Pick two at random, and see how many different inputs the group can find that satisfy the requirements.

Tracing Values (pairs/10)

Write a short program (10–15 lines); trade with a partner, and trace how the variables in the program change value over time. What differences are there in how you and your partner wrote down your traces?

Refactoring (small groups/15)

Form groups of 3–4 people. Have each person select a short piece of code (10–30 lines long) that they have written that isn’t as tidy as it could be. Choose one at random, and have everyone in the group tidy it up independently. How do your cleaned-up versions differ? How well or how poorly would you be able to accommodate all of these variations if marking automatically or in a large class?

Labelling a Diagram (pairs/10)

Draw a diagram showing something that you have explained recently: how browsers fetch data from servers, the relationship between objects and classes, or how data frames are indexed in R. Put the labels on the side, and ask your partner to place them.

Pencil-and-Paper Puzzles (whole class/15)

Butl2017 describes a set of pencil-and-paper puzzles that can be turned into introductory programming assignments, and found that these assignments are enjoyed by students and encourage meta-cognition. Think of a simple pencil-and-paper puzzle or game you played as a child, and describe how you would turn it into a programming exercise.

Counting Failures (pairs/15)

Any useful estimate of how much time an exercise needs must take into account how frequent failures are and how much time is lost to them. For example, editing text files seems like a simple task, but what about finding those files? Most GUI editors save things to the user’s desktop or home directory; if the files used in a course are stored somewhere else, a substantial fraction won’t be able to navigate to the right directory without help. (If this seems like a small problem to you, please revisit the discussion of expert blind spot in s:memory.)

Working with a partner, make a list of “simple” things you have seen go wrong in exercises you have used or taken. How often do they come up? How long do they take learners to fix on their own, or with help? How much time do you currently budget in class to deal with them?