Posts tagged ‘learning sciences’
I enjoy reading “Gas station without pumps,” and the below-quoted post was one I wanted to respond to.
Two of the popular memes of education researchers, “transferability is an illusion” and “the growth mindset”, are almost in direct opposition, and I don’t know how to reconcile them.
One possibility is that few students actually attempt to learn the general problem-solving skills that math, CS, and engineering design are rich domains for. Most are content to learn one tiny skill at a time, in complete isolation from other skills and ideas. Students who are particularly good at memory work often choose this route, memorizing pages of trigonometric identities, for example, rather than learning how to derive them at need from a few basics. If students don’t make an attempt to learn transferable skills, then they probably won’t. This is roughly equivalent to claiming that most students have a fixed mindset with respect to transferable skills, and suggests that transferability is possible, even if it is not currently being learned.
Teaching and testing techniques are often designed to foster an isolation of ideas, focusing on one idea at a time to reduce student confusion. Unfortunately, transferable learning comes not from practice of ideas in isolation, but from learning to retrieve and combine ideas—from doing multi-step problems that are not scaffolded by the teacher.
The problem with “transferability” is that it’s an ill-defined term. Certainly, there is transfer of skill between domains. Sharon Carver showed a long time ago that she could teach debugging Logo programs, and students would transfer that debugging process to instructions on a map (mentioned in post here). That’s transferring a skill or a procedure. We probably do transfer big, high-level heuristics like “divide-and-conquer” or “isolate the problem.” One issue is whether we can teach them. John Sweller says that we can’t — we must learn them (it’s a necessary survival skill), but they’re learned from abstracting experience (see Neil Brown’s nice summary of Sweller’s SIGCSE keynote).
Whether we can teach them or not, what we do know is that higher-order thinking is built on lots of content knowledge. Novices are unlikely to transfer until they know a lot of stuff, a lot of examples, a lot of situations. For example, novice designers often have “design fixation.” They decide that the first thing they think of must be the right answer. We can insist that novice designers generate more designs, but they’re not going to generate more good designs until they know more designs. Transfer happens pretty easily when you know a lot of content and have seen a lot of situations, and you recognize that one situation is actually like another.
Everybody starts out learning one tiny skill at a time. If you know a lot of skills (maybe because you have lots of prior experience, maybe because you have thought about these skills a lot and have recognized the general principles), you can start chunking these skills and learning whole schema and higher-level skills. But you can’t do that until you know lots of skills. Students who want to learn one tiny skill at a time may actually need to still learn one tiny skill at a time. People abstract (e.g., able to derive a solution rather than memorize it) when they know enough content that it’s useful and possible for them to abstract over it. I completely agree that students have to try to abstract. They have to learn a lot of stuff, and then they have to be in a situation where it’s useful for them to abstract.
“Growth mindset” is a necessity for any of this to work. Students have to believe that content is worth knowing and that they can learn it. If students believe that content is useless, or that they just “don’t do math” or “am not a computer person” (both of which I’ve heard in just the last week), they are unlikely to learn content, they are unlikely to see patterns in it, and they are unlikely to abstract over it.
Kevin is probably right that we don’t teach problem solving in engineering or computing well. I blogged on this theme for CACM last month — laboratory experiments work better for a wider range students than classroom studies. Maybe we teach better in labs than in classrooms? The worked examples effect suggests that we may be asking students to problem solve too much. We should show students more completely worked out problems. As Sweller said at SIGCSE, we can’t expect students to solve novel problems. We have to expect students to match new problems to solutions that they have already seen. We do want students to solve problems, too, and not just review example solutions. Trafton and Reiser showed that these should be interleaved: Example, Problem, Example, Problem… (see this page for a summary of some of the worked examples research, including Trafton & Reiser).
When I used to do Engineering Education research, one of my largest projects was a complete flop. We had all this prior work showing the benefits of a particular collaborative learning technology and technique, then we took it into the engineering classroom and…poof! Nothing happened. In response, we started a project to figure out why it failed so badly. One of our findings was that “learned helplessness” was rampant in our classes, which is a symptom of a fixed mindset. “I know that I’m wrong, and there’s nothing that I can do about it. Collaboration just puts my errors on display for everyone,” was the kind of response we’ve got. (See here for one of our papers on this work.)
I believe that all the things Kevin sees going wrong in his classes really are happening. I believe he’s not seeing transfer that he might reasonably expect to see. I believe that he doesn’t see students trying to abstract across lower-level skills. But I suspect that the problem is the lack of a growth mindset. In our work, we saw Engineering students simply give up. They felt like they couldn’t learn, they couldn’t keep up, so they just memorized. I don’t know that that’s the cause of the problems that Kevin is seeing. In my work, I’ve often found that motivation and incentive are key to engagement and learning.
I was at the Learning and Teaching in Computing Education (LaTICE 2016) conference in Mumbai in early April. It was one of my most memorable and thought-provoking trips. I have had few experiences in Asia, and none in India, so I was wide-eyed with amazement most of my time there. (Most of the pictures that I am including in this series of blog posts are mine or come from the LaTICE 2016 gallery.)
I was invited to join discussants at the LaTICE Doctoral Consortium on the day before the conference. LaTICE was hosted at IIT-Bombay, and IIT-Bombay is home to the Inter-disciplinary Program in Educational Technology (see link here). The IPD-ET program is an impressive program. Only five years old, it already has 20 PhD students. The lead faculty are Sahana Murthy and Sridhar Iyer who are guiding these students through interesting work. (Below picture shows Sahana with the DC co-chairs, Anders Berglund from Uppsala University and Tony Clear from Auckland University of Technology.) The Doctoral Consortium had students from across India and one from Germany. Not all were IDP-ET students, but most were.
Talking to graduate students was my main activity at LaTICE 2017. Aman Yadav (from Michigan State, in the back of the below picture) and I missed a lot of sessions as we met with groups of students. I don’t think I met all the IDP-ET students, but I met many of them, and wrestled with ideas with them. I was pleased that students didn’t just take me at my word — they asked for explanations and references. (I ripped out half of the pages of my notebook, handing out notes with names of papers and researchers.) I feel grateful for the experience of hearing about so many varied projects and to talk through issues with many students.
I’m going to take my blog writer’s prerogative to talk about some of the IDP-ET students’ work that I’ve been thinking about since I got back. I’m not claiming that this is the best work, and I do offer apologies to the (many!) students whose work I’m not mentioning. These are just the projects that keep popping up in my (still not sleeping correctly) brain.
Aditi Kothiyal is interested in how engineers estimate. Every expert engineer does back-of-the-envelope estimation before starting a project. It’s completely natural for them. How does that develop? Can we teach that process to students? Aditi has a paper at the International Conference of the Learning Sciences this year on her studies of how experts do estimation. I find this problem interesting because estimation might be one of those hard-to-transfer higher-order thinking skills OR it could be a rule-of-thumb procedure that could be taught.
Shitanshu Mishra is exploring question-posing as a way to encourage knowledge integration. He’s struggling with a fascinating set of issues. Question-posing is a great activity that leads to learning, but is practiced infrequently in classroom, especially by the students who need it the most. Shitanshu has developed a guided process (think the whiteboards in Problem-Based Learning, or classroom rituals in Janet Kolodner’s Learning-By-Design, or Scardamalia & Bereiter’s procedural facilitation) which measurably helps students to pose good questions that encourage students to integrate knowledge. When should he guide students through his question-posing process? Is it important that students use his process on their own?
Yogendra Pal is asking a question that is very important in India whose answer may also be useful here in the US: How do you help students who grew up in a non-English language in adapting to English-centric CS? India’s constitution recognizes 22 languages, and has 122 languages spoken by many Indian citizens on a daily basis. Language issues are core to the Indian experience. CS is very English-centric, from the words in our programming languages, to the technical terms that don’t always map to other languages. Yogendra is working with students who only spoke Hindi until they got to University, where they now want to adapt to English, the language of the Tech industry. I wonder if Yogendra’s scaffolding techniques would help children of immigrant families in the US succeed in CS.
Rwitajit Majumdar is developing visualizations to track student behavior on questions over time. Originally, he wanted to help teachers get a sense of how their students move towards a correct understanding over multiple questions during Peer Instruction. Now, he’s exploring using his visualizations with MOOC data. I’m interested in his visualizations for our ebooks. He’s trying to solve an important problem. It’s one thing to know that 35% of the students got Problem #1 right, and 75% got (similar) Problem #2 right. But is it the same 25% of students who got both wrong? What percentage of students are getting more right, and are there any that are swapping to more wrong answers? Tracking students across time, across problems is an important problem.
Overall, the LaTICE conference was comparable to SIGCSE or ITiCSE. It was single track, though it’s been dual-track at some instances. LaTICE is mostly a practitioner’s conference, with a number of papers saying, “Here’s what I’m doing in my class” without much evaluation. I found even those interesting, because many were set in contexts that were outside my experience. There are some good research papers. And there are some papers that said some things that I felt were outright wrong. But because LaTICE is a small (< 200 attendees, I’d guess) and collegial conference, I had one-on-one conversations with all the authors with whom I disagreed (and many others, as well!) to talk through issues.
My keynote was based on my book, Learner-Centered Design of Computing Education: Research on Computing for Everyone. I talked about why it’s important to provide computing education to more than computing majors, and how computing education would have to change for different audiences. Slides are here: http://www.slideshare.net/markguzdial/latice-2016-learnercentered-design-of-computing-education-for-all
The most remarkable part of my trip was simply being in India. I’ve never been any place so crowded, so chaotic, so dirty, and so vibrant. I felt like I took my life in my hands whenever I crossed the street after noon on any day (and given the pedestrian accidents that some conference participants reported seeing, including one possible fatality, I likely was taking a risk). I went out for three runs around Mumbai and across campus (only in the morning when the traffic was manageable) and enjoyed interactions with cows and monkeys. I was shocked at the miles and miles of slums I saw when driving around Mumbai. I got stuck on one side of a major street without any idea how I could possibly get through the crowds and traffic to the other side — on a normal Sunday night. The rich colors of the Indian clothing palette were beautiful, even in the poorest neighborhoods. There was an energy everywhere I went in Mumbai.
I’ve not experienced anything like Mumbai before. I certainly have a new sense of my own privilege — about the things I have that I never even noticed until I was somewhere where they are not given. Given that India has 1.2 billion people and the US only has some 320 million, I’m wondering about how I define “normal.”
In a recent blog post, I argued that problem-solving skills learned for solving problems in computational contexts (“computational thinking”) were unlikely to transfer to everyday situations (see post here). We see a similar pattern in the recent controversy about “brain training.” Yes, people get better at the particular exercises (e.g., people can learn to problem-solve better when programming). And they may still be better years later, which is great. That’s an indication of real learning. But they are unlikely to transfer that learning to non-exercise contexts. Most surprisingly, they are unlikely to transfer that learning even though they are convinced that they do. Just because you think you’re doing computational thinking doesn’t mean that you are.
Ten years later, tests showed that the subjects trained in processing speed and reasoning still outperformed the control group, though the people given memory training no longer did. And 60 percent of the trained participants, compared with 50 percent of the control group, said they had maintained or improved their ability to manage daily activities like shopping and finances. “They felt the training had made a difference,” said Dr. Rebok, who was a principal investigator.
So that’s far transfer — or is it? When the investigators administered tests that mimicked real-life activities, like managing medications, the differences between the trainees and the control group participants no longer reached statistical significance.
In subjects 18 to 30 years old, Dr. Redick also found limited transfer after computer training to improve working memory. Asked whether they thought they had improved, nearly all the participants said yes — and most had, on the training exercises themselves. They did no better, however, on tests of intelligence, multitasking and other cognitive abilities.
I facilitated a breakout group at the Dagstuhl Seminar on Assessment in Introductory Computer Science. We started talking about what students know and should know, and several of us started using terms like “notional machines” and “mental models” — and there were some strong disagreements. We decided to have a breakout group to define our terms, and came up with a fascinating set of issues and questions. It was a large group (maybe a dozen?), and I think there were some differences in attendance between the two days, so I’m not going to try to list everyone here.
We agreed on the definition of a notional machine (NM) as a set of abstractions that define the structure and behavior of a computational device. A notional machine includes a grammar and a vocabulary, and is specific to a programming paradigm. It’s consistent and predictive — given a notional machine and a program to run on that machine, we should be able to define the result. The abstract machine of a compiler is a possible notional machine. This definition meshes with duBoulay’s original one and the one that Juha Sorva used in his dissertation (which we could check, because Juha was there).
Note that a NM doesn’t include function. It doesn’t tell a user, “Why would I use this feature? What is it for?” Carsten Shulte and Ashok Goel both found that students tend to focus on structure and behavior, and significant expertise is needed before students can discern function for a program or a NM component.
In CS education, we care about the student’s understanding of the notional machine. Mental model isn’t the right term for that understanding, because (for some) that implies a consistent, executable model in the student’s head. But modern learning science suggests that students are more likely to have “knowledge in pieces” (e.g., diSessa). Students will try to explain one program using one set of predictions about program behavior, and another program in another way. They respond to different programs differently When Michael Caspersen tried to replicate the Dehnadi and Bornat paper (Camel has two humps paper, and its retraction), he found that students would use one rule set for interpreting assignment in part of the test, and another set of rules later — and they either didn’t care or didn’t notice that they were inconsistent.
An early form of student understanding of the NM is simply mimicry. “I saw the teacher type commands like this. So if I repeat them exactly, I should get the same behavior.” As they start to realize that the program causes behavior, cognitive load limits how much of the NM students can think about at once. They can’t predict as we would like them to, simply because they can’t think about all of the NM components and all of the program at once. The greatest challenge to understanding the NM is Roy Pea’s Superbug — the belief that the computer is in fact a human-like intelligent agent trying to discern our intentions.
We define student misconceptions (about the NM) as incorrect beliefs about the notional machine that are reliable (the student will use more than once) and common (more than one student uses it). There are lots of misunderstandings that pop up, but those aren’t interesting if they’re not common and reliable. We decided to avoid the “alternative conception” model in science education because, unlike natural science, we know ground truth. CS is a science of the artificial. We construct notional machines. Conceptions are provably correct or incorrect about the NM.
One of the challenging aspects of student understandings of NM is that our current evidence suggests that students never fix existing models. We develop new understandings, and learn new triggers/indices when to apply these understandings. Sometimes we layer new understandings so deeply that we can’t reach the old ones. Sometimes, when we are stressed or face edge/corner conditions, we fall back on previous understandings. We help students develop new understandings by constraining their process to an appropriate path (e.g., cognitive tutors, cognitive apprenticeship) or by providing the right contexts and examples (like in Betsy Davis’s paper with Mike Clancy Mind your P’s and Q’s).
Where do misconceptions come from?
We don’t know for sure, but we have hypotheses and research questions to explore:
- We know that some misconceptions come from making analogies to natural language.
- Teaching can lead to misconceptions. Sometimes it’s a slip of the tongue. For example, students often confuse IF and WHILE. How often do we say (when tracing a WHILE) loop, “IF the expression is true…” Of course, the teacher may not have the right understanding.Research Question (RQ): What is intersection between teacher and student misconceptions? Do teacher misconceptions explain most student misconceptions, or do most student misconceptions come from factors outside of teaching?
- Under-specification. Students may simply not see enough contexts or examples for them to construct a complete understanding.
- Students incorrectly applying prior knowledge. RQ: Do students try to understand programs in terms of spreadsheets, the most common computational model that most students see?
- Notation. We believe that = and == do lead to to significant misconceptions. RQ: Do Lisp’s set, Logo’s make/name, and Smalltalk’s back arrow lead to fewer assignment misconceptions? RQ: Dehnadi and Bornat did define a set of assignment misconceptions. How common are they? In what languages or contexts?
RQ: How much do students identify their own gaps in understanding of a NM (e.g., edge conditions, problem sets that don’t answer their questions)? Are they aware of what they don’t understand? How do they try to answer their questions?
One advantage of CS over natural sciences is that we can design curriculum to cover the whole NM. (Gail Sinatra was mentioned as someone who has designed instruction to fill all gaps in a NM.) Shriram Krishnamurthi told us that he designs problem-sets to probe understanding of the Java notional machine that he expects students to miss, and his predictions are often right.
RQ: Could we do this automatically given a formal specification for an NM? Could we define a set of examples that cover all paths in a NM? Could we develop a model that predicts where students will likely develop misconceptions?
RQ: Do students try to understand their own computational world (e.g., how behavior in a Web page works, how an ATM works, how Web search works) with what we’re teaching them? Kathi Fisler predicts that they rarely do that, because transfer is hard. But if they’re actively trying to understand their computational world, it’s possible.
How do we find and assess gaps in student understanding?
We don’t know how much students think explicitly about a NM. We know from Juha’s work that students don’t always see visualizations as visible incarnations of the NM — for some students, it’s just another set of confusing abstractions.
Carsten Schulte pointed out that Ira Diethelm has a cool way of finding out what students are confused about. She gives them a “miracle question” — if you had an oracle that knew all, what one question would you ask about how the Internet works, or Scratch, or Java? Whatever they say — that’s a gap.
RQ: How we define the right set of examples or questions to probe gaps in understanding of a NM? Can we define it in terms of a NM? We want such a set to lead to reflection and self-explanation that might lead to improved understanding of the NM.
Geoffrey Herman had an interesting way of finding gaps in NM understanding: using historical texts. Turns out Newton used the wrong terms for many physical phenomena, or at least, the terms he used were problematic (“momentum” for both momentum and velocity) and we have better, more exact ones today. Terms that have changed meaning or have been used historically in more than one way tend to be the things that are hard to understand — for scholars past, and for students today.
State is a significant source of misconceptions for students. They often don’t differentiate input state, output state, and internal states. Visualization of state only works for students who can handle those kinds of abstractions. Specification of a NM through experimentation (trying out example programs) can really help if students see that programs causally determine behavior, and if they have enough cognitive load to computer behavior (and emergent behavior is particularly hard). System state is the collection of smaller states, which is a large tax on cognitive load. Geoffrey told us about three kinds of state problems: control state, data state, and indirection/reference state.
State has temporality, which is a source of misconceptions for students, like the common misconception that assignment states define a constraint, not an action in time. RQ: Why? Raymond Lister wondered about our understanding of state in the physical world and how that influences our understanding of state in the computational world. Does state in the real world have less temporality? Do students get confused about temporality in state in the physical world?
Another source of misconceptions is state in code, which is always invisible. The THEN part of an IF has implicit state — that block gets executed only if the expression is true. The block with a loop is different than the block after a condition (executed many times, versus once) but look identical. RQ: How common are code state misconceptions?
Scratch has state, but it’s implicit in sprites (e.g., position, costume). Deborah Fields and Yasmin Kafai found that students didn’t use variables much in state, but maybe because they didn’t tackle problems that needed them. RQ: What kinds of problems encourage use of state, and better understanding of state?
RQ: Some functional curricula move students from stateless computation to stateful computation. We don’t know if that’s easier. We don’t know if more/fewer/different misconceptions arise. Maybe the reverse is easier?
RQ: When students get confused about states, how do they think about? How do they resolve their gaps in understanding?
RQ: What if you start students thinking about data (state) before control? Most introductory curricula start out talking about control structures. Do students develop different understanding of state? Different misconceptions? What if you start with events (like in John Pane’s HANDS system)?
RQ: What if you teach different problem-solving strategies? Can we problematize gaps in NM understanding, so that students see them and actively try to correct them?
SIGCSE 2016 Preview: Parsons Problems and Subgoal Labeling, and Improving Female Pass Rates on the AP CS exam
Our research group has two papers at this year’s SIGCSE Technical Symposium.
Subgoals help students solve Parsons Problems by Briana Morrison, Lauren Margulieux, Barbara Ericson, and Mark Guzdial. (Thursday 10:45-12, MCCC: L5-L6)
This is a continuation of our subgoal labeling work, which includes Lauren’s original work showing how subgoal labels improved learning, retention and transfer in learning App Inventor (see summary here), the 2015 ICER Chairs Paper Award-winning paper from Briana and Lauren showing that subgoals work for text languages (see this post for summary), and Briana’s recent dissertation proposal where she explores the cognitive load implications for learning programming (see this post for summary). This latest paper shows that subgoal labels improve success at Parson’s Problems, too. One of the fascinating results in this paper is that Parson’s Problems are more sensitive as a learning assessment than asking students to write programs.
Sisters Rise Up 4 CS: Helping Female Students Pass the Advanced Placement Computer Science A Exam by Barbara Ericson, Miranda Parker, and Shelly Engelman. (Friday 10:45-12, MCCC: L2-L3)
Barb has been developing Project Rise Up 4 CS to support African-American students in succeeding at the AP CS exam (see post here from RESPECT and this post here from last year’s SIGCSE). Sisters Rise Up 4 CS is a similar project targeting female students. These are populations that have lower pass rates than white or Asian males. These are examples of supporting equality and not equity. This paper introduces Sisters Rise Up 4 CS and contrasts it with Project Rise Up 4 CS. Barb has resources to support people who want to try these interventions, including a how-to ebook at http://ice-web.cc.gatech.edu/ce21/SRU4CS/index.html and an ebook for students to support preparation for the AP CS A.
I’m looking forward to these results! That interaction is better than video lectures is really not surprising. That it leads to better learning than even reading is quite a surprise. My guess is that this is mediated by student ability as a reader, but as a description of where students are today (like the prior posts on active learning), it’s a useful result.
Koedinger and his team further tested whether their theory that “learning by doing” is better than lectures and reading in other subjects. Unfortunately, the data on video watching were incomplete. But they were able to determine across four different courses in computer science, biology, statistics and psychology that active exercises were six times more effective than reading. In one class, the active exercises were 16 times more effective than reading. (Koedinger is currently drafting a paper on these results to present at a conference in 2016.)
Blog Post #2000: Barbara Ericson Proposes: Effectiveness and Efficiency of Adaptive Parsons Problems #CSEdWeek
My 1000th blog post looked backward and forward. This 2000th blog post is completely forward looking, from a personal perspective. Today, my wife and research partner, Barbara Ericson, proposes her dissertation.
Interesting side note: One of our most famous theory professors just blogged on the theory implications of the Parsons Problems that Barb is studying. See post here.
Barb’s proposal is the beginning of the end of this stage in our lives. Our youngest child is a senior in high school. When Barbara finishes her Human-Centered Computing PhD (expected mid-2017), we will be empty-nesters and ready to head out on a new adventure.
Title: EVALUATING THE EFFECTIVINESS AND EFFICIENCY OF PARSONS PROBLEMS AND DYNAMICALLY ADAPTIVE PARSONS PROBLEMS AS A TYPE OF LOW COGNITIVE LOAD PRACTICE PROBLEM
Barbara J. Ericson
Human Centered Computing
College of Computing
Georgia Institute of Technology
Date: Wednesday, December 9, 2015
Time: 12pm to 2pm EDT
Location: TSRB 223
Dr. James Foley, School of Interactive Computing (advisor)
Dr. Amy Bruckman, School of Interactive Computing
Dr. Ashok Goel, School of Interactive Computing
Dr. Richard Catrambone, School of Psychology
Dr. Mitchel Resnick, Media Laboratory, Massachusetts Institute of Technology
Learning to program can be difficult and can result in hours of frustration looking
for syntactic or semantic errors. This can make it especially difficult to prepare inservice
(working) high school teachers who don’t have any prior programming
experience to teach programming, since it requires an unpredictable amount of time for
practice in order to learn programming. The United States is trying to prepare 10,000
high school teachers to teach introductory programming courses by fall 2016. Most
introductory programming courses and textbooks rely on having learners gain experience
by writing lots of programs. However, writing programs is a complex cognitive task,
which can easily overload working memory, which impedes learning.
One way to potentially decrease the cognitive load of learning to program is to
use Parsons problems to give teachers practice with syntactic and semantic errors as well
as exposure to common algorithms. Parsons problems are a type of low cognitive load
code completion problem in which the correct code is provided, but is mixed up and has
to be placed in the correct order. Some variants of Parsons problems also require the
code to be indented to show the block structure. Distractor code can also be provided
that contains syntactic and semantic errors.
In my research I will compare solving Parsons problems that contain syntactic and
semantic errors, to fixing code with the same syntactic and semantic errors, and to writing
the equivalent code. I will examine learning from pre- to post-test as well as student
reported cognitive load. In addition, I will create dynamically adaptive Parsons problems
where the difficulty level of the problem is based on the learners’ prior and current
progress. If the learner solves one Parsons problem in one attempt the next problem will
be made more difficult. If the learner is having trouble solving a Parsons problem the
current problem will be made easier. This should enhance learning by keeping the
problem in the learner’s zone of proximal development as described by Vygotsky. I will
compare non-adaptive Parsons problems to dynamically adaptive Parsons problems in
terms of enjoyment, completion, learning, and cognitive load.
The major contributions of this work are a better understanding of how variants of
Parsons problems can be used to improve the efficiency and effectiveness of learning to
program and how they relate to code fixing and code writing. Parsons problems can help
teachers practice programming in order to prepare them to teach introductory computer
science at the high school level and potentially help reduce the frustration and difficulty
all beginning programmers face in learning to program.