The Case for Computation

In this series’ first essay, I make the case that there are two kinds of computer-based projects, digital and computational ones. I assert that the greatest educational value is to be found in computational projects. Surely, computational projects require experiences and skill development too often unavailable to students.
Our focus needs to be expanding the breadth, range, and depth of possible projects accessible to students. Therefore, a strong case can be made for adding computation to the educational diet of children. My paper, A New Paradigm for Evaluating the Learning Potential of an EdTech Activity , supports that argument without specifying computation as the secret ingredient.
The 1989 National Council of Teachers of Mathematics Standards made a stunning claim that “50% of all mathematics has been invented since World War II.” Common sense suggests that percentage has only increased in the intervening years. Educators should possess an insatiable desire to find new things for more kids to know in new ways.
Such new branches of mathematics are the result of two phenomena:
- The social science’s demand for number in a society awash in data
- Computation
That overlooked statement by the NCTM is no mere factoid, but rather a challenge, and urgent plea to reinvent the life of the classroom. Educators should possess an insatiable desire to find new things for more kids to know in new ways.
The realization that the world is changing rapidly and blessing us with new learning adventures motivates me to expect more of myself and my students.

New mathematical disciplines, including cellular automata, fractal geometry, number theory, information theory, combinatorics, cryptography, data science, as well as practical applications of computation like robotics, computer programming, physical computing, and artificial intelligence are now accessible to children. Their newness does not relegate them to post-graduate study. One need not endure 12-16 years of an asparagus diet before enjoying dessert.
This is the powerful idea behind Papert’s metaphorical Mathland, a “place” where mathematical fluency, power, meaning, and relevance comes as naturally as learning to speak French by growing up in France. Computation allows children to be mathematicians, rather than be taught a rigid sequence of tricks called “Math.”

Shoe-ber
Seven or eight years ago, a group of educators attending the Constructing Modern Knowledge (CMK) summer institute had an idea to invent a pair of shoes that when the heels were clicked together, a taxi would arrive.
In a traditional classroom setting, such fanciful ideas would result in a poster board or brochure displayed during a school’s “Invention Convention.” The teacher’s emphasis might be on entrepreneurship or oral presentation or desktop publishing, because realizing such a complex invention is out of reach.
Well, that may not be the case. We begin CMK by asking, “What do you want to make?” and take that question seriously as a provocation worth pursuing, regardless of the outcome.
A fellow participant offered a key bit of information. “The API for Uber is freely available,” they said. With that, a microcontroller, some craft supplies, a programming language, sufficient time, and a supportive culture, Shoe-ber was operational within just a few days!
Projects such as Shoe-ber and Papert’s stance creates all sorts of cognitive dissonance among the fans of taxonomies, literal interpretations of stage theory, and nonsense such as explicit direct instruction.
In this scenario and countless others, computation is what liberates fantastical ideas and transforms them into reality. Abstractions are concretized. The ceiling on human potential is elevated.

"If you remember rightly, the essence of the New Math was to say, let's make mathematics more rigorous, more formal, and we'll prove things. We'll have kids knowing rules. What it did was to take pure mathematics and make it even purer and what I'm going to suggest is that the right direction to go is to make it more applied – to connect it with real world problems." (Seymour Papert, 2005)
If mathematics is a way of making sense of the world, computation is a way of making mathematics. Whether you call it mathematical thinking, computational thinking, computing, computation, or computational making, there is an expanding universe of possible things to do and problems to solve.
The Benefits of Computation
- Learning to describe complex phenomena through formal representations
- Computation may be used produce action
- Makes project-based learning possible in math
- Embraces “hard fun”
- Models thinking as a generative process
- Creates opportunities for debugging
- Makes interactivity possible
- Bestows agency on the learner
- Amplifies our potential by making the computer working for us instead of us working for the computer
- Sustains democracy by preparing learners to think critically, anticipate multiple consequences, expect transparency, and develop what Weingarten and Postman called a highly tuned BS detector

Computational X, in Wolfram’s terms, not only represents the frontiers of every discipline, but the more interesting and potentially lucrative branches of those domains.
Developing a learner’s computational fluency prepares them to navigate an increasingly complex, technologically sophisticated, and uncertain future.
The first essay in this series introduces the paradigm of digital vs. computational projects. The following table (over) simplifies these distinctions in terms of the types of computer use found in schools.
Digital | Computational |
writing | computer programming |
drawing | robotics |
animation | modeling and simulation |
photography | data science |
multimedia presentations | computer-aided design (CAD) |
podcasting | fabrication |
video production | *music composition |
desktop publishing |
*Music composition may arguably belong in either column although it feels a lot like computation in my head.
Sometimes schools head fake towards computation while merely using digital technology to create a patina of innovation. The result is a curriculum left intact and zero evidence of progress.
Dr. Papert rightfully dismisses such incremental stunts.

Districts declare STEAM Day and have families color illustrations of scientists, or instruct kids to make propagandistic posters about grit.
“Let’s do Hour of Code in 45 minutes!” Let’s make the 1st grade “Digitech” curriculum about memorizing definitions of binary or pretend that making an imaginative sandwich is an application of algorithms.
Such Potemkin efforts waste time, deprive kids of richer experiences, reinforce the status quo, and insult our intelligence.
A New Standard
The project should be a teacher’s smallest unit of concern. All teaching should be focused on creating rich experiences for children, recognizing the Piagetian ideal that “knowledge is a consequence of experience.”
Rather than concerning ourselves with grading, ranking, or sorting students, a teacher’s focus should be on creating productive contexts for learning in which rich provocations and materials exist for all children to engage in personally meaningful project work.
Within that context, I find teaching to be most rewarding and delightful when students surprise me. Therefore, I humbly suggest a new aspirational “standard.”
The Stager Standard for project-based learning aspires for 10% of students to create something “interesting” and 5% doing something original that never occurred to the teacher or would astound curriculum writers.
This standard is much more attainable when computation is involved.
If you are looking for a collection of computational software environments for learners, you may find it here. However, no list would be complete without the remarkable new Wolfram Notebook Assistant, an environment in which you may interact in natural language with some of the most powerful computational system ever created.
The next essay in this series, Computation Makes Learning Visible, explores how computation makes thinking visible.
<– Read part one of this series. Read part three of this series — >