Math for Computer Science: Breaking down barriers to early computer science education


Eric Bennett, M.Ed., directs
Future Set Tech Camp, where creativity meets technology in project-based STEM summer camps, Saturday workshops, and after-school programs. He joins us on the blog to explain why he created a free online Math for Computer Science course for kids.

The idea that elementary-aged children will benefit from a course on a buzzy programming language is certainly appealing to well-intentioned parents: understanding the world around us increasingly means understanding technology; jobs in software engineering and information technology are both high-paying and in-demand; many children are naturally curious about technology. The problem with this idea is that writing even the most basic computer program requires an understanding of math concepts beyond the scope of a typical elementary curriculum. If students lack this math knowledge, computer science instruction will not have the intended benefit: students might be able to copy an instructor’s code but will not understand how it works or be able to produce code of their own.

Since math is used so extensively in computer science, is it possible that students will learn it through the process of writing a computer program or developing a video game? While the notion of learning math through games or in the context of a fun project is seductive, the reality is that mathematics is best learned through structured practice. Procedural fluency, as it is termed by the National Council of Teachers of Mathematics (NCTM), is a critical component to teaching mathematics, and fluency is only developed through repetition. Creative applications such as coding or game development will certainly enhance a child’s understanding but cannot replace more rigorous instruction.


For these reasons, mathematics has often been used as a prerequisite for computer science courses: students are allowed to enroll in a computer science course only after completing a particular mathematics course. While this approach ensures that students are prepared to reap the benefits of a computer science course, it also creates a barrier to entry. Thus, whether students simply lack math knowledge or it is enforced as a prerequisite, the benefits of courses in computer programming and video game development are limited for many interested students. Two solutions to this problem are clear: the first would involve selecting computer science curriculum that does not require this math knowledge; the second would be to deliver targeted mathematics instruction to interested students.

Front-end web design involves HTML and CSS, both of which are markup languages rather than programming languages. Just as a word processor can be instructed to adjust font sizes, spacing, and alignment, markup languages can be used to add structure to the words on a web page. While numbers can be used to specify sizes, dimensions, and positions within these markup languages, they cannot be expressed as variables, expressions, or equations. Thus, HTML and CSS are an excellent introduction to computer science for elementary-aged students. However, because most of these students are more interested in creating a fun game than an informative website, this solution may not be ideal.

The math concepts involved in computer programming and video game development are typically taught to older students, so this content should be presented to elementary students in a different way. Visual models and manipulatives are often used to assist struggling students and are promoted by the NCTM for their effectiveness in teaching conceptual understanding. These techniques, then, should serve elementary students well in tackling more advanced math concepts. Additionally, in computer programming, calculations are made by the computer program rather than the computer programmer. For the purposes of computer science readiness, then, tedious fraction and decimal arithmetic can be pushed aside in favor of integer operations and more abstract concepts like variables and variable expressions. For an example of a curriculum constructed according to these principles, check out Future Set Tech Camp’s Math for Computer Science, a free online course.

Rather than using mathematics as a barrier to entry, closing the door to many interested students, we can use computer science to motivate these students to learn specific, carefully presented math concepts. With so many children naturally drawn to technology and our job market’s demand for computer science skills stronger than ever, there are clear benefits in delivering computer science education to elementary-aged students. With the right mathematics and computer science curriculum, these benefits can be fully realized.

Eric Bennett

Austin’s STEM schools are fueled by kids’ and educators’ natural curiosity

The technology and engineering sectors are producing valuable jobs in Austin and the rest of the nation, and, perhaps as a result, a growing number of parents want to encourage a love of science and mathematics in their children. It makes sense that we’re seeing more and more schools promoting Science, Technology, Engineering, and Math (STEM) curricula. STEM courses and camps are popular in public and private schools, but as you might expect, the alternative schools in Austin offer some special twists. To learn more, I talked with local innovators who are taking STEM in new directions: Rebeca Guerrero and Dorothy and Kori McLain.

Geologists rock on at Copernicus.

Geologists rock on at Copernicus.

It’s important to be able to take a radio apart, and not get scolded!
—Rebeca Guerrero, Copernicus STEM, Language and Arts Academy

Rebeca Guerrero’s warm and supportive preschool, Copernicus STEM, Language and Arts Academy, has served children age 18 months to 5 years for the past two years.

Rebeca is a scientist herself, with a decade of experience as a microbiologist. When she realized that most young people today leave high school and head for college believing that science is too hard to master, and only for the smartest kids, she knew she had to try to make some changes. Rebeca’s own mother encouraged her to take an interest in the world and to ask questions and explore when she was very young. “As someone who used to take radios apart for fun, with my mother’s help, it was a shocking revelation that so many students are intimidated by science.”  

Invertebrates are awesome. (Copernicus)

Invertebrates are awesome. (Copernicus)

Rebeca moved into teaching and then, when her son was born a few years ago, decided to open her own preschool, allowing them to spend time together, playing and learning with other children. In the fall of 2015, Copernicus Academy started with four students, soon grew to 20, and today has about 50. The preschool combines STEM-focused play with learning in English and Spanish.

“Most of our kids speak English at home, but we have also had children who speak Korean and Farsi.” Parents at Copernicus understand the value of a bilingual education, says Rebeca, but “more than anything, families are looking for a place where kids can grow and feel supported emotionally.” With that supportive base, Copernicus educators pursue play-based learning with intention, making sure the students have experiences that spark a love of the natural world. For example, kids might spend a month learning about the solar system, including Earth’s rotation, the moon’s phases, integrating art and reading into their projects.

On an average day, you might find kids at Copernicus perfecting catapults made out of spoons, cooperating, experimenting, and showing off what they’ve done by launching pompoms. The usual routine includes time in the sun room or outside, snacks, small-group play, centers, and circle time. The staff joins in games and activities, asking questions but never telling the children what or how to play. And then there’s the music: “We sing and have dance parties every day,” says Rebeca. “We want to make sure that later in life they will say: ‘Science is not boring, it’s fun! Science is not for someone else—science is for me.’”


LTSA students on a NASA field trip.

LTSA students on a NASA field trip.

Everything is connected in our studies at LTSA,
like everything in our world is connected and integrated.

—Dorothy McLain, Lake Travis Stem Academy

At Lake Travis Stem Academy (LTSA), founder Kori McLain was not only inspired by her mother, she recruited her. Dorothy McLain spent most of her career as a college educator specializing in English composition and literature. Now she and Kori and the rest of the LTSA team are preparing about 25 students in Kindergarten through 9th grade for the 21st century, with a curriculum integrating STEM, critical thinking, and experiential learning. LTSA is now working on a partnership with UT High School that will allow older students to continue on at Lake Travis while benefitting from the resources the larger school can offer.

Dorothy has always believed in an interdisciplinary approach to learning. “It’s important to become well-rounded,” she says, citing a recent project in which middle-schoolers learned about the history, economics, politics, and culture of the Great Depression by writing and staging a three-act musical play.

Inspiration. (LTSA)

Inspiration. (LTSA)

“We are both experiential and project-based,” Dorothy explains. Students are engaged in hands-on, real-world activities that give them the opportunity to collaborate with each other and with outside experts to come up with solutions to problems or answer questions. At the end of each unit, instead of a traditional exam, students present their findings to the rest of the school and to the experts who have helped them. “They’re able to share their ideas with the rest of the community and have to think on their feet when the audience asks surprising questions!”

“We learn more from our failures than our successes,” adds Kori. If a model airplane a team has created doesn’t fly, then it’s back to the drawing board for more experiments. Just like in real life.

The overarching goals at both Copernicus and LTSA are to free the natural curiosity in each student and to keep them engaged and asking why? “They all see things around them and want to know more,” says Dorothy. “After that initial curiosity is aroused, we can then go deeper, encouraging them to think, ask more questions, and stay excited about learning.”

Shelley Sperry

Computer science is integral to a strong education

Lisa Zapalac is one of the co-owners of Long-View Micro School, an innovative new school in Austin that has a strong STEM focus. Lisa’s background in schools is extensive, as she has served as a principal, curriculum director, and teacher, working in both private and public schools, from preschool to high school. She is a dedicated proponent of early computer science and coding instruction and sees the results daily at Long-View.

We teach all children to write, but we don’t expect them all to necessarily become writers. In a world in which computing is ubiquitous and drives innovation in nearly every industry, it is important that we teach our children from an early age how to harness what is called “computational thinking.” Computer science is the broad area in which much of this would be taught to children, and computer science is now foundational to a strong education, right alongside reading, mathematics, science, and writing.

All kids will not end up as computer scientists, though we want many more to make that choice, as 71% of all new jobs in STEM are in computing and only 8% of STEM graduates are in computer science. However, most of our children will eventually find their jobs or their passions crossing over with computing. Whether they someday own a small business and recognize an app would accelerate revenue or they become a biologist who sees that the application of statistics, mathematics, and computer science holds the key to relations among several biological systems, computer science is key to being broadly educated and ensuring choice in future career pathways. This is sometimes referred to as the “double-deep” mandate, as the workforce will increasingly require sets of skills within technology and a secondary area, such as business, medicine, or sales.

Computer science is not just about sitting at a computer and coding. One might think of the relationship between arithmetic and mathematics (there is so much more to mathematics than only arithmetic!) when understanding coding and computer science. When taught properly, computer science will challenge students and teach them to approach problems in new and rigorous ways. It will stretch their logical thinking skills, and help them develop mindsets such as being curious and flexible. The core concepts and big ideas of computer science are broadly transferable, as CS is a discipline just like history, physics, or mathematics. It has a body of knowledge, and the thinking skills of the discipline will last students a lifetime. And there is ample evidence that the discipline of computer science is accessible to children in elementary school and onward.

What does it look like for young children to engage in a computer science class? Yesterday I watched a third grader, with a little bit of extra time on her hands, decide to challenge herself to code something she’d learned in math that day. She set forth to figure out how she’d write a program that allowed the user to consider two sets of numbers and then find the intersection of the two sets.

The third grader’s first thought was, “I don’t really know how to do that. The only thing I know for sure is that I can start with a print statement.” Using her knowledge of Python, she coded a few lines that would print onto the screen both sets of numbers, with six elements in each set. She then iterated her code by adding a line asking the user to consider both sets and then enter the value that represented the intersection of the two sets. After a peer tried out the fledgling program, the hard-working young computer scientist realized she had a problem to solve. What if the user inputted the wrong answer? How could she add to her program so the computer would respond by telling the user the answer was incorrect, and then allow for a new answer to be inputted?

The logical thinking and problem solving terrain that this young eight-year-old traversed, while also having to leverage her beginning knowledge of Python, is nothing short of remarkable. First and foremost, she was a curious learner who sought intellectual challenge. She found a starting point and had the stamina to continue breaking apart her problem. She was able to simultaneously think about the user’s experiences, the set theory she learned about in mathematics, and the coding language to which she’d been newly introduced. What a thinker!

As Jeannette Wing, Professor of Computer Science at Carnegie Mellon and VP of Microsoft Research, wrote in her seminal article in 2006, computational thinking “represents a universally applicable attitude and skill.” Her vision helped inspire innovation across the world, with England, as an example, leading as the first country to mandate computer programming instruction in primary and secondary schools. President Obama signed the U.S. education law called “Every Student Succeeds” and with it recognized computer science as a “critical academic field.” Our children live in a digital world, and we need to prepare them for the digital world by ensuring a baseline understanding. Computer science should be part of every child’s education experience.

Lisa Zapalac

Inspiring STEM learning in Austin youth

Alt Ed Austin doesn’t often publish guest posts from representatives of large corporations, but both the local Girl Scouts and the Microsoft Store staff were so excited to share the fun learning they’ve been doing together that we couldn't help but pass it along. Guest contributor Marco Cervantes is the store manager of the Austin Microsoft Store at The Domain, which offers free YouthSpark summer camps.

Brownies learn about the history of the computer to earn their “Computer Expert” badge in a recent workshop.
With all the available tech currently on the market, it’s easy for today’s youth to get sucked into a stream of unconscious thumb scrolling and finger tapping. As a manager at the Microsoft Store in Austin, I find frustrated parents sometimes pointing the finger at us, claiming that we are the source of their children’s lack of focus. However, our intention is quite the opposite. Microsoft is taking action to help involve today’s youth in meaningful and productive activities.

Amidst Austin’s booming tech scene, the next generation is deeply immersed in the digital world and will soon be the new employees managing projects and writing code. Yet these skills are seldom taught in elementary, middle school, and high school classrooms. To address this issue, the Microsoft Store at The Domain offers workshops to local youth to give them a head start in the fields of science, technology, engineering, and mathematics (STEM).

The Girl Scouts of Central Texas (GSCTX) is one of the many nonprofit organizations we have partnered with in the Austin area since the store opened in April 2012. To help meet the growing demands for hands-on STEM learning and to provide increased opportunity for girls, Microsoft has donated more than $500,000 in software to GSCTX. We host merit badge workshops two or three times a week for the Girl Scouts to teach them about internet safety, apps, and more. We extend free instruction to GSCTX staff members as well, with dedicated sessions to share Windows and Office proficiency tips so they can better organize and lead their troops.

“We strongly believe that investing in today’s youth and providing opportunities beyond the classroom are some of the most beneficial ways we can help set up the girls for a successful future,” says Lolis Garcia-Baab, director of marketing and communications at GSCTX. “We are helping to create the female leaders of tomorrow. By offering an outlet for youth to learn about technology, we are empowering them to reach their full potential, which may not be possible in many traditional classrooms.”

Microsoft’s dedication to helping the next generation extends far beyond the store walls. In addition to donations, our companywide YouthSpark initiative aims to create opportunities for 300 million youth around the world, including 50 million young people in the United States, by 2015. Through partnerships with governments, nonprofit organizations, and businesses, we connect them with education, employment, and entrepreneurship opportunities. For example, through our DreamSpark program, students gain access to professional developer and designer tools at no cost so they can get a head start on their careers or create the next big breakthrough in technology.

We are excited to help Austin youth create the world they want tomorrow, starting today. To learn more about Microsoft’s community and educational activities in Austin, please visit the store website.

Marco Cervantes