### Secondary School Students Are Learning Computational Thinking Skills at All Levels Thanks to Rutgers-Led, Teacher-Education Program

**“****I was thinking….”**

When these three words pass the lips of her third-grade students at the Lanesborough Elementary School, as they frequently do, Anna Mello allows a knowing smile.

Mello is teaching computational thinking skills to her 8-year-old charges, all of whom live in this small rural town close by the Berkshire Mountains in western Massachusetts.

That’s right, computational thinking, also known as CT.

Mello is among dozens of secondary school teachers who are bringing computer-age thinking skills into their elementary through 12^{th} grade classrooms in several states, thanks to an online instructional course developed by a Rutgers University-led group of education experts. The program, formally called *Integrating Computational Thinking in Mathematics and Science High School Teacher Professional Development*, is underwritten by a National Science Foundation grant.

As Mello and other elementary school teachers who took the course have demonstrated, computational thinking skills can be applied broadly at almost every educational level.

Ms. Mello, as her students call her, is teaching her students HOW to think using CT principles. More specifically, how to understand patterns and draw conclusions in a logical step-by-step manner. Her goal is to engage her students in this higher-level thinking process. That they are.

A 3rd grade student at Lanesborough Elementary School displays his graphic visualization of DNA sequencing, part of a computational thinking, pattern-recognition exercise.

*122 secondary school teachers in 8 states took the online computational thinking, professional-development course in its first 18 months. Interested?*

*Teachers: Go Here to **Learn More*

Indeed, her students are so engaged in their CT investigations, she says, that they rarely misbehave.

**Stepped Up Math**

Twenty-three hundred miles west of Lanesborough, in Helena, Montana, Andrew Roberts’s 7^{th} grade advanced math students are using computational thinking to solve recursive math problems. (Recursion is a method of solving a problem where the solution depends on solutions to smaller instances of the same problem.)

One such problem: Next to Roberts’s classroom are two flights of stairs. If you climb the stairway one step at a time or two steps at a time or any combination thereof, how many ways can you climb the steps without repeating any one pattern? And how do you show you have all the combinations?

To help his student visualize the problem, Roberts first had them climb the stairs in different patterns, and then transfer each pattern to graph paper. It soon became apparent that it would take forever to find the answer in this manner, and that all this running up and down steps would be too exhausting even for energetic 13-year-olds.

So, Roberts showed his students how to use CT thinking skills (including decomposition, pattern recognition, abstraction and algorithmic thinking) and mathematics (algebraic functions) to solve the problem by moving from graphs of data to tables of related data and finally to functions and equations.

In case you were wondering, there are 1,957 ways that 16 steps can be climbed going one or two steps at a time or any combination thereof.

According to one calculation (not provided by Roberts), running all the patterns would be equivalent to climbing the 1,860 steps of the Empire State Building in NYC 16 times!

“Computational thinking supports the kind of teaching we do now, but takes it to another level,” Roberts said, adding he believes it’s important to help students visualize the numbers, and understand how they connect to the real world, before moving to algebraic functions and equations.

“Everything in math is visual,” he said. “It’s not just memorizing some trick.”

In case you are interested, Roberts offers this recursive formula for solving the 16-step problem. It’s called The Fibinacci Rule: X_{n} = X_{n-1} + X_{n-2}, where X_{n }is the number of stairs, X_{n-1} is the previous term (the stage before or, the stairway with one less step), and X_{n-2} is the term before that (two stages before or, the stairway with two less steps).

7^{th} grade math students at the Helena, MT, Middle School walk up and down a stairway outside their classroom to start solving a recursive math problem.

Above: How one student started to solve the step problem visually, using a worksheet, with each “o” representing 1 step and each box representing 2 steps. The table shown here expresses the answer to the problem as a table containing two variables: the number of steps (16) and the number of ways each step can be climbed one and/or two steps at a time without repeating any one pattern.

**Privacy Violations**

Down the street and around the corner from Roberts, teacher colleague Kevin Ward has worked computational thinking into his AP Honors English class for juniors at Capital High School in Helena.

The central thrust of this particular course is how to write and evaluate nonfiction. Ward is using the privacy module provided by the CT online course to take his students on a deep dive into the world of big data and how companies use and abuse that data.

“By the end of the unit, we were discussing how companies use their algorithms to monetize their customers…and eventually abuse their privacy by selling our data to other companies,” Ward said.

Ward made the lesson personal by showing students how to download their Google search histories, a well-hidden but public archive of data kept by parent company Alphabet.

“The kids were most shocked when they downloaded the information Google had on them,” he said. “They found pages and pages of single-line search data. When you sign into Gmail accounts on any device, it all links to your searches. It continues to collect that information and gives you targeted ads.”

Google keeps an archive of every Internet search we make on all of our devices.

In Ward’s class, students learn not only how to write a research paper, but also how to develop a thesis and back it up with data. Along the way, students learn argumentation skills and how to present their case in a persuasive manner.

Ward begins his class with the basics: how to write a sentence and short thesis statement, how to develop a good paragraph, and then how to string together multiple paragraphs.

“We were doing this before (I introduced) computational thinking, but now we’re using CT words and phrases” to describe the structured thought process involved in the development of a thesis and data-supported paper to back it up.

One of the great values of the computational thinking process, he said, is that it breaks complex ideas into smaller “chunks” that are easier to work with.

“I have lots of kids who when I say we’re going to write a research paper, they’re terrified,” Ward said. “This sets them up so much more for success. On the surface, computational thinking is about pure math or science, but at the end, you’re having philosophical discussions that help them get morally and socially engaged.”

**What? School’s Over?**

Back at the Lanesborough Elementary School in Massachusetts, Ms. Mello is having her students complete an exercise in data collection and pattern recognition.

Taped onto the wall are large pieces of drawing paper, each prepared by a student, listing ten characteristics or clues about the identity of Revolutionary War heroes from Massachusetts.

Each hero profile contains similar information, such as their date of birth, their gender and their role in the Revolutionary war.

Of course, every student who prepared a profile knows who their hero is, but what about the other nine heroes? How can they determine from the clues given who the other mystery heroes are?

Third graders at the Lanesborough Elementary School try figure out which Revolutionary War heroes are depicted by reading ten clues about each one.

Mello does not tell them to look in the same social studies book from which all of the original clues or data came. Instead, she lets them talk to each other and figure it out themselves.

Before long, some boys are randomly flipping pages in the social studies book to find a match. Then a girl with her hair done up in a bun figures out it’s faster to use the index in the back of the book to look up the most important clues.

To the uninitiated outsider, who grew up sitting in orderly rows doing as he was told by his elementary school teachers, Mello’s classroom at first looks chaotic, with students walking here and there, talking to each other, trading information and figuring out how to solve problems.

But these students are learning how to ask questions, how to think for themselves, and how to work in teams

The most wonderful thing? They enjoy it, Mello said.

“At the end of the day, they say: “What? School’s over already?”

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