In this lesson, students will develop their problem-solving skills in the secondary context through computational thinking. Students are presented with challenges that require students to develop generalized strategies for addressing novel problems beyond the immediate scope of their understanding. Through the development of computational thinking, students are encouraged to step outside of their intellectual comfort zones and approach cognitive adversity with resilience.

**Grade Level:** 9-12

**Content:** Secondary Science

##### About the Author

Rick Lage is a science teacher and 2023-24 Kenan Fellow. The N.C. Department of Public Instruction supported his fellowship. Lage completed his industry immersion at TCOM in Elizabeth City.

##### About the Fellowship

Lage’s summer industry immersion at the aerospace technology company, TCOM, gave him insights into international engineering, programming, and manufacturing. While many of the particulars of this process are privileged information, Lage was able to focus on how problem-solving and computational skills were implemented and in demand across TCOM’s many operating departments and levels. Lage’s interviews with employees yielded many takeaways including the need for adaptive thinking and the ability to generalize problem solving. Repeatedly, across multiple fellowship and internship environments, it was echoed that “we can teach them the particulars” but that it was far more important to future engineers and programmers to be able to adapt and generalize their problem-solving process.

- Essential Questions
- Time Needed
- Standards
- Making Connections
- Background
- Materials
- The Activity
- Extensions
- Wrap Up and Action
- Resources
- Download

## Essential Questions

How should I approach a problem I don’t already know how to solve?

How can things I know help me solve new problems?

What does it mean to generalize a problem-solving process?

How can problem-solving algorithms help me better understand the way a problem works?

## Time Needed

Prep: 30-45 min.

Learn: ~2 90-minute periods (can be modified for a single class or 3-day learning unit)

Wrap Up: 15-20 minutes

## Standards

I incorporated this lesson into my scientific practices unit at the beginning of chemistry and physics classes.

However, I think this could be adapted to a wide range of standards by adjusting problem types to suit the learning unit.

**Part 3: Debrief**

- As a closure, bring students back together to discuss the problem strategies they found productive and unproductive.
- Remember to emphasize the algorithmic process of generalizing a problem-solving case.
- It may also be helpful to be ready to provide solutions to any of the puzzles students were stuck on, as usually there are a few that students are dying to know the answer to.
- It may also be helpful to close a class period by collecting students’ work and opening the next period with this wrap-up. This way, you can collect and provide feedback on their work and reference that during the wrap-up discussion.

## Making Connections

Before this lesson, students have been refreshed on some of the fundamentals of scientific inquiry. They also will be aware of nearly all the mathematical skills required to approach the problems presented to them such as solving 2-step equations, areas of simple geometric figures, basic probability, and others. Students will be asked to utilize those skills in conjunction with computational thinking and generalization outside of the scope of normal STEM instruction.

## Background

This lesson opens with the instructor facilitating a conversation about how to solve a problem for which students don’t already know the answer. This includes conversations about real-world problems and skills needed to adapt when there is not a predefined algorithm in place. Students are strategically placed into small groups. The size and strategy will likely vary, depending on the instructor’s particular needs – I worked with strategically well-rounded trios. Students are then asked to secure their phones and Chromebooks to avoid internet access as a solution to their forthcoming problems. Then, students are given their problem-solving challenges and resources to help them work on those problems. Students must be reminded that they can work the problems in any order and that evidence of their process is the primary objective for submission of the assignment (over final answers). For my group, this assignment was conducted with a problem set sufficient to allow for two days of exploration, so at the end of day one, I collected students’ problems and work thus far. On the second day, problems were returned and before the period ended, we came together for a debrief on problem-solving processes and the strategies students found insightful.

## Materials

For this assignment, I utilized:

- Printed handouts
- Chart Paper
- Rulers
- Calculators

If it would be advantageous for your instruction, it would be easy to substitute:

- Technology boards (e.g. SMART, Brightlink)
- Desmos
- Geogebra
- White Boards
- Virtual Collaboration tools (Padlet, Nearpod, etc.)

## The Activity

**Part 1: Opening (10-15 min)**

- Welcome students to class & the independent warm-up prompt “How do you attempt to solve a problem you’ve never seen before?”
- Allow students time to think and compose short replies
- Guide a class discussion on the prompt, allowing students to share and productively reply to each other’s answers.

**Part 2: The Challenge **

- Introduce the problem-solving challenge, being sure to give an overview of the rules, whether the challenge is collaborative or competitive, and what resources are and are
*not*allowed while students attempt to solve their problems. - Be sure to emphasize the problem-solving process as more important than any one solution.
- I utilized a phrasing something like: “Most of the problems are quite advanced and I wouldn’t be at all disappointed if you didn’t get a single one correct. The point of this exercise is to try your best and think about how you solve problems you don’t already know how to approach.”

- Overview of grouping strategy:
- As mentioned above, I think the educator will have the best insight into what is most productive & appropriate for their group of students. However, I do think this activity works best when students have at least one partner.

- Distribute the problem sets and provide access to the tools students may use to tackle their problems.
- I believe that providing students with small hints or validation of their problem-solving process can be very helpful in preventing students from getting overly discouraged.
- As mentioned above, I split this across two days so I could collect each group’s work into folders between class periods to discourage hunting for answers online.

- I believe that providing students with small hints or validation of their problem-solving process can be very helpful in preventing students from getting overly discouraged.

**Part 3: Debrief**

- As a closure, bring students back together to discuss the problem strategies they found productive and unproductive.
- Remember to emphasize the algorithmic process of generalizing a problem-solving case.
- It may also be helpful to be ready to provide solutions to any of the puzzles students were stuck on, as usually there are a few that students are dying to know the answer to.
- It may also be helpful to close a class period by collecting students’ work and opening the next period with this wrap-up. This way, you can collect and provide feedback on their work and reference that during the wrap-up discussion.

## Extensions

Additional opportunities include the school-wide puzzle challenges and other puzzle, codebreaking, and problem-solving challenges for students such as the Mathworks Math Modeling Challenge, the North Carolina State Math Competition, and others.

## Wrap Up and Action

Students were assessed both formally and informally in this lesson. In my case, students received a formal grade based on their effort during the challenge. Students with the most points earned solving puzzles were able to earn a few additional extra points (which helped motivate groups to solve the problems to the best of their ability) on other assignments. Additionally, students are informally assessed through their communication, collaboration, and problem-solving skills by the instructor as they work on their challenges.

## Resources

In working on these resources, I learned a lot from the published works of Martin Gardner, renowned puzzle author, mathematician, and Scientific American columnist.

The YouTube channels Numberphile and Computerphile both also proved valuable in developing many of these materials.

Code.org, codecademy, khanacademy, and stackoverflow all were instrumental in understanding some of the basics of computer programming and generalizing a problem to be solved by an algorithm.

## Download

Download the complete lesson for student pages and more details.