Challenge-based learning
inTASC 8: The teacher understands and uses a variety of instructional strategies to encourage learners to develop deep understanding of content areas and their connections, and to build skills to apply knowledge in meaningful ways.
Introduction
Challenge-based learning (CBL) is similar to project-based learning in many ways, but the key distinction lies in the outcomes. CBL provides much less structure and fewer restrictions on what results should look like. Students are pushed to explore and build connections to the content in more personal ways. These CBL Assignments are the Application focus of my weekly plans. For the most part, they are student-driven and many different approaches are appropriate.
The following Assignments are from Unit 2. They focus on the application of basic numeracy and foundational skills for linear functions.
Table of Contents
Fair Housing Wage Project
Assignment #1
In the Fair Housing Wage project, students analyzed the incomes of 6 different families in the City of Covington. This project would fit into the typical definition of project-based learning. Outcomes were prescribed in advance because the data were real and current data, but teams deviated in their analyses of the implications of it. What pushed the project toward challenge-based learning was the opportunity for students to budget the income of someone living in a similar situation. Students recognized the constraints of the circumstances given to them and used them to inform potential constraints in new and more relevant situations. It laid the foundation for the projects that followed by giving students concrete references for the exploration of the injustice of poverty and income inequality.
In the first stage of the project, teams created graphs to display the income of 6 different families. Beyond a few requirements, students were given no examples of how this graph should look. Creating the graph from scratch required teams to discuss the best way to represent the data. This was an indirect review of the features of a graph that students should be familiar with in an Algebra II class. The questions (shared below) required students to use the data they created to answer questions. They were pushed to form deeper understandings of the content and connect the learning they've done in math classrooms to real world scenarios and applications.
Teams worked on filling out relevant financial data for each of the families. They calculated the taxes owed and determined the cost of housing for all 6 families. These data were used to answer a series of questions about the implications of each family’s financial situation.
Students finished the project with a reflection about the project as a whole. This pushed them to internalize the key concepts and helped them track their own learning. Below are a few sample responses.
Career Research and exploration
Assignment #2
I want my students to engage with a tangible outcome of the financial topics we’ve been touching on in Algebra II. In this project, students researched careers. They found information about average pay, benefits, and availability of jobs in Northern Kentucky and created tables to track and compare different career paths. They used linear models to estimate the total income over a lifetime for each career. These models were used to start conversations about financial burdens that we often forget to account for.
This project provides a context for the high level math students engage with in Algebra II. Working through these problems, students implicitly uncover some foundational truths of math. Using Google Sheets to compile data allows students to use formulas to simplify the work they have to do. There is investment in finding the "easy way out" because they want to reach the answer more quickly. In doing so, students develop stronger concepts of input and output variables. This has benefits that translate into functions in Algebra II.
This approach prioritizes student engagement. Students are challenged to come up with a solution and often don't realize that they are learning mathematical concepts until after the fact. They are learning to apply the knowledge in a meaningful way first, then working backward to apply their thinking to the underlying mathematical skills. Using formulas in Google Sheets is a transferable skill that requires a deep understanding of variables and operations. The spreadsheet makes it more clear for students what functions are doing, and this connects directly to the work students are doing with linear and quadratic functions. Students are more able to express their understanding of variables and functions on worksheets, quizzes and tests because they learned it application-first. They had a context for their learning already, making it easy for me to teach function notation and transformations.
Assignment #3
Students dove deeper into a job they could have in the near future. They selected a job that they could have straight out of college and created a detailed budget of how money could be spent effectively. In addition to the transferable benefits of being more financially literate, this project helped students practice basic numeracy applied in a practical context.
Students had to fill out the table to the left with information that they researched about a single career. They had to find a job posting in the Northern Kentucky area and create a realistic budget for someone with that job. After accounting for their necessary expenses, they created a more personal budget for other needs on the second tab.
Students used these budgets to create flyers that advertise the careers. They addressed the finances and intangible benefits of their careers. The flyers were made using a website called Canva. Students summarized their learning from the projects in a brief presentation. This is an essential part of the project. Students not only have to process the learning of the unit, but they have to synthesize and express it in an effective way. This is excellent practice for summarizing mathematical concepts that don't have such clear and tangible applications.
This flyer was made by a student in our school's Construction Career Pathway. He did his own research to create a realistic vision for what his financial future will look like. It addresses some of the major takeaways from Assignment #3 and summarizes it in a digestible format. After presenting their flyer, it was hung around the school for students outside my class to benefit from.
Conclusion
An important aspect of these CBL Assignments is the time built in for reflection. This is where students are internalizing the information from the Assignment and understanding how math is present in their lives. Students often don’t realize they are doing higher-level math while working through the assignments. I like to highlight their growth by having them acknowledge their changes in thinking. This is what helps them not only build connections to other content areas and applications, but also recognize that they will never be done learning.
All three of the CBL Assignments in this unit built upon one another and led to students be able to express their financial expectations accurately. They developed deeper understandings of the math content involved and connected the experiences of others to their own decision making.