I know that some math teachers have been using problems (not math problems, but real world problems) for years. Some of the simplest versions of authentic uses for math sneak their way into quizzes and tests in the form of story problems. As a matter of fact, many math teachers use the terms “story problems” and “problem-based math questions” interchangeably. The major difference between using story problems to enhance the authentic side of mathematics and using PrBL in a math classroom is the timing—using authenticity from the beginning of the unit is the best way to engage math students with the WHY.

In a typical math classroom, the teacher instructs students on the skills they need to then complete some guided practice and then independent practice. This is usually followed up with a quiz over the material. Any effective teacher would then provide intervention or enrichment based on the quiz (formative) data and then a summative assessment would determine the mastery of the skills from the unit. Sound familiar? In a Problem-Based Classroom, an actual problem—a real life situation that is a problem for someone, is introduced to students before any instruction takes place. It is then the job of the teacher to give students the most minimal information and instruction possible, but just enough to get students off on the right track. Students would use their inquiry skills, critical thinking skills, and research skills to work through the math problem. The teacher would continue to track progress towards the answer, give formative assessments, and analyze the data to design small chunks of instruction and to give supplemental information as needed, until the students end up with a viable answer to the problem. This type of learning is less about product and more about process, which lends itself to the rigor required in the Common Core. Instead of saving the authentic learning for last by asking a story problem on a quiz, the authentic learning experiences of a PrBL classroom give students the answer to “Why do we need to know this?” on the very first day, and then allows students to think critically and solve problems more independently, with coaching from the teacher along the way.

Take a look at the following examples that illustrate the difference between story problems and PrBL math problems.

Story Problem: If an airplane leaves for Madrid, Spain at 7:00 A.M. and arrives in New York City at 8:00 P.M., how many hours is the flight, taking into account the Time Zones?

PrBL Problem:

Dear Students, This summer I was hoping to travel with the high school Spanish classes for a tour of Spain and Portugal. Since I am over 45 years old and I am on blood pressure medication, I am at risk for blood clots and other health issues if I choose to travel by air for long periods of time. I have been reading up on this and according to WebMD, I should not risk taking flights that last longer than 10 hours. Since we have not yet booked our flights, I would like for you to do some research to help me decide whether or not I should make this trip. You will need to use a website where airline tickets can be purchased to calculate how long the flight is from Columbus International Airport to Madrid, Spain. Please take into consideration layovers, where I could walk around the airport (which is suggested for those at risk for blood clots) and most importantly, be sure to consider the Time Zones. You will submit the math calculations and work you did to help me decide whether or not to take the trip. You will also write a paragraph explaining whether or not I should take the trip, and if I do, what types of flights (direct, 1 layover, etc.) I would need to book if I intend to go. Please help me make this important decision! I hope you can find a way to help me go on the trip of my dreams!

Sincerely,
Your Math Teacher

By framing the math problem as a practical application, students are more interested in figuring out an answer because they know that there are real consequences to the accuracy in their calculations.

Of course, not all of the PROBLEMS in a PrBL classroom have to be framed as a life or death situation like the one above. One of my math teachers, who is really getting the hang of the PrBL classroom, used a very simple but real problem with her students last week, and the results were amazing.

Mrs. Darla Wahl, who teaches Algebra I in New Tech Academy, wanted to find a “cool” way to teach inequalities in a deep enough way to satisfy the rigor of the Common Core standard for this skill. She could not find anything she deemed “cool” (in other words, engaging) and rigorous anywhere on the Internet, in textbooks, or in her master copy files. Since the newly adopted Common Core State Standards require that students are able to understand that solving inequalities is a process of reasoning, and then must be able to explain the process, Mrs. Wahl decided to use the technology skills of this generation of math students to her advantage.

Mrs. Wahl decided to leave it up to her students to add the “cool” to inequalities. She explained her PROBLEM to her students. “There just aren’t any engaging sites out there for students to use on this topic. We need to create a more engaging way for students to learn about the process of solving inequalities in one variable and graphing their solution set.” With the help of other teachers and her students, Mrs. Wahl decided to ask students to make a Prezi that would allow them to show each step of an example problem plainly and clearly. Students had one week to come up with a final product that could be published to the web to help students learn about the topic. Mrs. Wahl could not believe what her students were able to create without much prior experience with Prezi! The students were proud that they had helped Mrs. Wahl with her problem. Now, Mrs. Wahl will never have to search for “cool” materials for this topic again! The students are now interested in creating their own math website where students can submit math resources they make on their own.

I truly believe that if I would have had math teachers who used PrBL to teach me the skills I needed for the future, I wouldn’t have ever had to ask the dreaded question—the WHY. Just like Simon Cowell is looking for The X Factor, math students across the country are looking for the WHY factor. And so, now the question becomes, WHY not give it a try?