Audience: High school and middle school math teachers.

One concept a day. Two examples per class. Three practice problems per example. Four homework problems per example and one word problem. I held all the knowledge. My students had empty minds and it was my job to fill them.


Sound familiar? This is the exact structure all my middle school and high school math classes followed when I was a student. If I was able to learn in this environment, then my students should be able to as well. That was more than a decade ago and my students do not live in the same world that I grew up in. Education evolves slowly but today's students are changing faster than ever. New gadgets, gizmos, and trends daily. Technology has taken over everything and everyone, except education. As the saying goes, “If it ain't broke, then don't fix it.” It's broken. We are ignoring the fact that yesterday's education doesn't work in today's and tomorrow's world. We teach the way we were taught. And that doesn't work anymore.

It is 2010 and students are plugged in more than I could have imagined 10 years ago when I graduated high school. The important skills of an industrial society are those of yesterday. New skills are needed to be successful in today's post-industrial society. Students need to possess skills to problem solve, think critically, and collaborate - not regurgitate facts.

Standardized tests require students to remember facts and terms. In 1965, The Elementary and Secondary Education Act (ESEA) was the first major federal legistlation to award funds to U.S. school districts for designing and implementing programs intended to improve learning. The programs awarded money addressed increasgin students' basic skills. These programs needed a way to prove that they were working. As a response to this need, the Comprehensive Tests of Basic Skills became a popular way to evaluate a school's improvement (Popham, The Truth About Testing).

In 1965 knowledge was not as readily available as it is in 2010. Teachers no longer need are the main source of knowledge for students. Students possess hand-held technology that makes any fact available to them in seconds, anywhere. Testing student recall of factual knowledge is obsolete because any piece of information can be looked up easily. Standardized tests only assess a students' ability to remember the information that they look up in their daily lives.

If the need for memorizing basic knowledge is non-existent then what do we need to teach today's students? Today's and tomorrow's society requires it's members to be innovative, creative, problem solvers, and be able to work cooperatively. Skill and drill does not help student's gain these 21st century skills. Even though the year 2010 is the 21st century, education is stuck in the 20th century with its reliance on standardized test to evaluate student achievement and school effectiveness.

Unfortunately, standardized tests won't be going away anytime soon. What is going away is our students' desire to learn. What can we do as teachers to engage our students in meaningful, relevant learning? I would like to propose a shift from handing out knowledge to facilitating the solving a relevant problem. I would like to propose problem-based learning .

My Story:
Every student walks into class with more knowledge and experiences than the day before. My students are not empty but always half full. My challenge is to stop force feeding completely new knowledge and tap into their prior knowledge and connect with their real-life experiences. I intend to connect with my Algebra 2 students through the implementation of Problem-based learning.

Over the past four years I have struggled with my class of 30 eleventh grade students in Algebra 2. My students attend high school for a specialized performing art, such as dance, theatre, or music. They are on their way to college within the next two years but most for their chosen art. My students struggle on a daily basis trying to answer the question, “Why do I need to know this?” Frankly, I struggle with answering that question too.

Every other day, 30 students and I attempt to plow through the standards needed to score proficient on the state test in May. Every other day we go through the same routine. Example 1, practice, example 2, practice, questions, re-teach example 1, re-teach example 2, assign homework. The standards I find to be the most challenging for my students are found in the chapter on radicals and exponents. The argument is always the same. "Why can't we use our calculators to get the decimal?" "When will I ever need to simplify a root?" Some days I get so fed up with the questions of why, I honestly reply, "You won't. But the state says we have to." I try to get through this chapter as fast as possible with as many students understanding just enough to get by on the state test. It's like running from a pack of wolves with a steak in my hand. This chapter torments us both. They hate math class. I hate teaching Algebra 2. This year, I challenge myself and you to make a change. The system is broke and I am going to fix it, finally.

Problem-based learning starts with a complex problem encountered in the real world. This problem is the key in engaging students. If students see no use for the solution then they will continue to ask, “Why do I need to know this?” Collectively, the class or groups brainstorm what they know and what they need to know to come up with a solution. Students then go beyond their textbooks to pursue knowledge in other resources in between their group meetings. While students collaborate on their many solutions, the teacher's role is to facilitate group process and learning, not to provide easy answers. Through these group processes learning issues will ensue. Learning issues are the content standards that we desperately need students to retain for that dreaded state test. Finally, each group will prepare and follow a course of action to create a solution to the original problem. With the change in format comes different forms of assessment as well. These assessments may be group examinations, presentations, or products. This process is summarized in the diagram below. You may also want to view an example problem for graphing inequalities.

I am sure you have many questions about this challenge I am proposing. I know I do. I have listed my questions about Problem-based learning below and I have done my best to answer these question. To help answer the questions, I will make reference to examples provided by Dan Meyer. In his TEDx NYED talk, Meyer demonstrates how to restructure a typical example problem found in an Algebra 1 book into a Problem-based learning situation. He also explains simple ways to use technology in a meaningful way. Please watch the video below before reading further.


Questions & Answers:

What makes students want to answer a problem with math?
Students will use math when they see the need for it. Through patient problem solving we allow math to be secondary to the problem. Dan Meyer puts it best when he says, "Math serves the conversation, the conversation doesn't serve the math."

How do we engage the math intimidated student in a math word problem?
Students often fear answering questions in math class because they do not know correct vocabulary or terminology. Students also fear giving wrong answers. To engage a math-intimidated student, the first question should be as direct as possible and connect with their prior knowledge. For example, how long will it take to fill the water jug? When we ask a question that connects to students' prior knowledge (filling a container) we create a level playing field. The use of multimedia can help create this level playing field as well. By showing a video of the water jug being filled students are given the ability to make guesses based on only a few seconds of the video.

How do we engage students in thinking about how to solve the problem, instead of waiting for someone else to think for them?
These problems are used to engage students' curiosity and initiate learning the content subject matter. When a person is curious, they will automatically start to think of solutions. With this curiosity, students will not accept a prefabricated answer. They will have the drive to create an answer for themselves.

How do we influence students to use math to solve a problem?
Students need to view math the way their teachers do - as a tool to be more efficient. Guess-test-revise is not a problem solving method that is neither quick nor cost effective. Imagine wanting to repave your patio. First, I want to know the area. Then, cost of material per square foot. And finally, how long it will take for me to save enough money to make this home improvement. Now imagine using guess-test-revise as your problem solving method. The spaces looks to be about 10 by 10 and I pick out the most expensive brick. Get to work repaving but there is not enough material and not enough money to fund the project. So I make another guess and try again. Is this really a viable method to use to solve this problem?

How do we engage students in problem creation so they want to know the answers?
The problems used to teach content standards needs to be relevant to our student's lives. The best way to find out what your students are interested in is to ask them. Let the students ask the questions. You might have to mold the questions to fit the standard but ultimately the questions should come from them.

How do we structure word problems in a way that allows students to explore various problem solving methods?
Start with the shortest question possible. Then, involve students in developing the sub steps. Asking "which is the steepest," can be answered generally without applying math. As the conversation develops use math concepts and skills to answer the questions more specifically. The teacher might be incorporating the content standards but the students are supplying the questions and methods to solve the problem.

How can we use technology to enhance the experience?
Technology can be used to bring the real-world problem into the classroom. Instead of talking about a ski slope show a real-world picture or video. Then with that picture, overlay a coordinate plane. Use the technology to add depth and meaning to the conversation. The video provided below is an example of how to use Google Earth to enhance a lesson about area. The first half explains how to access the Google Earth App and the second half explains how to access the measurement tools within Google Earth.


Google Earth allows students to travel the world and collect information about the places they visit. The teacher speaking in the video mentions that his students love the Pentagon. Technology allows his students to have no constraints as to what or where they explore area and perimeter. In the past, we have been forced to work within the confines of our schools or homes and within the confines of our measuring tools. With the help of technology, this class travels to Washington, D.C. and measures a building that covers almost 30 acres of land. What if his class was obsessed with the Great Wall of China?

How can we use technology to encourage 21st century skills such as creativity, collaboration, and creation?
Previously, homework has been an isolated task for students. What if homework involved reading a friend's post, commenting, and creating a new original post? Sounds a lot like Facebook? Through the use of a wiki, students can share their ideas and findings about a problem and comment on the ideas of others outside of class and all while enjoying the socialization that technology provides. Many problem-based learning activities require more than just a discussion as presented by Dan Meyer. Many problems will require research, team work, and action plans. A wiki is a great place for students to collect their individual ideas for peer review and group ideas for assessment. Each page is easily editable by students. Each page also contains a discussion tool which can be used for communication between group members, other classmates and the teacher for feedback and guidance. Editing a wiki is as easy as writing in MS Word, posting a comment to Facebook, or posting a video to YouTube. Since using the wiki is simple, it allows students to use their time creating an innovative solution, instead of spending time arranging meetings with group members and writing down ideas. For an award winning example of a wiki check out Miss Baker's Biology Class Wiki. Take your time and look around. Check out posted videos, discussion boards, and the navigation tool bar to get a full overview of how to use a wiki. For some great ideas on how to use a wiki in your classroom check out Miss Baker's suggestions.

Problem-based learning is a student-centered instructional strategy in which students collaboratively solve problems and reflect on their experiences. The main defining trait of Problem-based learning is that the teacher provides the real world problem. I find this alternative particularly useful in math classes because the teacher can control which math standards the class focuses on.

I hope I have provided some insight into Problem-based learning. I have never been so excited to go back to school in September. I cannot wait to revamp every one of my lesson plan. Yes, embarking on the journey through problem-based learning will require more preparation than I am used to. However, the work will pay off. I predict that by mid-June next year I won't hate teaching Algebra 2 anymore. I accept this challenge. Do you?

Other Resources:
Short video outlining the process of PBL.

A math teacher explains how she applies PBL in her classroom.

Website explaining how math is used in an array of professions. Also provides real world problems to be solved with math.
When Will I Use Math?