Life presents us with few multiple choice tests. Our jobs and our lives are filled with more complex problems, often with no correct answer. We hope only for the best outcome, or at least one that will not result in an explosion, unless we wanted to blow something up.Â

One of the great problems we must solve as educators is teaching students to become problem solvers themselves–to assess information, consider options, experiment with outcomes and analyze results. I was intrigued to learn from two colleagues, eager to emphasize the value ofÂ developing problem solving skills,Â how problem solving took center stage in their classes the first day of school.

**Jennifer Mabe
**Jennifer Mabe introduced her students to the challenge of her advanced functions and modeling course by asking them to produce exactly seven cups of water from two unmarked pitchers measuring three and eight cups. She explains, “After filling up containers with water, dumping containers of water, and transferring water between pitchers(SEVERAL TIMES!!!!!) we were finally able to determine the correct method of getting 7 cups of water.”Â Student engagement, she observed, was extraordinarily high during that lesson.

**Jed Smith
**Jed Smith also wanted toÂ observe hisÂ physics students’ problem solving skills, so he challenged them with a simple building project. StudentsÂ received a few supplies–sheets of paper, paper clips, plastic cups–and one simple instruction: build the tallest free-standing structure you can. The task challenged students to analyzeÂ their materials and explore their knowledge of physics as they constructed their creations.

**A Paradigm Shift
**Mr. Smith and Ms. Mabe both understand the fact that to educate our students we mustÂ challenge them intellectually with the real problems of the world in which they live. We must

**engage them**not only as receivers of information, but as thinkers, as doers, as active participants with hands and eyes and brains. The video linked below–a speech by Sir Ken Robinson enhanced by anÂ artistic interpretation–explains this idea (and much more)Â brilliantly. I hope you will take a few minutes to view it.

Video link: Changing Education ParadigmsÂ

**Contest
**Let’s have another contest. Submit a brief description of an activity you have used or plan to useÂ that

**challenges the real-life problem solving skills**of your students. Submit your response by the end of the day onÂ Wednesday, Feb. 9Â either as a reply on this blog or via e-mail.

Prize: two gift cards for Panera

The winner will be determined by random selection.

Okay, sorry … but I LOOOOOOVVVVEEEEE panera! And yes, I do have another activity that I used in my AFM class to challenge my students to see the connection between real-life and the world of mathematics. This time, I was introducing the concept of limits – or, as most often referred to as by those who aren’t mathematicians, long-run values.

The only materials needed were water, pitchers, food coloring, measuring cups (in mL) and syringes (that measured mL). Our activity mocked the effect medicine has on one’s body. For example, I posed the question to students how many days they thought it would take for just ONE dose of medicine to completely leave their body. We put their guesses on the board … some thought 5 days, some thought 30 days, etc. As two volunteers “re-enacted” the job of a kidney, students soon began to change their predictions … they realized that because of the nature of the problem that the medicine would NEVER truly leave our body (only a percentage of the medicine left each time). It would, however, continue to approach the long-run value of 0 … thus, the idea of a limit is born

We also did the “experiment” to see what happens if more than one dose of medicine is given (the limit approaches a non-zero value). After all of the “ah-hah” moments, we brought the class back together to write our discoveries into mathematical terms (i.e. recursive formulas).

Had I simply discussed the ideas with students or explained to them the concept of limits, I truly believe they would still be left with a lack of true understanding and once again, math would still be some “stupid high school requirement that is totally useless in everyday life!”

Marie Lewis

After completing chapter 7 in my Honors Geometry class, my students will make an angle measuring device and go outside on the football field to measure the height of the flag pole there. They will not climb the pole. They will use their angle measuring device and right triangle trigonometry to complete the task. This activity is a fun way to re-enforce the concepts learned in the classroom.

In reference to real-life application and problem-solving, I have my students read Who Moved My Cheese? I know a lot of people do not see the value of this book, but I think it is a jewel and an awesome teaching tool. In the book, “Cheese” is what is important to you and the lesson is what would you do if your “cheese” disappeared or moved, etc. My main objective in beginning the year with this book is to teach my students the life is not always fair and you have to know and/or change your mindset to any situation that comes your way. I relate it to my course in that English may not be their “cheese”, but doing well in this course can put you on the right path to obtaining that thing in life that is indeed your “cheese.” I usually pair this book with a movie such as “Remember the Titans” as a way of showing my students how others overcame adversity and did well in life.

In the old days when we ESL teachers used to write our own curriculum, I made an economics/personal finance unit. Students had to research a job, determine it’s beginning salary and educational requirements. Then they spent a couple of weeks working on budgets using that salary. I created a couple of Powerpoint stations, where the students had to research prospective apartments in Greenville (the slides had the picture of the apartments and audio-links on topics such as “amenities,” “deposits and rent,” “location”) and use a decision-matrix to choose one to rent. They had to purchase groceries for a week, using grocery fliers (paper and on-line) and appropriate work clothes. They had to choose a car, again using options at the Powerpoint stations, and they had to calculate loan payments with interest. Anyway, I’m sure you get the idea. The purpose was to give them an idea of how much things actually cost in the U.S., to guide them in realizing that more education = more salary (as they found out when they researched their jobs), and to introduce them to economic/personal finance concepts (taxes, wants vs. needs, budgeting).

I’m still looking for a place to insert this unit back into our new “pre-packaged” curriculum because I think it was really effective. Students had to write about their trials and tribulations throughout the activities, and it was really interesting to see how it opened their eyes to the “real” world.

That’s my two cents worth.

In a physical science class, I presented my students with a scenario: We were asked, by a local business, to design a container for chemicals (in one class I told them it was sulfuric acid).

Each team had to come up with a design, decide which materials to use, build a scale model of their design, set the price for the construction, and submit a bid for the job.

Teams used their knowledge of chemical and physical properties to determine what materials they would use. They did have some difficulty with the scale. Most came up with a design that changed their perspective of why containers are constructed certain ways and with certain materials.

This lesson helped to reinforce their knowledge and how physical science is used in the “real world.” It also presented them with a tangible job opportunity that exist right here in our community.

Although that lesson is still being revised and tweaked, I think my students enjoyed the different approach to class and really took on the challenge before them. (One of my containers even had a butterfly for decoration!)

Rocketry:

In the 3rd marking period. I introduce my physical and Earth Science students to newton’s 3 laws of motion. I let them know that its these principles that governs how we design and create rockets. After this formal introduction I let them know their assignment is to create the perfect rocket. They can only use 3 designs using plastic soda bottles.. Their first design use anything. They main thing is that that they have to show progression of learning of what it means to construct a rocket. They have to take notes on what worked in building heir rocket and what didn’t. By the time the get to their final rocket design, they majority of the students understand the role of fins, center of balance and the right amount of water to create the correct thrust. Some groups even develop parachutes to keep their rockets in the air. This is done with a standard as well as honors class.