I teach Pre-algebra and Algebra students and focus on mathematical thinking. The weakness I see in many students is the inability to think through problems. They can quite often handle exercises from a book that rehearse algorithms taught in a lesson but given a unique true problem they hit a wall. My goal is to teach and inspire students to break through these walls and to use math as a metaphor of tackling life’s problems. I have entered the class with a toolbox and bring out many tools that a craftsman might use then share problem solving tools that mathematicians use. I share that thinking happens when they don’t know the answer. Only when students are placed in a situation where they cannot follow memorized algorithms will they use these tools and truly enjoy the adventure of thinking. If two people are seeking to strengthen themselves and one chooses to work out in gym and the other by hiking in a wilderness the one in the gym may get strengthened with the repetition but the other will get dirty, see more of nature, may get lost but have more stories to tell. This is the adventure of problem solving that I invite you to.
So with this in mind, I would like to present a column on thinking through problems. In this column I will present one problem a week and you, as a reader and fellow traveler and possible teacher, are free to present this problem to your students and respond with feedback of methods your students have used to solve the problem plus anecdotes of their adventure. Some will be easy and some more difficult but the aim is to discuss methods that elementary or middle school students would be able to use. Our goal is not to show off answers but to present the road on how to solve problems so that we can help students apply these tools to other problems. So let’s put on our hiking equipment and open up our toolkit and enjoy the adventure of problem solving!!
Are you ready for the first problem?
Discuss methods your students use to solve the following…
In a stationery store (these are stores not affected by earthquakes as one student piped in–ha, ha), pencils have one price and pens have another price. Two pencils and three pens cost 78 cents. But three pencils and two pens cost 72 cents. How much does one pencil cost?
You have one week to get into this conversation and share your stories before I share my experiences.