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We live in the Age of Information and Technology. Our access to knowledge seems to accelerate every few months. What was the quickest avenue to look up facts, or background material or context six or twelve months ago has given way to faster, technology-agedifferent paths to locate the information we seek. Only we “old folks”  “Google It” anymore. Young people find their information on “You Tube,” where they can instantly view multiple videos that provide them what they need. Computers, the Internet, iPads, Kindles, etc. offer ready access to vast amounts of information. Long before our students reach us, highly competitive parents have introduced our students to sites like,, and Older students are even more practiced at locating necessary information. It is time for us to catch up. We must realize that our students are already well-experienced at finding information.

As educators, we must come to grips with our new reality. We no longer “deliver” information to empty minds. Our job is to help our students learn to sift through the vast stores of facts available to them, help them organize that information into an age-appropriate whole, and be able to apply that information effectively in their personal environment. Study, after study, after overwhelmed teacherstudy emphasizes the principle that critical thinking – observation, analysis, synthesis and communication – is the essential tool that all students, regardless of age, need in order to be successful. I can hear you saying to yourself, “He’s wrong… He’s out of touch… I have to teach the fundamentals (counting, integers, negative numbers, coefficients, irrational numbers, differentials, factoids)… I have standards to meet and improvement to demonstrate…I have a principal who wants more math practice so that our yearly scores go up, not down.” Let me tell you that I know and I understand. I am NOT attempting to change what you need to do. I AM trying to change the way you get it done.

For years, the standard rule in math has been “practice and repetition;” introduce the principle, then practice over and over until “mastery” has been achieved. Nice theory. My question for you is, “How’s that working out for you?” My reading of the results Bad-Mathfrom standardized tests throughout the US indicates that the “Old Methods” are not working well. Students’ math scores have not significantly improved at any level since the NCLB mandated them. So, why do we continue to “practice and repeat” a system that by all empirical measures, does not work? (See The Cato Handbook for Education, 7th ed., 2009; Tim Walker, “PISA 2009..”, NEA Today, December, 2010, and National Research Council Report, “Standardized Testing and Education Improvement” 2011)

I am here to recommend that we “Engage to Change.” Specifically, I am advocating the use of artifacts – real objects from the present or the past – to teach math. Studies have demonstrated that students engage most in learning when they perceive that the lesson affects their daily lives.(See the work of Dr. Constance Steinkuehler on Adolescent Online Games and Reading, and the work of the Wisconsin Institute of Discovery). Early Childhood educators know this principle well, and have applied it for years. engagementThey have used “everyday things” to teach comparison, sorting and classifying, pattern recognition, meaningful counting, measurement, fractions, and on and on. “Promoting an attitude of delight and fascination with numbers encourages children to embrace rather than fear math, creating life-long math learners.”(Gretchen Damon, “Using Everyday Materials to Teach Math.”, Early Childhood News, 2007). These same principles can be applied beyond the K-5 classroom.

Why not employ Native American pottery to teach geometry? Why not use that same pottery to create algebra problems? “If the volume of this jug is 3 quarts and each person in a pueblo of 250 people uses 2 gallons of water each day,how many jugs of water jugwater are necessary to provide for the town?” “If the river is 1/2 mile from the pueblo, how many trips must be made each day to make sure that all the people have enough water?” “How many miles are traveled in a day? A week? A year?” What if Native American pottery does not engage your students? Well, then, how about “poop”? What student doesn’t like to say “poop” in class? Just change the basis of the equation and use a chamber pot.

Here is how you can accomplish the same end with a different artifact. Be sure that students understand the purpose of a chamber pot. Have them calculate the volume of the pot. Provide for them the number of chamber pots that a fChamber potamily of four would require. Place the pots at different levels of a 3-story house with 16 stairs between each floor. Now, create your math problems concerning time, distance, quantity, effort, etc. “But,” you say, “that is just another story problem.” The difference, and it is an important difference, is that the pot is in the room, in front of the students. They can see it, touch, lift it. Gauge its weight. Imagine using it. You have engaged them with the artifact, which also engages them in the problem solving.

Pick an artifact, place it in front of the students and turn them loose! How about using a compass or an egg beater to teach red marblestrigonometry? What could you do with a 12-candle, candle mold? Why not try a garden hose to teach algebra, and a set of marbles to teach everything from counting to calculus? I cannot provide you with an example for each and every math principle or math lesson. But, I can assure you that everyday objects – artifacts – contain the potential to engage your students. Stop and think. What can you trip over on the way to work that you can use to engage your students and make math enjoyable? These everyday things are artifacts and



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