This afternoon I came across a tall stack of Lego® boxes stored in my son’s closet; they reminded me of a lesson. (My son just turned 20 three days ago. I can still see him playing with his Lego sets for hours on end when he was younger. And when he ran out of floor space in his room, he took over our entire living room, and we were happy to let him.) Simple lesson — (I was looking around and this site cited the Mathematics Teacher, Vol. 92, No. 2 February 1999 titled “Promote Systems of Linear Inequalities with Real-World Problems” as source for this problem.) You own Funky Furniture, a store that makes tables and chairs out of Lego pieces to sell. A chair is made of one large and two small pieces. A table is made of two large and two small pieces. Currently you have 8 small Lego pieces and 6 large ones. If the profit for a table is $16 and for a chair is $10, then how many tables and chairs should you make to maximize profit for your Funky Furniture business?

I know there are a ton of “systems of inequalities” problems out there, but playing with Lego pieces is just more fun. Students can see the “tables” and “chairs” as they build them. I have the kids work in pairs, so each pair gets a Ziploc bag of 8 small pieces and 6 large pieces. Nobody leaves my room until all the pieces are back into the baggies and returned. If you don’t have Lego, maybe the kids can bring theirs in? Or you can just use centimeter cubes and inch cubes, or dice and cubes, or Cuisenaire rods and round counters. Or you can just print small and large rectangles on construction paper for them to cut out — flat models are better than no models. Anything they can manipulate is fine. We’ll be ready for this lesson next week as we just wrapped up systems of linear equations right before break. And I just remember this fun problem about Mrs. Murphy’s Missing Laundry. Have you seen it? There’s no manipulative involved, but kids like to solve mysteries too.

​Among many email solicitations we received in September was a letter from a textbook company welcoming us “back to the head of the classroom.” This struck us, not as odd, but as a disappointing reminder of the pervasive assumption about what is at the very foundation of teaching and learning.  The teacher’s role as the dispenser of knowledge in the classroom is axiomatic for most.   And the most efficient dispensing happens when she is at the front of the room. For math, this axiom is particularly strong.  On a recent trip to visit colleges, cheerful tour guides each stopped at classrooms, most of which consisted of desks or tables or lecture seats facing the front.  At one school, when asked about the configuration of most of the classrooms, the student shared her enthusiasm for the new tables and chairs in which the school had invested.  They allowed for professors to arrange classrooms creatively.  Many professors had chosen to place desks in a circle, for instance, to facilitate discussion, yet the desks could be returned to the front-facing configuration “for the math professors.”

In many ways, the pervasive notion of a teacher-centered classroom is not surprising.  For thousands of years, students have been learning from teachers.  The Socratic method, highly engaging and interactive though it might be, supposes that the teacher has the knowledge, asks the questions, and skillfully leads the student to the knowledge through those questions.  where can i buy chair glidesMore recent innovations like the flipped classroom move lectures from classroom time to homework time; best computer chair neck painyet, the lecture is still assumed to be integral.  rio beach chair replacement fabricIt seems as if all learning models, whether online or face-to-face, are predicated on the notion that learning happens through the delivery of content, from teacher to student.  wooden folding chairs at target

Even when we develop new and exciting content, innovative teaching is about finding new ways to deliver that content.  True innovation, ought to extend to the very foundations, instead.  Should we be delivering content at all?  Perhaps teaching can be more about creating an environment that fosters the discovery of content. The Harkness pedagogy, the hallmark of Phillips Exeter Academy in Exeter, New Hampshire, challenges us to establish such an environment.bean bag chair luxury It's a way of being: interacting with other minds, listening carefully, speaking respectfully, accepting new ideas and questioning old ones, using new knowledge, and enjoying the richness of human interaction.  used leather recliner chair for sale To implement this educational philosophy, members of the PEA Mathematics Department have composed problems for nearly every course that we offer.

The problems require that students read carefully, as all pertinent information is contained within the text of the problems themselves—there is no external annotation. The resulting curriculum is problem-centered rather than topic-centered. The purpose of this format is to have students continually encounter mathematics set in meaningful contexts, enabling them to draw, and then verify, their own conclusions. As in all Academy classes, mathematics is studied…with students [usually 12] and instructor seated around a large table. This pedagogy demands that students be active contributors in class each day; they are expected to ask questions, to share their results with their classmates, and to be prime movers of each day's investigations. The benefit of such participation in the students' study of mathematics is an enhanced ability to ask effective questions, to answer fellow students' inquiries, and to critically assess and present their own work. The goal is that the students, not the teacher or a textbook, be the source of mathematical knowledge .