My Classroom I believe that every student can learn. I teach them HOW to learn, for in their acadmic life, but also their whole life! Lyn Baier is a master educator specializing in working with students in the subject area of math. Her broad experience ranges from counseling to teaching students Kindergarten-Adult.
Change the objects under study. Remove a condition, or add new conditions. Remove or add context. Each of these potential changes is discussed in more detail below.
Change the Numbers This is the most obvious way to change a problem. Give your students one or more problems and ask them to identify any stated or implied numbers.
For example, in the cow problem, in addition to the three stated numbers, there are the following implicit conditions: We can change any of these numbers.
The geometry becomes much trickier in this final case.
Strategy games can be a good source of research problems and often have many alterable features. Two players take turns rolling a die. After each roll, that player must decide whether to add the value of the roll or ten times the value of the roll to his or her score e.
After seven rolls, the person with the highest total less than or equal to is the winner. A score over counts as 0. Again, ask your class to find all the stated and assumed numbers in this game. Stated values that might be changed include the number of players, the target totalthe number of turns, the multiples of the die result 1 or 10and the number of dice rolled per turn.
Assumed values include the number of faces on a die, the values on each face, and even the probability of each face appearing. When considering numerical changes to a problem, many different domains and representations can prove interesting.
For example, what if we limit the domain for some variable to whole numbers, or extend it to the reals? What if we allow negative or rational numbers? What happens for particularly small or large values?
What if we change base e. Can we change a finite quantity to an infinite one or a fixed quantity to an unlimited one e.
What if we change from zero to a non-zero value e. Change the Geometry Any problem with a geometric setting is ripe for new variants. The simplest problem-posing maneuver is to change the shapes involved. Different categories of shapes that suggest possible substitutions include polygons and their number of sides, regular versus non-regular polygons Is the cow problem with different tether lengths simpler with a square barn?
Try a shape that is more general but that includes the initial object of study, such as parallelograms rather than rectangles or more specific look at a subset of possibilities, such as regular solids rather than all polyhedra.
Changes of dimension can yield exciting challenges and patterns. What if we look at pyramids rather than triangles or hyper-cubes rather than squares? What if we reduce the dimension of our problem by considering cross-sections or projections e.Channakeshava, my math teacher at school, was the most inspiring teacher I had.
In this article dedicated I recount my experiences of being taught by him way back in the 80's. This apart, I have also described at length some of the topics we.
Sarah Burnett, a 4th-grade mathematics teacher in Pulaski County, thinks her experience in the classroom will help guide her decisions as head of the Education Professional Standards Board. © Iowa Board of Educational Examiners. Mathematics Itself: Formatics - On the Nature, Origin, and Fabrication of Structure and Function in Logic and Mathematics.
Yet faith in false precision seems to us to be one of the many imperfections our species is cursed with. Mathematics K–12 Learning Standards. Washington formally adopted the Mathematics and English Language Arts K–12 Learning Standards, also referred to as “the standards". May 01, · IMPORTANT: Educator Rules of Conduct and Responsibilities The Commission on Teacher Credentialing has provided through the link above immediate access to credential information.
The credential information serves as the official record of certification.