This observation led to a discussion
about systems of equations that could actually be solved more quickly, more accurately, and with more understanding using substitution rather than with matrices on the calculator (e.g., the system of equations y = 3x and y = x + 3).
The teachers felt that some students involved in lesson 1 were not capable of more advanced reasoning
about systems of equations and also felt that students could succeed on the state test by following a sequence of steps on the calculator without thinking much about them.
However, by not doing so in the given lesson, it seemed likely that they missed out on a teachable moment to help students reconcile the calculator output with their existing knowledge
about systems of equations.
Not exact matches
Through surveys and other analysis, they identified a long list
of factors that were interacting like a chemical
equation, which is the unsexy secret
about how education
systems usually work.
Using a pair
of governing
equations that assume swarmalators are free to move
about, along with numerical simulations, the group found that a swarmalator
system settles into one
of five states:
For example, the first inference drawn
about teachers» knowledge in this paper might motivate the formation
of items that measure teachers» knowledge
of using the graphing calculator to facilitate the exploration
of multiple representations and solution strategies for
systems of equations.
TOPICS The number
system Expressions and
equations Functions Geometry Statistics and probability INCLUDES Teacher resource guide 6 Sets
of small - group kits, each includes — 2 Sets
of Algebra Tiles 100 Pattern Blocks, ManipuLite 100 Color Tiles, ManipuLite 4 XY Coordinate Pegboards 200 Centimeter Cubes 2 Sets
of AngLegs Folding Number Lines Learning
About... Folding Number Lines Activity Guide
Whatever is known
about the properties
of spatio - temporal chaos in the solutions
of some
systems of partial differential
equations is not going to invalidate conservation laws or lead to rapid fluctuations in the energy content
of the earth
system.
That we even try to predict a
system as complex as the natural world with a bunch
of equations is, to me at least, the perfect example
of the hopeless search for an explanation which is everything that science should be
about.
Now the claims I make are: 1) The
equations are independent and the
system of random symbols has a unique solution 2) This solution uniquely determines the velocity, pressure and density fields in the steady 2 D case 3) If one
of the 2 fluids condenses then I obtain the dependences
of the fields on the condensation dynamics (rate, spatial distribution etc) what is actually what this whole thread is
about.
Namely that the first law
of thermodynamics, being an
equation of equilibrium thermodynamics, can not give information
about the dynamics
of the
system.
Everybody agrees that if there were no feedbacks in the climate
system, then the resulting climate sensitivity, as dictated by the S - B
Equation (using the effect radiating temperature
of 255 K for the earth) is
about 0.3 C per (W / m ^ 2).
The role
of stochastics is then even more crucial: (a) to infer dynamics (laws) from past data; (b) to formulate the
system equations; (c) to estimate the involved parameters; and (d) to test any hypothesis
about the dynamics.
Climate models are, at heart, giant bundles
of equations — mathematical representations
of everything we've learned
about the climate
system.
Imagine including the next nearest star
system in your
equations — the Centauri
system, which has three components that we know
about with a combined mass more than twice that
of our sun.