The first test in this course will take place in class on Friday, October 3. The test will cover everything that we have done in the class through Monday, September 29. This includes: The handout on number systems; Chapters 1, 2, 3, 10,and 11 of The Math Instinct; material from Sections 2.1, 4.1, 4.2, and 5.1 of Symmetry, Shape, and Space; and the material from Sections 1.1 and 1.2 of Symmetry, Shape, and Space that we covered in the first week of class.
On the test, you can expect some math problems similar to ones that you have done on homework. This might include, for example, area and perimeter problems, problems about polygons and angles in polygons, questions about tilings of the plane, and problems based on the Egyptian, Greek, and Babylonian number systems. If there is a question about one of these number systems, I will include a copy of the illustration from the handout for that number systems, so that you won't have to memorize the details.
You can also expect both short-answer and longer essay-type questions. These questions will make up at least half of the test, possibly as much as two-thirds. Some of the essay questions will be based on readings from The Math Instinct, probably about one-third of the test. The test will not ask about individual specific facts from The Math Instinct, but it will ask about general ideas and might ask you to mention some facts or examples from the reading to illustrate or support your answer. Besides the questions on The Math Instinct, there will be some essay-type questions about other material from the course.
Here is a list of some terms and ideas that you should know for the test:
area formulas for triangle, rectangle, and circle (πr2)
formula for circumference of a circle (2πr)
the Pythagorean Theorem (but not the proof)
number of degrees in a full circle (360o)
polygons
regular polygon
convex polygon
polygon names: triangle, quadrilateral, pentagon, hexagon, octagon, n-gon
equilateral triangle
the sum of the three interior angles in any triangle is 180o
the sum of the four interior angles in any quadrilateral is 90o
the sum of the n interior angles in any polygon is (n - 2)*180 degrees
an interior angle in a regular n-gon is ((n - 2)*180)/n degrees
path of a (frictionless) ball on a billiards table
the three regular tilings of the plane (by triangles, by squares, by hexagons)
semi-regular tilings
fitting regular polygons around a common vertex ("vertex configurations")
notations such as 3.3.6.6 and 12.5.12 for specifying vertex configurations
irregular tilings
ways of modifying a tile:
parallel translation
glide reflection
midpoint rotation
side rotation
what can you see in two mirrors facing each other?
what can you see in two mirrors held at an angle to each other?
tallies
moving from tallies to single symbols that represent larger numbers
translating numbers to and from the Egyptian, Greek, and Babylonian systems
how the Greek number system represents thousands and myriads (10000's)
how the Babylonian system uses multiples of 10 and multiples of 60
number bases in general; our Arabic number system uses base 10
arithmetical ability of infants; evidence for this ability
the difference between a natural "number sense" and abstract symbolic math
the question of whether dogs know calculus
the idea that math is the science of patterns
how street traders, supermarket shoppers, and others do math in daily life
street math versus school math
the difficulty people have with meaningless rules for symbol manipulation
the idea that math is largely a linguistic skill
neurological evidence about the way the brain does math
how counting may have started from counting on the fingers
Sumerian clay tokens and the development of the abstract idea of number
why our Arabic number system is superior to many ancient number systems
"why you are not sure what eight times seven is"
how Chinese/Japanese number names are easier to learn than ours