Math 104 Test 1 Review

Why the first math test is important

1. It can indicate one's level of skill in math- whether one needs help, etc 2. It can help bolster one's grade

Fibonacci sequence

A sequence of numbers in which each number is the sum of the preceding two.

arithmetic sequence

a sequence in which each term is found by adding the same number to the previous term

geometric sequence

a sequence in which each term is found by multiplying the previous term by the same number

Four things one must be able to do in a math course

1. Understand the material. 2. Process the material. 3. Apply what you've learned to solve a problem correctly. 4. Remember what you have learned in order to learn new material.

George Polya's Four-Step Problem Solving Strategy

1. Understand the problem 2. Devise a plan (translate) 3. Carry out the plan (solve) 4. Look back (check and interpret)

Variables contributing to Student Academic Achievement

50% Cognitive Entry Skills 25% Quality of Instruction 25% Affective Characteristics

Bad Math Attitude

Fear, anger, or hatred of math

Carl Gauss

German mathematician; When he was eight, he figured out how to add up all the numbers from 1 to 100

Ordering of Math courses

Math courses should be taken in order

Math as a skill subject

Math is a skill subject, which means it requires active practice.

Math as a speed subject

Math is a speed subject, which means that it is taught much faster than other subjects.

Affective Student Characteristics

Math study skills, test anxiety, motivation, locus of control, learning style, etc. (One's personal ability to learn math.)

Night Course Math vs. Day Course Math

Night Math courses are harder than Day Math courses

figurate numbers

Numbers that can be represented by dots arranged in the shape of geometric figures

Cognitive Entry Skills

Prior math knowledge, background knowledge

Read Word Problems Carefully

Read Word Problems Carefully (just do it)

Summer Semester vs. Fall/Spring Semester

Summer Semester Math courses are more difficult than Fall/Spring Semester Math courses

George Polya

The "Father of Problem Solving"

Self-Efficacy

The belief that one has the ability or skills to complete a specific task or overcome a particular challenge

Georg Cantor's Set Theory

The cardinality (numerical size) of a set is strictly less than the cardinality of its power set, or collection of subsets

Sequential Learning Pattern

The material learned on one day is used the next day and the next day, and so forth

Quality of Instruction

Classroom atmosphere, teaching style, lab instruction, textbook content/format, etc

Georg Cantor

German mathematician who formulated the theory of sets

Locus of Control

The person, place, or thing which one believes is responsible for their grades and behaviors

Carl Gauss' Sum of Natural Numbers

The sum of all natural numbers from 1 to 100 is 5050. Gauss added each number to get 101, then multiplied by 100 then divided by 2- to get 5050.