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informal assessment

observations & checklist

formal assessment

projects. papers, and portfolios rubrics essays tests

Performance-based assessments

ex: a lab experiment

authentic assessments

projects, anecdotal, portfolios

criterion-referenced tests

students can score 100 because they should understand the concept being tested

norm-reference test

A form of assessment in which the test takers' scores can be compared to the scores of a specified group of people, typically a group of the test takers' peers, such as students in the same grade.

percentile scores

the percentage of the population whose scores fall at or below the student's score.

raw scores

how many questions the student answered correctly -used to find the percentage score

normed scores

test scores that are compared to a specified group to determine how a student scored in comparision to the group

reliability

the ability of the instrument to give consistent results with repeated measurments. ex: a good bathroom scale gives the same # each time

Validity

does the test measure what it claims to measure

deductive reasoning

reasoning in which a conclusion is reached by stating a general principle and then applying that principle to a specific case (The sun rises every morning; therefore, the sun will rise on Tuesday morning.)

inductive reasoning

deriving general principles from particular facts or instances ("Every cat I have ever seen has four legs; cats are four-legged animals").

teaching deductively

the teacher gives the students the rule first and then practices it

teaching inductively

the students see many applications of the rule and then determine the rule themselves

inquiry lessons

start with a thought provoking question

set

a collection of things real or imagined related or unrelated

array

area method of representing a multiplication problem

multiples

numbers that a given number divides evenly into

reciprocals

two numbers whose product is 1

ex 8 X 1/8 = 1

ex 8 X 1/8 = 1

associative property for addition and multiplication

3+ (7+5) is the same as (3+7)+5 grouping does not make a difference

distributive property of addition and multiplication

6 X 47 is the same as (6X40) + (6X7)

natural numbers

The set of numbers 1, 2, 3, 4, ... Also called counting numbers.

factors

all whole numbers that divide evenly into a given number.

prime numbers

Numbers with exactly two factors, 1 and itself. Examples would be 2, 3, 5, 7, 11, 13, and 17

composite numbers

Numbers with more than two factors. Examples would be 4, 6, 8, 9, 10, etc.

rational numbers

any number that can be expressed as a fraction

integers

whole numbers and their opposites

fractions

part of a whole

irrational numbers

numbers that cannot be expressed in the form a/b, where a and b are integers and b =0, when written as a decimal it does not repeat or terminate

rational numbers

numbers that can be written as fractions, including terminating and repeating decimals, and integers

real numbers

all the numbers that can be represented by points on the number line

percent

out of 100

ratio notation

an alternative method for showing fractions 2/5 can be expressed as the ratio of 2 to 5 or 2:5

proportion

an equation stating that two ratios are equal ex 2/5 = N/10

congruent

if the measures of two angles are the same the angles are congruent

area

the number of square units needed to cover a flat surface

polygon

a closed plane figure bounded by straight sides

regular polygon

a closed plane figure with all sides and all angles equal

congruent polygons

the same size and shape

similar polygons

the same shape but different sizes; corresponding angles, have the same measure and the lengths of corresponding sides are porportional

tessellation

a repeating pattern of plane figures that completely cover a plane with no gaps or overlaps

scaling

a linear transformation that enlarges or reduces an object

measures of centeral tendency

mean- the average of the numbers

median- the middle number when the vaules are in order

mode-the value occurring most often

range- the largest number- the smallest number

median- the middle number when the vaules are in order

mode-the value occurring most often

range- the largest number- the smallest number

probability

a measure of how likely it is that some event will occur

P= number of ways the event can occur/ total number of possible events

P= number of ways the event can occur/ total number of possible events

problem solving strategies

estimation (2 level of blooms taxonomy- understanding)

guess and check

draw a picture

make a table or a chart

act it out

look ofr patterns

simplify the numbers

work backwards

guess and check

draw a picture

make a table or a chart

act it out

look ofr patterns

simplify the numbers

work backwards

volume

the amount of space an object occupies; 3-D

expository

method of instruction based on teacher-dominated activities, examples could include lecture, reading a story, showing video, etc.

discovery

takes place in problem solving situations where the learner draws on his own experience and prior knowledge and is a method of instruction through which students interact with their environment by exploring and manipulating objects, wrestling with questions and controversies, or performing experiments

guided inquiry

is carefully planned, closely supervised,

targeted investigation method of instruction

targeted investigation method of instruction

aptitiude test

predicts a student's ability

achievment test

determines a student's mastery of specific topics/concepts

enrichment

tiered lessons, learning centers, or other options which allow capable students to participate in extended learning opportunities

task analysis

when as assignment or skill is broken down into smaller sequential steps and each of those steps are taught one at a time

chunking

the strategy of breaking down information into bite-sized pieces so the brain can more easily digest new information

scope and sequence

design element of curriculum which includes decisions and planning about the information to be taught as well as an outline of the which sequence skills an concepts are taught

anticipatory set

opening activity of a lesson plan; prepares students for the upcoming lesson

direct instruction

general term for the explicit teaching of a skill-set using lectures or demonstrations of the material, rather than exploratory models such as inquiry-based learning

mastery learning

an instructional philosophy based on the idea of giving students more than one chance to demonstrate profeciency of content and skills.

extrinsic motivator

those that come from outside the individual; often tangible items e.g. money, prizes, stickers

intrinsic motivatior

those that come from within the individual; satisfaction, pride, feeling of accomplishment

equity

expectations and support for ALL students

constructivism

individuals create their own knowledge based on previous knowledge and controlled investigation

procedural knowledge

understanding of rules, routines, and tasks of mathematics

scaffolding

specialized instructional supports put in place in order to best facilitate learning when students are first introduced to a new subject.

ways students can respond to mathematical questions

concrete, picture, symbols, and/or oral

anecdotal notes

informal observational data recorded by a teacher as an assessment of how a student is performing on a learning concept, socially, etc.