Math Flashcards
used to gather data on all students. The purpose is typically to put students into groups, such as intervention groups.
universal screener
used to identify students’ specific strengths and weaknesses.
diagnostic assessment/pre-assessment
happen throughout instruction
flexible assessments that can be easily adjusted to fit the flow of the lesson
occurs through observation.
Informal assessments
happen both during and after an instructional unit
Ex: quizzes, tests, and projects or writing assignments scored with some kind of scale or rubric.
Formal assessments
are assessments for learning
used to guide instruction meaning they’re administered to assess students’ progress toward meeting a learning objective so teachers can adjust instruction as needed
“What do I teach next?”
Formative Assessments
are assessments of learning.
used to gauge instruction by determining whether or not students mastered a learning objective
“What did my students learn?”
Summative assessments
Criterion-referenced assessment
compare student performance to a predetermined standard,
ex: Tests administered at the end of an instructional unit and state achievement tests
compare students to each other and rank them according to performance
Ex: Scholastic Aptitude Test or SAT and Intelligence Quotient (IQ) tests.
Norm-referenced assessments
periodic assessments given to keep track of student growth toward a specific goal or objective
Progress Monitoring
Curriculum-Based Assessment
measures student progress using materials taken directly from the curriculum
Performance-Based Assessment
students apply knowledge or skills to complete a process or create a product
Portfolio
collection of student work to show growth over time
Exit Slip
short response completed and submitted at the end of a lesson
Write and say content / objectives
Use short, simple, specific sentences
Use gestures, pictures, and models
Have a “word wall” on which key terms are expressed in both English AND the student’s native language
Allow additional time to complete assignments/tests
Teach vocabulary intentionally and explicitly
Provide sentence stems for students to use when speaking
Use cooperative groups
Pair the student with another speaker of their language, if possible
Present notes bilingually, if possible
ELL and Engagement in math
ability to think critically about the processes that are used to arrive at an answer.
Mathematical reasoning
Teachers can help students develop mathematical reasoning skills through….
Explicitly teach students multiple strategies for solving a problem.
Encourage metacognition in students by asking students to explain their thought process and how they arrived at their answer.
Ask students to demonstrate another way that they can arrive at the correct answer.
Teach and remind students to ask themselves if their answer “makes sense.”
Ensure that students have a strong foundation in a skill before moving on to more abstract concepts such as algorithms
Piaget’s stages of development
Sensorimotor
Pre-operational
Concrete operational
Formal operational
birth-2 years
First stage of a childs mental development which mainly involves sensation and motor skills such as hearing, seeing, feeling, tasting, moving, manipulating, biting, chewing, etc.
In this stage the child does not know that physical objects remain in existence when out of sight
Sensorimotor Stage
2-7 years
In this stage children use their mental ability to represent events and objects in various ways like using symbols gestures and communication..
they are not yet able to conceptualize abstractly and need concrete physical situations to help with understanding concepts
Pre-operational Stage
7-11 years
At this stage the child starts to conceptualize, creating logical structures that explain physical experiences.
Abstract problem solving is also possible at this stage. Math problems can be solved with numbers not just with objects
Concrete operational stage
11- adulthood
Children become more systematic and reasonable
they reason tangibly and are also capable of reasoning and thinking in more abstract hypothetical and idealistic terms
Formal operational stage
Mathematics should be taught….
conceptually
This kind of instruction Is connected to students real experiences and uses activities that students see hear touch and taste
Concrete instruction
Manipulatives
are any object that can be touched or moved to assist understanding
When planning instruction the learning modalities that should be in use are …..
visual - Learn by seeing
auditory - Learn by hearing
kinesthetic - Learn by touch or movement
The different types of learning are …
Association
Concept
Principle
Problem solving
Words or symbols
Association
Relational or concrete attributes
Ex: similar figures have relational attributes. The corresponding angles are equal and the ratios of corresponding sides are equal
Concept
Generalizations, developed rules
Ex: The area of a trapezoid is developed from the concept of a trapezoid and the area of a triangles rectangles and or parallelograms
Principle
Putting together concepts and principles to solve a problem new to the learner
Ex: Given a composite figure the student determines the area using the areas of triangles and rectangles
Problem solving
Development of learning
Concrete- manipulative, models, hands on
Pictorial - pictures diagrams, graphs
Abstract- symbols, words
A general problem solving method that can be applied to many types of problems is …
Understand
Plan
Solve
Check
Inductive Reasoning
reasoning goes from specific to general
uses observations and patterns to infer a generalization
Deductive Reasoning
reaches conclusions based on accepted truths and logical reasoning
Goes from general to specific
assessment written to general content and performance on test is based on a comparison to other similar students who took the test
Ex: SAT ACT GRE
Standardized assessment
Instructional designs student placement monitoring student progress summative evaluation of a student accountability Validating student achievement True/false worked out problems essays fill in the blank matching multiple choice program evaluation
all describe the …
Purpose of assessment
the different kinds of assessment are…
reports applications models lab investigations projects always. sometime , never
addition
subtraction
multiplication
division
all are …
Basic arithmetic operations
Number sense is …
Having an understanding of how numbers work and the easier way to find an answer
Number models are…
using pictures or objects to show a problem
patterns are …
meaningful repetition in numbers pictures or objects
finding variables or unknown parts in a problem is..
Algebraic thinking
length
capacity
weight
describe …
measurement
how a digits location in a number affects its value is ..
place value
two dimensional and three dimensional shapes and their characteristics describes …
Geometry and spatial relations
Dividing whole numbers into parts describes …
fractions and decimals
This shows us how to use information (graphs and charts)
Data
This is an educated guess or rounding
Estimation
Solving problems in a logical way is …
Logical reasoning
instruction that begins with the desired outcome in mind
Backwards planning
Learning new behaviors based on the response they get to current behaviors
ex: If a student studies for a test (current behavior) and makes a good grade (response) they will learn to study for tests (new behavior).
Behaviorism
Learning new behaviors by connecting current knowledge with new knowledge
EX:If a student studies for a test by associating real-world examples with the concepts such as learning fractions by slicing a cake into equal parts, they will retain the information.
Cognitivism
Learning new behaviors by adjusting our current view of the world
EX:This is best used for brainstorming rather than test preparation as it requires students to use what they know to predict new applications of mathematical ideas.
Other uses for this approach are group work or research projects.
Constructivism
Tips for reinforcing mathematical vocabulary
Use language that is developmentally appropriate.
Model correct mathematical language.
Be sure that the language is understood by all students.
(An ongoing “Word Wall” following the format used in the student vocabulary notebooks/ Periodic assessments where students use their vocabulary notebooks will reinforce their importance and relevance..)
of sides and angles
how to classify triangles
have only two factors: one and themselves
2, 3, 5, 7, 11
prime numbers
are used to compare things between different groups or to track changes over time.
purpose of bar graphs
y=mx+b
y-intercept (where the line crosses the y-axis)
The m in the y=mx+b is the
m=y2-y1/x2-x1
slope intercept
the b in the equation
slope of the line (rise over run)
slope formula
a^2+b^2=c^2
pythagorean theorem
(slide) an isometry that maps all points of a figure the same distance in the same direction.
flip) an isometry in which a figure and its image have opposite orientations
translation
reflection
average
The middle number
The difference between the highest and lowest number in a set of data
The number that occurs most often in a set of data
mean
median
range
mode
the likelihood that an event will occur
equally likely chance of an event happening is the same as a __________ chance
a certain chance of an event happening is the same as a ______________ chance
an unlikely chance of an event happening is the same as approximately a ________________ chance
a likely chance of an event happening is the same as approximately ______________ chance
probability
1/2, 0.5, or 50%
1/1 , 1, 100
1/4, 0.25, or 25%
3/4, 0.75 or 75%
have more than exactly two numbers that divide them evenly
ex: 4 15 49
composite numbers
the sum of the numbers place values
1,729=1000+700+20+9
expanded form
changing the order of numbers being added or multiplied gives the same answer
ex: 12+7 gives the same answer as 7+12 and 3x9 gives the same answer as 9x3)
the grouping of the numbers in addition or multiplication does not change does not change the answer
Ex: (2x4)x3=2x(4x3)
multiplication and division may be distributed over addition or subtraction
ex: 10x(50+3)=(10x50)+(10x3)
(30-18)/3=30/3- 18/3
commutative
associative
distributive
straight one dimensional figure that has no thickness and extends forever on both ends
a line that starts at one end point and goes on forever to infinity ( two of these that share the sam endpoint make an angle)
lines that go in the same direction and never intersect
lines that intersect at 90degree angles
line
ray
parallel
perpendicular
two shapes can overlap each other completely with no gaps or extra pieces of symmetry
ex: equilateral triangles squares and hexagons
tessalation
uses general info to come to a specific conclusion
ex: sacrates is a man, all men are mortal, therefore socrates is mortal
deductive reasoning
