Number Sense Exam Flashcards
Number Sense Definition
A holistic concept of the ability to understand quantities, numbers, operations, and relationships among them which are applied efficiently and flexibly in making a mathematical judgment.
A person’s general comprehension of numbers and operations along with the ability and propensity to use this understanding flexibly.
The ability to quickly understand, estimate, and manipulate numerical quantities.
The foundation for students to understand formal math concepts.
What happens if you dont have number sense
A lack of understanding number will lead to obstacles that are difficult to overcome in mathematics learning.
Children who are not trained to use their senses in handling simple calculations tend to get stuck on rules that make their strategies and flexibility undeveloped.
Number sense is more acknowledged as an ability or knowledge, not intrinsic processes.
What is number sense not?
A rigid approach to manipulating numbers toward a specific solution
Memorization
Applications of algorithms without an understanding of the mathematical ideas embedded in problem solving
Why is developing number sense in the early years important?
“Early number sense is a strong predictor of later success in school mathematics.”
Dyson, Jordan, and Glutting(2011)
“What a 5- or 6- year old child knows about mathematics can predict not only their future mathematics achievement, but also their future reading achievement.”
Components of Number Sense
Students with number sense:
Have well-understood number meaning
Have developed multiple relationships among numbers
Recognize the relative magnitude of numbers
Know the relative effect of operating on number
Develop references to measure objects and general situations in their environment
Think and solve problems rationally, analytically, creatively, effectively, and flexibly
Find flexible and appropriate ways to solve a numerical problem
Easily identify numerical errors
Assess the truth of the obtained results when performing numerical calculations
Transfer their mathematical knowledge in and out of the school environment
See the world in terms of numbers and quantity (example: knowing when 100 is a lot and when 100 is a little)
Prefer to develop computational strategies such as mental calculations, calculator techniques, and estimations
Create procedures to solve a problem
represent numbers in various ways to suit the context and purpose
Identify benchmarks and number patterns
Understand the general nature of a numerical problem without performing standard calculations
What are the mathematical standards?
Content
Process
Proficiency
TEKS
Content Standards
WHAT we learn in math
Number and Operations
Algebra
Geometry
Measurment
Data Analysis and Probability
Financial Literacy
Process Standards:
HOW we learn in math
Problem solving
communication
connections
representation
reasoning and proof
Mathematical Proficiency
The goal!
Conceptual Understanding
Procedural Fluency
strategic competency
adaptive reasoning
productive dispostion
TEKS
Texas Essesntial Knowledge and skills
Your curriculum
cohesive and connected (aligned across the grades)
VERBS tell you what is expected, what your students need to be able to do
Nouns tell what your students need to know
What are basic facts for addition and multiplication
The basic facts for addition and multiplication are the number combinations where both addends or factors are 10 or less.
Students move throuugh three phases in developing fluency with basic facts
Counting strategies,
reasoning strategies, and
mastery.
What provides the basis for strategies that help students remember basic facts or to figure out unknown facts?
Number relationships
WHAT is not the answer when students struggle with basic facts?
Look at Big Idea #2: Drill removes the opportunity to focus on number relationships which is the basis for strategies.
WHAT is not the answer when students struggle with basic facts?
Look at Big Idea #1: Students move through 3 stages when learning basic facts. When the focus is on drill, the second stage of learning basic facts is neglected. The reasoning stage of learning basic facts is where conceptual understanding is established and connections are built.
WHY is drill not the answer to learning basic facts?
When we think about the developmental stages of learning math (concrete - representational - abstract), it makes sense. The abstract level is the drill. Drill is the 3rd stage of learning basic facts.
What is fluency
Fluency is being able to solve problems:
Flexibly
Efficiently
Accurately
What are the developmental stages for learning basic facts
Counting
Reasoning Strategies
Mastery
Prior knowledge for Counting strategies
Knowledge of number names
Sequencing of number names
1-1 correspondence
Concept of number sets
Basic manipulatives that help with the conceptual level (counting strategies)
Ten Frames
Number lines
Basic Fact Strings
Manipulatives -count sets
What is the second stage of developing basic fact fluency
Stage 2, Reasoning Strategies, is the 2nd stage of developing basic fact fluency.
Why is Stage 2 such an important stage of developing basic fact fluency?
The reasoning stage of learning basic facts is where conceptual understanding is established and connections are built.
it builds number sense
Examples of activities that focus on the 2nd stage, reasoning strategies
Categorizing facts
Activities to focus on categories
Flash cards
Categories Dice Game
Addition Fact Chart
addition fact categories
+ 0,1,2
+10
+9
Doubles
Neighbors
basic manipulatives for reasoning strategies
Ten Frames
Two Row Rek-N-Reks
Basic Fact Strings
Manipulatives
what is stage three of developing basic fact fluency
Mastery
what is stage one of developing basic fact fluency
counting strategies
Mastery- Just knowing: explain
This just happens after HOURS and HOURS and Years of working to COMPRESS the knowledge of facts through conceptual development, concrete experiences. THEN… as students enter into mastery where they are not needing the concrete models or the representations of those models as much… THEN is when you can begin working on speed of recall.
counter productive practices
Memorization and
timed tests
What do counter-productive approaches DO?
They are not just ‘un’-productive. They are ‘counter’-productive?
Why are they counter-productive?
because the actually contribute to the development of math anxiety, math trauma, fixed mindset, etc. and as a result,
students LOSE ground when using these approaches.
Skips Phase 2 (Reasoning Strategies)
of the developmental process resulting in limitations.
ARTICLE REVIEW
Name one unproductive strategy
name what makes it unproductive
Explain what to do instead
Pressing for speed
drives fluecy in the other direction, mentally implementing a strategy will take more time in the bringing so this strategy teaches kids to not use a strategy and only try to be fast
will also cause students anxiety and turn them away from loving math
instead: chose games that have each student solving a different problem and taking turns
don’t pit students against each other
provide low-stress meaningful practice
What makes counterproductive approaches inefficient? Know this…They are inefficient because:
Without an emphasis on strategies, students result to counting.
They do not help students build connections, identify number relationships; and
Defaulting to counting (using tally marks to do basic addition) demands time, concentration, and will often lead to frustration, loss of focus on the main idea of the problem, and result in incorrect solutions.
Counter productive practices= memorization + times tests Why are these approaches counter-productive?
100 isolated facts to memorize for each operation
Without an emphasis on strategies, students result to counting.
Misapplication of facts, students don’t check work because they don’t have strategies to help them check and confirm their work.
What is the real number system
The Real
Number System
consists of all of the numbers that we can put on the numberline.
Natural (counting)
Numbers: (1,2,3…)
Operations: Addition, multiplication
Whole
Numbers=+0 (0,1,2,3…)
Operations= addition + mutiplication
Integers
Numbers: +negative (… -2,-1,0,1,2,3…)
operations: additon multiplicatiion, subtraction
Rational
numbers added 1/2, 0.5
operations: addition multiplication, subtraction division
Irrational
numbers added square root of 2
opperations addition, multiplication, subtraction, division
iteration
repeated addition of the same value
partitioning
splitting into equal parts
benchmarks of fractions
0,1/2,1
there are three categories of models for working with fractions
area length set
students need many experiences estimating with fractions
to promote concept development and flexibility of thought NUMBER SENSE to develop an intuitive feel for and with fractions\
