Mathematics Instruction Flashcards
Place Value
The value of each digit in a number based on its location, or place
In 135, the 3 is in the tens place and has a value of 3 x 10 or 30.
Inquiry-Based Teaching / Student-Centered Learning
students drive instruction by asking questions and creating projects to answer the questions
Constructivism
Learning new behaviors by adjusting our current view of the world
Research projects
English Language Learners (ELLs)
Students who are learning the English language, or for whom English is not a first language
Manipulatives
Objects used by students to illustrate and explore mathematical concepts, such as to represent numbers in an equation
Blocks, Coins
Thematic Unit
a unit that has an overarching, uniting idea or topic, and incorporates skills into that theme. It can be within one subject-area or support cross-curricular instruction.
Behaviorism
Learning theory rooted in the notion that all behaviors are learned through interaction with the environment
Cognitivism
Learning new behaviors by connecting current knowledge with new knowledge
Teaching fractions by talking about pizza slices
Visual Learning
Learning primarily by seeing things
Written examples
Concrete Representations
Using physical pieces to represent mathematical problems
Manipulatives
Closure Activity
a time to summarize the learning for the day
What question(s) do you still have about today’s lesson?
Flexible Grouping
grouping students based on their learning needs or interests
After reviewing the student test results, a teacher can use flexible grouping to organize groups based on students’ areas of weakness.
Compartmentalized Teaching
concepts taught one at a time in isolation of other concepts (no longer recommended)
Visual Methods
Lessons using materials for students to view.
maps, images, political cartoons, multimedia presentations and graphs
Backward Design / Planning
Lesson planning that begins with the desired outcome in mind
Kinesthetic Learning / Tactile Learning
Learning primarily by touching things or doing an activity
create and act out plays or skits
Tactile Methods
Lessons using materials for students to touch and handle.
Encouraging students to take notes, use study sheets, build dioramas or models
Heterogeneous Group
group comprised of individuals working on various levels
A small group of students with varying academic abilities working together on a science project is a heterogeneous group.
Symbolic Stage / Representational Stage
Drawing pictures or symbols to represent numbers in an equation
Squares
Learning Style
The manner in which a student learns best
Visual Learning
Integrated Teaching
multiple concepts are used in problem-solving at once (current best practices)
Basic Operations
addition, subtraction, multiplication, and division
Math in early elementary school grades focuses on basic operations.
Counting
to name or list one-by-one in order to reach the total quantity
Popsicle sticks can be used by young children to practice counting. When there is a group of ten popsicle sticks, they can be grouped together with a rubber band as “one set of ten.”
Word Problems
a math question written as one sentence or more that requires children to apply their maths knowledge to solve a ‘real-life’ scenario
Jack had $10 and spent $4. How much money does he have left?
Small Group Instruction
a few members of the class learning together, as opposed to whole-group instruction
The students rotated through learning stations while the teacher pulled a few students to her table at a time for small group instruction.
Homogeneous Group
group comprised of individuals working on the same level
A small group of students reading a book together on the same reading level is a homogeneous group.
Culturally Responsive Teaching
an approach that recognizes the importance of including students’ cultures in all aspects of learning
Learning about students’ backgrounds and interests to cultivate authentic relationships in which students feel respected and valued is an example of culturally responsive teaching.
Texas Essential Knowledge and Skills (TEKS)
The state foundation curriculum developed by the State Board of Education, that requires all students to demonstrate the knowledge and skills necessary to read, write, compute, problem solve, think critically, apply technology, and communicate across all subject areas
Abstract Thinking
Using numbers or letter variables in an equation
13x = y
Auditory Methods
Lessons using materials for students to listen to.
speeches, music, or direct instruction
Auditory Learning
Learning primarily by hearing things
Lectures
Proportional Manipulatives
objects that are proportional to each other with respect to shape and size
tangrams
Concrete Operational Stage
the third stage of Piaget’s Theory of Cognitive development, occurring from 7 years old to adolescence, in which children begin to think logically and use inductive reasoning
Preoperational Stage
the second stage of Piaget’s Theory of Cognitive development, occurring from 2-7 years old, in which children think egocentrically and symbolically
Formal Measurement
uses traditional measurement tools to find value
ruler for length
Numeric Representation
A model using numbers to display a mathematical concept.
Verbal Representation
word problems and verbal descriptions of how to solve a problem or what the solution means
“We know that Sam gets $10 each week for allowance, so let’s make that a constant. And we know that Sam wants to save $150 to buy a new bicycle, so that’s a constant, too. But, what we don’t know is how long does Sam need to save - let’s make that X. So the equation is 10x = 150.”
Graphic / Pictorial Representation
A graph or picture that serves as a visual model of a mathematical equation.
Number line
Word Wall
An on-going bulletin board with common terms used frequently in the classroom. Vocabulary words are added as they are introduced
Search Engine
tool used to locate information on the internet
Google, Kiddle
Pie Chart
graph in which a circle is divided into sectors that each represent a proportion of the whole. Pie charts are helpful when displaying the relative distribution of categories.
App
a software application that is designed to perform a specific function for the user and can be utilized for teaching purposes
Remind, Canva, Kahoot
Number Line
a straight line where each number is equal distance from the next one
Presentation Software
used to display information with audio and visual components
Powerpoint, Google Slides, Prezi
Website
collection of web pages housed under a common domain name that are viewed on an internet browser
kids.nationalgeographic.com, learninglab.si.edu
Manipulatives
Objects used by students to illustrate and explore mathematical concepts, such as to represent numbers in an equation
Blocks, Coins
Concrete Representations
Using physical pieces to represent mathematical problems
Manipulatives
Blog / Discussion Board
platform for posts about various subjects and comments on the posts
Edublogs, Flipgrid
Non-proportional Manipulatives
objects that are not proportional to each other with respect to shape and size. Often all of the items are the same size.
counting tokens
Bar Graph
a visual representation of data which compares values in different categories
the number of people who prefer each genre of movie
Line Graph
a visual representation of data which shows change over time or in response to a manipulated variable
Informal Measurement
uses readily available objects to find value
arm for length
Collaboration Software
applications designed for multiple users to share and work on files and documents together
Symbolic Representation
A model using symbols or variables to display a mathematical concept.
Formula
Spreadsheet
A tabular view of data with columns and rows; the intersection of a column and row is called a cell.
Formal Assessments
a usually post-instruction assessment with the purpose of assessing student knowledge, retention, and application. Often involve the use of a standardized rubric or scoring guide based on several criteria.
chapter tests, semester tests
Criterion-Referenced Tests
Tests in which a standard has been set for the test taker to achieve in order to pass the test.
A multiple choice or short answer test on the content of a unit of study in which a 70% is needed to pass.
Informal Assessments
More flexible than formal assessments and can be adjusted to fit the situation and particular needs of the student being tested
observations during a lesson
Universal Screener
An assessment administered to all students to gather data and form groups, such as intervention groups
Exit Slips
A short formative assessment given by a teacher after completing a lesson to determine the degree to which students have learned the material taught in the lesson.
Norm-Referenced Tests
Tests that compare an individual’s performance/achievement to a group called the “norm group.”
An IQ test
Progress Monitoring
periodic assessments to monitor student growth and evaluate the effectiveness of instruction
The teacher prepared a progress monitoring assessment to see how much each student had improved and learn if his new instructional approach was effective. The teacher
Portfolio
A collection of student’s work and achievements that is used to assess past accomplishments and future potential; can include finished work in a variety of media and can contain materials from several courses over time
Diagnostic Assessment / Pre-Assessment
Assessment administered before instruction to determine students’ strengths and weaknesses
Summative Assessments
Assessment of learning. Given at specific points in time in order to determine what students know and don’t know. Summative assessments are generally formal.
State assessments, district benchmarks, semester or six weeks tests, and end of unit or chapter
Formative Assessments
Assessment for learning. Usually mid-instruction assessment with the purpose of assessing student progress and informing the teacher so instruction can be altered as needed.
graphic organizers, games
Curriculum-Based Assessments
testing the curriculum being taught
Performance-Based Assessment
A kind of assessment that requires students to show mastery of specific skills by demonstrating, producing, or performing something
designing and performing experiments, building models, writing poems or shorts stories, and developing portfolios
Division Property of Equality
If the quantities on each side of an equal sign are both divided by the same amount, the resulting statement will still be equal.
Metacognition
the ability to think about one’s own thought process
Conjectures
guesses without proof while doing mathematics
Multiplication Property of Equality
If the quantities on each side of an equal sign are both multiplied by the same amount, the resulting statement will still be equal.
Teacher Wait Time
the silence that often comes after a question has been asked but before students have finished considering their answer and/or find the courage to speak up
Subtraction Property of Equality
If the quantities on each side of an equal sign have the same amount subtracted from them, the resulting statement will still be equal.
Algorithms
systematic methods that always produce a correct solution to a problem
Area = Base x Height
Addition Property of Equality
If the quantities on each side of an equal sign have the same amount added to them, the resulting statement will still be equal.
Deductive Reasoning
using two or more known premises to draw a conclusion
Formal Reasoning
the use of logic and algorithms to reach conclusions
Informal Reasoning
used to answer questions and solve problems that are complex and open-ended (without a definitive solution)
Inductive Reasoning
generalizing knowledge from one area to another
Think-Pair-Share
Active learning activity in which the teacher provides a prompt, the students consider it individually (THINK), then pair up and brainstorm responses or solutions (PAIR), and then the students then share their results with the class (SHARE).
Estimating
rounding numbers or approximating them to quickly perform math operations
