Terms, Vocab, Resources 1 Flashcards
National Council of Teahers of Mathematics, NCTM
World largest mathematics education organization
Common Core State Standards, CCSS
Specify mathematic content
National Assessment of Educational Progress, NAEP
Data on students performance in mathematics
Trends in International Mathematics and Science Study, TIMSS
Mathematics studies performed on an internatoinal scale comparing different countries
No Child Left Behind, NCLB
Presses for a higher level of achievement, more testing, and increased teacher accountability
Professional Satandards for Teaching Mathematics, PSTM
Articulates a vision of teaching math based on the expection described in CES
Cirriculum and Evaluation Standards, CES
Sifnificant Math achievement is a viion for all students, not just a few.
Assessment Standard for School Mathematics, ASSM
Focuses on the importance of integrated assessment with instructionand indicates the key role that assessment plays in implementing change
Cirriculum Focal Point, CFP
Math taught at each level needs to focus, go into depth, and explicitly show connections.
Problem Solving standard
Describes peoblem solving through which students develop mathematical ideas.
The Reasoning and Proof standard
Emphasizes the logical thinking that helps us decide if and why our answers make sense.
The Communication standard
Points to the importanceof being able t talk about, write about, describe, and explain mathematical ideas.
The Connection stabdard
It is important to connect within mathematical ideas and mathematics should be connectedto real world and other disciplines.
The Representation standards
Emphasizes the use of symbols, charts, graphs, manipulatives, and diagrams as powerful methods of expressing mathematical ideas and relationships.
Learning Trajectories
The selection of topics at particular grades that refflects rigorous mathematics and learning progressions.
Persistence
The ability to stave off frustration and demonstrate persistence
Positive Attitude
Positive attitute towards math
Readiness for Change
Demostrate a readiness for change, even for changes so radical that it may cause desequilibrium
Reflection Disposition
Making time to be self-concious and reflective.
Doing Mthematics
It means generating strategies for solving problems, applying those approaches, seeing if they lead to solutions, and checking to see whether your answer makes sense.
Mathematics
The science of concepts and processes that have a pattern of regularity and logical order.
Explicit
The focus on students’ applying their prior knowledge, testing ideas, making connections and comparison, and making conjectures
Productive Struggle
A way of engagement in productive that struggle helps students learn mathematics
Constructivism
Rooted in John Piaget’s work, developed in 1930s, it is the notion that learners are not blank slates but rather creators(constructors) of their own learning.
Assimilation
Occurs when a new concept ‘fits’ with prior knowledge and the new information expands an existing network
Accomodation
Takes place when the new concept does not ‘fit’ with the existing network (causing what Piaget called disequilibrium) so the brain revamps or replaces the existing schema
Reflective Thought
The effort required to connect new knowledge to old knowledge
Sociocultural Theory
Mental processes exist between and among people in social learning sttings, and that from these social settings the learner mones ideas into his/her own psychological realm
Zone of Proximal Development, ZPD
Refers to range of knowledge that may be out of reach for a person to learn on his/her own, but is accessible if the learner has support from peers or more knowledgeable others
Semiotic Mediation
the mechanism by which individual beliefs, attitdudes, and goals are simultaneously affect sociocultural practices and institutions
Scaffolding
Based on the idea that a task otherwise outside os a students ZDP can become accessible if it is carefully structured
Tools
Any object, picture, or drawing that represents the concept or onto which the relationship for the concept can be impossed
Manipulatives
Physical objects that students and teachers can use to illustrate and discover math concepts, whether made specifically for math
Conceptual Understnading
Knowledge about relationships or foundational ideas of a topic
Procedural Fluency
Knowledge and use of rules and procedures used in carrying out math processes and also the symbolism used to represent math
Strategic Competence
Using different designs, trying different approachesto solving a given problem
Adaptive Reasoning
The capacity to reflect on your work, evaluate it, and then adapt, as needed.
Productive Disposition
it having a ‘can do’ attitude towards math problems phased
Teaching for Problem Solving
Teaching a skill so that a student can later solve a problem
Teaching About Problem Solving
Teaching studenta how to problem solve, which can include the process or strategies for solving a problem.
Teachinf Through Problem Solving
Students learn mathematics through real context, problems, situations and models
Problem
A task or activity for which a student have no perception or memorized rules or method, nor is there a perception by student that there is a ‘specifi correct’ solution method
Proceduralize Problem Solving
Avoid taking the problem solving from the student by offering startegies.
Concepts
Building on Ideas students already posess
Procedures
Teaching through problem solving where students determine the approach to computing the problem.
Cognitively Demanding
Involves higher-level thinking
Low-cognitive demand
Involving facts, following known procedures, and solving routine problems
Multiple Entry
A task having various degrees of challenge within it or it can be approached from a varity of ways
Multiple Exit Points
Various ways that students can demonstrate understanding of the lerning goals
Initiation-response-feedback, IRF
Does not lead to classroom discussion that encourage all students to think
Funneling
Continuos probing of students in orderto get them to a particular answer
Focusing
Pattern which uses probing questions to negotiate a classroom discussion and help students understand the math
Metacognition
concious monitoring and regulation of your own thought process
