NSF Glossary

Ableism: Ableism is the system of assigning value to people’s bodies and minds based on societally constructed ideas of normalcy, productivity, desirability, intelligence, excellence, and fitness. These constructed ideas are deeply rooted in eugenics, anti-Blackness, misogyny, colonialism, imperialism, and capitalism.

Ambitious mathematics instruction: In classrooms where teachers are enacting ambitious mathematics instruction, students are:  

  • actively involved in mathematical reasoning and sensemaking 
  • developing both conceptual understanding and procedural fluency  
  • flexibly using strategies to formulate, represent, and solve problems
  • developing productive dispositions and positive identities as doers of mathematics  

Conceptual understanding: Comprehension of mathematical concepts, operations, and relations 

  • Students with conceptual understanding recognize the importance of a mathematical idea and know the kinds of contexts in which it is useful. They have organized their knowledge into a coherent whole, which enables them to learn new ideas by connecting those ideas to what they already know. 

Cognitive apprenticeship: An instructional approach that makes the invisible practice of thinking visible to the student.

Cognitive flexibility: The ability to engage in perspective-taking and flexibly adapt to new situations or priorities 

Cognitive Load Theory (CLT): All humans have limited capacity at any given time to use their auditory, visual, and tactile inputs (independently or collectively) to acquire new information and store it in long-term memory. When available cognition is overwhelmed – which can be caused by any number of reasons – learning cannot occur.

Cognitive strategy: Cognitive strategies are specific enactments of cognition that learners can apply as needed. Examples related to understanding and solving word problems include visualizing the problem, identifying problem structure, or representing quantities concretely. 

Direct modeling: Representing a problem in some concrete way on fingers, with tally marks, or by manipulating counters 

Executive functions: Mental processes that enable us to plan, focus attention, remember instructions, and juggle multiple tasks successfully 

Extraneous cognitive load: Describes the strain on cognitive processes from sources unrelated to the task itself 

Funds of knowledge: Collections of knowledge and skills based in cultural practices that are a part of families’ traditions, work experience, or daily routine 

Inhibitory control: The ability to control our thoughts, behaviors, emotions, and attention and avoid impulsive actions 

Intersectionality: A term to describe the way that systems of oppression overlap to create distinct experiences for people with multiple identity categories. 

Intrinsic cognitive load: The processing needed to complete any learning task 

Marginalized: Marginalized populations are groups and communities that experience discrimination and exclusion (social, political and economic) because of unequal power relationships across economic, political, social and cultural dimensions.

Medical model of disability: Situates disability as individual deficits that need to be corrected 

Metacognition: An awareness of one’s thought processes and an understanding of the patterns behind them 

Metacognitive modeling: Thinking aloud about thinking in order to make a strategy, task, or process more accessible to students

Metacognitive strategy: A specific enactment of metacognition that learners can apply as needed. Examples include self-questioning, self-talk, self-reinforcement, and self-correction.

Problem type: All problems with the same set of quantities or salient features

Procedural fluency: Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately 

Productive disposition: The tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics 

Reasoning: The process of manipulating and analyzing objects, representations, diagrams, symbols, or statements to draw conclusions based on evidence or assumptions 

Schema: Previously learned information, organized in themed groups 

Self-Instruction: Talking oneself through a task or activity until the task is completed through the use of self-statements or “self-talk” 

Sensemaking: The process of understanding ideas and concepts in order to correctly identify, describe, explain, and apply them 

Social model of disability: A framework that acknowledges natural biological variation among individuals, but identifies social, environmental, and relational factors as disabling rather than an inherent characteristic of an individual 

Solving: The process of choosing and carrying out a strategy for finding the solution to a problem and then checking the answer for reasonableness 

Tape diagram: A visual model that uses rectangles to represent a mathematical relationship.

First Grade Tape Diagram

Unpacking: The process of making sense of the context and the action or situation of a problem to ensure that all students understand the problem 

  1. Reading and understanding the text;  
  1. Identifying what the problem is asking and the information needed to solve; 
  1. Representing the problem 

Word problems: Word problems in mathematics involve using text-based contexts to make sense of a mathematical situation. 

Working memory: The ability to hold and simultaneously manipulate information in our minds