Math Processes
Vocabulary
Supporting Diversity in the Classroom
Theorists
Helping Children Make Sense of Math
100
What math process involves students formulating, representing, and solving mathematical questions?
Problem solving (pg. 13)
100
What kind of knowledge is used to solve mathematical rules and algorithms?
Procedural knowledge (pg. 17)
100
How many strategies does the textbook provide for teachers who want to support diverse learners?
Five (pgs. 13-17)
100
How many stages make up Piaget's model of cognitive development?
Three (pg. 21)
100
True or False? The more involved children are in their learning of mathematics, the more likely they will develop confidence and other positive attitudes toward the subject.
True (pg. 24)
200
A geometry student completes a proof and provides justification for the answers they chose. What math process is this student using?
Reasoning (pg. 13)
200
What theory focuses on observable behaviors and external actions?
Behaviorism (pgs. 19-20)
200
What is one way teachers can help students better retain information?
Emphasize meaningful learning; have students physically manipulate objects/models; establish connections; periodically review ideas (pg. 17)
200
Name one similarity that Bruner, Piaget, and Dienes' works share with regard to the theory of constructivism.
Learners are actively involved in the learning process; several charactersistic and identifiable stages of thinking exist, and children progress through these stages as they grow and mature; learning proceeds from the concrete to the abstract; learners need opportunities for talking about or otherwise communicating their ideas with others (pg. 21)
200
What are three kinds of development that influence mathematics instruction?
Cognitive, physical, and social development (pg. 23)
300
According to the National Council of Teachers of Mathematics (NCTM), how many math processes are there and what are they?
Five; problem solving, reasoning, connections, communication, and representations (pg. 13)
300
What kind of development has to do with how a child thinks and reasons?
Cognitive development (pg. 23)
300
What is the definition of "mathophobia"?
A fear of mathematics or other negative attitudes toward mathematics (pg. 14)
300
What did psychologist William Brownwell propose?
That mathematics is a closely knit system of ideas, principles, and processes (pg. 20)
300
What is metacognition?
A concept that refers to someone thinking about their own trains of thought (pg. 25)
400
Students seek to understand connections between what three mathematical aspects?
Concepts, operations, and relations (pg. 13)
400
What are hypothesized learning experiences designed to build a deep and increasingly sophisticated understanding of core mathematical concepts and practices?
Learning trajectories (pg. 22)
400
To create a positive learning environment, make sure the classroom atmosphere is ____________ for learning mathematics.
Intellectually-stimulating (pg. 13)
400
Who are the 3 main advocates of the behaviorist perspective?
Edward Thorndike, B.F. Skinner, and Robert Gagné (pg. 19)
400
What are two tools that teachers use to help students learn mathematics?
Manipulatives and models (pg. 26)
500
What math process involves students believing in their own diligence and efficacy and seeing math as sensible/worthwhile?
Representation (pg. 13)
500
This theory, proposed by psychologist Lev Vygotsky, attempts to explain why children can accomplish certain tasks by themselves and not others.
Zone of proximal development (pg. 21)
500
What are five ways that teachers can help support diverse learners in their classrooms?
1) Create a positive learning environment, 2) Avoid negative experiences that increase anxiety, 3) Treat all students as equally likely to have aptitude for mathematics, 4) Help students retain mathematical knowledge and skills, and 5) Establish clear expectations (pgs. 13-17)
500
Who founded the theory of behaviorism?
John Watson
500
What are the four recommendations that help children make sense of mathematics?
1) Teach to the developmental characteristics of students, 2) Actively involve students, 3) Move learning from concrete to abstract, and 4) Use communication to encourage understanding (pgs. 22-27)
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