Math Methods Test 1

Front 1

What is mathematics?

Back 1

Mathematics is...
A tool
A language
A study of patterns and relationships
A way of thinking
An art

Front 2

Describe the three factors that influence what math is being taught

Back 2

The needs of the subject
o Topics are presented in a logical order. For example, length is studied before area.
o Technology has made some math obsolete and has opened the door for other mathematics to be accessible to students.

The needs of the child
o The developmental level of the child is a major factor in determining the sequence of the curriculum. Topics cannot be taught until children are developmentally ready to learn them.

The needs of society
o In Early America, math was only important for clerks and bookkeepers. By late 19th century, math was considered important for everyone.
o In reaction to the space race, math became much more important.
o In the 70s, emphasis was put on math for usefulness in the real world.
o By 80s, nobody knew what math would be important for the future, but problem-solving became key.

Front 3

What does the NCTM stand for?

Back 3

National Council of Teachers of Mathematics

Front 4

What were the principles and standards that NCTM set forth in 2000?

Back 4

o Equity Principle: strong support for all students
o Curriculum Principle: must be coherent, focused on important math
o Teaching Principle: understand what students know and need to learn and then challenge and support them
o Learning Principle: students must learn with understanding, building new knowledge from experience and prior knowledge
o Assessment Principle: should support the learning of important math and furnish useful info to both teachers and students
o Technology Principle: is important in learning math. Influences student learning

Front 5

What is the constructivist view of learning?

Back 5

Learners actively construct or create their own knowledge
Learning reflects a social process in which children engage in dialogue and discussion w/themselves as well as w/others as they develop intellectually

Front 6

What is the behaviorist view of learning?

Back 6

Behavior can be shaped through reinforcement
Practice promotes desired behavior

Front 7

What is Vygotsky's Zone of Proximal Development (ZPD)?

Back 7

The ZPD is the things that kids can do only with the help of scaffolding from somone who is older or more knowledgeable. The best learning takes place within the ZPD because it challenges the students.

Front 8

Describe investigative lessons

Back 8

Investigative lessons involve the teacher giving the students a problem and allowing them to work on their own with their own ideas to solve it. It develops problem-solving skills.
Launch: motivate the students and explain the problem
Investigate: allow kids to investigate and come up with solutions. The teacher observes and interjects questions/comments
Summarize: the class comes back together to discuss what they found and the diff strategies they used

Front 9

Describe direct instruction

Back 9

The teacher uses direct instruction to explain a specific concept, explain new vocabulary, or to teach certain procedures
The teacher has more control and the lesson is more focused

Front 10

What are the prenumber skills?
Briefly describe them.

Back 10

Classification: kids must be able to know what has to be counted.
Patterns:
o Early exploration with patterns help develop ordering, sequencing, and counting
o Later, patterns help students develop thinking strategies for basic facts
o Even later, these skills contribute to growth in graphing, number theory, and geometry

Comparisons: more than, less than, as many as. Leads to development of one-to-one correspondence
Conservation: the ability to understand that a number does not change
Group Recognition: can kids subitize?

Front 11

What is the sequence of pattern skills?

Back 11

Copying a pattern
Finding the next one
Extending a pattern
Making own pattern

Front 12

What is subitizing? Why is it important?

Back 12

It is the skill to see how many
We want kids to be able to subitize because it saves time, contributes to powerful number ideas, helps develop sophisticated counting skills, and helps with addition/subtraction

Front 13

What is conceptual vs. procedural knowledge?

Back 13

Conceptual knowledge is based on concepts
Procedural knowledge is based on rules, algorithms, and actions

Front 14

Describe review-teach-practice math lessons

Back 14

They are the most commonly used, but least effective.
Involves going over homework, introducing new concept, doing sample problems, and then assigning problem sets
Focuses on skill acquisition, not mathematical understanding

Front 15

What are proportional models of place value?
When should they def. be used?

Back 15

Proportional models should def. be used in grades 1-3.
In proportional models, 10 is 10 times the size of 1 and 100 is ten times the size of 10. Examples are base ten blocks, bundling straws. The kids can see the proportion.

Front 16

What are nonproportional models of place value?
When can they be used?

Back 16

They can be used in 4th-6th grade.
Nonproportional models do not have to visually show that 10 is 10 times the size of 1. Examples are chops, money, color tiles

Front 17

In what order must place value models be presented?

Back 17

Concrete physical
Semi-concrete organization
Symbolic representation

Front 18

Contrast nonstandard and standard units of measurement.

Back 18

Nonstandard units of measurement are not used in the real world. They include paper clips, toothpicks, pretzel rods, children, etc.
Standard units of measurement are inches, feet, pounds, miles, kilometers, centimeters, etc.

Front 19

Describe the application of measurement concepts.

Back 19

Measurement is extremely important because it is used in everyday life. Kids should learn measurement by doing it and actively engaging with it, not just by observing it.

Front 20

What is the concept of conservation?

Back 20

This is the concept that numbers do not change.
A young kid may see three piles of 5 blocks. He will know that each has 5 but might think that one has more than the other based on the arrangement or distribution of the blocks.

Front 21

Why is it important to teach w/math manipulatives?

Back 21

This helps kids understand math in a concrete way. Kids have to go through concrete interaction with materials to really develop a working understanding of the material. At a young age, kids can not jump straight to symbolic thinking about mathematical concepts.

Front 22

Compare CCS and ILS standards.

Back 22

The common core standards list by grade level what students should specifically be able to do. It also divides the skills by concept area (measurement, counting, geometry, etc.)
The ILS simply present grade bands and do not go into as many specifics about the skills or the grades in which students should learn them.

Front 23

Who were proponents of Behaviorism?

Back 23

Thorndike, Skinner, and Gagne

Front 24

Who were proponents of Constructivism?

Back 24

Bruner, Dienes, Brownell, and Piaget

Front 25

Define math anxiety

Back 25

an inconceivable dread of mathematics that can interfere with manipulating numbers and solving mathematical problems within a variety of everyday life and academic situations