Building Assessment into Instruction

Question 1

What Does It Mean to Learn Mathematic

Answer 1

Learning theory and research on how people learn.

Question 2

Constructivism:

Answer 2

The notion that learners are not blank slates but rather creators (constructors) of their own learning.

Question 3

Reflective Thought:

Answer 3

Effort to connect existing ideas to new information.

Question 4

Assimilation:

Answer 4

When a new concept “fits” with prior knowledge and the new information expands an existing network

Question 5

Accommodation:

Answer 5

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.

Question 6

Sociocultural Theory:

Answer 6

1) . Mental processes exist between and among people in social learning settings, and that from these social settings the learner moves ideas into his or her own psychological realm.
2) . The way in which information is internalized (or learned) depends on whether it was within a learner’s zone of proximal development.
3) . In a true mathematical community of learners there is something of a common ZPD that emerges across learners and there are also the ZPDs of individual learners.

Question 7

Zone of Proximal Development:

Answer 7

A “range” of knowledge that may be out of reach for a person to learn on his or her own, but is accessible if the learner has support from peers or more knowledgeable others. (Not a physical space but a symbolic space)

Question 8

Zone of Proximal Development {ZPD}:

Answer 8

A “range” of knowledge that may be out of reach for a person to learn on his or her own, but is accessible if the learner has support from peers or more knowledgeable others. (Not a physical space but a symbolic space)

Question 9

Sociocultural Perspective:

Answer 9

Learning is dependent on the new knowledge falling within the ZPD of the learner (who must have access to the assistance), and occurs through interactions that are influenced by tools of mediation (words, pictures, etc.) and the culture within and beyond the classroom.

Question 10

Foundational to Children’s Learning:

Answer 10

Classroom discussion based on students’ own ideas and solutions to problems.

Question 11

Problem-based Approach:

Answer 11

Where students explore a problem and the mathematical ideas are later connected to that experience.

Question 12

Inquiry-based Approach:

Answer 12

Students are activating their own knowledge and trying to assimilate or accommodate (or internalize) new knowledge.

Question 13

NCTM Assessment Standards:

Answer 13

Mathematics Standard
Learning Standard
Equity Standard
Openness Standard
Inferences Standard
Coherence Standard

Question 14

Mathematics Standard:

Answer 14

• Use NCTM and state or local standards to establish what mathematics students should know and be able to do and base assessments on those essential concepts and processes
• Develop assessments that encourage the application of mathematics to real and sometimes novel situations
• Focus on significant and correct mathematics

Question 15

Learning Standard:

Answer 15

• Incorporate assessment as an integral part of instruction and not an interruption or a singular event at the end of a unit of study
• Inform students about what content is important and what is valued by emphasizing those ideas in your instruction and matching your assessments to the models and methods used
• Listen thoughtfully to your students so that further instruction will not be based on guesswork but instead on evidence of students’ misunderstandings or needs

Question 16

Equity Standard:

Answer 16

• Respect the unique qualities, experiences, and expertise of all students
• Maintain high expectations for students while recognizing their individual needs
• Incorporate multiple approaches to assessing students, including the provision of accommodations and modifications for students with special needs

Question 17

Openness Standard:

Answer 17

• Establish with students the expectations for their performance and how they can demonstrate what they know
• Avoid just looking at answers and give attention to the examination of the thinking processes students used
• Provide students with examples of responses that meet expectations and those that don’t meet expectations

Question 18

Inferences Standard:

Answer 18

• Reflect seriously and honestly on what students are revealing about what they know
• Use multiple assessments (e.g., observations, interviews, tasks, tests) to draw conclusions about students’ performance
• Avoid bias by establishing a rubric that describes the evidence needed and the value of each component used for scoring

Question 19

Coherence Standard:

Answer 19

• Match your assessment techniques with both the objectives of your instruction and the methods of your instruction
• Ensure that assessments are a reflection of the content you want students to learn
• Develop a system of assessment that allows you to use the results to inform your instruction in a feedback loop

Question 20

Rubric:

Answer 20

A framework that can be designed or adapted by the teacher for a particular group of students or a particular mathematical task.

Question 21

Scoring:

Answer 21

Comparing students’ work to criteria or rubrics that describe what we expect the work to be.

Question 22

Grading:

Answer 22

The result of accumulating scores and other information about a student’s work for the purpose of summarizing and communicating to others.

Question 23

Performance indicators:

Answer 23

Task-specific statements that describe what performance looks like at each level of the rubric and, in so doing, establish criteria for acceptable performance.

Question 24

Tools for Tests:

Answer 24

Permit students to use calculators.
Use manipulatives and drawings.
Include opportunities for explanations.
Avoid always using “preanswered” tests.

Question 25

Tools for Tests:

Answer 25

Permit students to use calculators.
Use manipulatives and drawings.
Include opportunities for explanations.
Avoid always using “pre-answered” tests.

Question 26

Performance Assessment:

Answer 26

Real world problem solving activity.