Question 1

Which statement below captures the big idea from one of the Eight Guiding Principles outlines in the NCTM Principles to Action
A)Assessments that include ongoing observation and student interaction.
B)Learning mathematics with understanding is essential.
C)Look for both horizontal and vertical alignment to build coherence.
D)Problem solving will target student learning gaps.

Accepted Answer

C

Question 2

Which choice reflects two factors that influence the teaching of Mathematics effectively?
A)Manipulatives and an overhead projector.
B)Knowledge of standards and practices.
C)Internet sites and computer software.
D)Student records and interviews with experienced teachers.

Accepted Answer

Knowledge of standards and practices is essential for effective teaching of Mathematics as it helps teachers understand what is expected to be taught and how it should be taught. This knowledge helps them create lesson plans, assessments, and activities that align with the standards and practices. It also helps them monitor student progress and adjust instruction accordingly. The other choices may also be beneficial but do not reflect the two most important factors for effective teaching of Mathematics.

Question 3

Which of the following can be said to be true about the learning principle?
A)As long as students have their basic facts and procedures memorized,they do not have to understand how the mathematics works.
B)Due to technology,it is no longer necessary for students to practice computational skills.
C)Learning is strongly enhanced when students are encouraged to make and test their own mathematical conjectures.
D)To build confidence,students should be taught to focus on their own mathematical ideas and not the thinking of others.

Accepted Answer

Encouraging students to make and test their own mathematical conjectures is a well-known and effective learning principle supported by research. It encourages students to think deeply about the content and develop a better understanding. Option A is not true as understanding how mathematics work is critical for success, and not just memorization. Option B is not true as practicing computational skills is still necessary even with technology. Option D is not true as it is essential for students to learn and appreciate other people's reasoning and ways of thinking.

Question 4

The following statements represent the "thinking" behind the creation of the Common Core Standards for School Mathematics.Which statement is also true of the NCTM Principle and Standards for School Mathematics?
A)Represent the largest shift in mathematics content in the U.S in over 100 years.
B)A focused set of Mathematics content standards and practices.
C)Provide a coherent curriculum framework for content across the school year and grades.
D)Comprised of learning progressions that can inform instruction.

Accepted Answer

Both the Common Core Standards and the NCTM Principles and Standards emphasize a focused set of mathematics content standards and practices.

Question 5

What statement best reflects the Connectionsstandard of the Five Process Standardsfrom Principles and Standards for School Mathematics?
A)Students should be given opportunities to see how various mathematical ideas relate to one another and to a variety of real-life experiences.
B)Students should be able to interpret and create various symbolic representations of mathematical ideas.
C)Students should be able to connect personally to their fellow classmates in order to fully enjoy the learning process.
D)Students should be able to explain and justify the thought process behind their arguments.

Accepted Answer

The Connections standard emphasizes the importance of helping students see how mathematical ideas are related to each other and to real-life situations. Choice A reflects this emphasis. Choices B, C, and D do not directly address the Connections standard.

Question 6

The mathematical needs in society have changed and are influencing what should be taught in preK-8 mathematics classrooms.What statement below reflects a key factor in the change?
A)Teacher accountability through increased use of standardized assessments.
B)International perspective with ideas on how and what to teach.
C)Data on the performance of U.S.students in national and international studies.
D)Research on how students learn mathematics.

Accepted Answer

Data on the performance of U.S. students in national and international studies has shown that U.S. students are not performing as well as students in other countries. This has led to a re-examination of what is being taught in mathematics classrooms and how it is being taught.

Question 7

What are the main tenets of the Curriculum principle in the NCTM Principles to Action?

Accepted Answer

The answer of What are the main tenets of the...

Question 8

Identify the statement that completes this statement,"Learning progressions reflect current research and practice and they guide teachers in understanding…"
A)The essential big ideas and mathematics concepts for preschool-aged children.
B)What came before as well as what to expect next.
C)Progressions that are identical for all students.
D)What the vision is for the teachers their role in developing curriculum.

Accepted Answer

Learning progressions guide teachers in understanding what came before as well as what to expect next for their students in terms of knowledge and skills development. They are designed to be flexible and responsive to individual student needs, rather than being identical progressions for all students. The statement does not specifically mention mathematics concepts or the vision for teachers' roles in developing curriculum, so choices A and D are not the best answers.

Question 9

The six Principles and Standards for School Mathematics articulate high-quality mathematics education.What statement below represents the equity principle?
A)Mathematics today requires not only computation skills,but also the ability to think and reason.
B)Calculators and computers should be seen as essential tools for doing and learning mathematics.
C)Coherence speaks to the importance of building instruction around big ideas.
D)The message of high expectations for all is intertwined with every other principle.

Accepted Answer

The equity principle in mathematics education emphasizes high expectations and strong support for all students, ensuring that every student has the opportunity to learn and succeed in mathematics, regardless of their background or previous achievements. This principle is reflected in the statement that high expectations for all students are intertwined with every other principle, highlighting the importance of equity in providing quality mathematics education.

Question 10

The National Assessment of Educational Progress
A)Consists of data collected by individual school districts so they may assess their teachers.
B)Reported in 2013 that less than half of all fourth- and eighth-graders performed on a standardized mathematics test at the desirable levels of "proficient" or "advanced."
C)Showed dramatic decreases in U.S.mathematics scores over the last 30 years.
D)Produced results in 2009 that indicated U.S.students would likely reach the goal required by No Child Left Behind legislation that all students perform at or above a proficient level by 2014.

Accepted Answer

The National Assessment of Educational Progress (NAEP) reported in 2013 that less than half of all fourth- and eighth-graders performed on a standardized mathematics test at the desirable levels of "proficient" or "advanced." Therefore, option B is the correct answer. Option A is incorrect because NAEP consists of national data collected by the National Center for Education Statistics (NCES) under the U.S. Department of Education. Option C is incorrect because there have been fluctuations in math scores over the years, but no dramatic decreases have been reported. Option D is incorrect because the 2009 results showed progress, but not enough to reach the No Child Left Behind's goal by 2014.

Question 11

The Standards for Mathematical Practiceare
A)A component of the Common Core State Standards that outlines a series of important mathematical processes all students should be able to do regularly.
B)Important for students to be able to do,but are not actually a part of the Common Core State Standards.
C)A set of basic computation skills that students should have to enhance their problem-solving ability.
D)A series of common summative assessments to help teachers better understand their students' individual needs.

Accepted Answer

The Standards for Mathematical Practice are a key component of the Common Core State Standards for Mathematics. They describe the mathematical processes and habits of mind that students need to develop in order to become proficient in mathematical thinking and problem-solving.

Question 12

One of the statements below represents a method for developing the Reasoning and proof process standard.
A)Select meaningful mathematical tasks.
B)Give students opportunities to share ideas so others can understand.
C)Emphasize how mathematics is connected to students prior knowledge.
D)Create opportunities for students to evaluate conjectures.

Accepted Answer

Creating opportunities for students to evaluate conjectures allows them to use logical reasoning and evidence to support their conclusions, which is a key aspect of the Reasoning and proof standard.

Question 13

What are two ways that learning progressions can inform instructional planning?

Accepted Answer

The answer of What are two ways that learning progressions...

Question 14

What are examples of effective assessmenttechniques that will guide your understanding ofstudent knowledge?
A)Meaningful instructional tasks and practice.
B)Partnership for Assessment of Readiness for College and Careers and Smarter Balanced Assessment Consortium.
C)Feedback,on-going observation and continuous data gathering.
D)Grade-level content standards and the standards for mathematical practice.

Accepted Answer

Feedback, ongoing observation, and continuous data gathering are effective assessment techniques as they provide insight into a student's knowledge over time and allow for targeted instruction and interventions. Meaningful instructional tasks and practice, grade-level content standards, and the standards for mathematical practice are important components of instruction, but do not necessarily provide the same level of understanding of student knowledge as ongoing assessment. The Partnership for Assessment of Readiness for College and Careers and Smarter Balanced Assessment Consortium are standardized testing systems and may provide some insight into student knowledge, but are not tailored to individual student needs or provide the same level of ongoing feedback.

Question 15

As a practicing or prospective teacher each face the challenge of teaching mathematics from a problem solving perspective.This often requires some to confront personal beliefs about;
A)Teaching conceptual understanding and procedural fluency.
B)Allowing all students an equal opportunity to learn.
C)How technology can enhance student understanding.
D)What is means to do mathematics

Accepted Answer

The answer of As a practicing or prospective teacher each...

Quiz 1: Teaching Mathematics in the 21st Century

Which statement below captures the big idea from one of the Eight Guiding Principles outlines in the NCTM Principles to Action

Which choice reflects two factors that influence the teaching of Mathematics effectively?

Which of the following can be said to be true about the learning principle?

The following statements represent the "thinking" behind the creation of the Common Core Standards for School Mathematics.Which statement is also true of the NCTM Principle and Standards for School Mathematics?

What statement best reflects the Connectionsstandard of the Five Process Standardsfrom Principles and Standards for School Mathematics?

The mathematical needs in society have changed and are influencing what should be taught in preK-8 mathematics classrooms.What statement below reflects a key factor in the change?

What are the main tenets of the Curriculum principle in the NCTM Principles to Action?

Identify the statement that completes this statement,"Learning progressions reflect current research and practice and they guide teachers in understanding…"

The six Principles and Standards for School Mathematics articulate high-quality mathematics education.What statement below represents the equity principle?

The National Assessment of Educational Progress

The Standards for Mathematical Practiceare

One of the statements below represents a method for developing the Reasoning and proof process standard.

What are two ways that learning progressions can inform instructional planning?

What are examples of effective assessmenttechniques that will guide your understanding ofstudent knowledge?

As a practicing or prospective teacher each face the challenge of teaching mathematics from a problem solving perspective.This often requires some to confront personal beliefs about;