Question 1

All of the following statements regarding algebra are true, EXCEPT:

Accepted Answer

A) algebraic thinking can be seen on all grade levels as we move toward a problem solving emphasis in math. 
B) concrete thinkers generally do poorly in algebra, while more abstract thinkers generally do well. 
C) strong skills in algebra are necessary to develop higher level critical math skills needed in most workplaces today. 
D) using algebraic symbols, graphs, equations, etc., students learn to represent and analyze mathematical situations and see relationships between numbers.

Question 2

Based on large-scale assessments monitored by the National Assessment of Educational Progress in the United States from 2011 to 2013 (NCES, 2014), 36% of high school seniors lacked a basic understanding in math, and there is a sizable gap in achievement by ethnicity, family income, and disabilities. What recommendations would you make to raise the mathematical achievement of all students in general and special education and close the achievement gaps?

Accepted Answer

The answer of Based on large-scale assessments monitored by the...

Question 3

All of the following have contributed to the increased emphasis on mathematics education, EXCEPT:

Accepted Answer

A) Goals 2000: Educate America Act of 1994. 
B) Principles and Standards for School Mathematics. 
C) Reauthorization of IDEA, 1997. 
D) Common Core State Standards.

Question 4

Unlike other subject areas, a student's culture is irrelevant in the teaching of mathematics.

Accepted Answer

A) True 
 B)False

Question 5

In the 21st century the level of technical and mathematical skills required of everyone, regardless of whether or not they go to college, has:​

Accepted Answer

A) remained the same. 
B) increased. 
C) decreased. 
D) Diminished.

Question 6

Studies on gender and math has suggested all of the following, EXCEPT:

Accepted Answer

A) boys are inherently more skilled in math than girls. 
B) boys prefer to use spatial representations and memory to solve math problems. 
C) girls prefer math strategies paired with manipulatives to solve math problems. 
D) teachers may reinforce positive performance in math with attention and praise more often for boys than for girls.

Question 7

A student who understands that the word add is represented by the symbol + is demonstrating ability in:​

Accepted Answer

A) visual-motor skills. 
B) spatial learning.​ 
C) math literacy. 
D) computation fluency.

Question 8

Which of the following statements does NOT apply to best practice in teaching algebra to diverse learners?​

Accepted Answer

A) Advance organizers in the form of questions, prompts on a card or worksheet, etc. should be used 
B) Explicit instructions in self-monitoring, such as using "think alouds" to model your own thinking process, help students develop reasoning skills 
C) Strategies such as the STAR strategy help students to visualize how to solve an equation 
D) Assessment of prerequisite mathematical skills is not necessary when planning algebra instruction

Question 9

Explain how mathematics can be taught using UDL principles and give examples of the various tools and instructional techniques to support your answer.

Accepted Answer

The answer of Explain how mathematics can be taught using...

Question 10

Students who struggle with mathematics can increase their ability to reason in algebra through the use of guided practice, independent practice, frequent reviews, and corrective/positive feedback.

Accepted Answer

A) True 
 B)False

Question 11

Students who have difficulty understanding that the word quarter can be used to describe 15 minutes, twenty-five cents, or one-fourth of a whole have a problem with language ____________.​

Accepted Answer

A) phonology 
B) alphabetic principle​ 
C) semantics 
D) morphology

Question 12

Which group of students tends to find problem solving most challenging? Provide a rationale for your answer.

Accepted Answer

The answer of Which group of students tends to find...

Question 13

Learning to tell time, determining the outside temperature, cooking, and doing laundry all require the mathematical skill of:

Accepted Answer

A) algebra. 
B) geometry. 
C) measurement. 
D) computation fluency.

Question 14

Which type of formal assessment focuses more specifically on math skill areas and helps to determine strengths and needs within the math domain?​

Accepted Answer

A) Achievement tests​ 
B) Interest inventories​ 
C) Diagnostic tests 
D) Error analyses

Question 15

In order to be a good problem solver, students must possess all of the following characteristics, EXCEPT:

Accepted Answer

A) understanding there is only one right way to arrive at an answer. 
B) confidence.​ 
C) risk-taking. 
D) willingness to learn from mistakes.

Question 16

There is evidence to support all the following statements regarding second language learners and mathematics, EXCEPT:

Accepted Answer

A) Second language learners who have developed basic interpersonal communication skills in English will also have a sufficient math vocabulary. 
B) English language learners need exposure early to math vocabulary in order to accelerate their math performance. 
C) Difficulties with math can be overcome in time when an extra effort is made to learn the language and related math skills. 
D) Lower performances on math assessments by English language learners relates more to lack of exposure to mathematical words and phrases then to lack of mathematical skill.

Question 17

Explain what is involved in progress monitoring and why it is a critical component of math instruction for diverse learners

Accepted Answer

The answer of Explain what is involved in progress monitoring...

Question 18

Why is early number learning so critical for subsequent success in math, and what basic mathematical concepts should children learn at the preschool level?

Accepted Answer

The answer of Why is early number learning so critical...

Question 19

Students need to see how mathematical operations such as adding, subtracting, multiplying, and dividing are all connected so that later on they will be able to:​

Accepted Answer

A) pass addition tests. 
B) make reasonable predications and estimates. 
C) earn reasonable grades in math classes. 
D) improve their visual-motor skills.

Question 20

When students first understand that symbols, such as letters in algebra, can be used to stand for unknown numbers, they have moved to which of the following instructional stages?​

Accepted Answer

A) Concrete 
B) Representational 
C) Abstract 
D) Manipulative

Exam 14: Developing an Understanding of Mathematics in All Learners