Deck 14: Developing an Understanding of Mathematics in All Learners

Question 1

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

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.

Answer 1

C

Question 2

As students get older, risk-taking in math problem solving tends to:​

A)increase.
B)decrease.
C)be the same as when they were young.
D)change for the better.

Answer 2

B

Question 3

Many diverse learners need "hands on" math so they can see, hold, and move objects in order to grasp skills and concepts.

Answer 3

True

Question 4

Most students will need concrete experiences and at least some direct instruction to build a strong foundation in measurement.

Question 5

The current emphasis in mathematical education is now on the development of math literacy and conceptual knowledge.

Question 6

Math vocabulary should not be directly taught, but learned through authentic problem solving investigations.

Question 7

Good problem solvers must have all of the following characteristics, EXCEPT:

A)an ability to reason.
B)high levels of reading fluency.
C)a useful inner language.
D)an ability to evaluate and predict.

Question 8

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

Question 9

________________ has become the number one priority for math curriculum in both general and special education.​

A)Mathematical communication
B)Numbers and operations
C)Problem-solving.
D)Computation fluency

Question 10

In order to foster generalization of concepts and skill application, it is best to teach math through:​

A)skills taught in isolation.​
B)intensive direct instruction.
C)a focus on relevant stimuli as opposed to the big picture.
D)authentic, anchored learning.

Question 11

Children first learn how to order numbers and use them in operations and then progress to learning things like how to match objects, recognize groups of objects, and count.

Question 12

As cognitive and metacognitive challenges increase, the need for concrete representation, direct instruction, scaffolding, and task analysis conversely decrease.

Question 13

The standards-based reform movement in mathematics education has made teaching students _____________ a priority.​

A)to be critical thinkers
B)procedural knowledge
C)rule-driven knowledge
D)to be concrete thinkers

Question 14

It is estimated that between 20 and 25 percent of all elementary students struggle with learning mathematics.

Question 15

Students with ADHD appear to have the most difficulty with problem solving and calculation because:​

A)they also have cognitive deficits.​
B)they can only learn in real life settings.
C)they tend to focus on less relevant stimuli and miss the "big picture."
D)behavioral issues impede their learning of math concepts.

Question 16

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.

Question 17

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

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

Question 18

In mathematical communication, a student must be able to connect English words with symbols in order to develop math literacy.

Question 19

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

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 20

The impact of technology can be felt:​

A)in schools.
B)in the home at work.
C)in the community.
D)All of the choices are correct.

Question 21

In order to determine a student's working level in mathematics, _____________ should be used.​

A)informal assessments
B)a mixture of assessment tools
C)results from group administered achievement tests
D)standardized assessments

Question 22

Students with learning disabilities sometimes have great difficulty measuring:​

A)time and length.
B)length and direction.​
C)heights and direction.
D)direction and time.

Question 23

While grading John's addition and subtraction homework assignments and quizzes, the teacher notices that whenever John begins with an addition problem, he continues to perform addition on all of the problems, including those that are subtraction problems. Likewise, if the first question is a subtraction problem, John performs subtraction on all of the problems. The teacher has performed a(n)__________ of John's work.

A)diagnostic assessment
B)criterion referenced test​
C)error analysis
D)math interview

Question 24

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

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 25

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

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

Question 26

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:​

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

Question 27

Teachers need to show students how we use data analysis and probability in our everyday lives so:​

A)it doesn't seem so concrete.
B)they know we understand the concepts.​
C)it doesn't seem so abstract.
D)they are in compliance with standards based reform.

Question 28

Computational fluency refers to the ability to:​

A)use a number line.
B)work from right to left to solve column-form calculations.​
C)calculate accurately and efficiently.
D)line up computational problems in math.

Question 29

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

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 30

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?​

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

Question 31

Math vocabulary like "certain" or "impossible" are associated with:​

A)data analysis and probability.​
B)geometry and data analysis.
C)probability and algebra.
D)data analysis and measurement.

Question 32

Research has suggested that all of the following can help reduce math anxiety, EXCEPT:

A)providing peer models and social support.
B)assigning individual seat work.
C)discussing incorrect answers.
D)eliminating unnecessary competition.

Question 33

Informal math assessments can give us insights to student learning that we cannot get through any other means. Which of the following is NOT an example of an informal assessment?​

A)Criterion-referenced assessment
B)Curriculum based assessment​
C)Portfolio assessment
D)Error analysis

Question 34

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 ____________.​

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

Question 35

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

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

Question 36

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

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 37

Success in algebra requires students to be able to do all of the following, EXCEPT:

A)understand properties of numbers and recognize patterns.
B)identify symbols and understand the related language.
C)use reasoning abilities.
D)easily see pictures and shapes, or have visual spatial "intelligence."

Question 38

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

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

Question 39

All of the following group of students are likely to need extra supports in understanding geometry, EXCEPT students who are:

A)spatially-challenged.
B)physically-challenged.
C)verbally-challenged.
D)cognitively challenged.

Question 40

All of the following can occur when students have math anxiety, EXCEPT:

A)initial learning can be blocked.
B)working memory can be hindered.
C)demonstration of skills and concepts on assessments can be hindered.​
D)long term memory can be hindered.​

Question 41

Concrete instructional techniques that include using real clocks to teach time-telling, real coins to teach money skills, constructing grids that students can actually walk on, or constructing a 'Gallon Man' to teach units of capacity are useful in teaching students concepts of:​

A)algebra.
B)problem solving.
C)measurement.
D)geometry.

Question 42

Explain how teaching a math concept to a nonverbal student could help a teacher arrive at creative ways to teach the same concept to all students in the classroom. Give at least two examples to illustrate your answer.

Question 43

What can teachers do to help their students' progress through the three instructional stages in mathematical learning (e.g., concrete, representational, and abstract)?

Question 44

What kinds of mathematical skills and concepts do students need to have in order to successfully understand measurement?

Question 45

Which of the following is NOT helpful in promoting math communication in the classroom?​

A)Make sure math vocabulary is embedded  into the content, modeled, and used frequently as part of every lesson
B)For diverse students and English language learners, avoid mathematical vocabulary and teach using simpler terms
C)Use correct, universal mathematical terms when teaching, and put them on cards, posters, or labels
D)Use visual imagery, keyword mnemonics, and connections to prior learning

Question 46

What kinds of information can we gather on a student's mathematical abilities from formal assessments?

Question 47

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

Question 48

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

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 49

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

Question 50

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

Question 51

A study on early math skills of children concluded all of the following, EXCEPT:

A)no significant difference was found in the conventional math knowledge of four-year-old children according to their socioeconomic status.
B)the more "teacher talk" about mathematics that occurs the greater the overall achievement in math by all students.
C)early development in math has long term effects on math achievement.
D)promoting "best practices" in math instruction at the preschool level can set the stage for future math success.

Question 52

All of the following instructional techniques can help students in the problem solving process, EXCEPT:

A)creating a storyboard.
B)creating timed competitions.
C)using mnemonic strategies.
D)using multisensory manipulatives.​

Question 53

Geometry concepts can become more meaningful for diverse learners through the use of all of the following, EXCEPT:

A)concrete representations of geometric shapes.
B) independent practice worksheets and homework assignments to assist students in remediating weak and underdeveloped math skills.
C)posters, models, and computer presentations to represent geometric skills and concepts.
D)specialized computer programs such as Dynamic Geometry Software (DGS).

Question 54

All of the following statements on data analysis and probability are true, EXCEPT:

A)younger students enjoy collecting, organizing, analyzing, and displaying data but these are not age appropriate activities for older students.
B)data collection can easily occur in all areas of the curriculum, thus reinforcing mathematical concepts.​
C)graphing student preferences, such as favorite movies, music, etc., can activate the affective domain.
D)probability lessons lend themselves quite easily to employing multisensory learning.

Question 55

How can teachers support students who may struggle with problem-solving assignments?

Question 56

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?

Question 57

All of the following programs and techniques can help support students as they learn about numbers and operations, EXCEPT:

A)completed multisensory, TouchMath tools such as beans, foam dots, and pipe cleaner circles that can represent the relationship between numbers and values.
B)left to right subtraction algorithms to help students who have difficulty with right to left work or with regrouping.
C)lesson extensions where student are expected to intuitively be able to transfer the basic principles in math to real life problem solving.
D)the lattice multiplication method to break down large multiplication problems into small, manageable steps.

Question 58

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