Deck 9: Teaching and Learning: Tools and Technology

Question 1

Which of these is commonly involved in showing that a given hypothesis is not always true?

A)Justification.
B)Counterexample.
C)Procedure.
D)Conjecture.
E)Sample Case.

Answer 1

Counterexample.

Question 2

Principles to Actions (NCTM, 2014)uses which of the following words best describes the use of tools and technology in the teaching of mathematics?

A)Mandatory.
B)Optional.
C)Recommended.
D)Essential.
E)Unnecessary.

Answer 2

Essential.

Question 3

Which of the following are considered tools for teaching mathematics?

A)Computer software.
B)Manipulatives.
C)Puzzles.
D)Interactive electronic devices.20.For instructor use only.
E)All of these.

Answer 3

All of these.

Question 4

Research suggests that approximately what percentage of seventh graders is able to explain why decimals are "lined up" when adding or subtracting?

A)10%.
B)33%.
C)50%.
D)67%.
E)80%.

Question 5

When teaching a lesson on adding decimals in the middle school, which of the following are considered the "best" tools for a teacher to use?

A)Calculators.
B)Base ten blocks.
C)Rulers.
D)Money.
E)It depends on the situation.

Question 6

When using base ten blocks to explore decimals, if the "flat" represents 1, then what does the unit cube represent?

A)1/10.
B)1/100.
C)1/1000.
D)10.
E)100.

Question 7

When using base ten blocks to explore decimals, typically how would 4.83 be represented?

A)Four flats, eight longs, and three unit cubes.
B)Eight unit cubes, four flats, and three longs.
C)Four longs, eight flats, and three unit cubes.
D)Three longs, four unit cubes, and eight flats.
E)Four unit cubes, eight longs, and three flats.

Question 8

If students use graph paper to explore decimals and a 10 x 10 grid represents 1, then what would a single square represent?

A)100.
B)10.
C)0)1.
D)0)01.
E)0)001.

Question 9

If a teacher has the class use metric measurement to explore decimals with a decimeter representing a unit, then how would 6.93 be represented?ly.

A)Nine decimeters, six centimeters, and three centimeters.
B)Six millimeters, nine centimeters, and three decimeters.
C)Six decimeters, nine centimeters, and three millimeters.
D)Three centimeters, six decimeters, and nine millimeters.
E)Six centimeters, nine decimeters, and three millimeters.

Question 10

The authors of Mathematics Teaching Today (NCTM, 2007)asserted that there is no single "right way" to teach all mathematical topics and said that teachers must always balance knowledge of which of the following?

A)Mathematics, Textbooks, and Students.
B)Standards, Mathematics, and Pedagogy.
C)Textbooks, Students, and Pedagogy.
D)Psychology, Textbooks, and Students.
E)Mathematics, Pedagogy, and Students.

Question 11

Which of the following is NOT associated with Pedagogical Content Knowledge?

A)Interaction of subject matter and effective teaching strategies.
B)Thorough understanding of the subject matter.
C)Understanding of cultural backgrounds of students.
D)Access to appropriate teaching tools.
E)Prior knowledge of student experiences.

Question 12

If a teacher begins a lesson by using base ten blocks as a tool and finds that the majority of students are not understanding, what is the best route for a teacher to take?

A)Continue teaching the lesson as intended with the blocks.
B)Continue teaching the lesson as intended but without the blocks.
C)Stop the lesson and try a different tool with the class.
D)Try a different tool for individuals who need a different model.
E)Have students read the textbook explanation to supplement use of the blocks.

Question 13

Which of the following statements most accurately describes the role of manipulative and other tools in a successful mathematics lesson?

A)They are essential in the motivation section.
B)They are essential in the procedure section.
C)They are essential in the closure section.
D)They are essential throughout the lesson.
E)They are not essential in every lesson.

Question 14

What is the purpose of "freeplay" time with manipulatives?

A)To motivate the students.
B)To have students explore and experiment.nstructor use only.
C)To have students gain experience with working in groups.
D)To reward students for good behavior.
E)To reward students who complete a task early.

Question 15

How long and often should "freeplay" time with manipulatives be given, accordingto the author in Chapter 9?

A)About 5 minutes the first time students use them.
B)5-10 minutes at the end of the period, when appropriate.
C)15-20 minutes the first time students use them.
D)15-20 minutes at the end of the period, when appropriate.
E)One class period the first time students use them.

Question 16

What is the main reason that specific rules for the use of manipulatives should be established?

A)To replace the materials is costly.
B)The materials are shared between teachers.
C)The materials need to stay organized.
D)Students are tempted to exhibit off-task behavior.
E)Students need guidance on their use.

Question 17

Which of the following is NOT one of the Tips on Manipulative Use that is mentioned in the text?

A)Establish a process for distributing and collecting materials
B)Keep in mind that students "inherently" learn when they use manipulatives, so materials should be a regular part of the classroom routine.
C)Manipulatives are tools but are not the focus of instruction.
D)Students should not be asked to memorize procedures with the manipulatives.
E)Not every child will find manipulatives the "easiest" or the "best" way to solve certain problems.

Question 18

In Chapter 9, the author presents an example from the Hawaii Geometry Learning Project that asks how one would draw a picture to represent the position of a table before and after it was moved.The example focuses mainly on which two geometric concepts?

A)Translation and rotation.
B)Translation and reflection.
C)Reflection and dilation.
D)Reflection and rotation.
E)Dilation and rotation.

Question 19

What is important to remember about both the use of manipulatives and of technology?

A)Manipulatives and technology are always appropriate to use in teaching.
B)Manipulatives are always appropriate, and technology is sometimes appropriate to use in teaching.
C)Technology is always appropriate, and manipulatives are sometimes appropriate to use in teaching.
D)Manipulatives and technology are sometimes appropriate to use in teaching.
E)While manipulatives and technology are both very popular, research does not support their regular use in teaching.

Question 20

What are three main purposes for the use of technology in a mathematics classroom?

A)To explore, to check answers, and to teach.
B)To use as a reward, to teach, and to check answers.
C)To check answers, to explore, and to assess student progress.
D)To provide demonstrations, to teach, and to explore.
E)To teach, to explore, and to assess student progress.

Question 21

When assisting students with simple mental arithmetic such as 6 × 13 , a teacher can lead the students into thinking of the problem as 6(10+3)and adding 60+18 Which Property is being reviewed?

A)The Associative Property.
B)The Commutative Property.
C)The Distributive Property.
D)The Identity Property.
E)The Transitive Property.

Question 22

In which of the following instances would the use of a calculator MOST appropriate in the secondary or middle school classroom?

A)Graphing ordered pairs.
B)Multiplying 7 x 32.
C)Finding the circumference of a circle, in terms of ?, given a radius.
D)Simplifying 32/40.
E)Determining the next 10 terms in a geometric progression of numbers.

Question 23

Which Standard for Mathematical Practice is primarily involved in examining the
Distributive Property?

A)Make sense of problems.
B)Reason abstractly.
C)Look for and make use of structure.
D)Model with mathematics.
E)Attend to precision.

Question 24

The NCTM uses which of the following terms to describe technology?

A)Necessary evil.
B)Tool.
C)Crutch.
D)Option.
E)Unreliable.

Question 25

An application or device that has CAS Technology can always do which of the
Following?

A)Connect to the Internet.
B)Run without batteries.
C)Interface with a computer.
D)Manipulate algebraic symbols.
E)Draw geometric diagrams.

Question 26

Which of the following is NOT a function ordinarily associated with a device with CAS Technology?

A)Simplify a fraction.
B)Write a number in scientific notation.
C)Factor a trinomial.
D)Solve an equation.
E)Multiply polynomials.

Question 27

Which of the following Standards for Mathematical practice is being emphasized when a student explores a series of binomial multiplication problems to find a rule?

A)Look for regularity in repeated reasoning.
B)Model with mathematics.
C)Construct viable arguments.
D)Attend to precision.
E)Look for and make use of structure.

Question 28

In which setting was the interactive whiteboard first used?

A)Hospitals.
B)Businesses.
C)Schools.
D)Law enforcement agencies.
E)Courtrooms.

Question 29

Which of the following is NOT considered a significant use of an interactive whiteboard?

A)Projecting videoclips.
B)Marking up an image on the screen.
C)Recording a lesson.
D)Saving notes from a class.
E)Using a tool such as rolling dice on the screen.

Question 30

Which of the following is an example of a tool that is typically available on an
Interactive whiteboard?

A)Ruler.
B)Compass.
C)Algebra Tiles.
D)Graphing Grids.
E)All of these.

Question 31

Which of the following websites is known for featuring applets that can be displayed
And manipulated on an interactive whiteboard?

A)NCTM.org.
B)LearnZillion.com.
C)Mathforum.org.
D)NLVM.org.
E)Learner.org.

Question 32

Research on the use of interactive whiteboards in mathematics instruction suggests
That student engagement in the classroom only occurs under which condition?

A)The mathematics content is fairly easy to understand.
B)Students are directly involved with using the whiteboard.
C)The lesson includes virtual manipulatives.nstructor use only.
D)A limited amount of time is spent actually using the whiteboard.
E)The teacher provides considerable demonstration on the whiteboard.

Question 33

Research on the use of interactive whiteboards suggests which of the following
Drawbacks to their use in teaching mathematics?

A)Preparation time for lessons is increased.
B)Students display shorter attention spans.
C)Students are generally less engaged.
D)Whiteboards require more class time.
E)Classroom discourse is reduced.

Question 34

What does it mean for a school to have a BOYD policy?

A)The use of technology is not permitted.
B)The use of technology is permitted but limited.
C)Students are required to bring their own technological devices to class.
D)Schools provide the technology, but students sign contracts for its use.
E)Technology is not permitted to involve the use of the Internet.

Question 35

School districts with less wealth often struggle to provide adequate technology in
Classrooms.Which of the NCTM Principles does this most directly affect?

A)Curriculum.
B)Assessment.
C)Professionalism.
D)Teaching and Learning.
E)Access and Equity.

Question 36

Which of the following would be considered the LEAST creative use of a mobile
Device in the mathematics classroom?

A)Use the calculator feature to check an answer.
B)Take part in an online poll.
C)Play a game in an app.
D)Create a screencast of a problem solution.
E)Maintain a blog of learning.

Question 37

Which of the following uses of mobile devices can most readily be used to conduct
Formative assessment during class?

A)Playing a game.
B)Creating a screencast.
C)Writing a blog.
D)Taking part in a poll.
E)Manipulating a visual representation.

Question 38

The mobile device application known as ShowMe can be used to do which of the
Following?

A)Create a video with an explanation for a problem.
B)Generate a graph of poll responses.
C)Take a multiple-choice quiz.
D)Play an interactive mathematical game.
E)Write a blog.

Question 39

Research suggests that which of the following is the main challenge for using
Technology in the mathematics classroom?

A)Gaining reliable Internet access.
B)Affording to purchase the devices.
C)Determining how to use the technology most effectively.
D)Assessing whether students actually learned the intended content.
E)Teaching students how to use the technology.

Question 40

Which term refers most specifically to applications that can allow images, inputs, and
Parameters to be manipulated to observe the effects?

A)Changing.
B)Dynamic.
C)Justifying.
D)Visual.
E)Interactive.

Question 41

Dynamic software is perhaps most powerful when used in which of the following content areas?

A)Algebra.
B)Number.
C)Patterns.
D)Probability.
E)Geometry.

Question 42

Which of the following includes a popular dynamic geometry software application?

A)Action Grapher.
B)Problem-Attic.
C)Core Math Tools.
D)ShowMe.
E)Poll Everywhere.

Question 43

Which of the following is a relatively simple and low-cost but powerful tool used for projecting student work?

A)Interactive Whiteboard.
B)CAS Technology.
C)Dynamic Software.
D)Document Camera.
E)Mobile Projector.

Question 44

Which of the following is the LEAST creative use of a document camera in teaching mathematics?

A)Teacher writes notes on paper and projects them to a screen.
B)Students display their work after solving a problem.
C)Teacher takes a snapshot of a displayed image.
D)Manipulatives are demonstrated for the whole class.
E)Student uses a virtual pen to write on a saved image.

Question 45

Which of these is perhaps the greatest use of a document camera?

A)Teacher writes notes on paper and projects them to a screen.
B)Students display their work after solving a problem.
C)Teacher takes a snapshot of a displayed image.
D)Manipulatives are demonstrated for the whole class.
E)Student uses a virtual pen to write on a saved image.

Question 46

Which of the following is NOT suggested by research on the use of document cameras in teaching mathematics?

A)Teachers are able to spend more time discussing student thinking.
B)Teachers develop a deeper understanding of student thinking.
C)Students are more engaged in mathematics lessons.
D)The number of students able to share their work increases.
E)Students show an increase in confidence to do mathematics.

Question 47

Which term refers to the teaching approach that uses both on-line and classroom interactions?

A)Combined.
B)Associated
C)Dynamic.
D)Associated.
E)Blended.

Question 48

Which of the following strategies is most commonly used in a "flipped" classroom?

A)Students research a topic and teach it to one another.
B)Teacher creates videos that are shown in class.
C)Students create screencasts for homework.
D)Teacher uses videos for students to teach one another.
E)Students view videos for homework.

Question 49

Research on flipped classrooms suggests that student performance only tends to improve under which of the following conditions?

A)The teacher only occasionally uses the flipped approach.se only.
B)Students are highly motivated to learn independently.
C)The students are involved in making the learning videos.
D)The teacher also plans for how to increase the focus on conceptual understanding.
E)The content area under study is either number or geometry.

Question 50

Research suggests that what percentage of high school juniors and seniors are still operating at a concrete stage and need visual and hands-on experiences?

A)10%.
B)25%.
C)33%.
D)67%.
E)80%.

Question 51

List at least three tools that can be used to enhance classroom discourse.Discuss the context in which each of these tools might be used in the classroom.

Question 52

Explain how even a simple diagram or graph can be used in the teaching-and-learning process to generate rich mathematical discourse.

Question 53

Provide examples of what one may consider the appropriate use of a calculator in the mathematics classroom, contrasted with situations in which the calculator would not be necessary or may even inhibit the learning process.

Question 54

List and describe three different classroom technologies that can assist with teaching mathematics.For each, explain how the technology can be used, along with possible drawbacks to implementing the tool.

Question 55

List and discuss four different ways that an interactive whiteboard can enhance the teaching and learning of mathematics.

Question 56

Explain the meaning of "blended" and "flipped" classroom teaching strategies.For each, discuss the advantages and disadvantages of the strategy.