Question 1

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

Accepted Answer

A counterexample is a specific case for which the hypothesis does not hold, thus proving that the hypothesis is not always true.

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?

Accepted Answer

The NCTM (National Council of Teachers of Mathematics) in its "Principles to Actions" document emphasizes that the use of tools and technology is essential in the teaching of mathematics to enhance learning and understanding.

Question 3

Which of the following are considered tools for teaching mathematics?

Accepted Answer

All of these options (computer software, manipulatives, puzzles, and interactive electronic devices) are considered tools for teaching mathematics. They each offer unique ways to engage students and facilitate understanding of mathematical concepts.

Question 4

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

Accepted Answer

Research indicates that about 33% of seventh graders can explain the reasoning behind lining up decimals when performing addition or subtraction.

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?

Accepted Answer

The best tools for teaching a lesson on adding decimals can vary depending on the situation, such as the specific learning objectives, the students' prior knowledge, and the context of the lesson. Calculators, base ten blocks, rulers, and money can all be effective in different scenarios. For example, base ten blocks and money are particularly tangible and can help students understand the concept of place value and decimals in a hands-on way, while calculators might be more appropriate for older students focusing on more complex calculations. Therefore, the most effective tool depends on the educational context and goals.

Question 6

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

Accepted Answer

The answer of When using base ten blocks to explore...

Question 7

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

Accepted Answer

In base ten blocks, flats represent whole numbers, longs represent tenths, and unit cubes represent hundredths. Therefore, 4.83 would be represented by four flats (for the 4 whole units), eight longs (for the 0.8 or 8 tenths), and three unit cubes (for the 0.03 or 3 hundredths).

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?

Accepted Answer

A 10 x 10 grid represents 1 whole, so a single square, which is 1 out of 100 squares, represents 1/100 or 0.01.

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.

Accepted Answer

In the metric system, a decimeter is one-tenth of a meter, a centimeter is one-hundredth of a meter, and a millimeter is one-thousandth of a meter. Therefore, 6.93 meters would be represented as six decimeters (6.0), nine centimeters (0.9), and three millimeters (0.03), making option C correct.

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?

Accepted Answer

The correct balance involves understanding the subject matter (Mathematics), knowing how to teach it effectively (Pedagogy), and considering the needs and backgrounds of the learners (Students). This combination ensures that instruction is both effective and responsive to students' needs.

Question 11

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

Accepted Answer

Pedagogical Content Knowledge involves the integration of subject matter knowledge with effective teaching strategies, understanding students' backgrounds, and their prior knowledge, but not specifically access to teaching tools.

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?

Accepted Answer

The answer of If a teacher begins a lesson by...

Question 13

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

Accepted Answer

The answer of Which of the following statements most accurately...

Question 14

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

Accepted Answer

Freeplay time with manipulatives allows students to explore and experiment, fostering creativity and understanding through hands-on learning.

Question 15

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

Accepted Answer

The author suggests that 15-20 minutes should be given the first time students use manipulatives to allow them to explore and become familiar with the materials.

Question 16

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

Accepted Answer

Establishing specific rules for the use of manipulatives helps prevent students from engaging in off-task behavior, ensuring that the materials are used effectively for learning purposes.

Question 17

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

Accepted Answer

The incorrect statement is that students "inherently" learn when they use manipulatives, suggesting that simply using manipulatives guarantees learning. Effective use of manipulatives requires thoughtful integration into instruction, not just their regular presence in the classroom routine.

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?

Accepted Answer

Translation involves moving an object from one place to another without rotating it, and rotation involves turning the object around a fixed point. These two concepts are key to representing the position of a table before and after it was moved, as described in the example.

Question 19

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

Accepted Answer

Manipulatives and technology can be powerful tools in teaching, but their effectiveness depends on how and when they are used. They are not universally appropriate for every teaching situation or learning objective. The decision to use them should be based on their relevance to the learning goals and the needs of the students.

Question 20

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

Accepted Answer

Technology in a mathematics classroom is primarily used to teach concepts, explore mathematical ideas and problems, and assess student progress through various tools and applications.

Quiz 9: Teaching and Learning: Tools and Technology