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math concepts
| Question | Answer |
|---|---|
| According to the Principles and Standards for School Mathematics (2000), curriculum is more than a collection of activities, but rather is considered to be all of the following except: | formulated on standard methods. |
| According to the Teaching Principle defined by NCTM, effective mathematics teaching requires: | understanding what students know and need to learn. |
| The Technology Principle states that technology is essential in teaching and learning mathematics. | True |
| The NCTM standards provide a national curriculum for mathematics education. | False |
| The Principles and Standards for School Mathematics (2000) document makes which of the following statements about drill and practice. | Drill may produce short term results on traditional tests. |
| In order to create an environment for doing mathematics, the teacher's role is to: | create a spirit of inquiry, trust, and expectations. |
| Traditional teaching approaches lead children to accept all of the following except: | that making sense of mathematics is what is important. |
| All of the following statements are true about the desirable mathematical environment except: | students are working through practice problems to learn the mathematical strategy. |
| Repetitive drill is needed to do mathematics as you master the skills. | False |
| Teachers must continue teaching by telling. | False |
| Constructivist Philosophy has as a basic tenet that: | children construct their own knowledge. |
| The constructivist theory proposes all of the following except: | a safe environment is necessary to gain mathematical power. |
| Benefits of relational understanding include all of the following except: | it eliminates poor attitudes and beliefs. |
| Skilled use of procedures will lead to conceptual knowledge associated with that procedure. | False |
| he more ways a child is given to think about and test an idea, the less likely the child will form the idea correctly. | False |
| Every idea introduced in the mathematics classroom can and should be completely understood by every child. | True |
| Traditional problem solving lessons had a teacher explaining the math, students practicing the math followed by applying the mathematics to solving problems. Yet this rarely works because: | it assumes wonderful explanations produces understanding. |
| The four steps in evaluating and selecting a problem solving activity include determining: | the needed materials and how the activity can be completed. |
| All of the following are types of information that math teachers should provide their students except: | the preferred method. |
| n the final portion of the problem solving lesson, the students learn to engage in discourse and work as a community of learners. | True |
| Your textbook recommends structuring a lesson as explain-then-practice rather than before, during, afte | False |
| Several steps exist in planning a problem-based lesson. Which of the following is not one of them? | Begin with the textbook pages. |
| The primary criteria for using drill includes: | the need for automaticity with the skill or strategy as a desired outcome. |
| Drill can provide students with which of the following: | an increased facility with a strategy. |
| When drill is assigned for homework, which of the following is important to remember? | Keep the drill homework assignment short. |
| A game or repeatable activity may be a problem-based task if the activity causes students to reflect about new or developing mathematical relationships | True |
| When pairing students in need of help, it is advisable to randomly pair your student or allow them to select the students they want to work with. | False |
| A teacher should not repeat old ideas or pose tasks that students are not able to access without the teacher's guidance. | True |
| Addressing the needs of all students in a diverse classroom includes which of the following specific categories of students? | Students with specific learning issues Students from different cultures Students who are mathematically promising |
| When working with children who have learning disabilities, it is important to remember: | learning disabilities should be compensated for by helping students use their strengths. |
| Adaptations for students with attention deficits include all of the following except: | plan on students doing independent work in an environment that attracts their attention. |
| There are many ways to address cultural issues within the mathematics classroom including all of the following except: | studying mathematics concepts. |
| When working with learning disabled students, search for ways to adapt instructional strategies to avoid weaknesses and capitalize on strengths without major modifications to the curriculum | True |
| One modification in instruction is to partner the mentally disabled child with different students periodically who help the child with the same task or ideas. | True |
| All of the following are purposes of assessment except: | determining students' grades. |
| Deciding on a performance at different levels of your rubric requires all except: | knowing what ideas children will not use as they perform the task. |
| A good assessment program will allow students to demonstrate how they understand the concepts | True |
| A rubric is a scale used to judge performance on a series of exercises. | False |
| It is good to write out indicators of performance tasks after you use the task in class. | False |
| A teacher should make good use of calculators by using them for all of the following except to: | perform basic computations such as 7x3 when computation skills are the objective of the lesson. |
| In considering the use of the calculator, a teacher should: | teach children how to use the calculator as a commonplace tool effectively. |
| Features or characteristics that make software programs worthwhile additions to your classroom include all of the following except: | program comes with games. |
| Dynamic geometry software programs: | allow students to create and manipulate shapes. |
| hat technology is one of the six principles in the Principles and Standards in School Mathematics (2000) document highlights the importance that NCTM gives to technology. | True |
| Calculators interfere with the learning of basic facts. | False |
| Research has found that the average-ability learners can enhance their problem-solving abilities from calculator usage. | True |
| Story problems are an ineffective way to incorporate other subjects into the math classroom. | False |
| Literacy can be included in math instruction through which methods? | Reading entertaining stories which include math problems. Writing journal entries about problem solving processes. |
| Math and science are two subjects which cannot be easily integrated. | False |
| How could a unit on Egypt be incorporated into math class? | Answers will vary: discussion of pi, scale measurements, geometry (3D shapes), etc. |
| The ________ principle refers to recognizing that the last number counted names the quantity of the set. | Cardinality |
| Out of the four different types of number relationships that children can and should develop, which one refers specifically to working with fingers or ten frames? | Anchors of 5 and 10 |
| The multiplication property that explains a x ( b + c) = a x b + a x c is: | Distributive property |
| Which of the following statements is true? | Part-part-whole problems involve two parts that are combined into one whole. |
| Number line problems are a good model to teach addition to first and second graders. | False |
| Students should just think of remainders as "left over" amounts. | False |
| When students are able to use a strategy without recourse to physical models and are beginning to use it mentally, it is time to: | provide fact strategy drills. |
| One of the benefits of invented strategies is that: | students make fewer errors. |
| One should begin the instruction of addition and subtraction algorithms with: | models. |
| Any strategy other than the traditional algorithm and that does not involve the use of physical materials or counting by ones is called a/an ________ strategy. | invented |
| Models for fractions can be classified into categories. Which category includes pattern blocks, circle pieces, fraction squares? | Region/Area |
| One major requirement for understanding fractional parts of a whole is: | the whole must be made up of equal sized parts. |
| On explaining the top number and the bottom number, the bottom number tells what is being counted and can be called the divisor. | True |
| . "Find two equivalent fractions for 2/7." The first student provides this answer: 4/14 and 8/28. The second student answers: 4/9 and 5/10. Which of the following strategies should the teacher employ? | The teacher should allow both students to re-tell their strategies and discuss their method of obtaining the answer. |
| Focusing attention on fraction rules and answer-getting has two significant dangers, one of which is: | mastery is only short term. |
| The algorithm that relies on repeated subtraction for modeling division of two fractions with unlike denominators is called: | common-denominator. |
| When beginning work with multiplication of two fractions 1/2 x 2/3, you should tell students that: | just like in whole numbers such as 3x5 where we said 3 sets of 5, ½ x 2/3 means ½ of a set of 2/3. |
| Which of the following problems would not require the students to subdivide the parts in order to model the solution to the problem? | 2/3 x 3/4 |
| When connecting fractions to decimals, we should: | extend the base-ten decimal system to numbers less than one. |
| Before considering decimal numerals, it is wise to review old concepts. One of the most basic ideas relevant to decimal numerals is: | the ten-to-one relationship between the value of two adjacent positions. |
| To model 1/3 as an infinitely repeating decimal, students should first: | model 1/3 as a decimal by partitioning the whole square into 3 parts using strips and squares. |
| Any base 10 model can be a decimal model as well. | True |
| A ratio is defined as: | a multiplicative comparison of two numbers or measures or quantities. |
| Ratios can be all of the following except: | an equality of two fractional numbers. |
| All fractions are ratios because they both can be a comparison of parts-to-wholes. | True |
| Using physical materials versus paper and pencil activities in patterning activities: encourages better distinction of the core. | allows students to make changes and to extend patterns beyond the spaces on the page. |
| When teaching about growing patterns, students should be encouraged to do all of the following except: | make a pattern given a table or chart of numeric data. |
| The recursive relationship of a pattern implies: | how a pattern changes from step to step. |
| Which of the following is used as a symbol that represents a number or set of numbers? | Variable |
| Which is a true statement concerning a linear function? | All of the points on the graph lie on a straight line. |
| In 3B + 7 = A -- B, the equal sign means the quantity on the left is the same as the quantity on the right. | True |
| Conceptual knowledge that should be developed on measurement includes which of the following: | understanding the ways measuring instruments work. |
| Students should use a variety of informal units to begin measuring length, including: | plastic straws cut into smaller units that can be linked together with a long string. |
| In kindergarten, children should begin with direct, non-standard comparisons of two or more lengths. | True |
| Characteristics of the Van Hiele levels indicate: | levels are sequential. |
| In Van Hiele's level zero, Visualization, activities includes all of the following except: | hypothesizing about shapes. |
| General indicators that are more indicative of level two thinkers include all of the following except: | recognize shapes in the environment. |
| At level 0, the most important type of activity a teacher can have students work with is to: | find the similarities and differences of a wide variety of shapes. |
| Using smaller shapes or tiles to create larger shapes is a good level three activity. | False |
| Students at level two have a hard time seeing relationships among items other than disjoint classifications. | False |
| When no numeric ordering of the data is needed, you should use a: | bar graph. |
| When data is partitioned into parts of a whole it is best to use: | circle graphs. |
| Once a graph is constructed, the most important activity is to analyze the details of graph construction. | False |
| Deciding on the interval and scale can cause difficulties in histogram construction. | True |
| Older children, but not yet younger children, understand that chance: | means some results are more or less likely than others. |
| All of the following are true about probability except: | probability changes based on the number of trials. |
| In a probability experiment, an event: | is a subset of the sample space. |
| Independent events: | are when the occurrence or nonoccurrence of one event has no effect on the other. |
| he phenomenon of the law of large numbers means that a larger sample will provide a more accurate theoretical probability. | False |
| Supposing a student flips a coin three times and the results occur in the following ways: head, tail, tail. The student is then asked, "What is the probability that a tail is flipped next?" * | Tails occurred twice in three trials so it has a 66.67% chance of occurring again. 2/3 After tossing the coin 100 times, 32 times were tails and 68 were heads. 8/25 Since a coin has two sides, tails would occur 2 out of the 4 times. 1/2 |
| Children who have difficulty translating a concept from one representation to another: | should be given additional practice in the concept. |
| Procedural fluency leads to relational understanding. | False |
| Strengthening the ability to move between representations improves student understanding and retention. | true |
| The five representations of mathematical ideas include which of the following? | Pictures Written symbols Oral language Manipulative models Real-World Situations |
Created by:
hrodenbough