Math 340 Final Exam Review – Flashcards
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Which choice reflects two factors that influence the teaching of Mathematics effectively?
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Knowledge of standards and practices.
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The mathematical needs in society have changed and are influencing what should be taught in preK-8 mathematics classrooms. What statement below reflects a key factor in the change?
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Data on the performance of U.S. students in national and international studies.
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The National Assessment of Educational Progress
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Reported in 2013 that less than half of all fourth- and eighth-graders performed on a standardized mathematics test at the desirable levels of "proficient" or "advanced."
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The six Principles and Standards for School Mathematics articulate high-quality mathematics education. What statement below represents the equity principle?
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The message of high expectations for all is intertwined with every other principle.
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Which of the following can be said to be true about the learning principle?
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Learning is strongly enhanced when students are encouraged to make and test their own mathematical conjectures.
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Which of the following is an example of a statement spoken in the language of doing mathematics?
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"Explain how you solved the problem."
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Which statement below best describes the idea of mathematics as engaging in the science of pattern and order?
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Mathematical processes and concepts follow logical patterns and have a logical order. Students are capable of and should be allowed to explore this regularity and make their own sense of mathematics.
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Doing mathematics begins with posing worthwhile tasks. Which verbs align with activities that lead to higher-level thinking?
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Investigate, construct and formulate.
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To set up an environment for "doing" mathematics, teachers need to;
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Allow students to make engage in "productive struggle.
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There are many ways to model and solve problems and explore how others develop understanding. Which strategy would foster students examining multiple solutions to try other methods?
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Experimenting and explaining.
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Which statement best reflects the approach of teaching for problem solving?
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It usually involves students exploring alternative methods of solving a story problem.
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Which statement about the teaching through problem solving approach is most accurate?
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Requires a four-step approach to problem solving.
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Selecting problem solving tasks that require higher levels of cognitive demand should include which one of the following?
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Use of complex and non-algorithmic thinking.
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Problem solving tasks that have multiple entry and exit points exhibit what characteristics below?
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Varying degrees of challenge and methods to approach a solution.
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Children's literature can be a method of creating tasks with context students can connect to other subjects. What statement below demonstrates how a teacher made a connection?
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Today we are going to find out how numbers double with a Chinese magical
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When determining the mathematics content and learning goals for a lesson, the teacher should do all of the following EXCEPT:
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Plan goals that will take no longer than a day for students to accomplish.
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Planning a lesson for a classroom where inquiry and problem solving are emphasized requires a shift in the type of lessons being used. What statement below represents this shift in the agenda of a lesson?
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It should be a "thought experiment" to consider what might happen.
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The NCTM Principles and Standards stress two main ideas of integrating assessment into instruction. Identify the statement below that represents one of key NCTM ideas.
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Valuable tool for making instructional decisions.
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Three of the statements below are characteristic of formative assessment. What statement would be true of summative assessment?
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Identify the mastery of standards.
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What statement below denotes a limited point of view about the purpose of assessment?
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Assessment is tests and quizzes.
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The NCTM position statement on Access and Equity in Mathematics states that we
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All students should be held to high levels of performance regardless of race, ethnicity, gender and socioeconomic status and linguistic background.
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Teachers may be guilty of setting lower expectations for students when they suggest that the group is too unruly to work together or they don't have the reading skills to do problem solving. What "gap" does this represent?
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Instructional gap.
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The goal of equity is to offer all students access to important mathematics during the regular mathematics instruction in the classroom. Which group listed below would need a modification versus an accommodation?
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Students who are English language learners.
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What statement below is an example of an accommodation?
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Write directions in larger font.
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What statement below is the best description of what is meant by the term RTI ?
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A multi-tiered student support model that focuses on prevention, providing students with support before they begin to fail.
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Common features across RTI tiers include all of the following. Identify the statement that is related to instructions.
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Prompts, cues and environmental arrangements
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What statement represents a technology-enabled learning setting?
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Is an useful "add-on" part of your curriculum, when you are looking for a way to heighten student engagement.
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What is an example of a synchronous or asynchronous collaboration?
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Graphing calculators.
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NCTM's position on calculator use in elementary school includes which of the following ideas?
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Calculators should not be used until after students have developed mastery of basic facts.
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What phrase is the meaning of the term TPACK?
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Technology standards.
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All of the following are positive effects of using a calculator EXCEPT:
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Students become dependent on a tool they will not be able to readily access out in the real world.
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Which of the following is a description of Number Sense?
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Thinking about different sized quantities and use number relationships.
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Research-based recommendations for high quality learning activities in the first six years of life include all of the following EXCEPT:
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Thinking about different sized quantities and use number relationships.
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The National Research Council identified three foundational areas in mathematics content for early learners. Identify the core that is more applicable for experienced learners.
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Reasoning core.
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Children explore quantity before they can count. What is the word for children being able to "just" see how many there are without counting?
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Subitzing.
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Which of the following represents a true statement about the concept of 0?
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Developing understanding of 0 is important with its role in the base-ten number system.
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Verbal counting requires separate skills. Identify the statement that represents one of them.
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One-to-one correspondence.
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What statement identifies the importance of using contextual problems as a primary teaching tool?
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Children construct richer understanding of the operations.
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Identify the problem that represents the join, result unknown structure.
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Maryann had 3 library books before she checked out 2 more. How many did she have all together?
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Which problem represents the separate, start unknown structure?
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Maryann had some nonfiction books and 2 fiction. She now has 8 books. How many did she begin with?
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Which problem represents the compare, difference unknown structure?
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Maryann had 9 library books and Jim had 4. How many more did Maryann have than Jim?
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What statement below is the description of a Part-part-whole?
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Two parts that are conceptually or mentally combined into one whole.
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Problems with the join and separate structures, with the start or initial amount unknown, tend to be the hardest for students to understand and accurately solve. Identify the reason for they are more challenging for children to use.
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Children cannot use counters for the initial amount.
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What statement most accurately describes a person who has mastered basic facts?
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He or she has obtained a set of essential understandings and progressed through a set of stages so that she just "knows" the answers to certain basic fact problems.
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Three developmental phases for learning the basic facts are identified below. Which one is the initial phase?
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Counting strategies.
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Despite the fact that many learners in the past learned basic facts from memorization, there is strong evidence that this may not be the most effective strategy for all of the following reasons EXCEPT:
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Students are motivated when they are assessed with timed tests.
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Research shows that guiding students to use effective reasoning strategies can help them achieve mastery. Identify the explicit teaching strategy below.
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Use of known facts and relationships.
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Story problems can provide a valuable context to help students apply reasoning strategies for computation for all of the reasons EXCEPT:
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Become proficient with algorithms.
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Which of the problems below would provide an opportunity for students to apply the use of the Anchor Number reasoning strategy?
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Juan has 9 trading cards in his backpack and 6 more cards in his pocket. How many cards does he have altogether?
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Complete this statement, "Number sense is linked to a complete understanding of..".
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Place-value.
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What statement below would represent a child that has yet grasped the knowledge of recognizing groups of ten?
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Counts out sixteen objects and can tell you how many by counting each piece.
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All the examples below are examples of proportional base-ten models EXCEPT:
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Money
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What does the relational understanding of place value needs to begin with?
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Counting by tens and ones, making the model, saying and writing the numeral.
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What would be a strong indication that students are ready to begin place-value grouping activities?
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Students have had time to experiment with showing amounts in groups of twos, fives and agree that ten is a useful-sized group to use.
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Base ten riddles engage students in what type of mathematical demonstration?
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Equivalent representation
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Modern technology has made computation easier. Identify the true statement below.
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But mental computation strategies can be faster than using technology.
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All of the following provide an examples of a method used for computation EXCEPT:
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Discourse modeling
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One of the statements below would NOT be considered a benefit of invented strategies.
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They require one specific set of steps to use them, which makes them easier to memorize.
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Which of the following is a true statement about standard algorithms?
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In order to use them, students should be required to understand why they work and explain their steps.
