Math 391 Test 1 | Questions with Verified Answers

Math 391 Test 1 | Questions with Verified Answers Which choice reflects two factors that influence the teaching of Mathematics effectively? Knowledge of standards and practices. The mathematical needs in society have changed and are influencing what should be taught in pre K-8 mathematics classrooms. What statement below reflects a key factor in the change? Data on performance of U.S. students in national and international studies. The National Assessment of Educational Progress... reported in 2013 that less than half of all 4th and 8th graders performed on a standardized mathematics test as the desirable levels of "proficient" or "advanced". The six Principles and Standards for School Mathematics articulate high-quality mathematics education. What statement below represents the equity principle? The message of high expectations for all is intertwined with every other principle. What is true about the learning principle? Learning is strongly enhanced when students are encouraged to make and test their own mathematical conjectures. What statement reflects the Connections standard of the Five Process Standards from Principles and Standards for School Mathematics? Students should be given opportunities to see how various mathematical ideas relate to one another and to a variety of real-life experiences. One of the statements below represents a method for developing the Reasoning and proof process standard. Create opportunities for students to evaluate conjectures. The following statements represent the "thinking" behind the creation of the Common Core Standards for School Mathematics. Which statement is also true of the NCTM Principle and Standards for School Mathematics? A focused set of Mathematics content standards and practices. The Standards for Mathematical Practice are... A component of the Common Core State Standards that outlines a series of important mathematical processes all students should be able to do regularly. Which statement below captures the big idea from one of the Eight Guiding Principles outlines in the NCTM Principles to Action? Look for both horizontal and vertical alignment to build coherence. Identify the statement that completes this statement, "Learning progressions reflect current research and practice and they guide teachers in understanding..." What came before as well as what to expect next. As a practicing or prospective teacher each face the challenge of teaching mathematics from a problem solving perspective. This often requires some to confront personal beliefs about: Teaching conceptual understanding and procedural fluency. What are examples of effective assessment techniques that will guide your understanding of student knowledge? Feedback, on-going observation and continuous data gathering. What are two ways that learning progressions can inform instructional planning? -informing teachers of what came before -what to expect next as students reach key points -identity interim goals along the path to learning mathematical concepts -inform the order of instructional experiences What are the main tenets of the Curriculum principle in the NCTM Principles to Action? The tenets of the Curriculum Principle include a coherent curriculum build around big ideas in daily classroom instruction. The big ideas are links from one idea to another and help students see the integration and growth over grades versus an isolated series of bits and pieces. Which of the following is an example of a statement spoken in the language of doing mathematics? "Explain how you solved the problem." Which statement below best describes the idea of mathematics as engaging in the science pattern and order? 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. Doing mathematics begins with posing worthwhile tasks. Which verbs align with activities that lead to higher-level thinking? Investigate, construct, and formulate To set up an environment for "doing" mathematics, teachers need to: Allow students to make engage in "productive struggle". 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? Experimenting and explaining Which of the following represents an example of an effective way a teacher might help facilitate students' construction of mathematical relationships? Asking students, "How is today's topic related to the fraction multiplication we investigated last week?" What does it mean to be mathematically proficient? Identify the statement below that is true of students becoming mathematically proficient. The student will become mathematical proficient by following daily expectations for doing mathematics. The standards for mathematical proficiency state that we should want students to not only know the concepts but also to how to use them to problem solve. What statement below reflects how a proficient mathematical student might think? When I complete a problem I wonder if there are another answers that could be right. Identify the statement that reflects an educational implication of the learning theories discussed in Chapter 2 "Exploring What it Means to Know and Do Mathematics": Class activities and lessons should be designed with students' prior experiences in mind. Which statement best represents a method to expose students to multiple approaches to problem solving? Exposure to multiple approaches and the subsequent connections help students to recall the steps to complete mathematical processes. Your teaching of mathematics is controlled by what factor below? Personal theory and beliefs Identify the statement below that would represent a constructivist approach to a problem solving activity. Students are given resources that they can watch, touch, and listen in order to build new understandings. Vygotsky believed that learning was better achieved through social interaction. What statement best identifies a learning environment that represents this belief? Students are encouraged to work in groups and share problem solving strategies and solutions. What theory(s) allow a classroom culture to access prior knowledge, use tools to build knowledge? Constructivist Making connections among mathematical relationships improves student conceptual understanding. What statement is a tenet of this belief? Teacher scaffolds new content through the use of tools and peer assistance. Classroom culture influences the individual learning of students. What statement is an example of how a teacher can honor diversity? Value student ideas and approaches. Complete this statement, "Classrooms where students are making sense of mathematics do not happen by accident they happen because..." The teacher has practices and expectations that foster risk taking, reasoning, and sharing. The focus of connecting the dots between theory and practice require teachers to focus in opportunities. All of the statements below are true: -Plan and design instruction based on prior learning -Designate time for student reflection -Plan tasks that reflect the social and cultural makeup of the classroom. Manipulative materials have the potential to provide opportunities for connection and communication. What statement would be a non-example of how to utilize the materials? Encouraging students to converse about the model without knowledge of what the mathematical goal they are working on. All of the following statements regarding teaching for mathematical proficiency are true: -It requires students to memorize less -It allows students to more easily make connections to new concepts -It increases student enjoyment and attitudes towards mathematics. Name at least two examples of classroom culture that could be an environment for students to do mathematics and gain relational understanding of a concept. -Persistence, effort, and concentration are valued -Sharing of ideas among students -Students listen to each other -Students look for and discuss connections A mathematically proficient student would approach a challenging problem solving task with a certain disposition. Describe at least two examples of what that disposition would look and sound like in a classroom. -Students asking questions not only of the teacher by each other -Students trying multiple approaches when problem solving -Students recognizing errors and continuing to try other methods -Students that can communicate the how and why their answer makes sense -Students that believe learning mathematics is worthwhile and useful Conceptual understanding is a flexible web of connections and relationships within and between ideas, interpretations, and images of mathematical concepts. Give two ways that a spinner could be used to guide the understanding of the concept of "chance". -Models and compares possible outcomes -Models the relationship between frequency and all possible outcomes -Creates relative frequencies by observing the sections of the spinner -Configuration of the sections of spinner from easy to more complex Which statement best reflects the approach of teaching for problem solving? It frequently results in the instructor explaining a skill and providing practice and application of the skill Which statement about the teaching through problem solving approach is most accurate? Requires a four-step approach to problem solving. Selecting problem solving tasks that require higher levels of cognitive demand should include which one of the following? Use of complex and non-algorithmic thinking. Problem solving tasks that have multiple entry and exit points exhibit what characteristics below? Varying degrees of challenge and methods to approach a solution. 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? Today we are going to find out how numbers double with a Chinese magical pot. Which is the most accurate statement regarding posing a worthwhile problem? Teachers should select the problems that will help make relationships between mathematical concepts explicit for students. Which statement below best represents worthwhile features of tasks or problems for learning mathematics? Problematic, concepts and/or misconceptions, relevant Which of the following is an instructional example of teaching through problem solving? After students have conceptual understanding of the area of a rectangle, asking them to find the area of a triangle that was constructed by cutting a given rectangle in half and then to generalize their process to how they might find the area of any given triangle. Researchers have found that teachers benefit from using an intentional selection process to determine whether a task they chose is worthwhile. One of the criteria of the selection guide is "worthwhile features". Which statement below represents one of the categories in "worthwhile features"? Relevant context Drill and practice is present to some degree in every classroom. The definitions of drill and practice demonstrates how they are different and how they link. One of the statements below is representative of practice more than drill. An increased opportunity to develop conceptual ideas. Drill of skills has a place in helping students improve procedural knowledge but not conceptual knowledge. Before committing to a solution of "just drill" what do you need to know? The type of drill that will build understanding Facilitating classroom discourse requires that the teacher be aware of what factors that will affect the level of mathematical talk in the classroom. What statement below would impact the mathematical talk? The level of English proficiency of the students in the classroom. Effective use of classroom discussion has the teacher monitoring the students' strategies and asking questions. What question below would require the student to reflect on their specific strategy? What mathematical terms, symbols, or tools did you use to find a solution? Teachers can prompt productive classroom discussion through the use of five teacher talk actions. What statement below reflects the type of prompt to elicit student reasoning? Who also used similar strategy as Ricardo? How much to tell or not tell is a constant dilemma for teachers. What statement would be the type of information that teachers do need to tell? Help students clarify their ideas and point out related ideas The act of writing is a reflective process and involves students in metacognition. What statement is an example of a students' conscious monitoring of how and why they are doing something? Taking a timed multiplication test. *Looking back at problems previously worked incorrectly to examine the mistakes. Teaching through problem solving provides opportunities for all students to become mathematically proficient. Teaching through problem solving benefits all students in what way? Focusing on the single strategy needed to solve most problems. *Focusing students on ideas and sense making.