MATH 204 EXAM 1 QUESTIONS WITH VERIFIED ANSWERS LATEST UPDATE 2026

MATH 204 EXAM 1 QUESTIONS WITH VERIFIED ANSWERS LATEST UPDATE 2026 Why change the way we teach math? - Answers -for our students to be competitive in the global market -so students can understand the complex issues they must confront as responsible citizens The 5 Process Standards - Answers Problem-solving Reasoning & Proof Representation Communication Connections Six Principles and Standards for School Mathematics - Answers Curriculum Assesment Teaching Technology Learning Equity Curriculum Principle - Answers A curriculum in is more than a collection of activities: -it must be coherent -focused on important math -articulated across grades -connections to daily-life Assessment Principle - Answers Assessment should support the learning of important math and furnish useful information for teachers and students. -ongoing -student interaction & articulation Teaching Principle - Answers Effective math teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well. -provide strategies to enhance learning Technology Principle - Answers Technology is essential in teaching and learning math -influences the math taught -enhances student learning Learning Principle - Answers Student must learn mathematics with understanding -actively building new knowledge from experience & prior knowledge -individually & in groups Equity Principle - Answers Excellence in math education requires equity -high expectations & strong support Common Core State Standards - Answers Puts a coherent vision of standards across the states @ specific grade levels (Math & English) 5 Content Standards (Common Core) - Answers Numbers & Operations Algebra Geometry Measurement Data Analysis 6 Content Standards VA - Answers Number, Number Sense Computation and Estimation Measurement Geometry Probability & Stats Patterns, Function& Algebra Why didn't VA adopt Common Core? - Answers -Helped develop common core -Already developed their own standards -Standards weren't high enough What are the large groups in which Common Core divides the content expectations for students? - Answers Domains Many factors influence how mathematics are taught in a school system and which mathematics are covered. What are some of the most influential factors? A. National and international testing results B. The age of the students and their geographic location C. The presence of a new classroom textbook and a new teacher D. The size and wealth of the school system - Answers A. National and international testing results - The results of testing - at the local, national, and international levels strongly influence the direction of mathematics in education As a teacher... - Answers Knowledge of Math Life-long Learning Readiness for Change Positive Attitude Persistence Which of the following statements represents the equity principle? A. The message of high expectations for all is intertwined with every other principle B. Math today requires not only computation skills, but also the ability to think and reason C. Calculators and computers should be seen as essential tools for doing and learning mathematics D. Coherence speaks to the importance of building instruction around being ideas - Answers A. The message of high expectations for all is intertwined with every other principle -The equity principle is embedded in all of the other standards, as expectations for all students must be high in order to address the other components Although all are important, which of the following teacher characteristics is most essential to demonstrate in order to help students persevere, think to try other strategies, and check their answers to problems? A. Positive Attitude B.Persistence C. Reflective Disposition D.Lifelong learning - Answers B. Persistence - Persistence is most closely aligned to the behaviors students will need to demonstrate in order to persevere and make sense of problems and their answers Which of the following statements is the best definition for the term "school effects" as it pertains to mathematics education? A. Schools have no effect on students' leaning of math, and students' learning is completely determined by how they interact with math outside of the classroom B. Schools affect students' learning of mathematics by creating the daily schedule for when various content areas are taught C. For many students, school is the only place where they get to experience math. D. Some schools have better learning environments for mathematics than others - Answers C. For many students, school is the only place where they get to experience math -Although students are often exposed to reading, current/historical events, and science, math is commonly experienced only in school This makes the teacher's role significant in students' learning and understanding. What does it mean to DO Mathematics? - Answers -Generating strategies for solving problems -Applying those approaches, seeing if they lead to solutions -Checking to see whether your answers make sense Bloom's Taxonomy - Answers Promotion of higher-level thinking -Collaborate -Develop -Investigate -Formulate Tips for Solving Problems: - Answers -Searching for patterns -Analyzing situations -Generalizing relationships -Experimenting/Explaining -Rational understanding -Measuring with tools - manipulatives Three math tasks were shared in this section. Each of the tasks was an example of doing math because: A. it involved an open-ended problem. B. it required looking for patterns and order. C. it was fun. D. it engaged the learner in reasoning mathematically. - Answers B. it required looking for patterns and order -All of these answer choices correctly describe the three tasks, but what makes these tasks examples of "doing mathematics" is the fact that students had to notice mathematical patterns and sense of those patterns. Looking for patterns and order was necessary to reach an answer. Understanding - Answers the measure of quality and quantity of connections between new ideas and existing ideas Continuum of Understanding - Rational Understanding -Instrumental Understanding - Answers Richard Skemp -Knowing what to do and why -Doing something w/o understanding 5 Strands of Mathematical Proficiency - Answers Conceptual Uderstanding Procedural Fluency Strategic Competence Productive Disposition Adaptive Reasoning Conceptual Understanding - Answers Comprehension of mathematical concepts, operations, and relations Procedural Fluency - Answers Skill in carrying out procedures flexibility, accurately, efficiently, and appropriately Strategic Competence - Answers Ability to formulate, represent and solve mathematic problems Productive Disposition - Answers Habitual inclination to see math as sensible, useful, and worthwhile coupled with a belief in diligence and one's own efficacy Adaptive Reasoning - Answers Capacity for logical thought, reflection explanation, and justification PAPER SHREDDING PROBLEM: An old machine could shred a truckload of paper in 4 hours. The new machine could shred a truckload of paper in 4 hours. The new machine could shred the same truckload in only 2 hours. How long will it take to shred a truckload of paper if Ron runs both shredders at the same time? - Answers Which of the following is the best way to pose a task to students so that they experience doing mathematics? A. Give an example of how to do a problem that is similar to the one you have selected, but slightly easier, so the students know what to do. B. Share the problem, ask students to explore, stop them to see how they are doing, and let them keep going. C. Teach the skill that is needed to solve the problem first, then give this problem as an extension. D. Have the students take the problem home and solve it, then bring it back to school to discuss - Answers B. Share the problem, ask students to explore, stop them to see how they are doing, and let them keep going -To ensure the students get involved in doing mathematics, they would need to experience the problems much like you did. Choose problems for which students have the background, but to which all students (K-8) can apply meaningful and deep thinking with One Up, One Down. If the students are at home, you are not able to monitor, offer strategies, hear their thinking, or involve students in comparing strategies. Constructivist Theory -Assimilation -Accommodation/Disequalibrium - Answers Jean Piaget Learners are not blank slates but creators of their own knowledge Networks and cognitive schema are the products of constructing knowledge Reflective though is how people modify schemas to incorporate new ideas -new ideas fit within prior knowledge (blue dots) -new idea does not fit with existing knowledge Sociocultural Theory -Semiotic mediation - Answers Lev Vygotsky Mental processes exist between and among people in social interactions Learning (working in their ZPD) - how beliefs, attitudes, and goals are affected by sociocultural practices and institutions Implications for Teaching Math - Answers Build new knowledge from prior knowledge Provide opportunities to communicate about math Build opportunities for reflective thought Encourage multiple approaches Engage students in productive struggle Treat errors as opportunities for learning Scaffold new content Honor diversity All of the following statements about mathematical proficiency are true except which? A. Procedural fluency means being accurate and quick at using standard algorithms for each operation. B. A productive disposition, or a can-do attitude when it comes to solving a problem with no clear solution path, is one component of mathematical proficiency C. Conceptual understanding means having a flexible interconnected knowledge of a topic, such as ratios D. Mathematical proficiencies for students are described in the CCSS-M 8 Mathematical Practices - Answers A. Procedural fluency means being accurate and quick at using standard algorithms for each operation. -Procedural fluency involves selecting the most efficient strategy in any given situation, but that is not always the standard algorithm, as the examples in this section illustrate. If students' experience are limited to learning only standard algorithms, they do not develop a collection of strategies and are not able to develop strategic competence, such as picking the best strategy for the particular problem Constructivism and sociocultural theories have implication for teaching. Which of the following teaching strategies would be "weak" in terms of helping students learn based on these theories? A. Showing students two different samples of student work in which the answers were different and discussing publicly which one is correct (or are both correct) B. Introducing multiplication by reading a children's book about arrays, such as 100 Hungry Ants C. Illustrating how to fill a ten frame and then asking students to share how many counters they see and how they see it D. Having students sort the facts that they know and then work on the facts that they do not know by trying to memorize them - Answers D. Having students sort the facts that they know and then work on the facts that they do not know by trying to memorize them -Memorizing is not a method for students to connect their prior knowledge and build interconnected networks. However, sorting facts and identifying which ones still have their prior knowledge (for example, their known fact). If they know 5 + 5, how can they use that knowledge to solve an unknown fact, such as 5 + 7? Which of the following statement about dots are true? A. Red dots (new ideas) are best added to a person's network of concepts by being connected to blue dots (existing ideas). B. Learning theory describes various characteristics of learning, providing clear direction on how to teach mathematics. C. Teachers already have complete webs of blue dots, which enables them to show students how those dots are connected. D. Some students will not have blue dots to connect to red dots, so those blue dots will have to be developed through instruction - Answers A. Red dots (new ideas) are best added to a person's network of concepts by being connected to blue dots (existing ideas). - Having relational knowledge (well connected blue dots) is critical for understanding math, and includes conceptual understanding, procedural proficiency and other dispositions. Instruction that builds on existing ideas helps students to build this network. All students bring blue dots and all student' blue dots are different. As a teacher, you are still growing blue and red dots. the connections you can make within math, and between theory and practice, will inform and improve your ability as a teacher of mathematics. Problem Solving - Answers -Teach for problem solving -Teach about problem solving -Teach through problem solving