EDCI 3124 Midterm
Procedural knowledge refers to:
knowing how to complete an algorithm or procedure.
Learning center lessons may include all of the following except which?
The lessons may involve additional time in the after phase to share all solutions from each station.
The six Principles and Standards for School Mathematics articulate high-quality mathematics education. Which of the following statements represents the equity principle?
The message of high expectations for all is intertwined with every other principle
In this section of the chapter the authors have illustrated the decision-making process with a lesson on fixed area. Which statement below would be part of the planning for the during phase of the lesson.
A checklist for observing student products
What suggestion below would support the student that has a misconception and continues to make computational errors?
A problem solving task that the student has to apply knowledge to solve
The purpose of the eight research-informed teaching practices in the NCTM (2014) Principles to Actions was
Address issues of access and equity
What statement below would be an example of orchestrating productive discourse?
Ask follow up question whether the answer is right or wrong
Which of the following statements is true?
Begin with mathematical goals, consider student needs, and use these factors to create the three-phase lesson.
The during phase of a problem solving lesson is a great opportunity for the teacher to find out what students know. Three of the prompts below would help the teacher notice except one --- can you identify it?
Can I help you ____?
In teaching through problem solving, students are engaged in doing all the following except which?
Checking their answers with others or the textbook to confirm that it is correct
Using a "doing mathematics" verb in a lesson or unit plan lessons guides students to higher level thinking task. Identify the statement below that would invite students to think at a higher level.
Compare the problem solutions and determine what problem solving strategy was used and why.
Skills needed for the 21st-century workplace should be about designing solution strategies. Identify the skill below that does not fit with the 21st-century ideal.
Computation
A process standard refers to the mathematical processes that preK-12 students acquire and the mathematical knowledge they use. Identify the process standard that highlights how mathematical concepts relate to real-world and other subjects.
Connections
Mathematically proficient students demonstrate practices that show that they know the content and are able to apply that knowledge, which requires conceptual understanding. Identify the statement that represents conceptual understanding.
Connects knowledge of division to rates, and uses that to figure out unit prices
Which of the eight Standards for Mathematical Practice asks students to analyze situations by breaking them into cases and can recognize and use counter examples?
Construct viable arguments and critique reasoning of others
Problem-solving strategies are identifiable methods for approaching a task. Identify the method that students systematically account for possible outcomes in a situation and provide insights into its solution.
Create a list, table or chart
Homework should be a positive experience for students and their families. Identify the activity below that could be engaging for the parents and their child(ren).
Data collection of home tasks
Which one of the statements below would be considered a "doing mathematics tasks" versus a "procedures without connections"?
Demand self-monitoring of one's own cognitive processes
Identify the NCTM (2014) Principles to Actions practice that relates to students being the "doers" of the mathematics to develop skills that habits that are essential to becoming mathematically proficient.
Develops mathematical practices and processes
The Common Core State Standards divide the content expectations for students into large groupings called what?
Domains
Identify the teacher action that would happen in the before lesson phase.
Establish clear expectations.
Which of the following statements is the best definition for the term "school effects" as it pertains to mathematics education?
For many students, school is the only place where they get to experience mathematics.
Identify the major goal of the after phase of a problem-solving lesson
Formalize the main ideas of the lesson and make connections between strategies and mathematical ideas
What would be a way of addressing parents' questions about the mathematics curriculum and teaching practices?
Have Math Orientation Workshop
Constructivism and sociocultural theories have implications for teaching. Which of the following teaching strategies would be "weak" in terms of helping students learn based on these theories?
Having students sort the facts that they know and then work on the facts that they do not know by trying to memorize them
All the following are recommended teacher moves in a three-phase lesson plan format except which one?
Illustrating how to solve a problem to ensure that students are ready to practice
Three of the following statements are ways for teachers to maintain a positive disposition about mathematics. Which of the following would not contribute to that disposition?
In your heart you say, "I never liked math"
Learning theories are not teaching strategies. They are about how people learn. What strategy described below refers to scaffold new content?
Include the use of tools (manipulatives) and more assistance from peer
All of statements below are reasons to have multiple entry and exit points for problem solving tasks with the exception of which one?
Increase anxiety for English learners and struggling students
Teaching concepts and procedures through problem solving requires students to make connections among and between concepts and procedures. Which task below would connect to a measurement concept?
Jack and Jill were fetching a pail of water. Jack walked 5 yards every 25 seconds and Jill walked 3 yards every 10 seconds. Who will get the pail first?
Identify the statement below that would be an example of instrumental understanding.
Knowing the procedure for simplifying to
The George Pólya method of problem solving is still widely used today. Identify the step that is often overlooked.
Look back
If a lesson is well-aligned and worthwhile it will have the following components except which one?
Model and practice the right problem-solving method
Many factors influence how mathematics is taught in a school system and which mathematics is covered. What are some of the most influential factors?
National and international testing results
Which method below would be particularly useful in taking low cognitive demand tasks and turning them into high cognitive demand tasks?
Open questions
Classrooms that provide structures and supports to help students make sense of mathematics in light of what they know are employing what strategy.
Opportunities for reflective thought
Identify the method below involves students working on different task all focused on the same learning goal. This method is based on choice and helps students become more self-directed.
Parallel tasks
How much to tell and not tell is a dilemma for teachers with a range of experiences. The statements below represent three things that teachers should tell students, identify the statement that does not belong.
Patterns of reasoning
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?
Persistence
Below are three methods that will support children in learning mathematics at school and at home. Which method would parents be more familiar, based on their own school mathematics learning?
Procedural strategies
The purpose of differentiation is what?
Provide tasks that are accessible and challenging for all students
Which of the following statements about dots is true?
Red dots (new ideas) are best added to a person's network of concepts by being connected to blue dots (existing ideas).
Which of the following statements is true about features of worthwhile tasks?
Relevant tasks include ones that are interesting to students and that address important mathematical ideas; they may come from literature, the media, or a textbook.
Based on the discussion in this section, which of the following is the most effective way to pose a task to students so that they experience doing mathematics?
Share the problem, ask the students to explore, stop them to see how they are doing, and let them keep going.
Three of the following statements are pertinent of high-level cognitive demand. Which one would be a lower-level cognitive demand
Straightforward and routine
The value of student talk is vital to a mathematics lesson. All of the items below would be student actions as a result of classroom discourse except which one?
Supports making sense of students' reasoning
Teaching through problem solving requires a paradigm shift from traditional mathematics teaching. Which statement below would not be true of teaching through problem solving.
Teacher's role is less demanding
Three of the following are listed as important items to share with families related to mathematics. Identify the one that would not be considered important.
The amount of time their child should be drilling at home to ensure that they remember their skills
Why is it good practice for teachers to solve the problems they are asking their students to do?
To be aware of the varied ways the problem could be solved and still make sense
What is the goal of orchestrating productive classroom discourse?
To keep cognitive demand high
3. The National Council of Teachers of Mathematics has been transformative and influential in the changes in the teaching of mathematics. Three of the statements below are true about NCTM's contributions. Identify the one that is not true.
Trends in International Mathematics and Science Study
There have been significant reforms in mathematics that reflect the technological and informational needs of our society. What statement is a factor to consider in change?
U.S. student performance in national and international studies
All of the following questions with the exception of one would be helpful as a teacher is considering the needs of their students. Identify the one that belongs in an earlier step
What mathematical practices and processes will be developed?
The extent that a student understands why an algorithm works or connects relationships between concepts and procedures refers to
depth of understanding.
Identify the instructional approach that shortchanges students' ability to solve story problems, multistep problems, and solving higher-level tasks.
explain-practice-apply
