What are the 5 Process Standards addressed for each grade band in the Principles and Standards? Briefly describe each Process Standard. - ANSWER 1. Problem solving
2. Reasoning and proof
3. Communication
4. Connection
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What are the 5 Process Standards addressed for each grade band in the Principles and Standards? Briefly describe each Process Standard. - ANSWER 1. Problem solving
2. Reasoning and proof
3. Communication
4. Connections
5. Representation.
Summarize the section "A Changing World Economy" (p. 8-9). - ANSWER It pretty much just says that we need more individuals who are prepared to ride the ups and downs of the economy. It continues by saying that people need to be more well rounded and math oriented. As the world changes, we need to prepare our students for the complex changes and unpredictability of the job force and economy.
How do repeating patterns and growing patterns differ? - ANSWER Repeating patterns and growing patterns differ because in growing patterns, students not only extend or identify the core, but they look for a generalization or algebraic relationship that will tell them what the pattern will be along the way.
Briefly describe "relational understanding" and "instrumental understanding." These two ideas are sometimes described as "rules without reasons" and "knowing what to do AND why"; which is which? - ANSWER Relational understanding is knowing what to do and why. Instrumental understanding is doing something without understanding (rules without reason).
List the benefits VdW claims accompany relationship understanding. Choose two that you think are especially important and explain why those two benefits should result from an instructional approach that emphasizes relational understanding. - ANSWER VdW claims benefits that accompany relational understanding. The list consists of: Effective Learning of New Concepts and Procedures, Less to Remember, Increased Retention and Recall, Enhanced Problem-Solving Abilities, and Improved Attitudes and Beliefs.
Two of these that are most important to me are: Effective Learning of New Concepts and Procedures, and Increased Retention and Recall. These two benefits should result from an instructional approach because the more connections students are building, the more likely they can connect new ideas to existing conceptual ideas. Also, teaching students the "big ideas" enables students to have huge networks of interrelated concepts.
What are "attributes" and what are "values"? - ANSWER Attributes are the ways that materials can be sorted. For example: hair color, eye color, height, and gender, are attributes for people.
Values are the number of attributes there are. For example: red hair, blonde hair, brown hair, and black hair (Hair color is an attribute and has four values).
Three types of number relationships that help students develop number sense are introduced on p. 136. What are they? - ANSWER One and two more, one and two less, Anchors or "benchmarks" of five and ten, and Part-part-whole relationships.
What are "landmark numbers"? Describe how landmark numbers could be used in computing 53+34 and 53-27. - ANSWER Landmark numbers are usually multiples of 10, 100, and sometimes other special numbers like 25. They are often used as a resource to compute when students are between large units of numbers.
For example, in the problem 53+34, a student might say, "first I added 7 to get to 60, and then I added 20 to get to 80, and then I added 7 to get to 87." Additionally, in the problem 53-27, a student might say, "I will take 3 away from 53 which is 50, then I will take 20 away which is 30, and then I will take 4 away which is 26."
What does "subtraction think addition" mean? Write a think addition number sentence for 6-2=4. Why is this interpretation of subtraction important? - ANSWER Instead of using fact families and dropping the numbers into slots, the object of "think-addition" is to discover what is hidden. It is significant for mastering subtraction facts.
For example, if the total number of counters you have is 6, and 2 counters are removed, the child will think, "two plus what equals six?"
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