THE COMMON CORE STATE STANDARDS FOR MATHEMATICS:

Transcription

1 THE COMMON CORE STATE STANDARDS FOR MATHEMATICS: ASSESSMENT Depth of Knowledge (DOK) CCSS PD Grades K 5 Day 3 1

2 Complexity Difficulty 2

3 Rating Depth of Knowledge (DOK) Depth of Knowledge measures the degree to which the knowledge elicited from students on a classroom task or assessment is as complex as what students are expected to know (as stated in the standards) 3

4 Differing Levels of Cognitive Demand Selena s 1) How many minutes did it take her to do 3 problems? Answer: minutes 2) Selena continues to work at the same rate. How many problems will she do in 40 minutes? Answer: problems 4

5 4 Levels of Cognitive Complexity DOK 1: Recall & Reproduction DOK 2: Basic Application of Skills/Concepts DOK 3: Strategic Thinking and Reasoning DOK 4: Extended Thinking Based on the titles of the 4 levels of DOK above, what types of problems would match each level above? 5

6 LEVEL 1: Recall and Reproduction Basic recall of information, such as a fact, definition, term, or simple procedure and/or performing simple procedures. Reading a chart or graph and answering a simple question about what is seen. The task involves a relatively shallow understanding of the topic or text. 6

7 DOK 1: Recall or Reproduction Examples A pad of paper costs twenty-five cents. Kim gave the clerk three dimes to buy a pad of paper. Which picture shows how much change Kim should get? 7

8 DOK 1: Recall or Reproduction Examples 1. What is the place value of 9 in the number ? (a) hundreds (b) tenths c) hundredths (d) thousandths x 8 = 3. Write each of the following numbers in the circle where it belongs. 8

9 DOK 1: Recall or Reproduction Examples Grade 7 CST Released Item 41 Which equation shows the distributive property? A 43 ( + 6 ) = B = + ( ) 6 6 ( 4+ 3) C ( )+ = D = ( ) ( ) 9

10 LEVEL 2: Application of Skills & Concepts Includes the engagement of some mental processing beyond recalling or reproducing a response. Items require students to make some decisions as to how to approach the question or problem. Actions imply more than one mental or cognitive process/step. 10

11 LEVEL 2: Application of Skills & Concepts 1.Yoshi spent 1 and 1/3 hours reading and ¾ hour doing chores. How much time did Yoshi spend on these activities? 2.On a trip across the country, Justin determined that he would have to drive about 2,763 miles. What speed would he have to average to complete the trip in no more than 50 hours of driving time? 11

12 LEVEL 2: Application of Skills & Concepts What is the difference between the largest height and the smallest height? Why is this higher than a level 1? 12

13 LEVEL 2: Application of Skills & Concepts In which set are the numbers equivalent? 1 A 3, 3 27, 33% B 0.090, 90%, 0.90 C 88%, , D 0.66%, 2 3, 66.7% 13

14 LEVEL 3: Strategic Thinking Requires deep understanding exhibited through planning, using evidence, and more demanding cognitive reasoning. Requires some decision making and often also justification. The cognitive demands are complex and abstract. Questions that have more than one possible answer or require students to justify a response would most likely be a Level 3. 14

15 Strategic Thinking Example (DOK Level 3) Look at the drawing. The numbers alongside each column and row are the total of the values of the symbols within each column and row. What should replace the question mark? Answer Choices: A) 23 B) 25 C) 28 D) 30 E) 32 16?

16 Strategic Thinking Example (DOK Level 3) Brett needs to cut a piece of string into four equal pieces without using a ruler or other measuring instrument. Write directions to tell Brett how to do this. 16

17 Strategic Thinking Example (DOK Level 3) 1) Lori has a choice of two spinners. She wants the one that gives her a greater probability of landing on blue. Which spinner should she choose? A) Spinner A B) Spinner B Explain why the spinner you chose gives Lori greater probability of landing on blue. 17

18 Extended Thinking: Level 4 Requires time to think about, research, and process multiple conditions of the problem or task. Students are expected to make non-routine manipulations, connections across disciplines or content areas, or gather information from multiple sources. Students need to select or devise one approach among many alternatives on how the situation can be solved. Due to the complexity of cognitive demand, DOK 4 often requires an extended period of time. 18

19 Extended Thinking: Level 4 Students will visit 3 grocery stores and find the prices of 3 different sizes of the same product at each store. Determine the unit price for each item at the store and make a decision as to which is the best buy. Write a report chronicling your work and reporting which is the best buy; justify your decision with mathematical work. 19

20 Keywords that Signify DOK 4 Design and conduct an experiment Develop and carry out the project Create and prove conjectures Make connections between discoveries and related concepts/phenomena Combine and synthesize ideas into new concepts Critique plans and designs 20

21 How Many of Each Type of Problem? 21

22 What is the DOK Level? 2 22

23 What is the DOK Level? Fred s Rope Susan s Rope If Fred's rope is 12 inches long, about how long is Susan's rope? 16 inches 20 inches 24 inches 30 inches 2 23

24 What is the DOK Level? Which of these is equal to 8, ? A) 8,088 B) 8,808 C) 8,880 D) 8,

25 What is the DOK Level? If the pattern shown continues, could 375 be one of the products in this pattern? Product 2 2 = = = = 32 3 Yes No Explain why or why not. 25

26 What is the DOK Level? Selena s 1) How many minutes did it take her to do 3 problems? 1 Answer: minutes 2) Selena continues to work at the same rate. How many problems will she do in 40 minutes? 2 Answer: problems 26

27 What is the DOK Level? 2 27

28 What is the DOK Level? 2 1. Find 5 points that satisfy the equation y = 2x 3. Sketch the equation and the points ( 12) = 1 3. How many edges does this figure have? 28

29 What is the DOK Level? Ms. Jones keeps cats and canaries at her pet shop. This morning when she counted she had 30 heads and 80 legs altogether. How many of each animal does she have? 3 29

30 Same Verb 3 Different Levels of DOK Caution 1 DOK 1- Describe an isosceles triangle. (Requires simple recall.) DOK 2- Describe the differences between the three different types of triangles. (Requires cognitive processing to determine the differences.) DOK 3- Describe a model that you might use to represent the relationship between the three different types of triangles. (Requires deep understanding of polygons.) 30

31 Caution 2 DOK is about intended outcome, not about difficulty. DOK is a reference to the complexity of mental processing that must occur to answer a question, perform a task, or generate a product. Adding is a mental process. Knowing the rule for adding is the intended outcome that influences the DOK. Once someone learns the rule of how to add, is DOK 1 and is also easy. Adding 4,678, ,578,885 is still a DOK 1 but may be more difficult. 31

32 Review of 4 Levels of Cognitive Complexity DOK 1: Recall & Reproduction Recall a fact, information or procedure DOK 2: Basic Application of Skills/Concepts Uses information or conceptual knowledge; nearly always requires two or more steps DOK 3: Strategic Thinking and Reasoning Requires reasoning, developing a plan, or sequence of steps; some complexity and typically more than one possible answer DOK 4: Extended Thinking Requires investigation, time to think and process multiple conditions of the problems 32

33 Online Resources: 33

34 Thank You! 34