Task Development For Math Collection of Evidence

1. Task Development For Math Collection of Evidence Math Assessment Office of Superintendent of Public Instruction

2. The Quick Overview All Tasks will: • Reflect a real-world task and/or scenario-based problem • Integrate knowledge and skills from at least two (2) different reporting strands • Focus on no more that three (3) PEs • Lend themselves to multiple approaches • Include language that is clear, unbiased, and scoreable • Take a hard-working, C-level student 30-45 minutes to complete

3. How to Use this Presentation The next slide in this presentation contains the Course Module links. To jump to any Course Module simply select the link you wish to go to Each Course Module will have several slides. You can proceed through each section of the module simply by pressing the <Space Bar> OR you can return to the Course Module Menu by pressing the

4. Course Modules • Review of a Sample Task • Examples of Math Questions or Statements • Cognitive Complexity • Characteristics of a High Quality Task • Drafting a High-Quality Task • Mathematics Vocabulary by Grade/Course • Let’s Build a Task • Uploading Your Task for Review • Task Answer Key

5. Let’s Review a Sample Task On Demand Check Box Title of Task Reporting Strands/PEs The Setup and Background Data and Information Question – Labeled with #’s. Multiple part questions use 1a, 1b, ect. Return to Main Menu

6. Let’s Review a Sample Task Identifies the specific PE this question addresses. This must match with one of the PEs listed in the header Questions. Notice these questions do not both need PE references as both address the same PE. Be sure to provide adequate space for students to produce work. Provide lined space as needed or open space for diagrams and drawings This footer will be added by OSPI when the tasks has been edited and ready for uploading Return to Main Menu

7. Examples of Math Questions or Statements • Describe what the slope of the line represents in the situation? • Predict the greatest number of tracks (songs) you can record with a maximum of 50 minutes of playing time. Show how you used the equation to make your prediction. • Describe why a linear function best models the indicator you chose and why the other indicators are not best modeled by a linear function. • Using the equation of the line you wrote, predict how many seconds would pass between the lightning and thunder when the distance to a lightning strike is 4,500 meters. Show the steps you used to solve the equation. Return to Main Menu

8. Examples of Math Questions or Statements • Complete the table to determine the mass and acceleration of different objects when the same amount of force as used on the the 5 kilogram object is used. • Based on the data, which player better followed Trainer Sue’s weight plan? – Use specific data from the scatter plot and Trainer Sue’s plan to support your answer. Return to Main Menu

9. Cognitive Complexity The Test and Item Specifications for each content area best defines the “Depth-of-Knowledge” levels for Mathematics. It is best to review each of these levels prior to beginning the process of task development and writing. The four basic levels include; • Level 1 – Recall • Level 2 – Skill/Concept • Level 3 – Strategic Thinking • Level 4 – Extended Thinking A more complete review and explanation of each level can be found at the OSPI website in the Test and Item Specifications materials http://www.k12.wa.us/Mathematics/pubdocs/ItemSpec_A1.pdf Return to Main Menu

10. Cognitive Complexity Included in this section is a Table of Math Descriptors by Level. This table combines the work of Norman L. Webb from the Wisconsin Center of Educational Research (“Depth-of-Knowledge Levels) for Mathematics with the 2002 NAEP Mathematics Levels of Complexity, and other Descriptors Related to NECAP GLEs. The next set of slides provides you with a richer understanding of Cognitive Complexity. Each level is first explained in detail and then a table of math descriptors is provided to help with further development Return to Main Menu

11. Level 1 - Recall Level 1 (Recall) includes the recall of information such as fact, definition, term, or a simple procedure, as well as performing a simple algorithm or applying a formula. That is, in mathematics a one-step, well-defined, and straight algorithmic procedure should be included at this lowest level. Other key words that signify a Level 1 include "identify," "recall," "recognize," "use," and "measure." Verbs such as "describe" and "explain" could be classified at different levels depending on what is to be described and explained. Return to Main Menu

12. Level 2 – Skill/Concept Level 2 (Skill/Concept) includes the engagement of some mental processing beyond a habitual response. A Level 2 assessment item requires students to make some decisions as to how to approach the problem or activity, whereas Level 1 requires students to demonstrate a rote response, perform a well-known algorithm, follow a set procedure (like a recipe), or perform a clearly defined series of steps. Keywords that generally distinguish a Level 2 item include "classify," "organize," "estimate," "make observations," "collect and display data," and "compare data." These actions imply more than one step. Return to Main Menu

13. Level 3 – Strategic Thinking Level 3 (Strategic Thinking) requires reasoning, planning, using evidence, and a higher level of thinking than the previous two levels. In most instances, requiring students to explain their thinking is a Level 3. Activities that require students to make conjectures are also at this level. The cognitive demands at Level 3 are complex and abstract. The complexity does not result from the fact that there are multiple answers, a possibility for both Levels 1 and 2, but because the task requires more demanding reasoning. An activity, however, that has more than one possible answer and requires students to justify the response they give would most likely be a Level 3. Other Level 3 activities include drawing conclusions from observations; citing evidence and developing a logical argument for concepts; explaining phenomena in terms of concepts; and using concepts to solve problems. Return to Main Menu

14. Level 4 – Extended Thinking Level 4 (Extended Thinking) requires complex reasoning, planning, developing, and thinking most likely over an extended period of time. The extended time period is not a distinguishing factor if the required work is only repetitive and does not require applying significant conceptual understanding and higher-order thinking. At Level 4, the cognitive demands of the task should be high and the work should be very complex. Students should be required to make several connections-relate ideas within the content area or among content areas-and have to select one approach among many alternatives on how the situation should be solved, in order to be at this highest level. Level 4 activities include designing and conducting experiments; making connections between a finding and related concepts and phenomena; combining and synthesizing ideas into new concepts; and critiquing experimental designs. Return to Main Menu

15. Return to Main Menu

16. Characteristics of a High-Quality Task • Start with the math standard or skill developed around your highest level of expectation and then create your activity • This is the concept of beginning with end in mind It is generally not a good idea to begin with a ‘really cool problem’ or ‘this is my favorite task’ and try to adapt the standards to the problem or task Return to Main Menu

17. Characteristics of a High-Quality Task • Creating quality tasks is challenging. Once written, pilot your tasks with colleagues and students • Revise your tasks based on responses from students colleagues • You do not have to start from scratch. Here is a good website to use as a resource for task development: http://www.learner.org/workshops/missinglink/resources Return to Main Menu

18. Characteristics of a High-Quality Task • Essential(not tangential) • Aligned with math standards • Represents “big” math ideas • Students construct, refine, and use significant math models • Authentic(not contrived) • Directly involves meaningful, real-life uses of mathematics • Not artificially constrained in terms of the solution • Equitable(not biased) • Gives diverse students opportunities to use their talents and display growth • Students apply their own experiences and understandings to solve problems • Rich(not simplistic) • Contains numerous possibilities, including the potential for extensions and connections • Encourages students to understand the concepts underneath the mathematical formulas • Feasible(not impractical) • Safe and developmentally appropriate, can be done • Clear(not confusing) • States expectations clearly • Scoreable(not vague) • Has a scoring guide that is easily applied Return to Main Menu

19. Characteristics of a High-Quality Task • Active(not passive) • Student is the worker and decision maker • Student interacts with others • Student uses mathematical models to understand concepts • Accessible(not just for some students • Students with widely differing levels of mathematical ability can work actively and productively on the activity Return to Main Menu

20. Drafting a Quality Task • Core Concepts - What are the big mathematical ideas or concepts that students must know? Organized by Reporting Strand • Mathematical Skills – What are the skills that students must be able to do to demonstrate proficiency? • Essential Questions - What are the essential questions that tie the core concepts to the needed skills? The work students show in the problem will answer the essential question. Examples: • Core Concept – Scale Factor is a key to solving proportional situations. • Skill – Determine the scale factor in proportional situations. • Essential Question – How can you use scale factor to find a missing measure in a proportional situation? Return to Main Menu

21. Drafting a Quality Task • Problem Statement or Prompt • A sentence or paragraph that tells students what the problem is and what they need to do • Provides a clear invitation to students to demonstrate, as fully and powerfully as possible, what they know and can do mathematically • Involves essential mathematics • Exhibits characteristics of a high-quality performance task • Task Criteria • What do you hope to see? • What is your picture of an exemplary solution? • What work is necessary to demonstrate complete mastery and understanding? • How will the task solution be displayed or written up? Return to Main Menu

22. Mathematics Vocabulary The link provided allows you to view the spreadsheet which includes the terms used in the End of Course assessments for Algebra, Integrated Math 1 & 2, and Geometry. The spreadsheet also includes vocabulary for the MSP assessment http://www.k12.wa.us/Mathematics/pubdocs/MathAssessmentVocabulary.xls Return to Main Menu

23. So Let’s Build a Task! Reminders • Begin with the end in mind – Start with the Standards. This is in a header • Design a challenging and engaging task but one that students can accomplish • Review the current set of tasks to be sure you are not creating a duplicate task • Be aware of what level of cognitive complexity you are asking for in the task • Format the task so that is aligned to the current state tasks (Use of fonts, spacing, and PE notation) • Provide sufficient space for student work. You decide whether that space should be open space or lined space base on your request for information • Footers should be added to identify that fact this task is still under review Return to Main Menu

24. Step One – Starting with the Standards • Reporting Strand – Data and Statistics • Performance Expectation (PE) – A1.6.D Students are expected to: Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions Examples: Making predictions involves both interpolating and extrapolating from the original data set • Reporting Strand – Process • Performance Expectation (PE) – A1.8.G Students are expected to: Synthesize information to draw conclusions, and evaluate the arguments and conclusions of others

25. Step Two – Titles and Labels Standards /PEs Setup and Background Title Specific PE this question addresses Data Question with multiple parts and screened for bias and cognitive complexity Inserted Grid for student use Footer came installed with the Template

26. Step Three – Finish the Task Specific PE this question address Standars/PEs for this Task Multi-part question is numbered as 2a. and 2b. Questions are screened for bias and cognitive complexity Insert Response boxes. Decide if open space is needed or lined space. Sometimes a combination of both is required

27. So Now You Build a Task! • The Task Template has been loaded on the Moodle in the course for your use. Once you have completed the course you can use the template to help build an actual task. The template is the same for an Inclusion task or a Classroom Practice Task Clock Hours are available for task development. Please email Scott.Brittain@k12.wa.us for details Return to Main Menu

28. Uploading your Task for Review Once complete, be sure to upload your task for review using the Moodle. Follow these steps: • Go to Section Four (4) of the Math Collection of Evidence Moodle • Select the appropriate content for upload – Algebra or Geometry Task • Browse your computer to locate the file to upload • Make any notes necessary in the upload window about your file • Send File for Marking Return to Main Menu

29. Task Answer Key All Tasks accepted for the Inclusion Bank will require an answer key. You can choose to submit an answer key with your task when you initially submit your task for review or wait until after it has been reviewed. If your tasks is moved to an inclusion task, we will request you provide an answer key prior to posting it on the COE website. This is to assure we have the correct data tables, graphs, and necessary equations on the task prior to releasing the task for use as a student inclusion task Return to Main Menu