The Essential Skill of Mathematics Level 4 – Developing Good Problem-solving Tasks

Goals Participants will  Know how to select grade appropriate mathematics objectives  Know the key elements in a good mathematics work sample  Create a work sample that is complete and ready to use

The Essential Skill of Mathematics 3. Apply mathematics in a variety of settings  Interpret a situation and apply workable mathematical concepts and strategies, using appropriate technologies where applicable.  Produce evidence, such as graphs, data, or mathematical models, to obtain and verify a solution.  Communicate and defend the verified process and solution, using pictures, symbols, models, narrative or other methods.

Local Work Sample  Scored using Official State Scoring Guide  Two Mathematics Work Samples Required  Students must earn a score of 4 or higher in each dimension on each work sample

Mathematics work samples may provide the opportunity that some students need to show their math skills. Math Work Samples

Most students need instruction and practice in completing mathematics work samples Some students may need additional instruction or targeted coaching to demonstrate proficiency in all five dimensions Some students may need additional instruction to reach high school level math standards Mathematics Work Samples

Instructional Continuum  Whole group demonstration led by teacher with some student input  Whole group with lots of student input  Small group or pairs with reporting out and discussion/rework opportunities  Individual work with feedback

Give feedback – using scoring guide language regularly  Use scoring guide in class (student language version ok)  Provide scoring guide scores on all kinds of student work – not just on written responses to problem solving prompts  Use the language of the scoring guide often as an example of what is expected and how the language of the scoring guide applies to their work

Selecting Mathematics Topics and Objectives

Sorting Activity Organize the 4 versions of the sample task into any categories and in any manner you want. Be prepared to report out your group’s results as well as the reasoning behind your categories.

Guidelines for High School Mathematics Work Samples Definitions, Requirements and Recommendations

1.Select a Content Strand Algebra Geometry Statistics

2.Select Content Standards Problem Solving Tasks need to be tied to the standards  Common Core State Standards  or current District/Oregon Standards

Good tasks Tied to Standards  Oregon or  CCSS Tied to curriculum and recent instruction

Two types of tasks Stand alone Curriculum embedded

Types of Tasks Curriculum Embedded Part of current unit of study Real world connections especially to content area material Stand Alone Ideally related to curriculum May be specifically designed for Essential Skills proficiency

3. Select a Context for Problem May be tied to real-life applications of math Should be within students’ frame of reference

Elements of Good Tasks Thought-provoking Not routinely practiced Not immediately solvable (solution at a glance) Clearly worded

Good tasks elicit responses that Can be scored on all dimensions of the scoring guide Require the use of –NCTM Process Standards –CCSS Math Practices –Grade Level Appropriate Mathematics –Rich enough & complex enough when used for Essential Skills proficiency

ONE APPROACH Designing a Mathematics Problem Solving Task

Here’s how one person creates tasks the speedy way! Where to find ideas? I think about a concept I will be working on in the near future such as – extending patterns

Then I think about what students should be able to do What are the VERBS in the standard(s) being addressed? For Example : IDENTIFY patterns EXTEND patterns GENERALIZE patterns

Then I think about problems I have seen previously  TEXT BOOKS  PROBLEM BANKS  NCTM resources Could I adjust any of these to fit my needs?

Then I think of a context for the problem Like LIKE… I am sitting on my boat reviewing state math problems and I really need a break!!

I decide to go paddle boarding….. After I am 30 meters from the boat, I turn on my wrist GPS unit to track my progress so I can log it in my exercise journal when I am done.

After 3 minutes of steady paddling ( no falling in the water, stopping to admire the pretty fish or having a speed boat go by and knock me over with its wake) I am 69 meters from the boat.

Where am I? At this rate, how far will I be from the boat in 15 minutes?

Wow! I think I might have a problem-solving task! Next Steps.....

Confirm match to standards I check for a match. Later, I will identify all the appropriate standards and achievement level descriptors Since I started thinking about extending patterns, I am pretty sure this idea meets several of the CCSS, but just to be sure...

Time to Edit!

1. Read through and refine I AM SITTING ON MY BOAT REVIEWING STATE MATH PROBLEMS AND I REALLY NEED A BREAK! TOO MANY WORDS… Not important to the task – not something kids (or you) can relate to

More concise wording I decide to go paddle boarding. Joan is paddle boarding. She is 30 meters from the shore. After I am 30 meters from the boat, I decide to turn on my wrist GPS unit.

Continue Editing AFTER 3 MORE MINUTES OF STEADY PADDLING,( NO FALLING IN THE WATER OR STOPPING TO ADMIRE THE PRETTY FISHES) I AM JOAN IS A TOTAL OF 69 METERS FROM SHORE

Clarify the Question How far will Joan be from shore after 15 more minutes of paddling?

Now, work the problem! Find a solution Think about what kids might do with this problem Ask colleagues to work the problem and make suggestions REFINE SOME MORE….

Then try it out with students!

QUESTIONS TO ASK YOURSELF Does it really elicit the type of responses you were hoping for? Could you extend it and/or adjust it to meet needs of individual students? Are there multiple possible approaches or entry levels to the problem? Could you use different numbers (larger, smaller, decimals, fractions, etc.) and what effect would that have on the problem?

Give students feedback Give yourself more feedback Be nice to yourself Fix it, and move on! Try It Again...

 If the task is rich enough to elicit scores across the full spectrum of the scoring guide,  If it can be identified as the student’s own independent work,  If it applies developmentally- appropriate problem solving skills,  And if it’s tied to grade level standards... Remember …

Then it can be used as one of the two required work samples, to fulfill the Mathematics Essential Skill requirement

Let’s Go on a Walk- about!

Let’s try it! Choose a standard Highlight the verbs Brainstorm applications Draft a task Compare to the standard Do the task/have colleagues do the task Predict what students might do Check to see if expected responses could be scored in all dimension of the scoring guide Revise until it’s ready for students

Time to Share! Section 3

Carousel Activity Place your group’s problem solving task on the table. Make sure the task and any graphics are clear and easy to understand. Circulate among the tasks to give productive and constructive feedback. –Take 5 to 7 minutes to read and discuss each task. –Use the feedback form provided to share your thoughts with the creator(s) of the task.

Groups and individuals review feedback forms on their tasks Read and discuss feedback from carousel activity Make any changes adjustments to tasks based on this discussion or further thoughts that have “bubbled up” while reviewing the tasks written by other groups Provide Facilitator with a “final” version of your group task

Time to Debrief What did you learn? What support do you need?

Resources Oregon Department of Education Oregon Council of Teachers of Mathematics

Future Work Sample Trainings Level 2 Introduction  Dates: Level 3 In-Depth Training  Dates: Contact Information: