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Orange Belt:
Open-ended Tasks in Math
School Certification
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A Process of Discovery, Support and Mastery
THE NATIONAL PATHWAY
CONDITIONS FOR SUCCESSFUL IMPLEMENTATION
Vision Skills+ + Incentives + Resources + Action Plan = SustainableChange
Skills + Incentives + Resources + Action Plan = Confusion
Vision + Incentives + Resources + Action Plan = Anxiety
Vision Skills+ + Resources + Action Plan = Resistance
Vision Skills+ + Incentives + Action Plan = Frustration
Vision Skills+ + Incentives + Resources = Treadmill
Curriculum Mapping Implementation
Key Questions:Resources -- "Do we have tools, time, and training to map effectively?"Action Plan -- "Over the next three years, do we have attainabletimelines and goals? Who will be the responsible parties forimplementations, monitoring, and feedback?"
Vision -- "Why are we doing this?"Skills -- "How do we build effective maps?"Incentives -- "How will mapping improveteaching and learning?"
Plan
Plan
Plan
Plan
Plan
Vision: The “Why are we doing this?” to combat confusion.Skills: The skill sets needed to combat anxiety.Incentives: Reasons, perks, advantages to combat resistanceResources: Tools and time needed to combat frustration.
Plan: Provides the direction to eliminate the treadmill effect.
Knoster, T., Villa, R., & Thousand, J. (2000)
Learner Objectives• Understand the difference between a closed-
ended and open-ended task/question and how to identify them
• Understand the advantages of open-ended tasks
• Learn how to create open-ended questions and formulate open-ended tasks/projects
• Discover how open-ended tasks can promote communication, engagement and collaboration
• Learn how to implement a systematic protocol for responding to open-ended items in math
• Understand how to assess responses to open-ended questions and tasks
Part I: A Close Look at Closed-ended and
Open-ended Questions/Tasks
Open vs. Closed• Closed-ended: has a specific answer
o Example: 5+ 6 = _____o Often given as multiple choice or fill in the blank
• Open-ended: requires problem-solving skills; students must provide evidence to support their reasoningo Example: Elizabeth is 5 feet tall. She needs to be able to
comfortably reach books on the top shelf of a 12 foot wall.The shelves are placed approximately 1 foot apart. What do you think the height of the ladder should be if Elizabeth wishes to reach the books comfortably? Explain your reasoning.
How to tell the difference
Open-ended tasks:o Begin with words like “how”, “why”, and
“what do you think”o Include an expectation for students to
explain their reasoningo Elicit a range of responseso Can be scored using a rubricClosed-ended questions:o Can sometimes be answered with “yes” or
“no”o In math, require nothing more than
performing a calculation
Why Open-ended?o Differentiationo Connectionso Applicationo Reveal thinking processeso Build confidence
How to create open-ended tasks
o Take a closed-ended question and convert it to open-ended
• Example:o Closed: Which of the following numbers are not
squares - 4, 9, 11, 16?o Open: Explain why 15 is not a square.
How to create open-ended tasks
.o Use a closed-ended question as inspiration for an open-
ended task• Example:
o Closed: What is the volume of a cylinder that has a radius of 1.5’ and a height of 11’?
o Open: You have been hired to manufacture a cylindrical water tank which will hold a volume of 150 gallons. Sketch the cylinder, labeling its measurements.
What it looks like in your classroom?
Protocol for Solving Open-Ended Tasks
• Understanding of task• Sort the relevant information from the
irrelevant information• Make a plan• Reflect/re-evaluate• Test
What it looks like in your classroom?
What it looks like in your classroom?
“When children think, respond, discuss, elaborate, write, read, listen, and inquire about mathematical concepts, they reap dual benefits: they communicate to learn mathematics, and they learn to communicate mathematically.”
National Council of Teachers of Mathematics
Communication and Collaboration
Sparking Interest for Open-Ended Tasks
What it looks like in your assessment?
• Rubricso Analytico Holistico Vary in complexity, based on task
What it looks like in your assessment?
• Rubricso Find and adapto Even number of levelsoHigh to lowo Less is more
4 3 2 1
Part II: Stepping into the Classroom with Open-ended Tasks
What it looks like in your classroom?
Open-ended projects
What it looks like in your classroom?
Open-ended projects
Elementary
Example of Using Open Ended Tasks in
Grade 4-5
As You Watch…
o What makes the tasks the teacher asked open instead of closed?
o How did the teacher include an expectation for students to explain their reasoning?
o What strategies did the teacher select that elicit a range of responses?
What it looks like in your classroom?
Open-ended projects
Middle School
What it looks like in your classroom?
Open-ended projects
High School
What it looks like in your classroom?
Protocol for Solving Open-Ended Tasks
Engineering Design Algorithm
1)Identify the problem or design objective2)Define the goals and identify the constraints3)Research and gather information.4)Create potential design solutions.5)Analyze the viability of the solutions.6)Choose the most appropriate solution.7)Build or implement the design.8)Test and Evaluate the design.9)Repeat all steps as needed.
Example of an Open-Ended Project in
High School
As You Watch…
• How did the geometry project promote communication, engagement and collaboration?
• What strategies did the teacher include when designing the problem to build confidence for students?
Additional resource
Knowledge CheckQuestion: Which of the following is an open-ended question?
a)Alice has $1.78 in change. What combinations of coins might she have in her wallet?
b)Alice’s total at the grocery store came to $5.05. She has $1.78 more than she needs. How much money does Alice have in her wallet?
Knowledge CheckQuestion: Which of the following is an open-ended question?
a)Alice has $1.78 in change. What combinations of coins might she have?
b)Alice’s total at the grocery store came to $5.05. She has $1.78 more than she needs. How much money does Alice have in her wallet?
Knowledge CheckQuestion: The most important factor to consider when creating a rubric is:
a)Ensuring that the dimensions of the rubric are appropriate to the objectives.
b)Making sure to include items such as punctuation and grammar.
c) Creating as many criteria as possible to ensure that all facets of the objective have been covered.
d)Listing the values of each criteria with the lowest value first so students know the minimum requirements.
Knowledge CheckQuestion: The most important factor to consider when creating a rubric is:
a)Ensuring that the dimensions of the rubric are appropriate to the objectives.
b)Making sure to include items such as punctuation and grammar.
c) Creating as many criteria as possible to ensure that all facets of the objective have been covered.
d)Listing the values of each criteria with the lowest value first so students know the minimum requirements.
Partnership for 21st Century Skills (2011). ICT Literacy Maps http://www.p21.org/ict-literacy-maps
Open Ended Assessment in Math http://books.heinemann.com/math/nature.cfm
Table for 22: A real-world Geometry projectOpen ended tasks in the promotion of communication in
Mathematics, Viseu and Oliviera, International Electronic Journal of Elementary Education http://www.iejee.com/4_2_2012/IEJEE_4_2_Viseu_Oliveria_287_300.pdf
The Importance of Communication in Mathematics Classrooms http://www-users.math.umd.edu/~dac/650/huangpaper.html
Works Cited
Homework Assignments
• Create an open-ended project to use in your classroom. Apply real-world situations to increase engagement.
• Create a rubric to assess student work in the project.
• Bonus: Work with a teacher in another content area to create a cross-curricular project.
Homework Assignment
THANK YOU!
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