valerie mills ncsm president oakland schools, waterford mi
TRANSCRIPT
ASSESSING FOR UNDERSTANDING
BUMP IT UP! BUILD BETTER MATH TESTS
LEVERAGING INNOVATIVESHORT ITEM MODELS
Valerie Mills NCSM President
Oakland Schools, Waterford MI
THE WORK OF TEACHING AND LEARNING
“Learning is driven by what teachers do in classrooms. Teachers have to manage complicated and demanding situations, channeling personal, emotional, and social pressures of a group of 30 or more youngsters in order to help them learn immediately and become better learners in the future. Standards can be raised only if teachers can tackle this task more effectively.”
--Black and Wiliam, 1998
“Learning is driven by what teachers do in classrooms. Teachers have to manage complicated and demanding situations, channeling personal, emotional, and social pressures of a group of 30 or more youngsters in order to help them learn immediately and become better learners in the future. Standards can be raised only if teachers can tackle this task more effectively.”
--Black and Wiliam, 1998
THE WORK OF TEACHING AND LEARNING
GOALS
Activities in today’s session are designed to support an exploration of what it means to teach and assess
standards that include “understand”;
the features of short answer task "genres" that can be used to teach and assess student understanding of mathematical concepts.
possible implications for teaching and assessing in our classrooms and districts. 4
UNDERSTANDING IN CCSS
4.NBT Generalize place value understanding for multi-digit
whole numbers. Use place value understanding and properties of
operations to perform multi-digit arithmetic.4.NF
Extend understanding of fraction equivalence and ordering.
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Understand decimal notation for fractions and compare decimal fractions.
4.MD Geometric measurement: understand concepts of angle
and measure angles.
MAKING SENSE OF UNDERSTANDINGExamining Assessment Task Genre
6
Phil Daro
“Understand” is intended to mean that students can explain the concept with mathematical reasoning including concrete illustrations, mathematical representations, and example applications.
Students who understand a concept can:
a. Use it to make sense of and explain quantitative situations (“Model with Mathematics” in Practices)
b. Incorporate it into their own arguments and use it to evaluate the arguments of others (see “Construct viable arguments and critique the reasoning of others” in Practices)
c. Bring it to bear on the solutions to problems (see “Make sense of problems and persevere in solving them”)
d. Make connections between it and related concepts
- Phil Daro, CC writing team ppt. NCSM
7
MAKING SENSE OF UNDERSTANDINGExamining Categories Of Assessment Items
QUESTION… How well do our
current short answer tasks assess understanding?
What can we learn from the development of the consortia assessments to improve our items?
MAKING SENSE OF UNDERSTANDINGExamining Categories Of Assessment Items
http://sbac.portal.airast.org/
http://www.smarterbalanced.org/
MAKING SENSE OF UNDERSTANDINGExamining Assessment Task Genre
10
Compare and contrast the design features of a typical assessment task and a SBAC task.
Working with a partner/small group list the features of the task design that help to assess understanding.
Be prepared to share your thinking.
MAKING SENSE OF UNDERSTANDINGExamining Assessment Task Genre
11
Review the tasks in Set A (yellow) paying attention to the design features of these tasks.
Based on this set of tasks, add to or clarify your description of the design features for this genre of tasks.
How might tasks of this design better assess understanding?
MAKING SENSE OF UNDERSTANDINGExamining Assessment Task Genre
12
Review the new sets of tasks (pink, lavender, and grey).
Describe the design features in each set of tasks.
How might tasks modeled after each of these task “genres” better assess understanding?
MAKING SENSE OF UNDERSTANDINGExamining Assessment Task Genre
13
How do your teaching and assessment tasks support or hinder building and assessing understanding?
What implications do you see for your classroom and/or district?
MAKING SENSE OF UNDERSTANDINGExamining Assessment Task Genre
14
Phil Daro
“Understand” is intended to mean that students can explain the concept with mathematical reasoning including concrete illustrations, mathematical representations, and example applications.
Students who understand a concept can:
a. Use it to make sense of and explain quantitative situations (“Model with Mathematics” in Practices)
b. Incorporate it into their own arguments and use it to evaluate the arguments of others (“Construct viable arguments and critique the reasoning of others” in Practices)
c. Bring it to bear on the solutions to problems (“Make sense of problems and persevere in solving them”)
d. Make connections between it and related concepts
- Phil Daro, CC writing team ppt. NCSM
15
MAKING SENSE OF UNDERSTANDINGExamining Assessment Task Genre
CRITERIA FOR MATHEMATICAL GOALS
Goals and lessons need to focus on the mathematics concepts and practices
(not on doing particular math problems) be specific enough that you can effectively
gather and use information about student thinking
be understood to sit within a trajectory of goals and lessons that span days, weeks, and/or years
“Thinking of understandings as outcomes of solving problems rather than as concepts that we teach directly requires a fundamental change in our perceptions of teaching.”
-Hiebert et al. p.22, Making Sense
ADJUSTING MATHEMATICAL GOALS TO INCLUDE UNDERSTANDING
Describe the mathematical goal(s) that might be reasonably assessed using the each of the tasks we initially compared.
Traditional Task SBAC Task
ASSESSING MATHEMATICAL GOALSStandards for Mathematical Content4.OA Operations and Algebraic Thinking Gain familiarity with factors and multiples.
4. Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors.
Standards for Mathematical Practices 1. Make sense of problems and persevere in solving them
start by explaining to themselves the meaning of a problem and looking for entry points to its solution
analyze givens, constraints, relationships, and goals
3. Construct viable arguments and critique the reasoning of others. understand and use stated assumptions, definitions, and previously
established results in constructing arguments justify their conclusions, communicate them to others, and respond
to the arguments of others.
4. Model with Mathematics identify important quantities in a practical situation. analyze those relationships mathematically to draw conclusions. routinely interpret their mathematical results in the context of the
situation.
CREATING OPPORTUNITIES TO LEARN AND ASSESS UNDERSTANDING
19
Review tasks in the unit you are currently teaching.
Select an appropriate task you could modify to enhance learning and assessment opportunities around understanding.
Pick a task genre to use as a frame.
Modify the existing task AND identify mathematical goals for your revised task.
CREATING OPPORTUNITIESHow could you modify this problem to incorporate what we learned about teaching and assessing understanding?
Task as it appears:
CREATING OPPORTUNITIESHow could you modify this problem to incorporate what we learned about teaching and assessing understanding?Task as modified, connections among representations:
How do the goals you are teaching/assessing change with the modified task?
a) Represent 493 using the flats, longs, and little cubes in your base ten blocks.
b) Write an equation that matches what you have built to represent 493.
c) What is the greatest number of longs (i.e., tens) you would need to use if you didn’t have any flats (i.e., hundreds)?
d) Explain how you figured out the greatest number of longs (i.e., tens) you would need.
CREATING OPPORTUNITIES
How could you use this set of problems to forward elements of mathematical understanding?
Tasks as they appear:
How do the goals you are teaching/assessing change with the modified task?
CREATING OPPORTUNITIES
Sort the equations and explain how they chose to sort.
Solve the problems using tables, or graphs, not just manipulating symbols.
CREATING OPPORTUNITIES TO LEARN AND ASSESS “UNDERSTANDING”
24
Review mathematical goals and the tasks in the unit you are currently teaching. Select an appropriate
task you could modify to enhance learning and assessment opportunities around understanding.
Pick a task category to use as a frame.
Modify the existing task AND identify mathematical goals for your revised task.
A DUAL COLORED HAT
How did these activities help you think about what it means to teach and assess mathematical understanding?
How might activities such as these be used with teachers to help them reconsider what it means to teach and assess mathematical understanding?
25
SPECIAL THANKS TO MY COLLEAGUES!
Geraldine Devine
Dana Gosen [email protected]
Marie [email protected].
mi.us
Valerie [email protected]