Three(ish) things I want to remember from the sessions I went to on Friday and Saturday
Building Student Understanding of the Mathematical
Practices through INformative Assessment
Matt McLeod, Mary
Wedon (EDC)
 Assessing students’ use of structure (MP7) through
computation problems. In directions, write “avoid unnecessary computation”
 "Hidden Meaning" questions
 ex: 36(6^{5}) is
equivalent to 6^{7}. Explain or show why this is true.
 "Chunking" questions
 ex: Simplify the following: 8(99^{2}4)+3(99^{2}4)11(99^{2}4)
FakeWorld Math: When Mathematical Modeling Goes Wrong
Dan Meyer
 There are 5 steps of modeling. Students do a lot of steps
3 and 4 in textbooks. We should be doing a lot more of 1, 2, and 5. Students don’t need
to do all 5 steps every time you do modeling. Celebrate what students are
contributing at each level through praise, one clap, etc.
1. Identify
the variables
2.
Formulate models
3. Perform
operations
4.
Interpret results
5. Validate
conclusions
 When modeling, we need to be honest about whether the math
“works.” Have a discussion why the predicted height in cups with all accurate computation isn't the actual height in cups.
 Set up situations that require knowledge that students
don’t have yet. This creates a need for a “bigger boat” (Jaws reference) before
we give it to them.
Investigating the Pythagorean Theorem and Its Proofs
Robyn Carlin
 What is the definition of “proof” in the common core? Is
it enough for students to be looking at examples and then making
generalizations?
Reasoning Revisions Revolution
Patrick Callahan and Jessica
Murk
 In having students work on problems you don’t know the
answer to, you authentically cede authority and model reasoning and revision
 After having students/groups write and revise their own
rules, having all students write the same rule down at the end defeats the
purpose
 With peer feedback, the authority shifts from teacher to
student. Feedback expectations:
 it takes
practice
 giving
feedback is not the same as being mean
 think
about what you would find helpful
 avoid
opinions
 be
specific
What do my students know? How do they know it?
Barbara Dougherty and
Jeanette Olson
 Encourage students to show their thinking rather than
show their work. In doing so you open the door for valuing logical reasoning over
structured algorithms.
 Challenges of open response questions in progress
monitoring:
 students
couldn’t explain
 hard to
score
 students
often skipped
 In multiple choice, options have different point values
based on complexity of thinking required for the (wrong) option
Bringing the Standards for Mathematical Practice to Life
In Classrooms
Ruth Parker
 Daily objectives are too fragmented of a way to learn
math. Instead, there should be 6 to 8 units of study a year where you are looking at the same math on the first and last day of the unit (see
Phil Daro on grain size). Then, students
should be able to answer “what are you trying to figure out right now?” instead
of “what math are you learning today?”
 Big mathematical ideas are never fully mastered. They deepen
in complexity over time. Therefore, learners should encounter:
 fragile understandings
 periods of cognitive dissonance
 mistakes as sites of learning
 states of not knowing… yet
 Can You See? (Teacher starts by asking questions, then
turns it over to the student)





 2/5?
 2/3?
1 divided by 2/3 ?
 a way for students to gain
addition fluency
 after doing an example or two,
ask students to come up with their questions and explore them
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