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Megan W. Taylor 20133
“If you’re struggling with an equation while doing your algebra homework, more likely your parent will look over your shoulder, wrinkle a brow in puzzlement, then say something like ‘I never got that stuff either; do the best you can and try not to fail.’ This is an old problem. In effect, math instruction weeds out people.”
-Robert Moses & Paul Cobb, excerpt from Radical Equations
(Just a few of) The Problem(s) with“Teacher-Proof” Curricula
• no perfect curriculum yet exists– Or ever will?
• huge variability in how teachers use curricula
▫Teachers make a difference (duh)▫ In fact, teachers make the difference
Megan W. Taylor 2013 5
“Curriculum-Proof” teachers are effective because they…
• Design effective learning experiences regardless of textbook(s) being used
• Consider – and attend to – different kinds of knowledge• Maximize the effectiveness of given, existing curricula• In practice, this includes…
• considering ranges of student understandings• better assessment
Megan W. Taylor 2013 6
Intellectual activity anywhere is the same, whether at the frontier of
knowledge or in a third grade classroom…
The difference is in degree, not kind.
—Jerome BrunerMegan W. Taylor 2013 7
“Curriculum-Proof” teachers consider ranges of understanding
“Curriculum-Proof” teachers consider ranges of understanding
Megan W. Taylor 2013 8
Learning Goal: Draw a male human face.
“Curriculum-Proof” teachers consider ranges of understanding
Megan W. Taylor 2013 9
Learning Goal: Draw a male human face.
Megan W. Taylor 2013 10
A-REI.6 Solve systems of linear equations exactly and approximately.
Sprizon: Cost (per month) = $60 + .40/textT-Bell: Cost (per month) = $50 + .50/text
Which plan is a better deal?Justify your answer algebraically and graphically.
A-REI.6 Solve systems of linear equations exactly and approximately.
Megan W. Taylor 2013 11
Which plan is a better deal?
“T-Bell is cheaper if you text fewer than 100 times per month.”
Megan W. Taylor 2013 12
“It depends. If you don’t text that much, you should get T-Bell.”
Which plan is a better deal?
A-REI.6 Solve systems of linear equations exactly and approximately.
Megan W. Taylor 2013 13
“T-Bell is always better.”
Which plan is a better deal?
A-REI.6 Solve systems of linear equations exactly and approximately.
Megan W. Taylor 2013 14
Beginning Understanding ---------> Advanced Understanding
- graph both lines- estimate the point of intersection (solution) using a graph- give the solution as a coordinate (x,y)
“Curriculum-Proof” teachers consider ranges of understanding
Megan W. Taylor 2013 15
Beginning Understanding ---------> Advanced Understanding
- graph both lines- estimate the point of intersection (solution) using a graph- give the solution as a coordinate (x,y)
- solve a system using the “setting equal” or “substitution” method- explain why one solution method is more efficient than another
- solve a system using the “elimination” method- solve a three-equation linear system
“Curriculum-Proof” teachers consider ranges of understanding
“Curriculum-Proof” teachers use assessment more effectively
• Better assessment– Based on prioritized learning goals and ranges of
understandings– Allow ALL students to show what they know
• More frequent assessment• Better feedback
– For the teacher– For the students
Megan W. Taylor 2013 16