The document outlines the structure and content of an Agile Mind curriculum. It is divided into units that progress from functional thinking and graphing relationships between variables, to algebra, exponents, and quadratics. Some of the key points made are: - Units 1-3 focus on functional thinking and representing relationships between variables x and y. - Units 4-9 cover slope, intercepts, and linear models, including moving between table, graph, and equation representations. - Units 10-14 teach solving for unknowns using algebra and systems of equations. - Later units cover exponents, laws of exponents, quadratics, factoring, and finding roots. The document discusses challenges encountered

1. Structure of Agile Mind

2. Units 1-3: Functional thinking
x and y are variables linked by cause and effect, and this
relationship can be represented in various ways
Units 4-9: Slope, intercept, and linear models
Obtain fluency with moving between representations: tables,
graphs, and equations
Units 10-14: Solve for unknowns
Algebra and systems
Units 15-16: Sequences and patterns (we’re skipping)
Units 17-18: Exponents
Laws of exponents
Units 19-23: Quadratics
Factoring and finding roots

3. Units 1-3: Functional thinking
x and y are variables linked by cause and effect,
and this relationship can be represented in
various ways
Article: ‘Functional Thinking as a Route to Algebra
in the Elementary Grades’

4. An Example: The Trapezoid Problem
• Completed in Teacher Study Group
• Discussed in a class reading (Blanton & Kaput, 2003)
• How many people can sit if there are…
– Two trapezoids,
– 14 trapezoids,
– 127 trapezoids,
– n trapezoids?
• How do you know?
• Can you come up with multiple solutions?
7/07/2011 Sixth Annual Noyce Conference

10. Where we’re at this year
Semester 1:
Functional thinking & graphing
Semester 2:
Algebra, exponents, and quadratics

11. Where we need to be
Semester 1:
Finish unit 10 by December (currently not till
February).
Semester 2:
Systems, exponents, and quadratics
Bottom line: we fell a month behind in Nov/Dec

12. Structure of a Unit

13. M T W R F
Guided
Block 1 X Block 3 Assessment X
Block 2 X Test X

14. Classroom models for Agilemind
that work

15. Independent Practice
• Four students per
group
• Only one computer
out
• Students have class
sets of activity sheets

16. Direct Instruction
• NO computers out
• Either notebooks or
activity sheets
• For each slide, students
write / draw (especially
predictions), then check
it.
• Students share out
answers

17. Guided Practice
• Assignment is on
some instant-
feedback site
• Students write their
answers on
whiteboards, so the
teacher can monitor
• Teacher controls pace
of the questions, so
that any student who
doesn’t have answer
on whiteboard has to
finish it after
class/after school

18. Flipping
• Pre-recorded tutorial on a
problem is played on the
board (some teachers are
recording their own
videos or podcasts)
• Students solve either that
example, or work a similar
example at their desk
• Teacher roams the room

19. Simulation
• Student demonstrates
simulation on board,
then class does so
independently
• Students ‘act out’
simulation at end
• Article: ‘What levels of
guidance promote
engaged exploration
with interactive
simulations?

20. What doesn’t work
• Giving students an assignment from the agile
mind textbook and have them work at their seats
– This is the first thing you’d try
– It doesn’t work because the students don’t produce
anything
– It doesn’t work because you wind up being the
facebook police, not teaching
– Students can change their answers three times, so
they just wind up guessing
– You’ll get assignment results between 80 and 100%,
even though the students haven’t learned a thing.

21. Some examples of what I mean by
‘backwards’

22. From Unit 3 Test
Students must:
•Find the rate of change (before we’ve defined rate
or slope or practiced any such calculations)
•Find the intercept (before we’ve even defined it)
•Write an equation in slope-intercept form, even
though they’ve never even seen such an equation

23. Students must find equivalent expressions, before they
have seen a linear equation, been told what a like term
is, or even worked on order of operations.

24. The a-coordinate? Whoever heard of the a-
coordinate?
This problem ran throughout. Whenever
agilemind used ‘m’ to mean ‘miles’, for
example, students with a tenuous grasp of
slope got totally lost.

25. • Students have roughly two weeks to gain this
level of mastery, without the curriculum
mentioning algebra beforehand.

26. But don’t worry…
• Even though only the top 25% might grasp
these problems through intuition, agilemind
comes back and does the same problem again
once students have developed a formal
understanding

27. From Unit 3 Test
From Unit 7 Test
From Unit 9 Test

28. From Unit 1 Test
From Unit 11 Test

29. From Unit 2 Test
From Unit 10 Test

30. • From a math teacher’s normal perspective,
you don’t need to teach the same thing again.
The skill is the same.
• But I found, again and again, that what I
thought I was saying, and what the students
understood me to be saying, were totally
different.

31. It’s NOT because these skills were supposed
to be prerequisite
It’s the intention of the curriculum: students
gain a sense of what a function is (in a real-
world sense), and how variables are linked
by cause and effect.
Only after students have been given the
context several times, and in fact solved the
relevant problem, do they learn the
formalism

32. Q&A