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Strategies for Engaging Algebra Learners: Puzzles that Promote Mathematical Reasoning

Presentation for National Council of Teachers of Mathematics 2013
by

Mary Fries

on 28 March 2014

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Transcript of Strategies for Engaging Algebra Learners: Puzzles that Promote Mathematical Reasoning

Puzzles that Promote Mathematical Reasoning
Strategies for Engaging Algebra Learners
A Habits of Mind Approach
Transition to Algebra
a full-year intervention course designed to be taken
concurrently with first-year algebra
(aka double period algebra)
Why Puzzles?
Focuses on a few key mathematical ways of thinking or

Quickly gives students the
mathematical knowledge, skill,
and confidence to succeed in a
first-year algebra class
Puzzling and Persevering
Seeking and Using Structure
Using Tools Strategically
Describing Repeated Reasoning
Communicating with Precision
TTA is a 4-year research and development project funded by the National Science Foundation.
TTA has is also being used in other settings including
summer school and middle school as
pre-algebra
Mary Fries
,
mfries@edc.org
Paul Goldenberg,
pgoldenberg@edc.org
Jane Kang,
jkang@edc.org
ttalgebra.edc.org
mathematical habits of mind
Consistent with Common Core State Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Who Am I? Puzzles
You can make up your own puzzles using clues with relevant content.
parity: evens and odds
squares and roots
inequalities
algebraic expressions
factoring (shown right)
Mathematical Puzzles
:
are
genuine problems
support
number sense
encourage
logical reasoning
help students develop
strategy
in problem solving
are
fun
and engaging
allow for

social collaboration
in solving
encourage
perseverance
as solution method may not be known before starting
Bridge from mobile puzzles to systems of equations and properties of numbers and operations
Think of a Number
Tricks
Students
reason abstractly about variables
use notation logically
work with tables to organize information
How did I know your number?
Area Models
Mystery Number Puzzles
Students learn systems of equations intuitively
Mobile Puzzles
MysteryGrid Puzzles
Use the clues to fill in each grid so that every row and every column contains all of the numbers in the title.
provide a visual model for the distributive property
support "seeing" like terms
NCTM 2013
"[When] students were given the opportunity to look at a book, they would
immediately go for the puzzles
." - TTA Teacher
Students indicated that
area models
,

Think-of-a-Number tricks
, and
mystery grids
were among the
most useful
activities in helping them
understand algebra.
Classroom Use
Teachers who
taught both
algebra 1 and the intervention class
were better able to
make connections

between them.
Discussion
How was your experience exploring these activities today?

How do you see these experiences translating to students?

How do you see these ideas taking place in your school?
Full transcript