It’s Not the Math I Learned!
So how do I help my child?
What is Mathematics?
Traditional View
Negative Attitudes and Perceptions
Emphasis
Ignored
Rules and Procedures
Concepts and Big Ideas
Computation
Problem Solving
Answers
Thinking Processes
One “best” Way
Alternative Flexible Strategies
Listen, copy, memorize, drill
Explain, predict, justify, represent
The Cooking Analogy
“Arithmetic has usually been taught like it's
a recipe: Take the raw ingredients (the
numbers), follow a series of steps, and end
up with a tasty end result (the answer).
While an experienced baker knows why
you cream butter and sugar before adding
eggs, then add flour last, a beginner just
following the steps is in the dark. They
might know what to do, but they can't
explain why.” (Nelson, 2014)
What is the curriculum?
 Why the changes?
 Global economic concerns
 International comparisons
 College and career readiness
 78% of adults cannot explain how to
compute interest paid on a loan
 71% cannot calculate miles per gallon
 58% cannot calculate a 10% tip
Mathematics Advisory Panel Final Report, 2008
The Standards for Mathematical Practice
Overarching Habits of Mind
 Make sense of problems and persevere in solving them.
 Attend to precision.
Reasoning and Explaining
 Reason abstractly and quantitatively.
 Construct viable arguments and critique the reasoning of others.
Modeling and Using Tools
 Model with mathematics.
 Use appropriate tools strategically.
Seeing Structure and Generalizing

Look for and make use of structure.

Look for and express regularity in repeated reasoning.
What does it mean to be
“fluent”?
Accuracy
Efficiency
Flexibility
What does it mean to be
“fluent”?
9
50
Strategies vs.
Standard Algorithms
The Rule of Thumb
“If you can’t explain why
the method works, you
shouldn’t be using it.”
– John Van de Walle
Eastern Algorithm for
Multiplication
The Bottom Line
 Number sense is the strongest predictor of
success in higher level mathematics
(e.g., middle/high/college)
 Rote memorization, when emphasized over
sense-making, tends to inhibit the development
of number sense.
 Instead of simply asking, “What is 7 + 9?” consider
asking “How could you use 7 + 7 to help solve 7 +
9?”
The Arithmetic to Algebra Gap
 “Drill alone does not develop mastery of single-digit
combinations.” (Kilpatrick, Swafford, and Findell 2001, p. 192)
 Learning to decompose and recompose numbers in flexible
ways is integral to developing efficient computational strategies,
number sense, and ultimately, readiness for algebra. (Wheatley &
Reynolds, 1999)
Representation:
Arithmetic
𝟐𝟕𝟑
𝟏𝟑
= 21
Representation:
Algebra
𝟐𝒙𝟐+𝟕𝒙+𝟑
=
𝒙+𝟑
𝟐𝒙 + 𝟏
Relational Understanding
 Skemp (1978) defined an instrumental explanation as simply
stating what to do in order to solve a problem.
 In contrast, a relational explanation is characterized not only by
knowing what to do in order to solve a problem, but also
explaining why.
 Benefits
 Less to remember/recall
 Compression in the brain occurs when information is connected
 When you understand concepts, your brain uses LESS working memory
 Enhanced problem solving abilities (e.g., flexibility)
 Improved student attitudes/beliefs
“Why should my child use
drawings?”
Conceptual Understanding
 Multiple Representations
“Why should my child use
drawings?”
A student stands 12 feet ahead of the starting point on a line.
He takes 5 equal jumps and lands 27 feet beyond the starting
point. How long was each jump?
12 + 5j = 27
How Can I Help My Child?
• Be positive
• Don’t say “I was never good at math” or
“I hate fractions, too!”
• Ask questions
•
•
•
•
•
What do you think?
How do you know this? (Show me.)
Why do you think this?
Can you tell me more?
What questions can you ask your teacher?
How Can I Help My Child?
Help them master basic facts
• 3 phases of basic
fact mastery
• If using flash cards,
target/focus on a
few facts at a time
• Shoot for 4-5 sec.
for recall
How Can I Help My Child?
Support math homework
Avoid “doing it”
Ask your child what is confusing to
them – see if they can articulate it (this
supports adaptive reasoning and selfregulation).
If needed, work out a similar problem
as model for your child to reference
How Can I Help My Child?
 Encourage them to try mental math.*
 Look to a teacher’s itslearning page, the student work
book, or ask the teacher if your child does not
understand a concept.
 Help them solve word problems.
 Ask them to read and then paraphrase/summarize the problem
 Ask them to circle key information, the question being asked
 Ask them to VERIFY their solutions – “How do you know it makes sense?”
 Help them make sense of problems by asking, “Why
does this answer NOT make sense?” (ex: 9 – 7 ≠ 16)
 Make math a part of everyday life.
How Can I Help My Child?
If your child asks for help with a strategy, do NOT tell them,
“That’s not how you do it! I’ll show you the way I learned it,
which was much easier!”
 If your child asks for help with a strategy, do NOT tell them,
“That’s not how you do it! I’ll show you the way I learned it,
which was much easier!”
 Example:
Resources
Resources
• Video/audio (searchable by topic/standard)
• Interactive & adaptive (searchable by topic/standard)
• Virtual tools (for modeling math concepts)