I couldn't attach this article as a link but I think we need to read this regarding how math instruction needs to change:
Adjusting Mathematical Language to
the Common Core
In
this Kappan article, Valerie Faulkner
(North Carolina State University) presents a number of changes in the way
elementary mathematics is conceived in the Common Core. Implementing the new
standards means letting go of a lot of old habits:
• Old
habit to eliminate: Defining equality as “same as.”
The problem: This is mathematically incorrect
and leads to misconceptions.
New habit to adopt: Defining equality as
“same value as.”
For example, 3 + 4 tells a different math
story than 4 + 3, but they yield the same value of 7.
• Old
habit to eliminate: Calling digits “numbers.”
The problem: Failing to distinguish between
digits, numbers, and numerals
New habit to adopt: Clearly distinguishing
between numerals and numbers (which are essentially the same) and digits.
For example, 73 is a numeral that represents
the number value 73 and has two digits – 7 and 3.
• Old
habit to eliminate: “Addition makes things get bigger.”
The problem: When negative numbers are
introduced, the old habit has to be debugged.
New habit to adopt: Addition is about
combining.
• Old
habit to eliminate: “Subtraction makes things get smaller.”
The problem: As with addition, negative
numbers make this wrong.
New habit to adopt: Subtraction is about
difference.
• Old
habit to eliminate: When borrowing, saying, “We don’t have enough ones so we
need to go to the next place.”
The problem: Students don’t understand that
in the number 10, there are ten ones, but in the decimal system, we don’t “see”
them.
New habit to adopt: “We can’t see the ones we
need, and we need to find those ones.”
• Old
habit to eliminate: “You can’t take a big number from a little number.”
The problem: The statement is intended to
help elementary students deal with borrowing, but it’s mathematically
inaccurate and leads to problems later on.
New habit to adopt: “We could take a larger
number from a smaller number, but we would get a negative number. You will
learn about these later, but right now we will learn to solve this problem
using all positive numbers.”
• Old
habit to eliminate: “Let’s ‘borrow’ from the tens place.”
The problem: This doesn’t prepare students
for more-difficult borrowing and fractions.
New habit to adopt: Use “regrouping,”
“trading,” or “decomposing” instead.
• Old
habit to eliminate: Multiplication “makes things bigger.”
The problem: This is true only when using
positive whole numbers and will confuse students later on.
New habit to adopt: Teach the three
structures of multiplication: repeated addition; finding how many unique
possibilities there are when matching one set with another; and finding a total
amount or area when two sides are known.
• Old
habit to eliminate: Division “makes things smaller.”
The problem: As with multiplication, this is
not true a lot of the time.
New habit to adopt: Teach the different
structures of division: repeated subtraction of groups; answering the question
“how many for each one?”; and finding a side when an area and another side are
known.
• Old
habit to eliminate: “Doesn’t go into” (for example, 7 doesn’t go into 3).
The problem: Even elementary school children
understand intuitively that sometimes cookies need to be split up when they
don’t divide up exactly.
New habit to adopt: Prepare students for
later learning by using accurate mathematical language. A teacher might say,
“We could divide 3 by 7, but the result won’t be a whole number. When you begin
working with fractions, you will solve problems like this regularly. Here we
want to consider numbers that divide into other numbers without creating
fractional parts or leftover pieces.”
• Old
habit to eliminate: Saying “and” means decimal point.
The problem: In common parlance and math
parlance, “and” generally means to combine, add to, or augment. Insisting on
using “and” only when there’s a decimal buries the opportunity to have a
discussion that focuses on considering unit sizes and different ways to form a
number.
New habit to adopt: Don’t create false rules
for language. In other words, it’s not a big deal to call 145 “one hundred and
forty-five.”
• Old
habit to eliminate: Canceling out – for example, “These eights cancel out.”
The problem: Students don’t notice how often
properties are used and how important they are.
New habit to adopt: Explicitly use and
discuss the idea behind simplifying. A teacher might say, “Here I have an 8
divided by an 8, and we know that anything divided by itself equals 1. So you
can see here that we have simplified this expression without changing its
value.”
• Old
habit to eliminate: Referring to “the answer.”
The problem: If the goal is to find answers,
there’s a tendency to forget the most important part: How did we do that? Why
did we do that? How did you know that?
New habit to adopt: Use “the model” or “the
relationships” or “the structure” or “justify your answer.”
• Old
habit to eliminate: Guess-and-check as a strategy.
The problem: While this sometimes involves
using number sense, it’s not logical or mathematical and doesn’t prepare
students for more difficult challenges.
New habit to adopt: Teach systematic math
representations – bar models, for example – to teach students to think like
mathematicians.
- Superintendent Runcie and School Board Member Laurie Rich-Levinson will be here on Monday.
- Faculty Collaboration is scheduled for Tuesday afternoon. There are a few items to discuss.
- The next PTA General Meeting is Wednesday at 6:00 PM.
- Report Cards are due to your team leader on Tuesday and to Ms. Felton on Thursday.
- If you know before you arrive that you are going to leave early, please park in the Savannah parking lot. If you do need to leave early for an emergency, Mrs. Toth has a key that you can pick up and return to her when you move your car to the Savannah parking lot.
Quote of the Week -
Every child deserves a champion — an adult who will never
give up on them, who understands the power of connection, and insists
that they become the best that they can possibly be.
- Rita F. Pierson. When you have a moment please watch this video in which Ms. Pierson makes a plea for teachers to truly care about their students -
Every Kid Needs A Champion Are you a champion for your students?
Think Like a Detective - Can you determine the Gator Run teacher based on the following clues?
- Is from St. Paul, Minnesota
- Went to school at
University of Wisconsin & FAU
- Enjoys walking, reading and family time
- Her grandfather liked to invent things.
