It All Adds Up: Language in the Mathematics Classroom

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It All Adds UpLanguage in the Mathematics
Classroom

• Douglas Fisher Nancy Frey
• San Diego State University
• www.fisherandfrey.com
• .

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Increasing Specialization of Literacy
Shanahan Shanahan, 2008
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Math Reading

• Goal arrive at truth
• Importance of close reading an intensive
  consideration of every word in the text
• Rereading a major strategy
• Heavy emphasis on error detection
• Precision of understanding essential
• Conclusions subject to public argument
• Shanahan Shanahan, 2008

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Looking inside the math text

• Close reading required for precision
• Arriving at the truth
• Mastering technical vocabulary
• Rereading for error detection

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Mathematics Text

• 1.1 Introduction to Linear Equations
• A linear equation in n unknowns x1, xx, xn is
  an equation of the form
• a1x1 a2x2 anxn b,
• where a1, a2,,an, b are given real numbers
• For example, with x and y instead of x1
  and x2, the linear equation 2x 3y 6 describes
  the line passing through the points (3, 0) and
  (0, 2).
• Similarly, with x, y and z instead of x1,
  x2 and x3 the linear equation 2x 3y 4z 12
  describes the plan passing through the points (6,
  0, 0),
• (0, 4, 0), (0, 0, 3).
• A system of m linear equations in n unknowns x1,
  x2, , xn is a family of linear equations
• Shanahan Shanahan, 2008

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TEACHER RESPONSIBILITY
I do it
Focus Lesson
Guided Instruction
We do it
You do it together
Collaborative
You do it alone
Independent
STUDENT RESPONSIBILITY
A Structure for Instruction that Works
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In some classrooms
TEACHER RESPONSIBILITY
I do it
Focus Lesson
You do it alone
Independent
STUDENT RESPONSIBILITY
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In some classrooms
TEACHER RESPONSIBILITY
You do it alone
Independent
STUDENT RESPONSIBILITY
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And in some classrooms
TEACHER RESPONSIBILITY
I do it
Focus Lesson
Guided Instruction
We do it
You do it alone
Independent
STUDENT RESPONSIBILITY
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TEACHER RESPONSIBILITY
I do it
Focus Lesson
Guided Instruction
We do it
You do it together
Collaborative
You do it alone
Independent
STUDENT RESPONSIBILITY
A Structure for Instruction that Works
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Modeling in Math

• Background knowledge (e.g., When I see a
  triangle, I remember that the angles have to add
  to 180?.)
• Relevant versus irrelevant information (e.g.,
  Ive read this problem twice and I know that
  there is information included that I dont need.)
• Selecting a function (e.g., The problem says
  increased by so I know that Ill have to add.)
• Setting up the problem (e.g., The first thing
  that I will do is because )
• Estimating answers (e.g., I predict that the
  product will be about 150 because I see that
  there are 10 times the number.)
• Determining reasonableness of an answer (e.g.,
  Im not done yet as I have to check to see if my
  answer is makes sense.)
• Fisher, D., Frey, N., Anderson, H. (in press).
  Thinking and comprehending in mathematics
  classroooms.

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The sum of one-fifth p and 38 is as much as twice
p.

• Okay, Ive read the problem twice and I have a
  sense of what theyre asking me. I see the term
  sum, so I know that Im going to be adding. I
  know this because sum is one of the signal words
  that are used in math problems for a list of
  signal words see figure 2. I also know that
  when terms are combined, like one-fifth p, they
  are related because they make a phrase one-fifth
  of p so Ill write that 1/5 p. The next part
  says and 38, so I know that Ill be adding 38 to
  the equation. Now my equation reads 1/5p 38.
  But I know thats not really an equation. I know
  from my experience that there has to be an equal
  sign someplace to make it an equation. Oh, they
  say as much as which is just a fancier way of
  saying equal to. So, Ill add the equal sign to
  my equation 1/5p 38 . And the last part is
  twice p. And there it is again, one of those
  combined phrases like one-fifth p, but this time
  twice p. So Ill put that on the other side of
  the equation 1/5p 38 2p. Thats all theyre
  asking me to do. For this item, I just need to
  set up the equation. But I know that I can solve
  for p and I like solutions. I know that you can
  solve for p as well. Can you do so on your dry
  erase boards?

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Vocabulary Development

• Word walls on which teachers post 5-10 words on a
  wall space that is easily visible from anywhere
  in the room. The purpose of the word wall is to
  remind teachers to look for ways to bring words
  they want students to own back into the
  conversation so that students get many and varied
  experiences with the words.

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Vocabulary Development

• Word cards in which students analyze a word for
  its meaning, what it doesnt mean and create a
  visual reminder.

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Vocabulary Development

• Word sorts in which students arrange a list of
  words by their features. Word sorts can be open
  (students are not provided with categories) or
  closed (students are provided categories in which
  to sort).

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Vocabulary Development

• Word games in which students play with words and
  their meanings. For example, this might involve a
  bingo game of sorts where students write words
  from the class in various squares and then the
  teacher randomly draws definitions until someone
  gets bingo. We also like games such as Jeopardy,
  Who Wants to be a Millionaire, or 25,000 Pyramid
  as they allow students to review words while
  having a bit of fun. A great website that
  provides information about vocabulary games is
• jc-schools.net/tutorials/vocab/ppt-vocab.html

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Productive Group Work

• Individual Accountability
• Interaction
• Use of academic language

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