Writing in Mathematics

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Writing in Mathematics

• Carlos Rodriguez
• Area 11 Curriculum Instructional Coach
• Spring 2011

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Objectives

• Why math journaling?
• Key essentials?
• Establish a routine
• Choose a focus
• Model the process and expectations
• Models and anchor charts
• Establish a feedback protocol
• Implementation Strategy Scaffold
• Open end response (opinion, reflection,
  questions)
• Review and introduce math skills/concepts
• Problem solving (extended response)

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Why use Math Journals?

• Math journals are an effective way for teachers
  to understand a childs mathematical thinking,
  processes, strategic knowledge, and/or
  proficiency with skills and concepts. Journaling
  within the math class should reflect a gradual
  progression that include but are not limited to
  the following
• Response to Open-ended Prompts
• Solving Daily Math Problems
• Skills Review/Scaffolding
• Extended Response Problem Solving

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Start by

• Determine how and when to use the math journals
• Select several uses and discuss each with the
  students Ex. Daily problem solving, open
  response, exit slips, selected writing prompts,
  etc. MODEL, MODEL, MODEL!
• Determine when journals will be incorporated into
  the math lesson Ex. During the Warm-Up, during
  the wrap up, x number of days per week, etc.
• Develop a protocol for how journals will be
  assessed and shared Ex. Develop a schedule for
  feedback/assessment, encourage students to write
  with the intention to share with their
  classmates, create a rubric for assessment, etc.
• Determine how journals should be organized
  storage in the classroom, how they will be
  distributed when its time to use them, whether
  they are organized by unit, quarterly or a
  continuation of the whole year, etc.
• Support students writing by building anchor
  charts for concepts, creating math word walls,
  posting math problem solving strategies, etc.
• Increase the classroom discourse during math
  instruction students who are able to articulate
  their thinking will find it easier to translate
  their thoughts into writing.
• Encourage students to focus on their thought
  processes, not the right answer

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Implementation StrategiesOpen-Ended Response

• Begin implementation of journals with affective,
  open ended questions regarding the students
  feelings about a particular experience, concept,
  lesson and/or problem. This will give the teacher
  greater insight regarding how to develop each
  individual student and diagnose misconceptions
  and or areas of difficulty immediately
• Example 1 Reflect on your participation in
  class today and complete the following
  statements
• I learned that
• I was surprised that.
• Im not sure about.
• I noticed that.....
• Example 2 Have students write a paragraph about
  their math experiences in and out of school
• When you were younger, what didnt you like
  about math? What did you like?
• Did you have any tricks to help you remember
  certain concepts?
• Who was your favorite math teacher? What did
  he/she do to keep your interest?
• Can you remember a time when you learned
  something about math in school and then was
  able to use it outside of school? How did that
  make you feel?
• What is your earliest memory of being taught
  Mathematics?

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Implementation Strategies Reviewing Math
Concepts and Scaffolding New Concepts

• Once students are comfortable with writing their
  attitudes and feelings about mathematics, they
  are ready to write about simple and familiar
  concepts . Students should not be asked to write
  about a skill that is unfamiliar to them, it
  reduces their confidence which will have a
  negative impact on their attitude towards writing
  and mathematics. Instead, they should be asked,
  at this point, to write about a skill/concept
  that you are reviewing and/or a skill that was
  addressed during the lesson
• Examples
• Explain in your own words what subtraction
  means.
• How would you define a fraction to someone that
  you were teaching?
• Tell two ways to solve a division problem.
• When is it appropriate to use an estimate
  rather than the actual number?
• Draw your favorite shape and give the
  attributes of the shape.
• Describe some objects in your environment that
  have a measurement of less than 6 centimeters.
• Explain inverse operations and provide an
  example of how it works.
• Compare solving single-step equations to
  solving two-step equations, how are they alike
  and/or different?
• How are fractions, decimals and percents
  related?
• Which type of graph would be best to show
  change over time? Are there more than one?

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Implementation Strategies Problem Solving

• By this time, students should be accustomed to
  writing, students will now be asked to write
  solutions to math problems. They should be able
  to write about the solution they got as well as
  how they arrived at that solution. This will
  translate into higher scores for Math Extended
  Response as well as help teachers diagnose where
  the misconceptions or break down took place in
  the students thinking. When selecting problems
  for students to solve and write solutions,
  consider the following
• Selected Problems should
• Pin point a confusing or easily misunderstood
  concept or mathematical idea Example Write 0.2
  and 0.020 as a fraction. Are they equal? Explain
  your answer
• Have several solution strategies Example The
  Chicago Bulls won 8 out of 10 games. The Boston
  Celtics won 15 out of 18 games. Whose team won a
  greater fraction of games? Explain your answer.
• Encourage students to compare or debate two
  different solutions to the same problem Example
  Who is correct? The problem Which fraction is
  greater? 1/3 or 2/5? Jasons solution 2/5 is
  bigger because 15 is the LCD and 1/3 equals 5/15.
  2/5 equals 6/15. So 2/5 is greater. Blakes
  solution I used the calculator, I made them
  decimals and then compared the decimals. For 1.3,
  I divided 1 into 3 and got 3.0. Then I divided 2
  into 5 and got 2.2. 3.0 is bigger than 2.2 , so
  1/3 is greater.
• Use logical reasoning in determining if their
  answers or thoughts are appropriate for the
  question Examples Ms. James wants to treat her
  students to some cupcakes for their behavior.
  There are 30 students in the class. The cupcakes
  are sold in packages of 7 cupcakes per box. What
  is the least number of boxes Ms. James needs to
  purchase?
• Elicit students to think beyond applying
  procedures, but focus on contextual application
  Examples include situational problems that allow
  students to use background knowledge and
  experience to make the problem relative.

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Creative Writing

• Creative Writing allows students to broaden their
  view of mathematics and incorporate their own
  individual interest into mathematics instruction.
  One way to begin the implementation of creative
  writing in math is by reading math stories aloud
  (ex. Marilyn Burns), writing a math story
  together, using Math Mad-Libs (funny stories),
  and incorporating poetry.
• Examples of creative writing prompts
• If you were a centimeter high, what would you be
  able to do?
• Using magazine pictures and clips, write a
  problem or short story that the pictures could
  represent.
• Create your own shape, what would you name it and
  what are its attributes?
• Create a menu for your favorite restaurant, write
  a story detailing what you ordered, how much it
  costs, how much change was left, etc.
• Write a children's book explaining place value to
  a younger student.
• What would you do if you won 100, 1,000, 100,
  000, and 1,000,000?
• What if the number system did not contain 0,
  how would that effect people?
• Whats your favorite number, why?
• Create a Math Superhero or Math Fairy Tale
  character and write a story (be sure to include
  numbers, math symbols, vocabulary, etc.)

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Creative Writing Continued

• Examples of Math Poetry
• Math Haiku
• the season has come
• the days are getting longer
• minutes and hours
• Math Acrostics
• A.N.G.L.E.S- Acute less than 90 None are less
  than 0 Greater than 90 are called obtuse Lines
  that are 180 are called straight angles
  Equivalent angles measure the same Supplementary
  angles add up to 180
• Math Limericks
• There was a young student from Rye,
• Who worked out the value of p.
• "It happens," said he, "That it's just over 3,
• Though I'd rather you don't ask me why."

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Real World Connections

• Students must be able to connect their learning
  by understanding conceptually how the mathematics
  will be applied in a real world context. Teachers
  should make these connections daily (when new
  concepts are introduced) as well as through
  writing
• Examples
• Take students on math walk throughout the
  building or neighborhood to take photographs of
  mathematics (street signs, benches with parallel
  lines, obtuse angles created by branches of
  trees, slope of sliding board at the playground,
  etc.) Have students write a story or series of
  problems related to their observations and create
  a class book.
• Have students respond to the following types of
  prompts weekly, bi-weekly or monthly
• List all of the ways that you used math this
  week
• Write about something mathematical that you saw
  on television
• Name at least 10 things that you can do in a
  second, a minute, an hour, a day
• Make a graph and chart of how you spend your
  day. Write a narrative explaining the data.

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Helpful Reminders

• Talk to students regarding the purpose of their
  writing. Motivate students to write with positive
  praise, modeling and feedback!
• Consider allowing students to personalize their
  journals with stickers, pictures, etc. Make the
  process engaging and exciting for students, not
  laborious and tedious.
• Keep journals in the classroom, do not send home
  for homework.
• Set a timer for journal entries to focus
  students.
• Decide on a system for identifying journal
  entries, do not spend time having students write
  the prompt each time. Use a numbering system,
  print prompts on strips of paper to staple to
  their journal pages, etc.
• Do not focus heavily on grammar and spelling
  initially, build up to improvement in their
  overall writing
• Periodically allow for peer collaboration such as
  brainstorming ideas and providing collaborative
  feedback.
• Regularly allow students to share entries with
  the class
• Respond to students writing, personalized
  responses will encourage students to want to
  improve.
• Allow students to suggest prompt ideas
• Use students responses to evaluate your
  instruction
• Begin the year writing EVERYDAY in math, once
  students are accustomed to the various types of
  entries, 2 to 3 times a week is sufficient.

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Conclusion

• A comprehensive student math journal will display
  samples from each of the fore mentioned writing
  styles it will also display a progression of
  improved content throughout the year. As with any
  new concept, journal writing is a skill that will
  require patience for proper implementation, so
  focus on quality, not quantity!

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Additional Resources for Math Writing Prompts

• http//www.myteacherpages.com/webpages/jgriffin/jo
  urnal.cfm
• http//www.superteacherworksheets.com/journal-prom
  pts.html
• http//www.quincy.k12.mi.us/qms/PDF_2009_2010/
• http//letsplaymath.net/2007/08/21/writing-to-lear
  n-math/
• http//www.mathpower.com/funstuff.htm
• http//www.mathlibs.com/
• http//www.teach-nology.com/worksheets/language_ar
  ts/madlibs/