Math Matters: Results that Add Up for Teachers and Students

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Math Matters Results that Add Up for Teachers
and Students

• Presenters Bonnie Warren-Kring, Deborah
  McAllister and John Graef, University of
  Tennessee at Chattanooga

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Teacher Ed Faculty Partner with A S Faculty

• Math, Science, Social Science and English faculty
  devise lesson plans and learning strategies for
  students in low areas of performance on TCAP
  tests.
• Faculty will focus on the thinking/reading skills
  needed for success in each of these areas.

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Literacy Instruction in the Content Areas
Getting to the core of middle and high school
improvement (Heller Greenleaf, 2007)

• Students need advanced literacy skills for the
  intellectual work that the academic disciplines
  require,
• such as conducting and reporting scientific
  experiments,
• analyzing historical sources, or
• proving mathematical theorems.

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Reading Difficult Text

• If teachers want their students to be able to
  handle such assignments, they would do well to
  help them become more competent in reading
  difficult texts in general.

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For content area teachers, a key challenge is to
articulate and make concrete the skills,
knowledge, and concepts

• they may take for granted but that many students
  need to be shown explicitly
• To become an expert is to internalize specific
  disciplinary standards and to learn how to do
  certain things more or less automatically

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Content area teachers

• need to understand what is distinct about reading
  and writing in their own discipline, and how to
  make those rules, conventions, and skills
  apparent to students

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They may need to help their students to see that
such disciplinary styles exist,

• and that each discipline uses vocabulary, text
  structures, stylistic conventions, and modes of
  analysis and debate that are very different from
  the language students hear at home, or among
  their friends or elsewhere in school (Heller
  Greenleaf, 2007, p.22).

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Partnering

• Reading is thinking and problem-solving. Content
  area teachers (math, science, history, English)
  read, think and write about their discipline in a
  certain way.
• These strategies that content area teachers
  employ can be translated into strategies to help
  their students understand the text they read,
  think and write about in their discipline.

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Thinking/Reading in Content Areas

• The challenge is to make these strategies
  explicit, first to yourself and then to your
  students. This process is known as metacognition.
• Education and Arts Science faculty will partner
  to think about their thinking processes in order
  to help middle schools students begin thinking in
  similar ways about the thinking in different
  content areas.

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Beginning Stages of Process

• Have asked the Hamilton County Director of
  Evaluation to share the 8th grade areas of lowest
  performance.
• We will then develop thinking/reading processes
  to apply to those areas of weakness.

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Possible Difficulties

• Specific schools have specific areas of need. One
  size does not fit all.
• Just because we come up with what looks like a
  good plan, doesnt mean it will be successful
  when implemented in the classroom. Pilot lessons,
  implementation, and evaluation would be
  necessary.

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Incongruencies between Curriculum Testing

• Students at this Title I school were all in
  Algebra I or Algebra 1a.
• They were all being taught using the Cognitive
  Tutor and Carnegie Learning.
• However, the TCAP tests other state standards not
  addressed in the Cognitive Tutor curriculum.
  Therefore, they would not do as well in those
  areas.
• They also take the Algebra 1 Gateway test.

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Sample Mathematics Lesson

• 8th Grade TCAP - SPI 8.4.8 Solve problems
  involving scale factors using ratios and
  proportions
• Design supplemental instruction to address gaps
  in students knowledge not covered by the
  Cognitive Tutor but tested on the 8th grade TCAP.

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Scale Factors

• Begin the lesson with the motivational book, If
  You Hopped Like a Frog by David Schwartz. (Show
  book)
• Using vivid pictures and concrete examples, this
  book captivates and engages students with its
  real-life examples of scale factors and begins
  the thinking processes related to ratios and
  proportions.

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If You Hopped Like a Frog

• you could jump from home plate to first base in
  one mighty leap!
• Frogs are champion jumpers. A 3-inch frog can hop
  60 inches. That means the frog is jumping 20
  times its bodys length. Lets suppose you are 4
  ½ feet tall. If you, like a frog, could hop 20
  times your body length (your height), you would
  be able to sail from home plate to first base, 90
  feet in all!

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Sample cont.

• How tall are you? If you could jump 20 times your
  body length, how far could you go? Measure your
  height and multiply by 20 to find out!
• The book goes on with many such intriguing
  examples. This hooks the students into thinking
  about using ratios and proportions.

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Next you

• use Chattanooga Math Trail Community
  Mathematics Modules designed by Deborah
  McAllister to bring math concepts to life in the
  Chattanooga community.
• Example Carousel at Coolidge Park
• In this math module, students explore the
  restored carousel to solve a variety of
  mathematics problems.

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16. Measure the length, width, and height of
one of the carousel animals.

• Compare the measurements to those of a live
  animal (collect data or use resource material) or
  a porcelain figure or a plastic toy. What is the
  scale of the carousel animal, as compared to the
  live animal or figure/toy? Is the carousel animal
  in proportion to the actual animal (i.e., are all
  three dimensions at the same scale)?

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Sample data
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Connect to text

• After being given this introductory material to
  scale factors using ratios and proportions,
  students are then ready to connect what they have
  just experienced to the mathematics text that
  they are using in their classroom.
• With math ratios and proportions made real to
  them, students are better able to begin thinking
  and reading about them from their text.

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Partners will Develop

• At this point, the AS and Education partners
  will develop an explicit process of thinking
  about ratios and proportions that teachers can
  use to guide students in their understandings.
• This thinking process could be used as an
  evaluation tool to verify the students
  understanding.

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Community Mathematics

• Found at this web site
• www.utc.edu/Faculty/Deborah-McAllister/
• Click on the Chattanooga Math Trail to find the
  Community Mathematics Modules

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Geography Example

• TCAP SPI 6.1 Trace the stages of Americas
  westward growth through the analysis of maps and
  primary source accounts.
• Thinking/reading about maps reading/thinking
  about primary documents as they relate to
  Americas westward movement.

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Faculty and Metacognition

• Developing metacognition
• Notice what is happening in your mind in everyday
  situations
• Identify various thinking processes you engage in
  a variety of everyday situations

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Metacognition cont

• Notice where your attention is when you read
• Identify all of the different processes going on
  while you read
• Choose what thinking activities to engage in
  direct and control your reading processes
  accordingly

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Faculty Partners

• Education and AS faculty work together to make
  conscious their own reading/thinking processes
  concerning development of mapping skills in
  students.
• As faculty become more aware of their own
  processes, they gain new appreciation for the
  reading/thinking difficulties students may face.

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Scaffolding Students

• Faculty can then begin to scaffold the students
  in their classes into the reading/thinking about
  maps and geography by making their own normally
  invisible comprehension processes (metacognition)
  visible to their students.
• Faculty will develop concrete activities to make
  the students thinking/reading concerning map
  skills visible.

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Additional Content Areas

• Thinking/reading about English literature
• Thinking/reading about areas of science.

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Application of Lessons

• Faculty can apply what they have learned about
  their own thinking processes to scaffolding
  students in their classes to become better
  thinker/readers in their content areas.
• I will share the four lesson areas with my
  content area students to use as models for them
  when they teach.

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THEC Application

• These lessons can be further developed into units
  and used as workshops for teachers in public
  schools. A THEC grant proposal could be written
  to provide for materials, time, and money to
  accomplish these workshops for middle school
  teachers.

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Areas of Possible Difficulties

• Just a beginning.
• These content lessons would need to be
  implemented within the classroom setting and TCAP
  given to see if the format of these lessons did
  increase the knowledge, understandings and skills
  in each of the four content areas tested on the
  TCAP.
• THEC proposal would have to be accepted in order
  to further this study.

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Reading Content Area Text Teachers for a New
Era Mini-grant

• Reading in the Content Area Course
• Pre/post Preservice Teacher Attitude Survey
• Education students tutor middle/high students in
  reading comprehension skills
• Pre/post Bader Inventory with students they tutor
• Comparison group tested but NOT tutored
• Science and history trade books at CSAS and
  Orchard Knob Middle School libraries
• AS and Education Faculty Partner