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Math Matters: Results that Add Up for Teachers and Students


Math Matters: Results that Add Up for Teachers and Students Presenters: Bonnie Warren-Kring, Deborah McAllister and John Graef, University of Tennessee at Chattanooga – PowerPoint PPT presentation

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Title: Math Matters: Results that Add Up for Teachers and Students

Math Matters Results that Add Up for Teachers
and Students
  • Presenters Bonnie Warren-Kring, Deborah
    McAllister and John Graef, University of
    Tennessee at Chattanooga

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
  • Faculty will focus on the thinking/reading skills
    needed for success in each of these areas.

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
  • such as conducting and reporting scientific
  • analyzing historical sources, or
  • proving mathematical theorems.

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.

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

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

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).

  • 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.

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.

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

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

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
  • They also take the Algebra 1 Gateway test.

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

Scale Factors
  • Begin the lesson with the motivational book, If
    You Hopped Like a Frog by David Schwartz. (Show
  • 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

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!

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.

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.

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)?

Sample data
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.

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

Community Mathematics
  • Found at this web site
  • Click on the Chattanooga Math Trail to find the
    Community Mathematics Modules

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.

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

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

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

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.

Additional Content Areas
  • Thinking/reading about English literature
  • Thinking/reading about areas of science.

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.

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

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
  • THEC proposal would have to be accepted in order
    to further this study.

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