Working Together to Achieve the Vision In Utah

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Working Together to Achieve the Vision In Utah

• Johnny W. Lott, Director
• Center for Excellence in Teaching and Learning
• University of Mississippi
• jlott_at_olemiss.edu

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• Each of us, teachers, parents, policymakers,
  organizations, and community members, has an
  obligation to aid mathematics teaching and
  learning in schools. 

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• To improve student learning, all need to consider
  contributions that can be made and how each part
  fits into the whole. 

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• What can you contribute to mathematics teaching
  and learning, regardless of your role in the
  community?

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Roles of Teachers

• Teachers must shift their perspectives about
  teaching from a process of delivering information
  to that of facilitating students sense making
  about mathematics.
• Martin, (p.5)

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Teachers must be proficient in

• Designing and implementing mathematical
  experiences that stimulate students interests
  and intellect

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NOTE I said interest.
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What interests students?

• Depends on grade level
• Math. Students can develop important math skills
  while they classify and compare quantifiable
  characteristics and performance numbers (e.g.,
  prices, speeds, sizes, weights, duration) of the
  things they find fascinating.

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What interests students?

• Math. Students can create and compute statistics
  for their sports heros accomplishments, such as
  home runs, batting averages, rebounds, and
  touchdowns. They can create a budget using their
  heros salary.

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François Morellet
10 Lignes au hasard, 1971
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François Morellet
10 Lignes au hasard, 1971
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Roles of teachers

• Teachers must orchestrate classroom discourse in
  ways that promote the exploration and growth of
  mathematical ideas.
• ?Martin, (p.5)

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Establishing a Frame of Reference

• Sequence 1
• What is the sum of the reciprocals of the prime
  or composite factors of 28?
• Truxaw, Mary , "Orchestrating Whole Group
  Discourse to Mediate Mathematical Meaning"
  (2005). TERC Documents. Paper 2.

(See Figure 3-A)
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Establishing Common Language

• Sequence 2
• What are prime numbers?
• What are composite numbers?

(See Figure 3-B-1)
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Exploration Toward Building Common Understanding

• Sequence 3
• Both Exploratory and Structured Discourse used to
  yield...
• The sum of the reciprocals of the prime and
  composite factors of 28 equals 1
• 1/2 1/4 1/7 1/14 1/28
• 14/28 7/28 4/28 2/28 1/8 28/28 1

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Sequences 1 3 Serve as a Springboard for
Sequence 4

• Sequence 4
• I wonder if thats always true. Im going to try
  another...
• The sum of the reciprocals of the prime or
  composite factors of 6 is investigated.
• The sum of the reciprocals of the prime and
  composite factors of 6 equals 1!

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A Hypothesis is Suggested
Hankins Hypothesis The sum of the reciprocals
of the prime or composite factors of any number
equals 1.

• Small group discourse is used to test the
  hypothesis

(See Figure 3-B-3 3-C)
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New Understanding Used as a Foundation to Test
Hypotheses

• Corollaries to the theorem are presented
• Vargas Corollary The hypothesis doesnt work
  for primes
• OConnor Corollary The hypothesis doesnt
  work for perfect cubes
• David says, It didnt work for 36, which is an
  abundant number.
• This provokes discussion of abundant numbers
  then deficient numbers.

(See Figure 3-D)
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Roles of Teachers

• Teachers use, and help students use, technology
  and other tools to pursue mathematical
  investigations.
• Martin (p. 5)

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Using Technology for Investigation

• How might you use technology for this problem?

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Could you simulate what is expected?

• How would you do it?

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Box-and-Whisker Plots

• Consider life expectancies of all countries in
  Africa.
• Consider life expectancies of all countries in
  North America. This includes Caribbean
  Islands.
• Draw separate box plots.
• What do you see? Why?
• Problem suggested by James Rubillo, Executive
  Director, NCTM

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Roles of Teachers

• Teachers must assess students existing
  mathematical knowledge and challenge them to
  extend that knowledge.
• Martin (p. 6)

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What do we teach?

• Do we still teach what students already know?
• Do we still teach what students have already been
  taught?

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If re-teaching, then modify and enhance!
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Roles of Teachers

• Teachers must foster positive attitudes about the
  aesthetic and utilitarian values of mathematics.

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Show them that math matters.
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Show them that math matters.
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Roles of Teachers

• Teachers must engage students in opportunities to
  deepen their own understanding of the mathematics
  being studied and its applications.

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Troy Jones Salt Activity
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Roles of Teachers

• Teachers must reflect on the value of classroom
  encounters and take action to improve their
  practice.
• Martin (p. 6)

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Reflecting on Practice
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Roles of Teachers

• Teachers must foster professional and collegial
  relationships to enhance their own teaching
  performance.
• Martin (p. 6)

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Enhance Yourself!

• Take classes
• Form interest groups
• Socialize with each other
• Talk mathnot students
• Read with an eye to math
• Be professional

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Responsibilities of Policymakers

• Support decisions made by math ed professionals
  that set directions for curriculum, instruction,
  evaluation, and school practice.

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But speak so that people understand you!
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Policymakers

• Provide resources and funding for the
  implementation of high-quality school mathematics
  programs that reach all students.

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Money doesnt solve everything, but

• without it, we have no hope.
• Salaries are from the 2006-2007 Jordan
• School District reflect entry level wages.
• Average Teacher Salary
• Bachelors Degree 28,939
• Masters Degree 32,455
• PhD 36,512

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Responsibilities of Business/Industry

• Provide assistance in, developing, and
  implementing high-quality school mathematics
  programs that reach all students.
• Participate in partnerships at all levels to
  improve teaching and learning of math.

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Math/Science Partnerships

• MESA Utah is a great example from what I read
  online.

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Responsibilities of Schools

• Understand the goals for math ed of all students.
• Recruit qualified teachers of math.
• Provide mentoring and support system for
  teachers.
• Make teaching assignments on basis of
  qualification.

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Responsibilities of Schools

• Involve teachers in designing and evaluating
  professional development programs.
• Support teachers in self-evaluation, in
  analyzing, evaluating, and improving teaching.

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Responsibilities of Schools

• Provide adequate resources, equipment, software,
  instructional materials, time, and funding for
  math.
• Allow teacher input in selecting all teaching
  materials with time and resources to do
  selection.

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Responsibilities of Schools

• Establish outreach activities with parents,
  care-givers, and community to build support for
  math programs.
• Promote excellence in teaching math by
  establishing an adequate reward system.

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Responsibilities of Universities

• Establish a reward system for joint
  appointmentsmath ed.
• Provide a workplace environment to support
  teacher education.
• Facilitate faculty collaboration to improve
  teacher preparation.
• Ensure adequately qualified individuals teach
  teacher prep courses.

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Responsibilities of Faculty

• Spend time in schools.
• Collaborate with teachers.
• Engage in inquiry-oriented analyses of personal
  practices.
• Offer appropriate graduate courses for teachers.

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Responsibilities of Faculty

• Provide leadership in conducting and interpreting
  math ed research for schools.
• Cooperate with precollege educators to articulate
  K-16 programs.
• Make concerted efforts to recruit and retain
  high-quality diverse teacher candidates.

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References

• http//www.prufrock.com/client/client_pages/GCT_Re
  aders/Strategies/Ch._14/Motivation_Traps_for_Gifte
  d_Children.cfm
• Truxaw, Mary , "Orchestrating Whole Group
  Discourse to Mediate Mathematical Meaning"
  (2005). TERC Documents. Paper 2.
  http//digitalcommons.uconn.edu/terc_docs/2/
• http//radicalart.info/AlgorithmicArt/scatter/inde
  x.html
• http//timiddlegrades.com/activitiesmath/290
• http//hub.mspnet.org/index.cfm/9142
• Martin, T. (ed.). (2007). Mathematics Teaching
  Today, Improving Practice, Improving Student
  Learning (originally published as Professional
  Standards for Teaching Mathematics, 1991.).
  Reston, VA National Council of Teachers of
  Mathematics.