Mathematics for Middle School Teachers: A Program of Activity-Based Courses

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Mathematics for Middle School Teachers A Program
of Activity-Based Courses

• Portland State University
• Nicole Rigelman
• Eva Thanheiser

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What is the Mathematics for Middle School
Teachers Program?

• Graduate Certificate Program Undergraduate
  Minor
• Housed in mathematics department
• Relevance of the mathematics learned
• Activity based learning
• Discussion of childrens mathematical thinking

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The certificate program consists of 8 courses 

• Computing in Mathematics for Middle School
  Teachers
• Experimental Probability and Statistics for
  Middle School Teachers
• Problem Solving for Middle School Teachers
• Geometry for Middle School Teachers
• Arithmetic and Algebraic Structures for Middle
  School Teachers
• Historical Topics in Mathematics for Middle
  School Teachers
• Concepts of Calculus for Middle School Teachers
• Teaching and Learning in the Middle School
  Mathematics Classroom

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2009 2010 2011 2012 2013 2014
Winter MTH 4/593 MTH 4/590 MTH 4/591 MTH 4/594 MTH 4/592 MTH 4/595
Spring MTH 4/594 MTH 4/592 MTH 4/595 MTH 4/596 MTH 4/510 MTH 4/593
Summer MTH 4/591MTH 4/592MTH 4/510 MTH 4/593MTH 4/594MTH 4/595 MTH 4/590MTH 4/592MTH 4/596 MTH 4/591MTH 4/595MTH 4/510 MTH 4/593MTH 4/594MTH 4/596 MTH 4/590MTH 4/592MTH 4/510
Fall MTH 4/596 MTH 4/510 MTH 4/593 MTH 4/590 MTH 4/591 MTH 4/594
With careful planning it is possible to complete
the program in 3 consecutive summers, 2 academic
years and the intervening summer, or 3 academic
years.
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The graduate certificate admission requirements
are

• Completed B.A. or B.S. degree.
• GPA 3.0 cumulative undergraduate, or 3.0 for
  upper division courses, or 3.0 in all graduate
  credit courses (a minimum of 12 credits).
• Completion of Mth 111 (College Algebra) and Mth
  211 (Foundations of Elementary Mathematics I) or
  the equivalent.

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Philosophy of the Graduate Middle School
Certificate Program

• Problem solving activities that promote
  exploration and experimentation and which allow
  students to construct (and reconstruct)
  mathematical understanding and knowledge
• Development of multiple strategies or approaches
  to problems - discussing and listening to how
  others think about a concept, problem, or idea
• Small group work and cooperative learning
• Integration of childrens mathematical thinking
• Supportive and cooperative class environment

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Discussion of Childrens Mathematical Thinking

• Connecting
• Mathematics
• Childrens mathematical thinking
• Practice of teaching
• Activities
• Interviewing children
• Assessing whole classes
• Viewing videos
• Participating in Family Math Night

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Example

• 4 ½ - 1 ½
• Solve the problem as many ways as you can
• How could a 6th grader justify 3 as an answer?
• How could a 6th grader justify 2 as an answer?
• Show a video clip and make sense of the students
  reasoning

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Example

• 4 ½ - 1 ½
• Solve the problem as many ways as you can
• How could a 6th grader justify 3 as an answer?
• How could a 6th grader justify 2 as an answer?
• Show a video clip and make sense of the students
  reasoning

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Example

• 4 ½ - 1 ½
• Solve the problem as many ways as you can
• How could a 6th grader justify 3 as an answer?
• How could a 6th grader justify 2 as an answer?
• Show a video clip and make sense of the students
  reasoning

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Justification for 4 ½ - 1 ½ 2
S1 4-1 3 and ½ - ½ 0 so the answer is 3
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Justification for 4 ½ - 1 ½ 2
S1 4-1 3 and ½ - ½ 0 so the answer is 3
S2 he did 4-1 was 3, and then he said the 2 halves dont equal anything
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Justification for 4 ½ - 1 ½ 2
S1 4-1 3 and ½ - ½ 0 so the answer is 3
S2 he did 4-1 was 3, and then he said the 2 halves dont equal anything
S3 4-1 3 and ½ ½ 1 and 3-12
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Justification for 4 ½ - 1 ½ 2
S1 4-1 3 and ½ - ½ 0 so the answer is 3
S2 he did 4-1 was 3, and then he said the 2 halves dont equal anything
S3 4-1 3 and ½ ½ 1 and 3-12
S4 States you cannot combine ½ ½ if you have 4 ½ - 1 ½ you dont combine that
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4 ½ - 1 ½ 2
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4 ½ - 1 ½ 2

• Heres the 4 by itself, no, ok, nobodys ripped
  in half yet, its just them, so those 2 halves are
  taken out, so its 4 -1 is 3
• and then they surgically clip that guy back
  together

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4 ½ - 1 ½ 2

• Heres the 4 by itself, no, ok, nobodys ripped
  in half yet, its just them, so those 2 halves are
  taken out, so its 4 -1 is 3
• and then they surgically clip that guy back
  together

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4 ½ - 1 ½ 2

• Heres the 4 by itself, no, ok, nobodys ripped
  in half yet, its just them, so those 2 halves are
  taken out, so its 4 -1 is 3
• and then they surgically clip that guy back
  together

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4 ½ - 1 ½ 2

• Heres the 4 by itself, no, ok, nobodys ripped
  in half yet, its just them, so those 2 halves are
  taken out, so its 4 -1 is 3
• and then they surgically clip that guy back
  together

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Use of video clip

• Address
• Models of subtraction and their representation
• Take away vs. comparison
• Fractions
• How do students think about fractions?
• How do students think about mixed numbers?
• Appropriate models for a context
• What do teachers need to know?
• To understand student thinking
• To build on student thinking
• to facilitate class discussion

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Why does it work?

• Preservice In-service teachers working together
• Exploration of mathematics in small groups
• Connection to real childrens mathematical
  thinking
• Relevance

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Student Quotes

• I really have enjoyed the class discussions and
  activities. These were very amazing to me as it
  has really helped me to experience looking at and
  analyzing others approaches to problems that I
  may not have seen or even been able to understand
  at first glance.
• Even though they are hard to schedule, I have
  learned a lot from the student interviews. Seldom
  do we have the chance to sit down with one child
  for 45 minutes and explore their mathematical
  thinking. This has been a small luxury and very
  illuminating.

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Secondary Mathematics Methods

• Develop views about how adolescents learn
  mathematics and how to facilitate learning via
  the tasks posed, the classroom norms established,
  the questions asked, etc.
• Analyze and adapt tasks/lessons and plan for
  implementation that promotes high level thinking
  and reasoning for each student.
• Apply learning from course in the field
  experience.
• Navigate different points of view about teaching
  and learning.
• Reflect critically on developing instructional
  practice.

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Course Structure

• Engage in mathematical tasks as learners.
• Examine student work and students at work (video
  and written cases).
• Discuss teacher moves that facilitate learning
  both as modeled by the instructor and as modeled
  in the classroom cases.

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Course ProjectsAnalyzing Classroom Talk

• Plan and teach a lesson. Then analyze a
  transcript of the classroom talk for
• the types of questions asked and the purposes
  they served,
• the student understanding evidenced in student
  responses, and
• the role questions play in student learning.

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Course ProjectsLesson Study

• Collaborate with 1-2 others to create a mini-unit
  that reflects the learning from
• the readings,
• class discussion, and
• other teaching/learning settings
• about Standards-based instructional practices.

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Course ProjectsVideo Analysis

• An opportunity to plan, implement and reflect
  deeply on teaching.   
• Analysis draws upon evidence from the video and
  includes
• intended and actual student mathematical
  learning,
• ways the teacher supported or inhibited student,
  and
• teacher candidate learning and implications.