Numerical Reasoning for Pre-service Teachers Rachel Cochran, Center for Educational Accountability Jason Fulmore, Center for Educational Accountability Bernadette Mullins, Birmingham-Southern College www.math.uab.edu/GBMP

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Numerical Reasoning for Pre-service
TeachersRachel Cochran, Center for Educational
AccountabilityJason Fulmore, Center for
Educational AccountabilityBernadette Mullins,
Birmingham-Southern Collegewww.math.uab.edu/GBMP
The Greater Birmingham Mathematics Partnership
is funded by NSF awards DUE-0632522 and
DUE-0928665. The opinions expressed herein are
those of the authors, and not necessarily those
of the National Science Foundation.
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Greater Birmingham Mathematics Partnership
Partner Students Minority Red. Lunch MS Gr. 6-8
Birmingham City Schools 27,440 99 83 1 358
Fairfield City Schools 2,307 100 83 1 512
Homewood City Schools 3,510 39 29 1 799
Hoover City Schools 13,194 35 22 2 2,241
Jefferson County Schools 35,669 49 51 4 3,236
Shelby County Schools 28,029 26 32 3 1,716
Tarrant City Schools 1,295 90 94 1 318
Trussville City Schools 4,183 13 11 1 1,011
UAB 17,543 36
Birmingham-Southern College 1,412 16
Mathematics Education Collaborative
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GBMP Activities

• Summer Courses
• Mathematics Support Teams
• Professional Learning Communities
• Administrator Sessions
• Community Mathematics Nights
• Revised Courses at UAB and BSC for
  Pre-service Teachers

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Challenging Courses and Curricula

• Big mathematics ideas
• Inquiry and reflection
• Productive disposition
• Communication

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Numerical Reasoning course for BSC pre-service
teachers

• Number talks (mental computation, estimation)
• Whole numbers and operations, place value
• Multiple models for fractions, story problems
• Equivalent fractions, ordering fractions
• Operations on fractions
• Decimals, percents
• Ratios, proportional reasoning
• Integers
• Real numbers

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Numerical Reasoning Task

• The Marriage Problem
• In a certain town, 3/5 of the women are married
  to 2/3 of the men.
• What fraction of the adults in the town are
  married?

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The Marriage Problem

• Sample 1
• Since 3/5 of the women are married to 2/3 of the
  men, 5/8 of the adults are married.
• Sample 2
• 3/5 2/3

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The Marriage Problem

• Sample 3
• 3/5 of the women are married
• to 2/3 of the men are married
• so 19/30 of the adults are married.

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The Marriage Problem

• Correct Solutions
• Geometric approaches
• Numerical approaches
• Algebraic approaches
• Graphical approaches
• Verbal approaches

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Numerical Reasoning Task 1½ ½

• There were 1½ pizzas left over. Juanita shared
  the leftovers with her friend, Rachel. How much
  pizza did they each get?
• Yan has1½ ounces of gin and it takes ½ an ounce
  of gin to make a cosmo. How many drinks can she
  make?
• It takes Kamal 1½ hours to clean his room. His
  bother said they could each do ½ the work. How
  long did it take them?
• I have a total of 1½ square yards of fabric. The
  fabric is ½ yard wide. How long is the fabric?
• Bobby has 1½ feet of rope. Thats enough for ½ a
  skipping rope. How much rope is needed for a
  whole skipping rope?

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Objective Pre-Post Assessment

• Content Knowledge for Teaching Mathematics (CKTM)
• Learning Mathematics for Teaching Project,
  University of Michigan, Deborah Ball et. al.
• 15 item instrument
• Mean gain of 3.4 from pre-test to post-test

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Student Achievement 2006-2007
Implementation Level 2006 Mean Std Dev 2007 Mean Std Dev N
High 57.0 21.4 60.3 22.2 1097
Moderate 55.4 21.2 56.4 21.6 6704
Low 56.6 20.8 55.0 21.3 15022
Total 56.2 20.9 55.7 21.4 22823
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Student Achievement 2007-2008
Implementation Level 2007 Mean Std Dev 2008 Mean Std Dev N
High 57.1 21.1 60.0 21.0 3305
Moderate 55.1 20.8 55.1 20.9 6215
Low 57.8 20.8 56.4 20.9 14506
Total 57.0 20.9 56.5 21.0 24026
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Student Achievement 2008-2009
Implementation Level 2008 Mean Std Dev 2009 Mean Std Dev N
High 59.5 20.7 61.6 21.3 3620
Moderate 54.6 20.2 54.8 20.4 7217
Low 57.7 20.4 57.1 20.7 8537
Total 57.1 20.5 57.1 20.8 24872
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Student Achievement 2009-2010
Implementation Level 2009 Mean Std Dev 2010 Mean Std Dev N
High 53.8 19.6 56.9 19.9 1221
Moderate 58.5 20.9 58.7 21.1 2441
Low 57.7 20.4 56.7 20.2 4255
Total 57.3 20.5 57.4 20.5 7917
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Numerical Reasoning for Pre-service
TeachersRachel Cochran, Center for Educational
AccountabilityJason Fulmore, Center for
Educational AccountabilityBernadette Mullins,
Birmingham-Southern Collegewww.math.uab.edu/GBMP
The Greater Birmingham Mathematics Partnership
is funded by NSF awards DUE-0632522 and
DUE-0928665. The opinions expressed herein are
those of the authors, and not necessarily those
of the National Science Foundation.