Effects of engagements in non decimal numeration systems on the understanding of place value
Download
1 / 21

Effects of Engagements in Non-Decimal Numeration Systems on the Understanding of Place Value - PowerPoint PPT Presentation


  • 89 Views
  • Uploaded on

Effects of Engagements in Non-Decimal Numeration Systems on the Understanding of Place Value. Aaron Trocki November 14, 2011. Stage Setting. Need for Highly Qualified Teachers (NCTM, 2000) Call for Conceptual Understandin g in Elementary School (Common Core, 2010)

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Effects of Engagements in Non-Decimal Numeration Systems on the Understanding of Place Value' - phil


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Effects of engagements in non decimal numeration systems on the understanding of place value

Effects of Engagements in Non-Decimal Numeration Systems on the Understanding of Place Value

Aaron Trocki

November 14, 2011


Stage setting
Stage Setting the Understanding of Place Value

  • Need for Highly Qualified Teachers (NCTM, 2000)

  • Call for Conceptual Understanding in Elementary School (Common Core, 2010)

  • “Explain why addition and subtraction strategies work, using place value and the properties of operations” (Common Core, 2010)


Stage setting1
Stage Setting the Understanding of Place Value

  • Since at least the 1960’s it has been posited that study of non-decimal numeration systems can increase foundational mathematical understanding and this notion is still evident in current research (it just won’t go away!) (include personal note here)

  • Purpose: Synthesize the research on place value understanding related to engagements with non-decimal numeration systems

  • Organization: Set Stage, Furnish Framework, Map Method, Report Results, Finish with Findings, Include Implications

  • Define Non-Decimal Numeration System


Furnishing the framework
Furnishing the Framework the Understanding of Place Value

Research on Knowledge for Teaching

  • Need for content knowledge (Shulman, 1986)

  • Specialized Content Knowledge (Ball, 1988, 2008)

    Teacher Knowledge Related to Student Achievement

  • 1st and 3rd grade student achievement positively correlated to specialized knowledge for teaching (Hill, Rowan, Ball, 2005)

  • Place Value knowledge of teacher positively correlates to:

    • Types of activities afforded to students (contructivist, in depth, student creativity, etc.)

    • Student Achievement (Tanase, 2011)


Furnishing the framework1
Furnishing the Framework the Understanding of Place Value

Research on Pre-Service Teachers and Pre-Service Teachers’ Training

  • Prospective teachers’ knowledge upon entering college (Ball, 1990)

  • Prospective teachers’ knowledge at end of college (Ball, 1988)

  • 1) Build on currently held conceptions; 2) model teaching for understanding; 3) focus on connections between content knowledge and other types of knowledge (Thanheiser et al., 2010)

  • Teach to ‘unpack’ learning goals when analyzing mathematical tasks (Morris, Heibert, and Spitzer, 2009)


Furnishing the framework2
Furnishing the Framework the Understanding of Place Value

Demonstrate Importance and Difficulty in Understanding Place Value

  • Place value understanding is difficult to acquire even in a familiar context of dealing with money (Chandler and Kamii, 2009)

  • A lack of place value understanding can inhibit and slow conceptual understanding of algorithms (Cooper and Tomayko, 2011)


Mapping the method

Mapping the Method the Understanding of Place Value

Include articles that assess the effects of non-decimal numeration system engagements

Does not include simple activity descriptions such as in most practitioner articles


Mapping the method1
Mapping the Method the Understanding of Place Value

  • ERIC and Google Scholar

  • Sample search terms

    • Non-decimal

    • Numeration systems

    • Alternate bases

    • Place value

    • Pre-service

    • Conceptual understanding


Reporting the results
Reporting the Results the Understanding of Place Value

Two basic categories emerged

Studies Done with Children

Studies Done with Pre-Service Teachers


Reporting the results1
Reporting the Results the Understanding of Place Value

Kavett (1969)

  • 4th and 6th grades, 430 students

  • Trained 18 teachers in non-decimal numeration systems

  • Significant differences found on retention between control and experimental groups

  • Recommendation to teach non-decimal systems in late elementary school


Reporting the results2
Reporting the Results the Understanding of Place Value

Diedrich & Glennon (1970)

  • Test Dines’ “Mathematical Variability Principal”

  • Four 4th grade classes

  • Researcher guest taught

  • Posttest treatment effect found but not at a statistically significant level

  • Speculated that student interest in mathematics increased


Reporting the results3
Reporting the Results the Understanding of Place Value

Senger (1997)

  • 5th grade, 13 students

  • Qualitative in nature

  • Students created their own non-decimal number systems

  • Understanding on difference between number and number symbol increased


Reporting the results4
Reporting the Results the Understanding of Place Value

McClain (2003)

  • Class of Pre-Service Teachers

  • Hypothetical Learning Trajectory Proposed on Place Value and Multidigit Addition and Subtraction

  • Includes work in Base 8

  • Results showed increased conceptual understanding of place value and addition and subtraction


Reporting the results5
Reporting the Results the Understanding of Place Value

Radin (2007)

  • Two classes of pre-service teachers

  • Different Instructors

  • Pre and Posttests and comparisons between classes

  • Significant differences found in systematic unfamiliar problem types but not in overall test scores


Reporting the results6
Reporting the Results the Understanding of Place Value

Khoury and Zazkis (1994)

  • 124 Pre-Service Teachers

  • Understanding multiple representations of fractions depends on understanding of place value

  • Tests implemented and interviews conducted

  • Most pre-service teachers believed the value of a fraction changed when represented in a different numeration system

  • Need for conceptual understanding of place value and fractions for pre-service teachers


Reporting the results7
Reporting the Results the Understanding of Place Value

Zazkis (1993)

  • 82 Pre-Service Teachers

  • Investigated problem solving strategies and systematic errors in place value and rational number understanding

  • Unfamiliar domain of non-decimal numeration systems

  • Common strategies for interpreting place value were found

  • Only 12 pre-service implemented a correct strategy


Finishing with the findings
Finishing with the Findings the Understanding of Place Value

What do these studies tell us?


Finishing with the findings1
Finishing with the Findings the Understanding of Place Value

  • Engagements with non-decimal numeration systems have been shown to increase student understanding of place value but results have been inconsistent and not necessarily generalizable

  • Student interest in and attitude toward math may improve through such engagements


Finishing with the findings2
Finishing with the Findings the Understanding of Place Value

  • The evidence suggests that engagements with non-decimal numeration systems increases teachers understanding of place value and representations of fractions

  • Engagements with non-decimal numeration systems may serve as a profitable window to uncover pre-service teacher understanding or lack thereof of place value and representations of fractions


Including the implications
Including the Implications the Understanding of Place Value

  • Engagements in non-decimal numeration systems are potentially powerful to increase understanding

  • Mathematics educators should consider using these engagements as many are available (include some of the 9 articles found)


Including the implications1
Including the Implications the Understanding of Place Value

  • More studies are needed to assess the effects of engagements in non-decimal numeration systems with both pre-service teachers and students

  • More research needs to be conducted to address where non-decimal numeration system study should be included in the learning trajectory on place value


ad