Conceptual Development in Area Measurement Funda Gonulates, Lorraine Males, & Nic Gilbertson Strengthening Tomorrow’s Education in Measurement (STEM) Project Michigan State University MCTM Conference 2010 Dakota High School

Welcome We’d like to take some time for everyone to introduce themselves  Name  Position  Grade level  District/School 2STEM MCTM Conference

Area Take some time to think about and share your answer to the following: 3STEM MCTM Conference  What is area?  What issues or difficulties do you think students might have with area measurement?

Pentagon Task STEM MCTM Conference4 1)Find the area 2)Draw a second pentagon with the same area

Pentagon Task STEM MCTM Conference5 With a partner, 1)Share your solutions 2)What might students have difficulties with in solving this problem? 3)What would students need to know in order to solve this problem?

Pentagon Task – NAEP results STEM MCTM Conference6 Scoring Rubric: Incorrect (both parts a & b incorrect) Partial (either a or b correct) Correct (both a & b correct) Omitted Off Task

Pentagon Task – NAEP results STEM MCTM Conference7 Scoring Rubric: Incorrect (both parts a & b incorrect)…48% Partial (either a or b correct)…47% Correct (both a & b correct)…2% Omitted…2% Off Task… (rounded to 0%)

Pentagon Task – NAEP results STEM MCTM Conference8 Grade 8 – 2005 Scoring Rubric: Incorrect (both parts a & b incorrect)…48% Partial (either a or b correct)…47% Correct (both a & b correct)…2% Omitted…2% Off Task… (rounded to 0%)

STEM – Who, Where, and When Who:  PI: Dr. Jack Smith  Research Assistants: Dan Clark, Kuo-Liang Chang, Leslie Dietiker, Hanna Figueras, Nic Gilbertson, Funda Gonulates, Pat Greeley, Jia He, Kosze Lee, Lorraine Males, Aaron Mosier, Matt Pahl, Gulcin Tan Sisman, Shannon Sweeny, Alexandria Theakston When:  2007 – present Where:  Michigan State University  Work beginning in various districts throughout Michigan including Eastern UP, Grand Rapids, Jackson, Kalamazoo, & Oakland 9STEM MCTM Conference Strengthening Tomorrow’s Education in Measurement

STEM – What What: Research  analyzing the capacity of three written elementary curricula to support robust learning of spatial measurement (length, area, volume) Professional Development  worked with pre-service teachers during their year- long internship on measurement lesson study  working with facilitators throughout Michigan who are in turn working with teachers in their areas 10STEM MCTM Conference

STEM – Three Curricula The three carefully chosen curricula are:  Scott Foresman- Addison Wesley Mathematics  UCSMP’s Everyday Mathematics  Saxon Math 11STEM MCTM Conference

STEM – Our Analysis In our analysis we are looking at every lesson, problem, and activity of teach curricula for two important aspects:  Knowledge elements - Spatial measurement knowledge (conceptual, procedural, conventional)  Textual elements - The ways in which this knowledge is expressed (statements, demonstrations, worked examples, questions, problems, games) 12STEM MCTM Conference

STEM – Area Core Principles  Area as a measurable quantity  Conservation under partitioning.  Conservation under motion  Identical Units  Unit iteration  Transitivity  Spatial structure of rectangular arrays  Multiplicative composition from lengths 13STEM MCTM Conference

STEM – Area Analysis Flow of Area Topics 14STEM MCTM Conference “Grain-size perception of area” the ability to exploit the structure “Holistic perception of area” to understand the structure of a region Array of Objects (Numbers, counting) Arrays of Tesselating Objects Rectangles Visual Judgment Cover Measure and Cover Measure w/ Grid w/out Array Structure Measure w/ Array Structure Compute LxW Std. vs Non std. Units Visual Estimation of Area Partition Analysis of area content in all curricula K-4 (Gonulates & Mosier, 2010)

Area Lesson Analysis: SFAW Grade 3, P.468A 15STEM MCTM Conference What knowledge is required What is in curricula

Area Lesson Analysis: SFAW Grade 3, P STEM MCTM Conference What knowledge is required What is in curricula

STEM MCTM Conference17 SFAW GR3 Area Lesson Analysis Objectives of the Lesson P. 468AP. 468 Conceptual Knowledge Procedural Knowledge Connections Reflection

STEM MCTM Conference18 SFAW GR3 Area Lesson Analysis Objectives of the Lesson Estimate or find the areas of figures in square units. P. 468AP. 468 Conceptual Knowledge Area as a measurable quantity (Definition and meaning of area measure) Order/Equity Unit Measure Compensation Area as a measurable quantity (Definition and meaning of area measure) Procedural Knowledge Measure area (G, RC) Draw a region Measure area (G, covering, counting, grid) Visual estimation Read an area Draw a region Connections Reflection

Thank you! We want to thank the National Science Foundation for funding this work We want to thank you for coming! Please take a few minute to fill out our evaluation. For more information starting this fall you can go to: If you have any questions please us at: STEM MCTM Conference19