Definitions and Meaning for Future Teachers in Spatial Measurement: Length, Area, and Volume

U.S. students have consistently demonstrated poor performance in spatial reasoning in standardized testing (e.g., National Assessment of Educational Progress). One possible reason is students\u27 lack of conceptual understanding of measurement concepts (length, area, volume, capacity). This paper describes different ways that mathematics textbooks written for future elementary teachers define meanings of measurement concepts, especially the meaning of measure, area, and the measurement process (generally and for area). We base the analysis of definitions and construction of complete definitions using several definitions of each concept from mathematics textbooks written for future elementary teachers (e.g., Beckmann, 2012; Sowder, Sowder, & Nickerson, 2010). Although not one mathematics textbook provided a complete definition, together the definitions present a detailed and in-depth look at the measurement process and area measurement

Selecting, Sequencing, and Connecting: Using Technology to Support Area Measurement through Tasks, Strategies, and Discussion

This paper supports grades 3-5 mathematics teachers and considers how technology in the classroom can be used to support low threshold, high ceiling tasks and productive discussion. We present a description of a card-sorting task to support the “5 Practices of Productive Mathematics Discussions” focused on an online task designed to: be open to multiple levels of strategies, reveal misconceptions, and support students in developing more sophisticated conceptual understandings of area measurement. We present a sampling of strategies created by teachers (who were pretending to be elementary students) in past activities. We discuss approaches to connecting strategies for deeper understanding of area measurement

Using Google Forms to Inform Teaching Practices

Kay and LeSage (2009) conducted a literature review of research on use of student response systems in university courses (typically Science, Technology, Engineering, and Mathematics courses) and categorized benefits into classroom environment, learning, and assessment. The objectives of the proposed session are to discuss how using Google Forms will benefit those three above categories. Examples of Google Forms used to gather data, receive in-the-moment feedback to students and instructors, engage students’ learning, and assess their learning will be shared throughout the paper. Limitations of Google Forms will also be discussed. This session can be beneficial to all K-College educators

Definitions and meaning for future teachers in spatial measurement: Length, area, and volume

U.S. students have consistently demonstrated poor performance in spatial reasoning in standardized testing (e.g., National Assessment of Educational Progress). One possible reason is students\u27 lack of conceptual understanding of measurement concepts (length, area, volume, capacity). This session will engage participants in activities that compare and contrast different ways to define meanings of measurement concepts. We share card sorts that use several definitions of each concept from mathematics textbooks written for future elementary teachers (e.g., Beckmann, 2012; Sowder, Sowder, & Nickerson, 2010) and from elementary mathematics curricula (e.g., Saxon Math, Everyday Math, Scott Foresman-Addison Wesley). Participants will gain a deeper understanding of these concepts and reflect on how various definitions may affect future elementary teachers\u27 and elementary students’ understanding of measurement concepts

Conceptualizing and Interpreting Mean and Median with Future Teachers

Mathematical Education of Teachers II (METII), echoed by the American Statistical Association publication, Statistical Education of Teachers, recommended teacher preparation programs support future teachers in developing deep understandings of mean and median, such that middle grades teachers may use them to “summarize, describe, and compare distributions” (Conference Board of Mathematical Sciences, 2012, p. 44; Franklin et al., 2015). Georgia Standards of Excellence require statistical reasoning from students beginning as early as 6-7 years old, including interpretation of measures of center and statistical reasoning about best measures of center (Georgia Department of Education, 2015). This level of understanding and interpretation of measures of center, however, has been a persistent struggle for students and their teachers (e.g., Jacobbe & Carvalho, 2011). Jacobbe and Carvalho argued that an over-reliance on computation with little focus on conceptual understanding has created these barriers to statistical reasoning. To impact students’ understanding, a starting point is to address teachers’ understanding, particularly by supporting conceptual understanding of measures of center in teacher preparation programs (Jacobbe & Carvalho, p. 207). Our research question was: What conceptual understandings of mean and median do preservice teacher candidates (PSTs) exhibit when presented with a mean and median statistical task? We present findings from a two-part study, comparing PSTs’ responses to a task written to elicit conceptual understandings and statistical reasoning in one semester, with PSTs’ responses to a revised task in a second semester, both given at the end of a senior-level Statistics for K-8 Teachers course