How to Be a Mathematician: Complexifying Mathematical Smartnesses

This presentation was given at the Twelfth Annual Georgia Association of Mathematics Teacher Educators Conference

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

Supporting Spatial Reasoning: Identifying Aspects of Length, Area, and Volume in Textbook Definitions

Length, area, and volume share structural similarities enabling flexibility in reasoning for real-world applications. Deep understanding of structures can help teachers connect these concepts to support their students’ mathematical reasoning and practices involving real-world situations. In mathematics textbooks designed for future teachers, definitions of length, area, and volume vary from procedural (e.g., use a ruler to measure side lengths, use formulas to calculate measures) to conceptual (e.g., construct appropriate n-dimensional units that tessellate the n-dimensional space) to formal (e.g., construct a function mapping qualitative size to a quantity of appropriate units). Most textbooks describe length, area, and volume as quantitative measurements and provide examples of standard units. Definitional aspects such as describing size as an attribute or measurement, identifying dimensionality of a space, or constructing appropriate nonstandard units are inconsistently acknowledged across textbooks. Attending to definitional aspects of spatial attributes and their quantification can open conversations about the structure and essential meanings of length, area, and volume

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

Pre-Service K-8 Teachers’ Learning of Measurement Unit Conversion Problems

This presentation was given at the Twelfth Annual Georgia Association of Mathematics Teacher Educators Conference

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

This session supports grades 3-5 mathematics teachers and coaches in considering how technology in the classroom can be used to support low threshold, high ceiling tasks and productive discussion. In this session, participants will interact with and share resulting strategies from 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 will present a sampling of strategies created by teachers (who were pretending to be elementary students) in past activities. Participants will select and sequence these strategies to align with chosen learning outcomes. We will discuss approaches to connecting strategies for deeper understanding of area measurement. Participants will gain access to a set of online tasks that are free and work on any internet-capable device. (Bring an Internet-capable device to the session!

Journal Staff

The aluminum–zinc-vacancy (Al Zn −V Zn ) complex is identified as one of the dominant defects in Al-containing n -type ZnO after electron irradiation at room temperature with energies above 0.8 MeV. The complex is energetically favorable over the isolated V Zn , binding more than 90% of the stable V Zn ’s generated by the irradiation. It acts as a deep acceptor with the (0/− ) energy level located at approximately 1 eV above the valence band. Such a complex is concluded to be a defect of crucial and general importance that limits the n -type doping efficiency by complex formation with donors, thereby literally removing the donors, as well as by charge compensation

Mathematics Learning, Teaching, and Equity in Policy and Programs: The Case of Secondary Mathematics Teacher Education in the United States

Professional organizations have provided recommendations for mathematics teaching and learning; however, few studies have investigated the practical integration of those recommendations into mathematics teacher education programs. In this study, we examine how the reported “big ideas” of courses in secondary mathematics teacher education programs emphasized the content and teaching practices necessary for future mathematics teachers, as recommended by policy documents. As part of a larger study, we conducted a series of interviews in secondary mathematics teacher education programs at four universities (names are descriptive pseudonyms): Great Lakes University (GLU), Midwestern Research University (MRU), Midwestern Urban University (MUU), and Southeastern Research University (SRU). We selected the institutions and programs based on their Carnegie Classification, the types of communities in which they were situated, the average number of graduates from a program, the departmental homes of their secondary mathematics education programs, and the demographics of their student populations. The analysis of data collected from 12 courses across four universities revealed specific ways in which big ideas in secondary mathematics teacher education programs emphasized areas related to mathematics learning, teaching, and issues of equity and access

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

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-themoment 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 KCollege educators