Understanding graphicacy : students’ making sense of graphics in mathematics assessment tasks

The ability to decode graphics is an increasingly important component of mathematics assessment and curricula. This study examined 50, 9- to 10-year-old students (23 male, 27 female), as they solved items from six distinct graphical languages (e.g., maps) that are commonly used to convey mathematical information. The results of the study revealed: 1) factors which contribute to success or hinder performance on tasks with various graphical representations; and 2) how the literacy and graphical demands of tasks influence the mathematical sense making of students. The outcomes of this study highlight the changing nature of assessment in school mathematics and identify the function and influence of graphics in the design of assessment tasks.

Diversity in mathematics assessment equals diversity in opinion?

We undertook a study to investigate the views of both students and staff in our department towards assessment in mathematics, as a precursor to considering increasing the diversity of assessment types. In a survey and focus group there was reasonable agreement amongst the students with regards major themes such as mode of assessment. However, this level of agreement was not seen amongst the staff, where discussions regarding diversity in mathematics assessment definitely revealed a difference of opinion. As a consequence, we feel that the greatest barriers to increasing diversity may be with staff, and so more efforts are needed to communicate to staff the advantages and disadvantages, in order to give them greater confidence in trying a range of assessment types.

Large-scale mathematics assessment : looking globally to act locally

In this paper, I will argue that it is possible to use data from large-scale international and national mathematics assessment programmes, whose attention is on summative achievement, to provide formative information that informs teachers about the effects of their classroom practice. However, to have impact on, and be useful for, classroom practitioners, these achievement data need to be reworked and re-presented in ways that are plausible, provide a basis for inferences about practice, and be appropriate for the intended audience. This paper examines achievement-focused assessment programmes in terms of their aims and approaches, and develops the argument that formative assessment possibilities are present, within these programmes, although usually hidden. Examples are drawn from several sources to support this argument, and demonstrate a variety of approaches that have been taken in the past. Suggestions for further action are made.

The Levels of mathematics achievement : initial performance standards for the 1990 NAEP mathematics assessment /

"November 1991"--Vol. 3.

Mathematics assessment report, Spring 1977 /

WI docs. no.: Ed.3/2:9320

A collaborative development of quality mathematics assessment tasks to promote preservice teachers’ professional eye

The Mathematics Teacher Education Collective (MTEC) — a self-study group based at the University of British Columbia, Canada — collaborates to enhance our pedagogical practice in mathematics teacher education through analysing, constructing, and reflecting on variations to assessment tasks. The theoretical framework underlying the establishment of the MTEC is based on Lave and Wenger’s (1991) view of learning through a Community of Practice (CoP). “Communities of practice are groups of people who share a concern or a passion for something they do and learn how to do it better as they interact regularly” (Wenger-Trayner, 2011, http://wenger-trayner.com/theory/). Three characteristics are viewed as crucial to the CoP: domain, community, and practice. The shared domain for MTEC is a commitment to gaining a deeper understanding of practice as mathematics teacher educators. In particular, as members we are interested in better understanding the role and development of tasks for learning to teach mathematics. As a community MTEC engages “in joint activities and discussions, [that] help each other, and share information” (Wenger-Trayner, 2011, http://wenger-trayner.com/theory/), with the goal to build relationships that provide members with opportunities to learn from one other. MTEC members are practitioners in the field. The success of the MTEC is based on the sharing, evaluation and critical reflection of assessment tasks and pedagogical approaches refined by the CoP.

Assessment in tertiary mathematics

There is a growing consensus among many educators that the goals of teaching and learning mathematics are to help students solve real-life problems, participate intelligently in daily affairs, and prepare them for jobs (Gardiner, 1994; Roeber, 1995). These goals suggest that the role of routine procedural skills should be diminished while more emphasis ought to be placed on learners gaining conceptual insights and analytical skills that appear essential in real-life mathematical problem solving (Schoenfeld, 1993; Stenmark, 1989).

An instrument for assessing primary students’ knowledge of information graphics in mathematics

Information graphics have become increasingly important in representing, organising and analysing information in a technological age. In classroom contexts, information graphics are typically associated with graphs, maps and number lines. However, all students need to become competent with the broad range of graphics that they will encounter in mathematical situations. This paper provides a rationale for creating a test to measure students’ knowledge of graphics. This instrument can be used in mass testing and individual (in-depth) situations. Our analysis of the utility of this instrument informs policy and practice. The results provide an appreciation of the relative difficulty of different information graphics; and provide the capacity to benchmark information about students’ knowledge of graphics. The implications for practice include the need to support the development of students’ knowledge of graphics, the existence of gender differences, the role of cross-curriculum applications in learning about graphics, and the need to explicate the links among graphics.

A framework for mathematics graphical tasks : The influence of the graphic element on student sense making

Graphical tasks have become a prominent aspect of mathematics assessment. From a conceptual stance, the purpose of this study was to better understand the composition of graphical tasks commonly used to assess students’ mathematics understandings. Through an iterative design, the investigation described the sense making of 11–12-year-olds as they decoded mathematics tasks which contained a graphic. An ongoing analysis of two phases of data collection was undertaken as we analysed the extent to which various elements of text, graphics, and symbols influenced student sense making. Specifically, the study outlined the changed behaviour (and performance) of the participants as they solved graphical tasks that had been modified with respect to these elements. We propose a theoretical framework for understanding the composition of a graphical task and identify three specific elements which are dependently and independently related to each other, namely: the graphic; the text; and the symbols. Results indicated that although changes to the graphical tasks were minimal, a change in student success and understanding was most evident when the graphic element was modified. Implications include the need for test designers to carefully consider the graphics embedded within mathematics tasks since the elements within graphical tasks greatly influence student understanding.

Assessment of microInductors for DC-DC converters

There are increasing demands on the power density and efficiency of DC-DC power converters due to the soaring functionality and operational longevity required for today's electronic products. In addition, DC-DC converters are required to operate at new elevated frequencies in the MHz frequency regime. Typical ferrite cores, whose useable flux density falls drastically at these frequencies, have to be replaced and a method of producing compact component windings developed. In this study, two types of microinductors, pot-core and solenoid, for DC-DC converter applications have been analyzed for their performance in the MHz frequency range. The inductors were manufactured using an adapted UV-LIGA process and included electrodeposited nickel-iron and the commercial alloy Vitrovac 6025 as core materials. Using a vibrating sample magnetometer (VSM) and a Hewlett Packard 4192A LF- impedance analyzer, the inductor characteristics such as power density, efficiency, inductance and Q-factor were recorded. Experimental, finite element and analytical results were used to assess the suitability of the magnetic materials and component geometries for low MHz operation.

Assessment of a robust opportunistic routing for video transmission in dynamic topologies

Mobile multimedia ad hoc services run on dynamic topologies due to node mobility or failures and wireless channel impairments. A robust routing service must adapt to topology changes with the aim of recovering or maintaining the video quality level and reducing the impact of the user's experience. In those scenarios, beacon-less Opportunistic Routing (OR) increases the robustness by supporting routing decisions in a completely distributed manner based on protocol-specific characteristics. However, the existing beacon-less OR approaches do not efficiently combine multiple metrics for forwarding selection, which cause higher packet loss rate, and consequently reduce the video quality level. In this paper, we assess the robustness and reliability of our recently developed OR protocol under node failures, called cross-layer Link quality and Geographical-aware OR protocol (LinGO). Simulation results show that LinGO achieves multimedia dissemination with QoE support and robustness in scenarios with dynamic topologies.

Assessment of Collimator Jaw Optimization in Reducing Normal Tissue Irradiation with Intensity Modulated Radiation Therapy

Purpose: To evaluate normal tissue dose reduction in step-and-shoot intensity-modulated radiation therapy (IMRT) on the Varian 2100 platform by tracking the multileaf collimator (MLC) apertures with the accelerator jaws. Methods: Clinical radiation treatment plans for 10 thoracic, 3 pediatric and 3 head and neck patients were converted to plans with the jaws tracking each segment’s MLC apertures. Each segment was then renormalized to account for the change in collimator scatter to obtain target coverage within 1% of that in the original plan. The new plans were compared to the original plans in a commercial radiation treatment planning system (TPS). Reduction in normal tissue dose was evaluated in the new plan by using the parameters V5, V10, and V20 in the cumulative dose-volume histogram for the following structures: total lung minus GTV (gross target volume), heart, esophagus, spinal cord, liver, parotids, and brainstem. In order to validate the accuracy of our beam model, MLC transmission measurements were made and compared to those predicted by the TPS. Results: The greatest change between the original plan and new plan occurred at lower dose levels. The reduction in V20 was never more than 6.3% and was typically less than 1% for all patients. The reduction in V5 was 16.7% maximum and was typically less than 3% for all patients. The variation in normal tissue dose reduction was not predictable, and we found no clear parameters that indicated which patients would benefit most from jaw tracking. Our TPS model of MLC transmission agreed with measurements with absolute transmission differences of less than 0.1 % and thus uncertainties in the model did not contribute significantly to the uncertainty in the dose determination. Conclusion: The amount of dose reduction achieved by collimating the jaws around each MLC aperture in step-and-shoot IMRT does not appear to be clinically significant.