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An Introduction To Discourse Analysis Theory And Method

Our paper is an analytical review of the design, development and reporting of learning progressions and teaching sequences. Research questions are: (1) what criteria are being used to propose a ‘hypothetical learning progression/trajectory’ and (2) what measurements/evidence are being used to empirically define and refine a ‘hypothetical learning progression/trajectory’? Publications from five topic areas are examined: teaching sequences, teaching experiments, didaktiks, learning trajectories in mathematics education and learning progressions in science education. The reviewed publications are drawn from journal special issues, conference reports and monographs. The review is coordinated around four frameworks of Learning Progressions (LP): conceptual domain, disciplinary practices, assessment/measurement and theoretical/guiding conceptions. Our findings and analyses show there is a distinction between the preferred learning pathways that focus on ‘Evolutionary LP’ models and the less preferred but potent...

Learning progressions and teaching sequences: a review and analysis

Assessments, understood as tools for tracking what and how well students have learned, play a critical role in the classroom Developing Assessments for the Next Generation Science Standards develops an approach to science assessment to meet the vision of science education for the future as it has been elaborated in A Framework for K-12 Science Education (Framework) and Next Generation Science Standards (NGSS) These documents are brand new and the changes they call for are barely under way, but the new assessments will be needed as soon as states and districts begin the process of implementing the NGSS and changing their approach to science education The new Framework and the NGSS are designed to guide educators in significantly altering the way K-12 science is taught The Framework is aimed at making science education more closely resemble the way scientists actually work and think, and making instruction reflect research on learning that demonstrates the importance of building coherent understandings over time It structures science education around three dimensions - the practices through which scientists and engineers do their work, the key crosscutting concepts that cut across disciplines, and the core ideas of the disciplines - and argues that they should be interwoven in every aspect of science education, building in sophistication as students progress through grades K-12 Developing Assessments for the Next Generation Science Standards recommends strategies for developing assessments that yield valid measures of student proficiency in science as described in the new Framework This report reviews recent and current work in science assessment to determine which aspects of the Framework's vision can be assessed with available techniques and what additional research and development will be needed to support an assessment system that fully meets that vision The report offers a systems approach to science assessment, in which a range of assessment strategies are designed to answer different kinds of questions with appropriate degrees of specificity and provide results that complement one another Developing Assessments for the Next Generation Science Standards makes the case that a science assessment system that meets the Framework's vision should consist of assessments designed to support classroom instruction, assessments designed to monitor science learning on a broader scale, and indicators designed to track opportunity to learn New standards for science education make clear that new modes of assessment designed to measure the integrated learning they promote are essential The recommendations of this report will be key to making sure that the dramatic changes in curriculum and instruction signaled by Framework and the NGSS reduce inequities in science education and raise the level of science education for all students

Developing Assessments for the Next Generation Science Standards.

Science educators increasingly seek to support students’ participation in scientific practices, particularly epistemic practices, that is, those that ground authority for knowing in the discipline. Argumentation is one practice that has received significant attention in the research literature. However, scholars who take a sociocultural stance increasingly suggest that current conceptualizations are not sufficient for characterizing and supporting important aspects of scientific practice. In this article, I explore how students’ argumentation can be brought into closer alignment with that of scientists. I identify consequential differences in the contexts in which scientists and students typically enact argumentation and discuss how these differences have been addressed in the literature. Finally, I propose several directions for further research: embedding argumentation in uncertain scientific activity, supporting students to contest both what they know and their means of knowing, building more carefully...

Representing Student Argumentation as Functionally Emergent From Scientific Activity

For the past 15 years, pre-university students in many countries including the United States have encountered data analysis and probability as separate, mostly independent strands. Classroom-based research suggests, however, that some of the difficulties students have in learning basic skills in Exploratory Data Analysis stem from a lack of rudimentary ideas in probability. We describe a recent project that is developing materials to support middle-school students in coming to see the “data in chance” and the “chance in data.” Instruction focuses on four main ideas: model fit, distribution, signal-noise, and the Law of Large Numbers. Central to our approach is a new modeling and simulation capability that we are building into a future version of the data-analysis software TinkerPlots. We describe three classroom-tested probability investigations that employ an iterative model-fit process in which students evaluate successive theories by collecting and analyzing data. As distribution features become a focal point of students’ explorations, signal and noise components of data become visible as variation around an “expected” distribution in repeated samples. An important part of students’ learning experience, and one enhanced through visual aspects of TinkerPlots, is becoming able to see things in data they were previously unable to see.

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Reconnecting Data and Chance

New capabilities in TinkerPlots 2.0 supported the conceptual development of fifth- and sixth-grade students as they pursued several weeks of instruction that emphasized data modeling. The instruction highlighted links between data analysis, chance, and modeling in the context of describing and explaining the distributions of measures that result from repeatedly measuring multiple objects (i.e., the height of the school’s flagpole, a teacher’s head circumference, the arm-span of a peer). We describe the variety of data representations, statistics, and models that students invented and how these inscriptions were grounded both in their personal experience as measurers and in the affordances of TinkerPlots, which assisted them in quantifying what they could readily display with the computer tool. By inventing statistics, students explored the relation between qualities of distribution and methods for expressing these qualities as a quantity. Attention to different aspects of distribution resulted in the invention of different statistics. Variable invention invited attention to the qualities of “good” measures (statistics), thus meshing conceptual and procedural knowledge. Students used chance simulations, built into TinkerPlots, to generate models that explained variability in a sample of measurements as a composition of true value and chance error. Error was, in turn, decomposed into a variety of sources and associated magnitudes—a form of analysis of variance for children. The dynamic notations of TinkerPlots altered the conceptual landscape of modeling, placing simulation and world on more equal footing, as first suggested by Kaput (Journal of Mathematical Behavior, 17(2), 265–281, 1998).

Supporting the Development of Conceptions of Statistics by Engaging Students in Measuring and Modeling Variability

Although variability and structure are often considered as antonyms in many everyday settings, a mathematically disciplined view contradicts this opposition. To initiate fifth- (10 years old) and sixth-grade (11 years old) students in this disciplinary view, we engaged students in practices of modeling data. These practices included inventing and revising data displays, inventing and revising measures of centre and variability, and inventing and revising models of chance to account for variability. Here we focus on prospective correspondences between students’ invented measures (statistics) of variability and those favoured by the discipline. We suggest that inventing measures positions students to transform their vision of variability from mere difference to more structured forms, some of which coordinate centre and spread. By tracing interactions among an inventor, her classmates, and the teacher, we trace how structuring variability and constituting its measure cooriginated during the course of negotiations about the meaning of the measure. Consideration of the coherency, transparency and generalisability of a statistic, all of which are valued by the discipline of statistics, emerged during the course of invention.

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Structuring variability by negotiating its measure

Students often learn procedures for measuring, but rarely do they grapple with the foundational conceptual problem of generating and validating coordination between a measure and the phenomenon being measured. Coordinating measures with phenomenon involves developing an appreciation of the objects and relations in each as well as establishing their mutual correspondence. We supported students’ developing conceptions of statistics by positioning them to design measures of center and of variability for distributions that they had generated through repeated measure of a length. After students invented and explored the viability of their measures individually, they participated in a public (whole-class conversation) forum featuring justification and reflection about the viability of their designed measures. We illustrate how individual invention enticed students to attend to, and to make explicit, characteristics of distribution not initially noticed or known only tacitly. Conceptions of statistics and of relevant characteristics of distribution were further expanded as students justified and argued about the utility and prospective generalization of particular inventions. Teachers supported student learning by highlighting prospective relations between characteristics of measures and characteristics of distribution as they emerged during the course of activity in each setting.

Developing conceptions of statistics by designing measures of distribution

This article compares students' critiques within a class discussion about an invented statistic to STEM professionals' critiques from interviews to better understand how the situated meanings of a statistic are similar and different across student and professional worlds. We discuss similarities and differences in how participants constructed meaning for the statistic, and argue that disciplinary practices in schooling will always have an approximate, and somewhat indeterminate, relation to the figured worlds of professional practice.

Min-Joung Kim

Papers

Supporting the Development of Conceptions of Statistics by Engaging Students in Measuring and Modeling Variability

Structuring variability by negotiating its measure

Developing conceptions of statistics by designing measures of distribution

Critiquing Statistics in Student and Professional Worlds