Adding interactive graphic organizers to a whole-class slideshow lesson

This study examines the effects of including interactive graphic organizers into a whole-class PowerPoint lesson as an instructional approach intended to improve student engagement and generative learning in schools. A software application was developed and integrated into PowerPoint that makes it possible for the instructor to fill in empty graphic organizers during PowerPoint projection mode. The participants were 152 fourth-grade students selected from three schools that were grouped in four classrooms. Each classroom was divided in two groups—graphic organizer and content-based. The graphic organizer group was taught using an 11-slide PowerPoint presentation on a social study topic that included two empty graphic organizers plus two additional slides explaining how to make a comparison. The content-based group was taught using the same presentation but without these additional slides plus a set of questions students had to answer as a class activity. The lessons were recorded and the verbal statements between instructor and students examined using the Flanders Interaction Analysis System. Results indicated significant differences in how instructors and students interacted in each group, including more questions asked by teachers (d?=?1.99) and more students participating in the classroom discussion in the graphic organizer group (d?=?1.76). Learning outcomes showed that the graphic organizer group outperformed the content-based group on a memory test (d?=?.45) and a comprehension test (d?=?.44). These results encourage the use of graphic organizers as an instructional approach, and are consistent with a generative theory of learning.     

Using graphic organizers to attain relational knowledge from expository text

Many students with learning disabilities (LD) experience difficulties with extracting relationships from expository text, especially if they are implicit. Results from studies with K-12 participants have been inconclusive regarding the potency of the graphic organizer (GO) as a comprehension tool. This study attempted to address some of the concerns with GO research by examining the effects of using GOs with middle school students with LD to convey and cue relational knowledge, using a longer intervention and using written essays to assess the students' attainment of relational knowledge. The results lend support for using GOs with students with LD to gain relational knowledge from expository textbooks. When factual knowledge was assessed via multiple choice tests and quizzes, no differences were found between treatment and control conditions. As in other GO studies, both groups demonstrated attainment of facts and concepts. But when relational knowledge was assessed, the two groups responded differentially. On essays that required application, the GO group provided significantly more relational knowledge statements than students in the No GO group did.     

Students’ understanding of the number line / Estudiantes pensando en la recta numérica

We studied the conceptions of students coming from secondary education and university regarding the number line as a representation of real numbers. In the context of a wider questionnaire, 307 students were presented with a task consisting of two verbal items and one graphic item related to the number line. The students were all at different levels in their study of mathematics (in the third, fourth or fifth year of secondary education, or at the beginning or advanced stage of a university degree in mathematics, biology or physical education). A gradient in the depth of the students’ conceptions, associated with the level of their studies in mathematics, was found. This gradient extends from the estrangement of facing the problem or a conception of a drawn or physical matter line, which was associated with students with a lower level of mathematical studies, passing through a vision centred around potential numeric density or a line containing points (discrete), up to an instrumental conception of the line as supportive of magnitudes in advanced students of biology and focusing on continuity sustained by advanced students of mathematics.     

Photo-elicitation: reflexivity on method,analysis, and graphic portraits

In this methodological discussion, the authors detail and reflect on the processes of using photo-elicitation interviewing as a way to align with positive qualitative methodologies, to gain access to participant beliefs and values, and to highlight participant voices through their choices of words and visuals. A review of the literature and an overview of the educational research experiences leading to the discussion are included. Next, the discoveries regarding what is methodologically new and/or valuable concerning this visual method is presented. In the final section, the authors reflexively contemplate aspects of visual methodological processes in an effort to address methodological crossroads of potential and tension including: (1) the potential of decontextualized photos, (2) photos as metaphors of meaning, (3) photos as representations of inherent meaning, (4) participant empowerment, and (5) graphic representation or graphic portraits.     

ITEM-RACE INTERACTION ON A TEST OF SCHOLASTIC APTITUDE1

Several samples of black and white students were drawn from the 1970 PSAT administration in Georgia and studied for item x race interaction on both the verbal and mathematical sections of the test. When subsamples of candidates were drawn from their respective racial groups, matched on mathematical for the study of verbal items and matched on verbal for the study of mathematical items, there was an observable decrease in the size of the item x race interaction, suggesting that one factor contributing to that interaction was simply the difference in performance levels on the test shown by the two races. Further analyses demonstrated a moderate item x group interaction for blacks native to different cities and a moderate item x group interaction for blacks native to areas of different population density.     

Implementing Confidence Assessment in Low-Stakes,Formative Mathematics Assessments

Confidence assessment (CA) involves students stating alongside each of their answers a confidence rating (e.g. 0 low to 10 high) to express how certain they are that their answer is correct. Each student’s score is calculated as the sum of the confidence ratings on the items that they answered correctly, minus the sum of the confidence ratings on the items that they answered incorrectly; this scoring system is designed to incentivize students to give truthful confidence ratings. Previous research found that secondary-school mathematics students readily understood the negative-marking feature of a CA instrument used during one lesson, and that they were generally positive about the CA approach. This paper reports on a quasi-experimental trial of CA in four secondary-school mathematics lessons (N = 475 students) across time periods ranging from 3 weeks up to one academic year, compared to business-as-usual controls. A meta-analysis of the effect sizes across the four schools gave an aggregated Cohen’s d of –0.02 [95% CI –0.22, 0.19] and an overall Bayes Factor B₀₁ of 8.48. This indicated substantial evidence for the null hypothesis that there was no difference between the attainment gains of the intervention group and the control group, relative to the alternative hypothesis that the gains were different. I conclude that incorporating confidence assessment into low-stakes classroom mathematics formative assessments does not appear to be detrimental to students’ attainment, and I suggest reasons why a clear positive outcome was not obtained.

     

Mathematical Modeling in the Elementary Grades: Developing and Testing an Assessment

Mathematical modeling is a high-leverage topic, critical for college and career readiness, participation in STEM education, and civic engagement. Mathematical modeling involves connecting real-world situations, phenomenon, and/or data with mathematical models, and in this way applies across various STEM disciplines, including mathematics, engineering, and science. Although research has begun to explore mathematical modeling instruction in the elementary grades, questions remain about how to assess student learning at the elementary level. We addressed this need by designing an assessment of mathematical modeling competencies for students in grades 3 through 5. Informed by international research, our assessment includes a hybrid structure to assess mathematical modeling competencies holistically (as students engage in the complete modeling process) and atomistically (as students engage in different components of the modeling process, including making sense of phenomena and real-world situations, setting up and operating on mathematical models, and interpreting results in relation to the real-world context). We conducted student interviews, followed by two rounds of pilot testing to inform item development and ensure acceptable psychometric properties. The final assessment included 13 items (9 multiple choice, 3 open-response, and 1 complete modeling task). We describe our assessment development process, and provide sample assessment items and detailed coding rubrics. We summarize quantitative analyses which established high reliability and low standard error for our assessment, supporting its use for grades 3 to 5. Implications of our framework and assessment for mathematical modeling instruction and future research on STEM learning are discussed.

     

Can the English Baccalaureate act as an educational equaliser?

ABSTRACT

Ensuring equal access to a broad and balanced curriculum for all students is a key component of a socially just education system. Yet in England, the freedom that 16-year-old students have to choose the GCSE subjects they study has created divisions in the pathways taken by students from different backgrounds. In 2010, a new accountability measure, the English Baccalaureate (EBacc), was introduced to encourage more disadvantaged students to study the ‘core academic’ GCSE subjects. This paper investigates the success of this initiative by analysing the relationship between free school meal (FSM) eligibility, studying the EBacc subjects and GCSE attainment. The findings are used to illustrate the complexities of balancing equal access to academic subjects against fair access to future opportunities, which often depend on good grades, when trying to deliver social justice in an education system that has an entrenched attainment gap.     

Second Graders Learn Animal Adaptations through Form and Function Analogy Object Boxes

This study examined the use of form and function analogy object boxes to teach second graders (n = 21) animal adaptations. The study used a pretest–posttest design to examine animal adaptation content learned through focused analogy activities as compared with reading and Internet searches for information about adaptations of animals followed by making an informative puppet play. Students participated in six week‐long lesson sets, each addressing adaptations of two animals, which alternated between the two conditions. In the analogy condition, students matched cards explaining form and function analogies of animal body parts or homes to analogous manufactured items. They mapped analogies, thought of alternate manufactured items, and created new analogies. Students scored similarly on material to be taught through both conditions on the pretest, but made significantly higher posttest mean scores (76.1% analogy versus 57.2% traditional condition) with large effect size (partial η² = 0.58) on animal adaptation content learned through the analogy activities. This study shows the usefulness of form and function analogies in teaching product innovations to second‐grade students, indicating that early childhood students are able to successfully engage in sophisticated analogy activities. Efficacy of the analogy activities was related to objects that focused attention, motivated, and gave concrete representations of concepts; to cards and graphic organizers for organization, connections, and memory; and to complex thinking activities that challenged students and promoted peer interaction.     

Building a versatile understanding of algebraic variables with a graphic calculator

Algebra has been recognised for some time as a difficult topic for many secondary school students. Discovering the best way(s) of introducing algebra into the students' experience and fostering understanding has stimulated much discussion and research. It is our belief that an understanding of the concept of variable is fundamental to further student progress in algebra. This paper describes a study using a module of work based on a graphic calculator which provided an environment where students could experience some aspects of variables and hence begin to build an understanding of them. The graphic calculator proved to be an instrument for achieving a significant improvement in student understanding, something which has often proved difficult previously.This revised version was published online in September 2005 with corrections to the Cover Date.     

The effectiveness of graphic organizers for three classifications of secondary students in content area classes.

Previous research concerning the graphic or visual display of information with academically handicapped students has not addressed the instructional conditions that exist in mainstream settings. This article investigates the effectiveness of graphic organizers for three classifications of secondary students enrolled in content area classes: students with learning disabilities, remedial students, and students in regular education. The results of three separate experiments indicated that graphic organizers, whether teacher-directed, student-directed with text references, or student-directed with clues, produced significantly higher performance than self-study for each group of students. Several practical issues involving the use of graphic organizers with heterogeneous groups of secondary students are discussed.     

Using Confirmatory Factor Analysis and the Rasch Model to Assess Measurement Invariance in a High Stakes Reading Assessment

The psychometric properties and multigroup measurement invariance of scores across subgroups, items, and persons on the Reading for Meaning items from the Georgia Criterion Referenced Competency Test (CRCT) were assessed in a sample of 778 seventh-grade students. Specifically, we sought to determine the extent to which score-based inferences on a high stakes state assessment hold across several subgroups within the population of students. To that end, both confirmatory factor analysis (CFA) and Rasch (1980 Rasch, G. 1980. Probabilistic models for some intelligence and attainment tests, Chicago: The University of Chicago Press (Original work published 1960).  [Google Scholar]) models were used to assess measurement invariance. Results revealed a unidimensional construct with factorial-level measurement invariance across disability status (students with and without specific learning disabilities), but not across test accommodations (resource guide, read-aloud, and standard administrations). Item-level analysis using the Rasch Model also revealed minimal differential item functioning across disability status, but not accommodation status.     

Teaching functions in a graphic milieu: What forms of knowledge enable students to conjecture and prove?

In many countries, the first concepts of calculus (such as functions)are taught by looking at examples, noticing their properties and generalizing from them in some implicit ways. Students have no means to discuss the general truth of a statement, or to examine the validity of a theorem, relative to the mathematical field. This knowledge is nonetheless required by teachers at the university level. The question is, therefore, if it is possible to organize activities for beginning calculus students, which would nevertheless lead them to working on statements and validity of theorems. This paper presents a teaching approach related to the concept of function, which aimed at leading students working within a graphic milieu to producing, discussing and testing the validity of mathematical statements and theorems. The intention of the approach was to use the procedural aspect of the graphs to provide a favorable milieu for linking the intuitive and the formal knowledge(such as required at the university for establishing proofs). The approach was experimented with a group of students. After the experiment, the students indeed became able to think of functions as objects and to engage with questions of validity of mathematical statements.This revised version was published online in October 2005 with corrections to the Cover Date.     

Using Graph Talks to Engage Undergraduates in Conversations Around Social Justice

Abstract

We present a mathematical activity called graph talks as a new pedagogical routine to intertwine social justice issues and mathematics. Adapted from number talks, graph talks involve students analyzing, interpreting, and discussing real-life data represented in graphs. Graphs may be strategically selected to both highlight a relevant social justice issue while also reinforcing the mathematics content of the course. We report on experiences using graph talks in undergraduate mathematics content courses for future teachers in the USA, and provide examples of the undergraduates doing mathematics while analyzing the social justice context of the graphs.     

Factors Causing Failure in Teaching

Abstract

This study was undertaken to examine two fundamental questions related to the use of graphic organizer instruction with fifth-grade, normal-achieving students: (a) Does graphic organizer instruction facilitate comprehension, recall, and transfer of information contained in an expository textbook? and (b) To what degree is explicit instruction necessary for independent generation and use of graphic organizers by students? In four experimental conditions, participants read social studies information with or without the graphic organizer. The conditions were further separated by the presence or absence of explicit instruction. Participants in the control condition received traditional basal instruction, as prescribed by the teacher's manual of the district-adopted textbook. Participants in all groups performed comparably on acquisition and retention measures. However, when required to read and recall novel social studies content, participants receiving the graphic organizer and explicit instruction performed better on the measure of transfer than students who received traditional basal instruction did.     

On mathematics teaching for future engineers—in the digital era

Current changes, especially the wide application of information technology, in all fields of our life, mean that mathematical knowledge becomes necessary in almost every domain. It implies new expectations for mathematical education. An urgent need of a new mathematical literacy for all—also a new mathematical literacy for engineers—is evident. It is necessary to consider a process of mathematics learning at tertiary level from the epistemological perspective and to investigate students’ ways of mathematical thinking. This epistemological knowledge is especially indispensable when students use information technology. In this article current requirements regarding mathematical education are discussed, especially those for future engineers. Analysis of examples of learning elementary statistics, using graphing calculators as supporting tools, leads to the formulation of essential aims for mathematics educators concerning mathematics teaching for future engineers.     

Effects of graphic organizers in online discussions: comparison between instructor-provided and student-generated

The current experimental study examined the effects of graphic organizers in a collaborative learning context where students constructed knowledge during online discussions. As the results could vary depending on how students interacted with the graphic organizers, this study compared two different approaches: instructor-provided versus student-generated graphic organizers. Thus, the purpose of this study was to investigate the effects of receiving or generating graphic organizers on students’ engagement in online discussions. Thirty-six graduate students enrolled in an online graduate course participated in the study. While analyzing an instructional design case, students were asked to discuss design issues in a randomly assigned group. There were three conditions: control condition without graphic organizers, instructor-provided, and student-generated graphic organizers. Major findings revealed that both generating and receiving graphic organizers facilitated students’ higher levels of cognitive engagement, and encouraged students to consider alternative views during the discussions. Without the graphic organizer, students tended to simply summarize previous messages or raise new issues rather than elaborating on previous topics. There was a significant finding regarding the ways of interacting graphic organizers. Students discussed more topics when they were given instructor’s graphic organizers rather than when they were asked to generate them.     

Science career aspiration and science capital in China and UK: a comparative study using PISA data

ABSTRACT

The concept of science capital has a growing influence in science education research for understanding young people’s science trajectories. Popularised in the UK, this paper aims to extend and evaluate the applicability of science capital in the context of China by drawing on PISA2015. More specifically, we make use of existing items in the PISA2015 survey as a proxy for operationalising the construct of science capital to explore the science career aspirations and attainments of 15-year-old Chinese and UK students (n?=?23,998). Our findings indicate that science capital has more explanatory power for understanding UK students’ science career aspirations than for Chinese students, where science attainment seems most important. We raise the potential challenge for Chinese students to convert their science capital into scientific self-efficacy and science career aspirations as we highlight the importance of recognising cultural and national differences in operationalising science capital.     

On the Road to Graphicacy: The learning of graphical representation systems

This article examines the learning of different types of graphic information by subjects with different levels of education and knowledge of the content represented. Three levels of graphic information learning were distinguished (explicit, implicit, and conceptual information processing) and two experiments were conducted, looking at graph and geographical map learning. The graph study (Experiment 1) examined the influence of the variables' numerical relationship structure on adolescent students with different levels of education and knowledge of social sciences and also assessed their proportional reasoning skills. The map study (Experiment 2) looked at the learning of a geographical map studied spontaneously by secondary school and university students with different geographical knowledge (experts and novices) and also assessed their spatial skills. The results of both studies show that graph and map learning performance improves with the subjects' educational level. The groups' differential performance varied according to the type of information involved (explicit, implicit, or conceptual). The subjects' knowledge of the domain in question determined the level at which they processed the information. Verbal and superficial processing of graphic information were also found to predominate. This has important educational implications, suggesting the need for differential treatment in teaching different types of information. The results of the study also raise interesting issues regarding the type of expertise involved in learning graphic information: expertise related to the content represented, to knowledge of the syntax (graphicacy), and/or the system of knowledge graphically represented – spatial in the case of maps, numerical in the case of graphs.     

The effects of resilience in learning variables on mathematical literacy performance: a study of learning characteristics of the academic resilient and advantaged low achievers in Shanghai,Singapore, Hong Kong,Taiwan and Korea

Abstract

Many students from disadvantaged homes participating in Programme for International Student Assessment (PISA) 2012 were classified as academic resilient (called disadvantaged high achiever, the DHA in this study). In comparison with peers of comparable home background status, there were also students from advantaged homes performing far behind standard in mathematical literacy performance (called advantaged low achiever, the ALA). Drawing data from the PISA 2012, this study sought to examine the similarities and differences in learning mathematics characteristics (ie gender, family and academic background, and resilience in learning variables) amongst students of the top five high-performing Asian economies, ie Shanghai, Singapore, Hong Kong, Taiwan and Korea. The results of the logistic regression analyses showed that variables like family and academic background, as well as resilience in learning mathematics variables (eg familiarity with mathematical concept, mathematics self-efficacy, mathematics self-concept and mathematics anxiety) are able to predict whether a student of comparable disadvantaged (or advantaged) home background is more likely to be classified as DHA (or ALA) or not. The findings are important to shed light on the principles and methods of mathematics education so as to help the low achievers, whether advantaged or disadvantaged, to advance to higher level of mathematical literacy attainment.