A teaching experiment to foster the conceptual understanding of multiplication based on children's literature to facilitate dialogic learning

The importance of conceptual understanding as opposed to low-level procedural knowledge in mathematics has been well documented (Hiebert & Carpenter, 1992). Development of conceptual understanding of multiplication is fostered when students recognise the equal group structure that is common in all multiplicative problems (Mulligan & Mitchelmore, 1996). This paper reports on the theoretical development of a transformative teaching experiment based on conjecture-driven research design (Confrey & Lachance, 1999) that aims to enhance Year 3 students’ conceptual understanding of multiplication. The teaching experiment employs children’s literature as a motivational catalyst and mediational tool for students to explore and engage in multiplication activities and dialogue. The SOLO taxonomy (Biggs & Collis, 1989) is used to both frame the novel teaching and learning activities, as well as assess the level of students’ conceptual understanding of multiplication as displayed in the products derived from the experiment. Further, student’s group interactions will be analysed in order to investigate the social processes that may contribute positively to learning

Education students' views on the integration of ICT into their undergraduate learning experiences

It is well understood that university graduates, regardless of discipline, must have appropriate information and communication technology (ICT) competencies to function and be employable in the modern world. Universities have been encouraged to develop action plans for ICT literacy and to introduce means of auditing ICT literacy levels of students. In addition, education graduates have had additional responsibility to develop ICT competencies to support student learning. The extent to which this is actually being achieved is less well understood. This paper reports on the second phase of a research project to audit the ICT experiences of teacher education undergraduates. The first phase collected survey data that explored the students' competence with ICT applications and their confidence with ICT integration in their teaching pedagogy, and is reported elsewhere. This paper reports on interviews with students to provide in-depth understanding of their ICT experiences as undergraduates. It supports survey findings that considerable difference exists between individual experiences within and between programs depending on course selection, study plans and personal inclination. It also raises serious questions about the capacity of many graduates to undertake ICT aspects of their profession without extensive and immediate further professional development. The paper concludes by exploring how some of this variance can be addressed to ensure that graduates are more ICT capable

Upper primary students, intelligence and technology: An investigation of interventions designed to develop students' creativity and domain-specific intellectual abilities

The major goal of this study was the creation of two unique intervention programs for upper primary students, based around the National Profile and Statement (Curriculum Corporation, 1994a, 1994b) for the Key Learning Area (KLA) of Technology. The intervention programs comprised discrete units or projects, each of which ran for a full school term, and each of which thematically integrated the other seven KLAs. Both intervention programs were identical in content and implementation techniques, with the exception that the second program aimed to seamlessly integrate classroom computer resources with the curriculum units of work. The two intervention programs, called Program Only (PO) and Program+ Computers (P+C), were implemented for a period of one school year and their effectiveness in facilitating positive student learning products and processes was assessed using mixed-method procedures. This thesis views the KLA Technology as basically an intellectually creative problem solving process which can be applied in a range of culturally valued domains. Thus, this study proposed that it is imperative that intervention programs dealing with Technology be strongly linked to the accumulated psychological research into intelligence and intellectual development, in order to provide the programs with a sound theoretical basis for development, implementation and assessment. Therefore, the literature pertaining to intelligence and intellectual development was reviewed, and a theoretically sound conceptual model of intelligent functioning within the classroom context was proposed. Further, the relationship between intelligence and other valued human capacities such as creativity, problem solving and metacognition were also examined. The conceptual model used in this study contained three major dimensions: Learning Context, Learning Processes and Learning Products. It was largely based on the work of Gardner (1993a) and Biggs & Moore (1993). The interventions, based on this model, endeavoured to develop students' creativity and domain-specific intellectual abilities, through use of the problem solving heuristic Investigate (I), Design (D), Make (M) and Evaluate (E). The definition of intelligence, that was used in this study, is that intelligence is a unique set of proclivities, which afford the individual the capacity to solve problems, or to create novel products, valuable in the specific cultural setting in which they were created. Intelligence was therefore viewed as a pluralistic cognitive construct (Gardner, 1993a). Further, this research took a distributed view of intelligence, whereby it was assumed that an individual's intelligence is composed of both in-the-head and out-of-the-head elements. An individual's creative output can be perceived therefore, as the mirror through which to view their intellectual ability in specific domains. Nine research questions were asked pertaining to the effectiveness of the interventions to positively impact upon learning process and product components of the conceptual model. Eleven measurement instruments and/or procedures were utilised to answer the questions and accept or reject the eight hypotheses that were based on the research questions. The Approach to Learning Inventory (ALI), the Classroom Environment Questionnaire (CEQ) and the Creativity Checklist are new instruments that were designed and psychometrically validated for use in this study. The Upper Primary Classroom Computer Attitude Inventory (UPCCAI) was designed and validated by this researcher in a previous study, and its reliability was confirmed as part of this study. Other instruments include the MICUPS and COSMIC (McGrath & Noble, 1995) and the Self-Concept Questionnaire that was developed from Burnett's research (1994). All of these instruments were psychometrically validated as part of this study. Qualitative data were also collected to triangulate, complement, develop and expand the data collected with the quantitative measures (Greene, Caracelli & Graham, 1989). The qualitative data took the form of teacher Feedback Sheets at the completion of each project/term; teacher interviews at the end of the implementation period; student Process Folios for each project; and student written responses to two questions about their own learning. The study involved 24 upper primary classes in seven schools in Brisbane, Queensland, Australia. Fourteen of the classes from five schools were evenly distributed between the two interventions and the remaining ten classes in two schools acted as a non-intervention control group. The study utilised an Intervention (3) by Time (3) repeated measures MANOVA design to investigate the quantitative impact of the three treatment programs (2 interventions, 1 control). Initially 580 students were pre-tested and 455 completed data sets were collected at the post-test. At the treatment group level, interactions between the groups and time were achieved for both the MICUPS and the COSMIC which measured students' relative intellectual strengths; the Creativity Checklist which measured the students' personal creativity characteristics; and the Upper Primary Classroom Computer Attitude Inventory (UPCCAI), which measured students' attitude to their classroom computers. In fact, the students in the P+C group were perceived by their teachers to have significantly enhanced personal creativity characteristics at the post-test, in contrast to the other two groups. All three groups reported liking their classroom computers less at the end of the trial than they did at the start. However, only minor differences were reported at the .01 level of significance among the three groups with respect to the students' intellectual ability profiles. Further, the results of the teacher interviews and Feedback Sheets indicated that there were differences among the implementation approaches used by the individual teachers within the same intervention program. These difference were more related to teacher and school variables than they were related to the intervention program itself. They also undoubtedly impacted upon the results obtained at the treatment group level of analysis, and required investigation at the class level, hence the unit of analysis was moved to individual classes within the two intervention groups. At the class level, there were interactions between the seven PO classes and time for the COSMIC and the UPCCAI. Interactions between the seven P+C classes and time were reported for the COSMIC, the Creativity Checklist, the Approach to Learning Inventory (ALI), the Self-Concept Questionnaire (S-CQ), and the UPCCAI. It would appear from these results that differences were more apparent among classes within interventions, than they were among the three treatment groups as a whole. Another compounding issue of the study reported here relates to the non-convergent results which were obtained between the quantitative and qualitative data with respect to the students' approach to learning, self-concept and perceptions of their classroom environment. An explanation is provided for this non-convergence in the study's concluding chapter. However, further research will be required in order to establish the reasons for the anomalies obtained in this study's results. Overall, the results obtained in this study indicate that the intervention programs were a wise investment of classroom time, as students achieved positive learning outcomes in a number of areas. Further, the purposeful integration of computer technologies seems to have had a significant impact on the personal creativity characteristics of the students in the P+C group. Generally, the teachers involved in the trial of the intervention programs reported a positive impact on their pedagogical thinking and practices. They felt that the intervention programs were a valuable addition to their classroom curriculum programs and they would not hesitate to use the programs again with other class groups

Integrating concrete and virtual materials in an elementary mathematics classroom : a case study of success with fractions

This paper describes an approach to introducing fraction concepts using generic software tools such as Microsoft Office's PowerPoint to create "virtual" materials for mathematics teaching and learning. This approach replicates existing concrete materials and integrates virtual materials with current non-computer methods of teaching primary students about fractions. The paper reports a case study of a 12-year-old student, Frank, who had an extremely limited understanding of fractions. Frank also lacked motivation for learning mathematics in general and interacted with his peers in a negative way during mathematics lessons. In just one classroom session involving the seamless integration of off-computer and on-computer activities, Frank acquired a basic understanding of simple common equivalent fractions. Further, he was observed as the session progressed to be an enthusiastic learner who offered to share his learning with his peers. The study's "virtual replication" approach for fractions involves the manipulation of concrete materials (folding paper regions) alongside the manipulation of their virtual equivalent (shading screen regions). As researchers have pointed out, the emergence of new technologies does not mean old technologies become redundant. Learning technologies have not replaced print and oral language or basic mathematical understanding. Instead, they are modifying, reshaping, and blending the ways in which humankind speaks, reads, writes, and works mathematically. Constructivist theories of learning and teaching argue that mathematics understanding is developed from concrete to pictorial to abstract and that, ultimately, mathematics learning and teaching is about refinement and expression of ideas and concepts. Therefore, by seamlessly integrating the use of concrete materials and virtual materials generated by computer software applications, an opportunity arises to enhance the teaching and learning value of both materials

Integrating Concrete and Virtual Materials in an Elementary

This paper describes an approach to introducing the concept of fractions using generic software suites such as Microsoft Office to create "virtual" materials to use in Mathematics teaching and learning. This approach replicates currently used concrete materials and integrates virtual materials with current traditional (i.e. non-computer) methods of teaching elementary students about fractions. The paper reports a case study of one student from a Year 7 class (12-13 year olds) who had an extremely limited understanding of fractions and had formed misconceptions that were hindering his mathematical understanding. By integrating on-computer and off-computer activities involving the manipulation of concrete and virtual materials, and by alternating between these two representations of fractions, it was possible for the student to acquire a basic understanding of simple common fractions and to reject his previously held misconceptions in a single session

Measuring the use of information and communication technologies (ICTs) in the classroom

In 2003, the “ICT Curriculum Integration Performance Measurement Instrument” was developed froman extensive review ofthe contemporary international and Australian research pertaining to the definition and measurement of ICT curriculum integration in classrooms (Proctor, Watson, & Finger, 2003). The 45-item instrument that resulted was based on theories and methodologies identified by the literature review. This paper describes psychometric results from a large-scale evaluation of the instrument subsequently conducted, as recommended by Proctor, Watson, and Finger (2003). The resultant 20-item, two-factor instrument, now called “Learning with ICTs: Measuring ICT Use in the Curriculum,” is both statistically and theoretically robust. This paper should be read in association with the original paper published in Computers in the Schools(Proctor, Watson, & Finger, 2003) that described in detail the theoretical framework underpinning the development of the instrument

Measuring cognitive and dispositional characteristics of creativity in elementary students

This article describes the theoretical underpinning and development of a measurement instrument that provides teachers with a tool to observe the personal creativity characteristics of individual students. The instrument was developed by compiling a list of characteristics derived from the literature to be indicative of the personal characteristics of creative people. The list was then reduced by grouping like characteristics to 9 cognitive and dispositional traits that were considered appropriate for elementary students. The 9-item instrument was then administered in 24 classrooms to 520 Year 6 and Year 7 students. Factor analysis using maximum likelihood extraction with an oblimin rotation revealed a single factor with an eigenvalue greater than 1 and accounting for 63% of the variance. All 9 items on this factor loaded at .72 or greater. The results indicated that the Creativity Checklist has very high internal consistency and is a reliable measurement instrument (a = .93)