Promoting basic arithmetic competence in early school years–using a response to intervention model

This study investigated whether mathematics education based on a multi-tiered response to intervention (RTI) model can support students' arithmetic competence in primary schools in Sweden. The intent was to identify and support students at risk of failure. In this study, 113 students participated in the intervention, and 30 students participated in the control group. Both groups were followed from Grade 1 to the end of Grade 2 and compared. During the first semester in Grade 1, all students were taught basic addition and subtraction with explicit instructions in Tier 1. Those who did not respond to Tier 1 after one semester were provided support within Tier 2 during the second semester. The same was repeated in grade 2 and the students that did not respond to Tier 2 were supported within Tier 3. At the end of Grade 2, students in the intervention group performed significantly higher on the basic arithmetic competence in the number range 1–9 than the control group. No significant difference was found in a test measuring basic arithmetic competence in the number range 10–19. This study shows that using multi-tiered RTI might be sufficient to identify and support students at risk in early arithmetic competence.     

Learning statistics with interactive pictures using R Shiny: Generally preferred,but not generally advantageous

Constructing interactive web apps has become more accessible for instructors, for example, by using the R package Shiny. Here we explored learners' preferences and the efficiency of interactive simulations versus static pictures in acquiring statistics knowledge of Cohen's d and standard normal distribution. Results revealed that students' spontaneous interaction with pictures was infrequent (pilot study, N = 26). While prompts (Exp. 1, N = 152) effectively ensured the manipulation of simulations, student exposure to interactive simulations led to longer learning times though similar test performance compared with student exposure to static pictures. Multiple interactive representations led to lower test performance than single interactive and static representations (Exp. 2, N = 117). Though no advantage was gained regarding learning outcomes, participants preferred the interactive variant (Exp. 3, N = 119). Taken together, this study demonstrates that the superiority of interactive pictures cannot be assumed to hold in general. Further work should evaluate how mental model construction can be effectively scaffolded by interactive simulations.     

Inclusive practice within the lived cultures of school communities: research case studies in teaching,learning and inclusion

This paper provides an account of a teacher's use of theory as a tool to develop inclusive practice through a social studies programme in a new entrant class. The account illustrates the ways in which the teacher drew on research to assist in the facilitation of an inclusive educational environment. Presented are research case studies the teacher encountered in an in-service teacher education programme, and the ‘social constructionist’ and ‘personal tragedy’ models that were used as theoretical tools to assist the teacher's planning and teaching practice. Mounted cameras, broadcast microphones and pre- and post-unit interviews with the teacher and students were used to explore the lived culture of the classroom, and the nature and effectiveness of the strategies the teacher used. An ‘interrupted narrative’ methodology engages the reader in the interplay between research and theory in the research case studies. Four major strategies used by the teacher have been identified and these are presented as theoretical tools for other teachers and teacher educators to use, critique and develop to support inclusive practice in their own contexts.     

Not Read,but Nevertheless Solved? Three Experiments on PIRLS Multiple Choice Reading Comprehension Test Items

Multiple-choice (MC) reading comprehension test items comprise three components: text passage, questions about the text, and MC answers. The construct validity of this format has been repeatedly criticized. In three between-subjects experiments, fourth graders (N ₁ = 230, N ₂ = 340, N ₃ = 194) worked on three versions of MC items from the Progress in International Reading Literacy Study 2001 reading comprehension test with relevant components successively deleted: “original version” (text, questions, MC-answers), “version without text” (questions, MC-answers), “version without text and without questions” (only MC-answers). Answering correctly the MC items became more difficult as the relevant information was eliminated. In the two narrative fictional texts presented, the students' performance of the version without text was not better than chance. Conversely in the informational (fictional) text, the students' performance of the version without text was better than chance. In the third condition, students' performance was never better than chance.     

Diagnosing Teachers’ Understandings of Rational Numbers: Building a Multidimensional Test Within the Diagnostic Classification Framework

We report a multidimensional test that examines middle grades teachers’ understanding of fraction arithmetic, especially multiplication and division. The test is based on four attributes identified through an analysis of the extensive mathematics education research literature on teachers’ and students’ reasoning in this content area. We administered the test to a national sample of 990 in‐service middle grades teachers and analyzed the item responses using the log‐linear cognitive diagnosis model. We report the diagnostic quality of the test at the item level, mastery classifications for teachers, and attribute relationships. Our results demonstrate that, when a test is grounded in research on cognition and is designed to be multidimensional from the onset, it is possible to use diagnostic classification models to detect distinct patterns of attribute mastery.     

Following Young Students’ Understanding of Three Phenomena in which Transformations of Matter Occur

In order to develop successful teaching approaches to transformations of matter, we need to know more about how young students develop an understanding of these processes. In this longitudinal study, we followed 25 students from 7 to 13 years of age in their reasoning about transformations of matter. The questions addressed included how the students’ understanding of transformations of matter changed and how we can make sense of individual learning pathways. In interviews performed once or twice every year the students described and explained three situations: fading leaves left on the ground, a burning candle, and a glass of water covered with a glass plate on which some mist had formed. When analysing the interviews, we found a common pathway of how the students’ ideas changed over the years in each one of the situations. When analysing individual student’s interviews with Ausubel’s assimilation theory we could discern subordinate, superordinate and combinatorial learning. How these findings can contribute to an improvement of teaching about transformations of matter is discussed.