This article reports on a post hoc study using a randomised controlled trial with 31,842 students in the Netherlands and an instrument consisting of 21 paired problems. The trial showed a variability in the differences of students’ results in solving contextual mathematical problems with either a descriptive or a depictive representation of the problem situation. In this study the relation between this variability and two task characteristics is investigated: (1) complexity of the task representation; and (2) the content domain of the task. We found indications that differences in performance on descriptive and depictive representations of the problem situation are related to the content domain of the problems. One of the tentative conclusions is that for depicted problems in the domain of measurement and geometry the inferential step from representation of the problem situation to the mathematical problem to be solved is smaller than for word problems.
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This paper reports on an experiment comparing students’ results on image-rich numeracy problems and on equivalent word problems. Given the well reported problematic nature of word problems, the hypothesis is that students score better on image-rich numeracy problems than on comparable word problems. To test the hypothesis a randomized controlled trial was conducted with 31,842 students from primary, secondary, and vocational education. The trial consisted of 21 numeracy problems in two versions: word problems and image-rich problems. The hypothesis was confirmed for the problems used in this experiment. With the insights gained we intend to improve the assessment of students’ abilities in solving quantitative problems from daily life. Numeracy, word problem, image-rich problem, randomized controlled trial, assessment
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The aim of this study is to contribute to the body of knowledge on the use of contextual mathematical problems. Word problems are a predominant genre in mathematics classrooms in assessing students’ ability to solve problems from everyday life. Research on word problems, however, reveals a range of difficulties in their use in mathematics education. In our research we took an alternative approach: we designed image-rich numeracy problems as alternatives for word problems. A set of word problems was modified by systematically replacing the descriptive representation of the problem situation by a more depictive representation and an instrument was designed to measure the effect of this modification on students’ performance. The instrument can measure the effect of this alternative approach in a randomized controlled trial. In order to use the instrument at scale, we made this instrument also usable as a diagnostic test for an upcoming nationwide examination on numeracy. In this article we explain and discuss the design of the instrument and the validation of its intended uses.
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Early detection of reading problems is important to prevent an enduring lag in reading skills. We studied the relationship between speed of word recognition (after six months of grade 1 education) and four kindergarten pre-literacy skills: letter knowledge, phonological awareness and naming speed for both digits and letters. Our sample consisted of 178 pupils divided over seven classes. In agreement with the literature, we found that all four kindergarten tests were related to speed of word recognition in grade 1. We also performed a multiple regression analysis with a set of background variables and the four kindergarten tests. The model explained 53% of the variance in speed of word recognition. However, only letter knowledge and naming speed for digits had a significant direct effect. Our conclusion is, nevertheless, that all four kindergarten tests should be used to identify children at risk for reading problems.
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This textbook is intended for a basic course in problem solving and program design needed by scientists and engineers using the TI-92. The TI-92 is an extremely powerful problem solving tool that can help you manage complicated problems quickly. We assume no prior knowledge of computers or programming, and for most of its material, high school algebra is sufficient mathematica background. It is advised that you have basic skills in using the TI-92. After the course you will become familiar with many of the programming commands and functions of the TI-92. The connection between good problem solving skills and an effective program design method, is used and applied consistently to most examples and problems in the text. We also introduce many of the programming commands and functions of the TI-92 needed to solve these problems. Each chapter ends with a number of practica problems that require analysis of programs as well as short programming exercises.
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Torpedo is a digital learning environment for developing mathematical problem-solving ability through self-study for pre-service teachers in primary teacher education. To achieve this, Torpedo supports and challenges pre-service teachers’ reflection during and after solving non-routine mathematics problems. To investigate the feasibility of the Torpedo approach, 271 pre-service teachers used Torpedo during one month in a pilot study. They used and evaluated Torpedo’s reflective elements differently. The results varied from pre-service teachers who experienced that reflection really contributed to the development of their problem-solving ability, to pre-service teachers who hardly reflected. The last group consisted of those who found the problems too difficult to reflect upon and those who used Torpedo to prepare for the National Mathematics Test and preferred to do so by drill and practice. As a conclusion, the study provides clues for improving Torpedo so that it invites more reflective self-study behaviour. For pre-service teachers who consider reflection valueless, however, self-study in a digital learning environment may be insufficient to change this attitude.
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Peer discussions play a major role in students’ collaborative problem-solving activity. These discussions provide researchers and teachers with a wealth of information about the students' reasoning. To analyse such discussions, different theoretical lenses are available, such as Schoenfeld’s problem solving model, the Florida Taxonomy of Cognitive Behaviour, and the Scheme for Educational Dialogue Analysis. The question is, however, how these three perspectives can complement each other. To investigate this, the discussion between four students was analysed through the three lenses. Results indicate that these frameworks are both complementary and connected. This connection allows an in-depth analysis of the discussion and reveals possibilities and limitations for an integration of the three models, which will guide future discussions’ analyses in our study.
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The colour-word Stroop task and the picture-word interference task (PWI) have been used extensively to study the functional processes underlying spoken word production. One of the consistent behavioural effects in both tasks is the Stroop-like effect: The reaction time (RT) is longer on incongruent trials than on congruent trials. The effect in the Stroop task is usually linked to word planning, whereas the effect in the PWI task is associated with either word planning or perceptual encoding. To adjudicate between the word planning and perceptual encoding accounts of the effect in PWI, we conducted an EEG experiment consisting of three tasks: a standard colour-word Stroop task (three colours), a standard PWI task (39 pictures), and a Stroop-like version of the PWI task (three pictures). Participants overtly named the colours and pictures while their EEG was recorded. A Stroop-like effect in RTs was observed in all three tasks. ERPs at centro-parietal sensors started to deflect negatively for incongruent relative to congruent stimuli around 350 ms after stimulus onset for the Stroop, Stroop-like PWI, and the Standard PWI tasks: an N400 effect. No early differences were found in the PWI tasks. The onset of the Stroop-like effect at about 350 ms in all three tasks links the effect to word planning rather than perceptual encoding, which has been estimated in the literature to be finished around 200-250 ms after stimulus onset. We conclude that the Stroop-like effect arises during word planning in both Stroop and PWI.
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Publicatie bij de rede van Femke Kaulingfreks, uitgesproken bij de aanvaarding van de functie van lector aan Hogeschool Inholland in Amsterdam op 21 mei 2019.
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This study focuses on revealing and developing personal constructs regarding problem behaviour in classrooms. Twenty-nine teachers (initial and in-service students) took part in the project. The main idea is that teachers opinions about their pupils and themselves influence the way they act in their classrooms. Their thoughts and ideas about students - their personal constructs - are generally unconscious. To clarify and to develop teachers constructs, we used Kellys repertory grid technique and Garmans reflective approach. Both methods give a powerful impulse to the development of thinking and acting of teachers. They can use the experiences as an integral part of their own action research. & I am one of the teachers who took part in the constructs research.A personal set of fifteen constructs on twenty-eight pupils was collected. These constructs showed me what kinds of constructs I have (mainly social-emotional and cognitive ones) and made me reflect. They also made clear to me that I think less positively on problem children. Participation in this research includes coaching, theoretical orientation and continuous reflection, making me conscious of what (problem) behaviour I like or dislike and what I should change to get a professional, holistic view. Then problem behaviour will be more easily tolerated by me and I can teach my colleagues about my new insights in intercommunicative sessions and by personal counselling.
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