The Influence of Interactive Learning Materials on Solving Tasks That Require Different Types of Mathematical Reasoning

Norqvist M., Jonsson B., Lithner J., Qwillbard T., Holm L.

Imitative teaching and learning approaches have been dominating in mathematics education. Although more creative approaches (e.g. problem-based learning) have been proposed and implemented, a main ...

Radović S., Radojičić M., Veljković K., Marić M.

ABSTRACTThe rapid growth in diversity of information and communication technologies (ICT) enables a range of teaching methods, learning support strategies, and education settings to be developed. Q...

Radišić J., Baucal A.

The study explores how teachers perceive and go about students’ thinking in connection to particular mathematical content and how they frame the notion of applied mathematics in their own classrooms. Teachers’ narratives are built around two released PISA 2012 mathematics items, the ‘Drip rate’ and ‘Climbing Mount Fuji’ (will be referred to as the Fuji item). Teachers show concordance as to the reasons that could make either of the items difficult for students and are able to provide more examples justifying their reasoning for the ‘Fuji’ item. Suggestions linked to making the items more familiar to the students mostly relate to de-contextualization of the items’ content towards a more formal mathematical record. The teachers agree that students need only basic mathematical knowledge, at a level learned during elementary school, in order to solve these problems. Yet, at the same time, many teachers have difficulty clearly verbalising which procedures students are expected to follow to be able to solve the tasks. Disagreement among the teachers is noticeable when labelling the most difficult part(s) of each of the selected items. Mathematics teachers show openness for learning on how to create math problems we examined in this study, but question the purpose and meaning in incorporating more such problems in their own teaching.

Pepin B., Choppin J., Ruthven K., Sinclair N.

In this conceptual review paper we draw on recent literature with respect to digital curriculum resources (DCR); we briefly outline and explain selected theoretical frames; and we discuss issues related to the design, and the use (by teachers and students) of digital curricula and e-textbooks in mathematics education. The results of our review show the following. Firstly, whilst there are some contrasting tendencies between research on instructional technology and research on DCR, these studies are at the same time predominantly framed by socio-cultural theories. Secondly, whilst there seems to be a continuing demarcation between the design(er) and the use(r), there is at the same time an emerging/increasing understanding that design continues in use, due to the different nature and affordances of DCR (as compared to traditional text curriculum resources). Thirdly, there is an apparent weakening of traditional demarcations between pedagogy and assessment, and between summative and formative assessment techniques, due to the nature and design of the automated learning systems. Fourthly, there is an increasing need for understanding the expanded space of interaction associated with the shift from static print to dynamic/interactive DCR, a shift that has the potential to support different forms of personalised learning and interaction with resources. Hence, we claim that DCR offer opportunities for change: of understandings concerning the design and use of DCR; of their quality; and of the processes related to teacher/student interactions with DCR—they provide indeed the foundations for change.

Norqvist M.

Studies in mathematics education often point to the necessity for students to engage in more cognitively demanding activities than just solving tasks by applying given solution methods. Previous st ...

Brunner E., Konietschke F., Pauly M., Puri M.L.

Jäder J., Sidenvall J., Sumpter L.

Lithner J.

This paper presents (1a) a research framework for analysing learning difficulties related to rote learning and imitative reasoning, (1b) research insights based on that framework, (2a) a framework for research and design of more efficient learning opportunities through creative reasoning and (2b) some related ongoing research.

Takači D., Stankov G., Milanovic I.

In this paper we present a modern approach of teaching mathematics based on the computer supported collaborative learning (CSCL) of calculus contents. The collaborative learning was used in calculus course at the University of Novi Sad, Serbia, for examining functions and drawing their graphs. In 2012 the authors decided to improve the collaborative learning introducing GeoGebra application. Small four member groups were formed by using Kagan's (1994) principles. Two groups of students, the experimental, and the control one were observed. The students in the experimental group learned with the help of GeoGebra, and the students in the control group learned without using GeoGebra.Comparison between those two groups of the first year calculus students, regarding their way of learning and the results achieved, is described below. Before the students' collaborative learning, they were tested with a pre-test and their knowledge necessary for examining functions was verified. The pre-test showed that there was no significant statistical difference between the experimental and the control group. The experimental group worked with the help of the computer and the control one without it. After the collaborative learning, the students were tested with a test (colloquium) and the results of the experimental group were significantly better than the results of students in the control group. At the end of the course the students did their exams (post-test), and the results of the experimental group were significantly better than the results of students in the control group.Some students from the experimental group had to answer questions in an interview related to the use of GeoGebra during their collaborative learning. In order to see the students' difficulties in solving problems, students in the experimental group were asked to cross out incorrect parts of solutions, not to erase them. The teachers reviewed the students' tasks done during the collaborative learning and after that the students who had corrected their mistakes were invited for an interview about using GeoGebra for overcoming their difficulties. Based on the students' results in the tests, answers in the questionnaire and in the interview, it can be concluded that GeoGebra has enabled an easier learning of this material. The GeoGebra package enables the students to check whether each step in the process of solving a task was correctly done or not. The results of our research show that GeoGebra can help those students having insufficient knowledge (necessary for solving those tasks) to improve it.We can say that our research shows that the students' learning achievement in examining functions and drawing their graphs is better when they use GeoGebra, working in collaborative groups than without using it. Also, GeoGebra enables creation of effective learning environment for examining functions and drawing their graphs. We present an approach of teaching mathematics based on computer supported collaborative learning (CSCL) of calculus contents.We examine how GeoGebra package helps the students' learning in CSCL.We examine the using GeoGebra in CSCL as learning environment.

Granberg C., Olsson J.

The present study investigates how a dynamic software program, GeoGebra, may support students' collaboration and creative reasoning during mathematical problem solving. Thirty-six students between ...

Chiu T.K., Churchill D.

Literature suggests using multimedia learning principles in the design of instructional material. However, these principles may not be sufficient for the design of learning objects for concept learning in mathematics. This paper reports on an experimental study that investigated the effects of an instructional approach, which includes two teaching techniques – (a) variation theory and (b) representations of subject matter – on the design of learning objects for secondary school algebra concept learning. The results of this study showed that the experimental group performed significantly better than the control group on algebra learning achievement. The results also showed that only the experimental design with the addition of the instructional approach resulted in higher-order mathematical thinking skills and improved procedural skills of the students. Further analysis reveals that concept learning was simplified when multimedia learning principles were applied and the information was presented by the ins...

De Witte K., Rogge N.

ICT infrastructure investments in educational institutions have been one of the key priorities of education policy during the last decade. Despite the attention, research on the effectiveness and efficiency of ICT is inconclusive. This is mainly due to small-scale research with weak identification strategies which lack a proper control group. Using the 2011 ‘Trends in International Mathematics and Science Study’ (TIMSS) data, we define by a Mahalanobis matching a control group with similar student, teacher, school and regional characteristics. The results indicate that accounting or not accounting for these characteristics, may considerably alter the estimated impact of ICT. This suggests that a correction for characteristics related to the student population, teaching staff, administrative personnel and school management is warranted in the evaluation of the impact of ICT.

Boesen J., Helenius O., Bergqvist E., Bergqvist T., Lithner J., Palm T., Palmberg B.

This study investigates the impact of a national reform in Sweden introducing mathematical competency goals. Data were gathered through interviews, classroom observations, and online surveys with n ...

Bergqvist T., Lithner J.

This paper presents a study of the opportunities presented to students that allow them to learn different types of mathematical reasoning during teachers’ ordinary task solving presentations. The c ...

Shahbari J.A., Rubel L.H.

Brnic M., Greefrath G., Reinhold F.

AbstractThe integration of dynamic visualisations, feedback formats and digital tools is characteristic of state-of-the-art digital mathematics textbooks. Although there already is evidence that students can benefit from these technology-based features in their learning, the direct comparison between the use of a comparable digital and printed resource has not yet been sufficiently investigated. We address this research gap by contrasting the use of an enriched digital textbook that includes these features and comparable printed materials without them. To do so, we investigate the achievement of 314 students in a pretest-posttest control group design in a five-hour series of lessons on conditional probability. Using the Rasch model and mixed ANOVA, the results indicate that students can benefit from digital textbook features, especially compared to the use of comparable printed materials. In line with other studies on mathematical achievement and the use of digital resources, our study also shows differences between boys and girls. It seems that particularly girls benefit from the use of the digital textbook, whereas, for the boys, it does not seem to make a difference what kind of resources they use. The group and gender differences are discussed against the background of other studies considering that, especially in Bayesian situations, the way statistical situations are visualised can be decisive for a student’s performance.

Huang H., Tang X., Zhang Y., Sun Y., Zhang X., Salmela-Aro K.

The Covid-19 Pandemic has affected school learning broadly, and particularly for students from low socioeconomic status families. The present study aimed to quantify the heterogeneous learning loss in mathematical learning due to the pandemic, and more importantly, to understand whether parents' involvement or adolescents' aspiration is more responsible for the learning gap. Using the Propensity Score Matching method, 678 adolescents aged 10–15 in China were selected from the 2016 and 2020 China Family Panel Study database (339 for each year) and controlled for demographic variables, educational aspirations, family socioeconomic status (SES) and parental involvement. The results showed that during the pandemic, (1) learning loss in mathematical reasoning skill was about 12 % among Chinese adolescents, and the loss was more significant for low SES adolescents (20 %) than high SES adolescents (8 %); and (2) adolescents' educational aspiration directly mediated the association between SES and mathematical reasoning skill, whereas parents' involvement in academics only had an indirect effect through aspiration. Findings implies that facilitating adolescents' educational aspiration can be a more effective strategy to buffer the pandemic-induced mathematics learning loss. Thus, parents, especially those from low SES families, are advised to facilitate adolescents' aspiration than simply involving in adolescents' learning.

Yuan Z., Liu J., Deng X., Ding T., Wijaya T.T.

Dynamic mathematics software, such as GeoGebra, is one of the most important teaching and learning media. This kind of software can help teachers teach mathematics, especially geometry, at the elementary school level. However, the use of dynamic mathematics software of elementary school teachers is still very limited so far. This study analyzed the factors influencing elementary school teachers’ usage behavior of dynamic mathematics software. Four independent variables, namely performance expectancy (PE), effort expectancy (EE), social influence (SI), and facilitating conditions (FC) from the united theory of acceptance and use of technology (UTAUT), were used to understand elementary school teachers’ usage behavior of dynamic mathematics software. A questionnaire survey was conducted in the Hunan and Guangdong provinces of China. Two hundred and sixty-six elementary school mathematics teachers provided valid questionnaire data. The partial least squares structural equation modeling (PLS-SEM) approach was used to analyze the data. The results showed that facilitating conditions and effort expectancy significantly affect elementary school teachers’ usage behavior of dynamic mathematics software, and facilitating conditions were the biggest factor that affected user behavior. The moderating effects of gender, major, and training on all relationships in the dynamic mathematics software usage conceptual model were not significant. This study contributes by developing a model and providing new knowledge to elementary school principals and the government about factors that can increase the adoption of dynamic mathematics software.