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In the contextual field of environmental composition in kindergarten, transforming it into a space for cognitive, social, emotional, i.e., holistic formation and development of the child, multimodality operates with authenticity, magnetism, multilevelity, multidimensionality, and dynamism to overcome schematicity and linearity of thinking, thus stimulating imagination. Leading the way is the understanding that the environmental composing of multimodality in kindergarten is the foundation of quality for the child’s cognitive, affective, sensory cognition and self-knowledge. This paper outlines the parameters of evaluating multimodal digital resources designed by students preparing for future kindergarten teachers. The starting points for their expertise in the relations of autonomy, coherence, justification, adequacy and authenticity as subjectively significant and objective wholes of multimodal composing are argued. Criteria and indicators for the expert evaluation of digital resources for multimodal environmental composing in kindergarten, as modeling and provoking and enriching the individual sensory experience of the child, as an opportunity to stimulate cognitive and personal activity are derived. It is necessary to conclude that through the design of multimodal digital resources, the existing contradictions in the starting conditions of the pedagogical interaction in the kindergarten will be overcome. The main recommendation points to the need for specific training of future children’s teachers for multimodal environmental composition of educational practices in kindergarten, synergizing different modalities, rather than their linear sequential environmental combination.

IntroductionThis article analyses parents' and children's attitudes toward the different literacy practices across three different contexts (at home, in a community project, and, indirectly, at school) and how they perceive the interaction between these practices and the development of competences in the Heritage Language (HL). We investigate the relevance of family and community, and how mainstream school influences the co-construction of literacy practices that affect the development of HL, while at the same time supporting the development of the majority language, and especially in broadening the understanding of the notion of language exposure.MethodsSemi structured interviews with parents and focus groups with children (aged 4–14) were carried out in Munich, Germany, between May 2018 and February 2020. Data from the verbal interactions, in a total of 12 h of recorded audio with the parents and 8h with the children, was transcribed and the excerpts were coded in Nvivo. In a first moment, a data and theory driven thematic analysis with open data coding was undertaken; subsequently, discourse analysis was used to analyze selected excerpts individually and reconstruct the meaning the participants were attaching to their literacy practices. Three thematic strands were identified.ResultsWe make the case that exposure to literacy practices in the majority language is interpreted and (re)appropriated by families and communities to support the development of complex and integrated literacy practices involving the different languages of children's repertoires. We shed light on how families construct bilingual input safe spaces at home, i.e., spaces where continuities between formal, informal and non-formal literacy practices in both German and Portuguese are assured.DiscussionThe results bring a critical perspective on the ecology of literacy practices and highlight the added value of seeing those practices interconnected holistically from a co-developmental viewpoint. Such interconnectedness has a potential positive impact not only in children's HL but also in the majority language, and possibly in the languages learnt at school.

The increasingly digital and multicultural 21st-century society requires future teachers to be prepared for the changes and challenges they may encounter. Not only language and digital competences, but critical-thinking and problem-solving skills are needed. Moreover, well developed socio-affective abilities, empathy among them, are also key when dealing with others. This is even more relevant when teachers are to work with a non-mainstream population, such as adult migrants with low literacy levels, and to design student-centered curricula or activities. Empathy is a multifaceted process involving, among others, perception, intellection, affect and other sensory aspects of the lived experience. It has been argued that the first-person perspective-taking involved in empathic engagement must necessarily involve rational computation and cognitively mediated processing. Training future teachers in the Pedagogy of Multiliteracies is a means to integrate multimodal digital instruction and aggregate cognitive as well as socio-emotional features to the education of future language teachers.MethodA mixed-method pre-post study was conducted with 48 trainee teachers who participated in stand-alone digital multiliteracy interventions, in which they were encouraged to envisage themselves as future teachers of low-literate migrants. Policy documents such as the reference guide on Literacy and Second Language Learning for the Linguistic Integration of Adult Migrants, journal articles, audiovisual resources as well as examples of existing educational materials aimed at the target audience, were made available to them on an online platform. In two separate studies, trainees were encouraged to collaboratively produce two different multimodal outputs. The Revised Scale of Ethnocultural Empathy was administered before and after the intervention, subjecting the data obtained to quantitative analysis. Qualitative data was also collected to gain a better understanding of the affective and cognitive processes experienced by the participants.ResultsSimple statistical analysis coupled with the comparison of means was used to respond to the research questions. Statistical hypothesis testing, including correlations and non-parametric statistics were used to analyze the relationship between each of the factors within the RSEE and the participants, considering the different interventions applied. Non-parametric tests (U-Mann Whitney) were used to compare the differences between the levels of ethnocultural empathy of the participants in the two studies. Significant differences were found in Factor 3 (Empathy) and Factor 5 (Anxiety) between the groups and their post-intervention results, with a p value of 0.053 and 0.038, respectively. The effect size r was calculated, obtaining a size effect of 0.625 for Factor 3 (Empathy) and 0.674 for Factor 5 (Anxiety). These results indicate that the significant differences and the size effect between both groups are large. U-Mann Whitney non-parametric analysis also revealed gender differences in Factor 3 (Empathy), showing females higher levels than males. Effect size r analysis showed a large size effect of 0.708 for Factor 3 (Empathy). The findings pertaining to gender-related differences in empathy levels confirm the conclusions drawn by previous studies. When contrasting study 1 and 2, statistical differences were also shown after the intervention for the ‘Anxiety and Lack of Multicultural Self-efficacy’ factor. The qualitative data analysis was carried out with Atlas.ti v.8, in order to isolate and categorize the broader themes and the most significant explanatory quotes extracted from the participants’ records and interviews. The results reveal the learning strategies that each group of learners applied to successfully complete the task at hand, as well as the participants’ deployment of their critical thinking skills and the awakening of a sense of awareness of their own professional competence development process.ConclusionThis study set out to compare how effective two digital multiliteracy interventions were in developing future language teachers’ ethnocultural empathy and cognitive abilities when appraising the educational needs of low-literacy migrants. Despite the small sample size, the study certainly adds to our understanding of the impact of multimodal tasks involving critical thinking skills on trainees’ cognitive and affective abilities. Besides, it expands the growing body of research that points to the desirability of embedding digitally-based content creation tasks in training curricula for future language teachers.

Рассматривается практика применения метода «исследование в действии» (action research) при решении исследовательских задач. На основании истории появления и развития метода «исследование в действии», анализа примеров его использования в научных трудах сформировано описание метода, а также принципы его применения, которыми можно руководствоваться при проведении педагогического исследования. Метод получил широкое распространение в англоязычных исследованиях, как и феномен мультиграмотности, однако поиск среди множества научных источников в открытых ресурсах показал, что он редко применяется в контексте отечественных педагогических исследований. Обосновывается использование метода «исследование в действии» при изучении феномена мультиграмотности как интегративной личной характеристики, необходимой для взаимодействия с текстами новой природы. С помощью применения представленного метода описаны умения мультиграмотного человека, формируемые при освоении соответствующего онлайн-курса. Изучение практики освоения мультиграмотности как нового для русскоязычного педагогического дискурса феномена было дополнено актуальными данными, получено наиболее полное представление обо всех этапах его реализации. Описанный в статье этап диссертационного исследования позволил решить одну из поставленных в нем задач. Автор приводит не только преимущества применения метода «исследование в действии», но и риски, которые могут возникнуть. Применение данного метода позволяет произвести анализ практических действий, ведущих к формированию научных положений педагогического исследования и внести вклад в методологию педагогики.

This study aimed to analyze the Arabic book for the 10th grade of Madrasah Aliyah, published by the Ministry of Religious Affairs of the Republic of Indonesia in 2020, based on the multiliteracy concept. The primary data source in this study is a 10th-grade Arabic textbook, whereas the secondary data is literature on the subject themes. The data analysis technique employs content analysis. The results reflect the context, which frequently refers to the situational context. The At Ta'am wa Sharāb chapter explores a natural science theme. The multimedia element includes both text and visual media. As for audio for listening learning, it is not yet in all chapters. As for the multicultural aspect, most of them contained Indonesian culture. There is one theme that contained Arab culture and one that contains American culture. Based on the analysis results, Arabic books are not optimal in containing the concept of multiliteracy.

The distribution of disinformation in online environments poses an increasing risk for pupils to be confronted with manipulated content. As a pedagogical strategy for schools, phenomenon-based learning (PhBL) is said to train a variety of required digital competences. This article aims to describe PhBL as practical teaching intervention to address disinformation in secondary schools. PhBL is a cross-curricular and subject-unspecific teaching intervention with a suggested duration of 8-12 teaching lessons and an appropriate age starting from 12/13 years. This investigation included that teacher organized project-oriented activities. The evaluation comprised semi-structured interviews with pupils (n=36) and their teachers (n=8) as well as video-based classroom observations in six classes with 107 pupils. The findings indicate that this teaching approach supported pupils to compare information sources, evaluate credibility indicators, and act criticaly as online consumers. After the intervention pupils said that they felt more sceptical of online and social media information.

This paper presents tools which can be used to measure multimodal literacy and metasemiotic awareness in students. The results are interesting within the context of multiliteracy development both in terms of the individual student over time or in comparison to other students within a specific course, as well as when comparing data from larger cohorts for example differences in level or orientation of education, age, regional, territorial, national and so on to see patterns or strengths and weaknesses in multimodal literacy within a wider perspective.

The ongoing pandemic has significantly transformed the educational landscape, necessitating the design of curricula that seamlessly integrate innovative technologies and pedagogies to support students in a multimodal world. As a result, teacher-training programs must prioritize the development of pedagogical and technological skills for new educators. This investigation explored the utilization of computer-based technology (CBT) by pre-service teachers during classroom instruction and its integration for promoting multiliteracy in science education. The study connected CBT applications to Gardner's multiple intelligences theory and employed the Multiliteracy Pedagogy framework to analyze the technology used, adhering to the 7Es instructional model. Employing case study research and observation methodologies, the study assessed pre-service science teachers' demonstrations.The findings revealed that pre-service science teachers incorporated CBTs into their instruction, addressing various intelligences. Examples of CBTs included digital interactive whiteboards, virtual laboratories, video sharing websites, presentation software, and online quiz platforms. Although these tools accommodated diverse learners, the integration of CBTs into contextualized and localized approaches remained limited. Consequently, the results highlight the necessity for systematic strategies that enable pre-service teachers to effectively incorporate CBTs into various learning experiences. Such approaches facilitate a smooth transition from training to professional practice and promote the consistent use of technology at all levels of education

This study investigated the influence of multiliteracy in opaque orthographies on phonological awareness. Using a visual rhyme judgement task in English, we assessed phonological processing in three multilingual and multiliterate populations who were distinguished by the transparency of the orthographies they can read in (N = 135; ages 18–40). The first group consisted of 45 multilinguals literate in English and a transparent Latin orthography like Malay; the second group consisted of 45 multilinguals literate in English and transparent orthographies like Malay and Arabic; and the third group consisted of 45 multilinguals literate in English, transparent orthographies, and Mandarin Chinese, an opaque orthography. Results showed that all groups had poorer performance in the two opaque conditions: rhyming pairs with different orthographic endings and non-rhyming pairs with similar orthographic endings, with the latter posing the greatest difficulty. Subjects whose languages consisted of half or more opaque orthographies performed significantly better than subjects who knew more transparent orthographies than opaque orthographies. The findings are consistent with past studies that used the visual rhyme judgement paradigm and suggest that literacy experience acquired over time relating to orthographic transparency may influence performance on phonological awareness tasks.

Today's educators should be well-aware of the world of the 21st century; a world that is characterised by a constant technological advancement, a fierce economic competition, a diversified digital village at the end of a fingertip, and unforeseen pandemics and crises. Teachers need to develop innovative methods to allow their learners to successfully cope with the requirements of the 21st century. At present, students are digitally-oriented in need of skills and competencies that empower them to smoothly understand and critically engage in dialogue with the world they live and work in. A vivid incarnation of the principles of multiliteracy approach is the edited book entitled Films, Graphic Novels and Visuals: Developing Multiliteracies in Foreign Language Education- An Interdisciplinary Approach by Daniela Elsner, Sissy Helff and Britta Viebrock.

This article emerged from my study of three alternative-certification teachers, or teacher learners as they tried to enact culturally responsive practices while navigating their first year of teaching and taking graduate courses for initial certification. These teacher learners worked to develop their understanding and capacities to enact a culturally responsive pedagogy but found that standardization of content and conceptions of what constitutes “good students”, appropriate classroom conduct, and micro-managed professional learning communities all created environments hostile to their attempts to develop as equity-minded educators and culturally responsive practitioners. However, their experiences changed once the COVID-19 pandemic closed these teacher learners’ schools to in-person instruction and sent them home to instruct online for the remainder of the spring 2020 semester. Free from the constrictive macro-structures and socio-political contexts in their physical workplaces, their planning showed them employing more culturally responsive practices and considering those practices more deeply. Once outside the cultures of practice, formed around neoliberal conceptions of success and measuring learning, these teacher learners became the sole mediators of the conflicting knowledge sources of their jobs and their university methods courses. On their own they began to confront the ways educational institutions stubbornly cling to hegemonic concepts of their communities and valorize work centered on concepts of knowledge and ways of knowing that bear little resemblance to society’s current reality. Away from the wider cultures of their schools during the COVID-19 lockdown and aided in mediating their own development using a dialogically structured lesson planning template inspired by—the Heuristic for Thinking About Culturally Responsive Teaching (HiTCRiT)—the teacher learners focused their instruction on their students making both their students’ learning and their own conceptions of CRP more real and their students’ learning more equitable.

This article introduces a flexible and adaptable Map Composition assignment to promote cartographic literacy. With applications to composition and writing across the curriculum, this assignment promotes students’ awareness of the rhetorical nature of maps, which is important as maps inform and influence public discourse on wide-ranging issues. Student work shows how composing a map can lead them toward improved rhetorical awareness, cartographic literacy, and engagement with place-based civic issues. The article acknowledges limitations of teaching maps in writing classes and concludes with discussion of how this assignment can be adapted to a range of courses to promote cartographic literacy in support of broader literacies and civic engagement.

The researchers used a duo-ethnographic approach to examine mathematics and science teacher-candidates (TCs) experiences with a Multiliteracies Across the Curriculum course during the pandemic and how the shift to online delivery impacted their attitudes. Through one researcher’s course reflections and students’ anonymous course survey comments in 2020, the research revealed that some TCs lack of exposure to literacy-based teaching impacted their literacy identities and initial resistance to the course. However, the shift to online learning, increased course relevance, exposure to diverse online methodologies and multiliterate tools seemed to have positively impacted mathematics and science TCs attitudes toward Multiliteracies Across the Curriculum compared to previous years.

Competence-based education is a widely implemented educational approach, but more research is needed into the relationship between transversal competences and individual disciplines. In this article, we present the results of a study focusing on how the transversal competence of multiliteracy is contextually defined in Finnish local curricula in the disciplines of mathematics and social studies. The article offers new insights into the discussion between content- and competence-based educations by introducing the concept of disciplinary contextualisation. Based on the qualitatively analysed data, four different types of disciplinary contextualisation are presented and further discussed. The study also engages with the discussion in the field of multiliteracy by offering insights into the ways in which multiliteracy is rationalised, defined, and developed in the analysed disciplines. Multiliteracy contextualisations share features, but also differences, between the disciplines, illustrating the importance of taking into account the disciplinary perspective when discussing the development of competences in basic education.

The article aims to discuss about how to teach make up for the beginner through an organized event. The researcher explains about step by step to make a great event such as AISMAWARI. The research is descriptive qualitative. The researcher describes the study briefly. The researcher posts and analizes, and explains the pictures briefly from pre-event, the main event, and the post event. The research reveals the phenomenon that collaboration is needed to make a big events. It also collaborates with a hundred of make up artists, a hundred of designers, and a hundred of models. It involves many supporters. It is held at Atrium Istana Plaza Bandung, in Pasir Kaliki Street no. 121-123. The due date is March 8th, 2019. It related to the primary education pedagogy. It is because the researcher tries to teach the beginner although it is covered by multiliteracy and multiagendas in a big events. The goal is to ask the participants or beginners to think in higher level. The researcher wants to educate the beginner not only to hear the material, but also do the action. As it is believed, practices make perfect.

In this article, we present a case study of digital making as an example for constructing social participation around multiliteracy learning in Finnish early years settings. Digital making is explored and evaluated through the practices and experiences from workshops conducted with four- to five-year-old children in one day care centre in the Helsinki metropolitan area in Finland. Reflections scrutinize children’s social interaction with digital technologies and aim to examine shared meaning-making in the design process. We explain how innovative technologies mediate and enable social interaction and what leads children to either collaborate or work individually while making meaning digitally. Our study indicates that although social participation can be intentionally achieved by children themselves, early childhood education and care (ECEC) professionals and pedagogical practices play a pivotal role, especially when the cultural tools used in learning are new and unfamiliar to children, in this case tablet computers and smartphones.

The objective of the research was to promote a new model of designing activities in the lesson plan of English teachers. The model was derived from the phases of the Multiliteracy pedagogical Framework. It was qualitative research with documentation techniques for collecting data. The source of data was the document of lesson plans made by teachers of English. The data was statements on teaching-learning activities in the lesson plans. The author identified the lesson plan of teachers from Al Islam senior high school in Krian, Sidoarjo. The activities statements were categorized using the four phases and cognitive process of the Multiliteracy Framework; Situated Practice (Experiencing), Overt Instruction (Conceptualizing), Critical Framing (Analysis), and Transformed Practice (Applying) promoted by Cope and Kalantzis with New London Group in 1996. The result showed that the teachers just included two phases; Situated Practice (Experiencing) and Overt Instruction (Conceptualizing), no Overt Instruction (Conceptualizing), Critical Framing (Analysis), and Transformed Practice (Applying) yet in their teaching-learning activities. The teachers should change the old phases in their lesson plan with the four phases of the framework to guide them in applying multiliteracy in English language teaching. The next researcher could focus on teachers’ knowledge or belief about the multiliteracy framework to assure the implementation

Through the description of two (notably different) research programs dedicated to the inclusion of Oceanian languages in New Caledonia’s diglossic context, the aim of this paper is to study the processes and implications of co-development when it comes to building knowledge. This comparison raises and enlightens many epistemological and ethical questions. We believe action research in education should be built as in cooperative approach gathering teachers in training, practicing teachers and researchers from various disciplinary fields. However, the relationship between research teams and teachers is still fragile (Nusbaum, 2008: 127). In addition, research implies an act of power as it constructs social realities and legitimizes them through scientific popularisation (Heller 2002) sometimes without everyone’s consent. Action research that integrates interventions seems more efficient to us on both ethical values and the construction of knowledge.

The need to improve English proficiency and inclusion of social media in language teaching have resulted in teachers having to develop new teaching strategies incorporating digital tools. In South Africa, English teachers in township settings have to develop teaching strategies suitable for teaching English using social media platforms, especially in resource-constrained secondary schools. From literature and education policies, teaching of digital literacy is strongly recommended, but teachers in some township environments are not pedagogically capacitated to teach and use social media in teaching English. To explore the experiences of such teachers, this study explored the use of social media for the teaching of English as a second language in township schools. The study used an interpretivist qualitative approach in an exploratory case-study design to understand teachers’ initiatives and strategies in teaching English as a second language using social media. Data collection was done using semi-structured interviews with open-ended questions and document analysis. Teachers’ voices, actions and documents on the use of social media were analysed inductively and thematically. The research findings indicate that the sampled English teachers used social media for collaboration, networking, communication and out-of-school digital literacy practices as their initiatives. These digital initiatives lead to the utilisation of digital connection platforms for socialisation and teaching and learning English. In addition to dividends of connectivism, visual communication and cyber linguistics were found to have become critically important practices for learners learning English as a second language. The implication is that the education policy-makers and planners in South Africa need to revisit the policy on e-learning and Information Communication Technology (ICT) usage in schools to incorporate the methodological requirements and competences for teachers to use in the teaching of English using social media. In addition to improvements in policy measures, English teachers in resource-constrained township secondary schools need to improve their digital literacy skills to line up themselves for online and out-of-school literacy learning requirements.

As digital communication has been challenging traditional monomodality, and as tourist offer has been increasing over the last decades, the language of tourist promotion in the Web has progressively been evolving into a multilayered and multiliteracy model, bridging verbal and visual language in a new semiotic integration code, which includes impactful, highly persuasive mass and multimedia products, such as tourist promotion websites. As a consequence, LSP students are nowadays confronted with increasingly complex semiotic artefacts. The pedagogical significance of multimodal analysis to the work/practice of learners/teachers of LSP, tourism discourse and Web communication thus comes into focus. This paper addresses the mixed-media strategies constructing the LEGOLAND theme park website as a recreational destination on the Web as a significant case study for multiliteracy communication. Drawing from the metafunctions (i.e., ideational, interactional, textual) of Systemic Functional Grammar, from socio-semiotic multiliteracy analysis, and from multimodal genre analysis of tourism and communication discourse, the paper will investigate the textual/visual strategies through which audience engagement is created in the LEGOLAND website. In particular, at the ideational level, the paper will analyse the key role played by the representation of informative meanings in the website’s promotional purposes; at the interactional level, the metadiscursive strategies maximizing audience involvement will be investigated; and at the textual level, the thematic structure and Information Unit patterning of the LEGOLAND website will be explored, in order to examine the specialzed meaning-making resources which should be made accessible to tourism and communication discourse learners.

The purpose of this study is to build a trisila character (reciprocal, compassionate, caring) in order to strengthen heterogeneity through multiliteracy-based multicultural education. The method used in this study is a literature review. The results of this study can be concluded that multiliteracy-based multicultural education is education that is oriented towards building heterogeneity through four multicultural approaches and five multicultural dimensions combined with multiliteracy learning. Multiliteracy learning will be a tool for the success of multicultural education with its progressive character in utilizing students' potential and environmental conditions. So that the Trisilas character (Reciprocation of Asah, Reparation of Asih, Reparation of Asuh) which is a national character that will strengthen heterogeneity will grow and develop within each student.

The aim of this paperis to analyse video as an instrument of motivation in the foreign language class, considering that motivation is very important in language learning. The hypothesis is that video enhances students’ motivation in the classroom. The research is qualitative and the theoretical framework is based on John Keller’s ARCS model, on Kress e van Leeuwen’s Visual Grammar and on the concepts of multiliteracy of The New London Group. In order to collect the data, the following methodology was used: in the first moment, the students watched a video from YouTube; and in the second moment, they produced their own video and posted it on YouTube. The data analysis showed that the use of video enhances students’ motivation in foreign language learning.

Educational policy is an emerging area of the interdisciplinary research in educational science. This article is focused on a specific topic related to competence pedagogy and includes a critical analysis of the relationships among concepts and their definitions. The aim of the article is to present a literature reviews of what has been publishing by UNESCO and European Commission related to educational policy in order the prove the hierarchy of educational policies. The main objectives of the article are to convey to the reader what ideas have been established on the topic of educational policy and what their strengths and weaknesses are. The research issue: What is an educational policy in European context? is solved through a synthesis of a set of summaries of what is and what is not known in the interdisciplinary area of educational policy. The controversies rely on reality and norms of competence pedagogy.

Finnish basic education faces a significant change with the 2016 commissioning of the renewed core curriculum, which introduces a new transversal competence, termed multiliteracies—a concept closely related to media literacy. This systematic literature review examines the research literature on media literacy and multiliteracies, analysing and comparing the nature of knowledge constructed and the varying definitions of the two concepts. Previous review articles (Marten 2010; Potter 2010) found little consensus among scholars regarding the definition of media literacy. This review examines the research literature published in international peer-reviewed academic journals between 2010 and 2014 to investigate whether a mutual understanding of the concept has since been established. The article argues that significant differences exist between the concepts of media literacy and multiliteracies and, further, that Finnish core curriculum defines multiliteracies differently than the research literature defines the term. In line with previous research, this article finds no consensus on the definition of media literacy in the research literature. Based on the multifaceted nature of the concept, this article rejects attempts to establish a universal definition of media literacy and presents a theoretical framework for conceptualising media literacies based on their abstraction levels. The article aims to facilitate understanding of the concept and its operationalisation in research and practice and discusses future opportunities for research on media literacy and multiliteracies.

The purpose of this study is to present a multimodal languaging model for mathematics education. The model consists of mathematical symbolic language, a pictorial language, and a natural language. By applying this model, the objective was to study how 4th grade pupils (N = 21) understand the concept of division. The data was collected over six hours of teaching sessions, during which the pupils expressed their mathematical thinking mainly by writing and drawing. Their productions, as well as questionnaire after the process, were analyzed qualitatively. The results show that, in expressing the mathematical problem in verbal form, most of the students saw it as a division into parts. It was evident from the pupils’ texts and drawings that the mathematical expression of subtraction could be interpreted in three different ways. It was found that the pupils enjoyed using writing in the solution of word problems, and it is suggested that the use of different modes in expressing mathematical thinking may both strengthen the learning of mathematical concepts and support the evaluation of learning.