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It is well known that primary school children may face difficulties in acquiring mathematical competence, possibly because teaching is generally based on formal lessons with little opportunity to exploit more multisensory-based activities within the classroom. To overcome such difficulties, we report here the exemplary design of a novel multisensory learning environment for teaching mathematical concepts based on meaningful inputs from elementary school teachers. First, we developed and administered a questionnaire to 101 teachers asking them to rate based on their experience the learning difficulty for specific arithmetical and geometrical concepts encountered by elementary school children. Additionally, the questionnaire investigated the feasibility to use multisensory information to teach mathematical concepts. Results show that challenging concepts differ depending on children school level, thus providing a guidance to improve teaching strategies and the design of new and emerging learning technologies accordingly. Second, we obtained specific and practical design inputs with workshops involving elementary school teachers and children. Altogether, these findings are used to inform the design of emerging multimodal technological applications, that take advantage not only of vision but also of other sensory modalities. In the present work, we describe in detail one exemplary multisensory environment design based on the questionnaire results and design ideas from the workshops: the Space Shapes game, which exploits visual and haptic/proprioceptive sensory information to support mental rotation, 2D–3D transformation and percentages. Corroborating research evidence in neuroscience and pedagogy, our work presents a functional approach to develop novel multimodal user interfaces to improve education in the classroom.

As content-specific educational coaches, elementary mathematics specialists (EMSs) have emerged as school-based professionals who are needs-driven and work closely with school stakeholders in regard to mathematics teaching and learning. While leading mathematics education organizations have identified the specialized knowledge and skills required for EMS positions, how to best prepare these individuals is knowledge that the field is still exploring. This paper first presents a theoretical model for EMS preparation that aligns an emerging coaching tool, the Decision-Making Protocol for Mathematics Coaching (Baker & Knapp, 2019, [DMPMC]) with the Professional Development Design Framework (Loucks-Horsley et al. in Designing professional development for teachers of science and mathematics, Corwin Press, 2010). The paper then presents a descriptive case study that examines the application of this model in an EMS preparation course. The findings indicate that assessing the coaching situation fostered administrative partnerships, revisiting goals increased specificity of anticipated outcomes, and applying research-informed practices increased EMS self-efficacy and advanced coaching agendas. Taken together, these findings suggest that integrating the DMPMC into an EMS preparation course led to positive changes in EMS candidate learning of professional development design. Notably, this is one of the first studies that documents the influence of a coaching education tool on EMS candidates’ professional development design.

This article reports on a second national survey of higher education institutions in the USA to answer the question “Who teaches mathematics content courses for prospective elementary teachers, and what are these instructors’ academic and teaching backgrounds?” and addresses valuable information not collected with the first survey conducted in 2010. We surveyed 1740 institutions and a faculty member from each of 413 institutions (23.7%) participated in the survey. The survey results demonstrate that the majority of these institutions are not meeting the recommendations of the Conference Board of Mathematical Sciences (2012) and the Association of Mathematics Teacher Educators (2017) for prospective elementary teachers to take at least 12 semester-hour credits of mathematics content designed specifically for them. The data do indicate that there is movement toward more activity-based approaches for these courses as compared to the 2010 survey. Additionally, there is an increase in these courses having instructors with doctorates in mathematics education as well as an increase in instructors having grades 7–12 teaching experience. Most instructors for these courses do not have elementary teaching experience and have likely not had opportunities to think deeply about the important ideas in elementary mathematics. While most institutions still do not provide training and/or support for these instructors, formalized support and training appear to be increasing since the 2010 survey.

Around the globe, young students are expected to learn about time, yet how is it that they themselves make sense of this topic? From a sociocultural perspective, sense-making about time emerges in ...

This multi-case study examines how three elementary mathematics methods instructors, in the same teacher education program, provide their prospective teachers with learning opportunities. Qualitative data were collected through interviews, classroom observations, and artifacts. The findings suggest that the instructors’ beliefs associated with teaching philosophies influence both the content that prospective teachers have the opportunity to learn (what) and the nature of the prospective teachers’ opportunities to learn (how). Through analytic induction, three assertions were developed to understand and explicate: similarities in opportunities to learn, differences in opportunities to learn, and perceptions about the purpose of the methods courses across the three cases. Specifically, the first assertion examines how all three methods instructors focused on developing conceptual understanding and combating mathematical misconceptions for which prospective teachers most often experience opportunities to learn through representations and approximations. The second and third assertions place more emphasis on differences across the cases based upon observed instructor actions and their beliefs. This study is significant because it helps us gain a deeper understanding about prospective teachers’ opportunities to learn within one teacher education program, and therefore, may point toward what can be done in the future to better prepare teachers in elementary mathematics education and the development of ambitious instruction. Additionally, this study unpacks how prospective teachers in the same teacher education program may have varying experiences and thus varied access to opportunities to learn.

This study analysed elementary mathematics specialists’ stories of work to examine how these disciplinary-specific teacher leaders engage in their practice. This paper examines the ways in which el...

Measurement is a critical component of mathematics education, but research on the learning and teaching of measurement is limited. We previously introduced, refined, and validated a developmental p...

Recent scholarship around teaching elementary mathematics supports the learning of early algebra with 5- to 12-year olds. However, in spite of the recognition of the affordances of early algebra, issues about how to introduce it remain open. Within this context, Davydov’s work is often cited as a source of impressive demonstration of young learners’ capacity for algebraic thinking. This work requires further exploration in order to yield a clearer picture of a very particular teaching approach, which focuses on early abstractions and symbolic language. We argue that in order to fully understand how Davydov’s work contributes to current conversations and what Davydov was trying to do, we need to shed light on the context- and time-specific discourse of the 1960 Soviet educational reforms that made it possible for Davydov to develop his vision about algebraic thinking and to set in motion appropriate teaching approaches for young learners. In this paper, we look back to the Soviet debates that unfolded in Russia on the integration of early algebra in elementary school word-problem solving. Drawing on these debates and the results of Davydov’s school experiments, we lay out the developmental axes of capacity building. This can be done by emphasizing ascent from the abstract to the concrete using a variety of representational modeling tools to support the emergence of algebraic thinking while targeting particular habits of mind within carefully designed learning activities. We conclude with some insights about current arithmetic-algebra debates, and how these could be enriched and deepened by Davydov’s work, which yet remains open to future discussion and reflection.

This study explored the efficacy of a Tier 2 intervention within the context of the Response to Intervention (RtI) model implemented by Spanish first- to third-grade primary school teachers to improve at-risk students’ early math skills. Teachers were instructed in the administration of a math curriculum-based measure composed of 5 isolated measures (quantity discrimination, missing number, single-digit computation, multidigit computation, and place value) to identify at-risk students and to monitor their progress; and in the implementation of a systematic and explicit instructional program to improve basic math skills in at-risk students. Implementation fidelity was analyzed using direct observations and self-reports. The intervention was conducted with adequate fidelity and had a significant positive impact on all grades. Significant differences were found between experimental and control students at risk of math failure in the improvement rate of quantity discrimination, missing number, and place value in all grades. Experimental at-risk students showed a monthly improvement, assessed using a combination of screening and progress monitoring measures. In conclusion, Spanish first to third graders at risk of math failure benefited from a Tier 2 intervention based on basic math skills, implemented by in-service teachers.

It has been shown that the emotional state of students plays an important role towards learning; for instance, engaged concentration is positively correlated with learning. This paper proposes Inductive Control (IC) for educational games. Unlike conventional approaches that only modify the game level, the proposed technique also induces emotions in the player for supporting the learning process. This paper explores a fuzzy system that analyzes the players’ performance and their emotional state for controlling the level and aesthetic content of an educational video game. The emotional state of the player is recognized through voice analysis. A total of 40 subjects played a video game designed to practice basic math skills; for each trial, a student plays twice in a row the same game but each time the game was controlled by one of the two approaches—Dynamic Difficulty Adjustment (DDA) and IC, the playing order was assigned randomly. Results show that when the proposed approach is used the participants changed faster from unpleasant–low to pleasant or high emotions. These experiments demonstrate that the inductive control technique improves the learning effectiveness through detection and stimulation of positive emotions.

The focus in this paper is on the analysis of student-centered discourse through applying a discourse analysis tool that I developed to analyze data from an elementary mathematics classroom. The purpose of the analysis tool is to understand the impact of the complex learning system on the emerging classroom discourse. The minimum conditions for complexity created an invitational space for students that allowed interactions and meaningful exchanges to flourish through exploration of mathematical concepts and collective participation in classroom discourse. The analytic lens provides the teacher with a tool to understand more clearly the dynamics of meaningful exchanges identified as sharing, building, exploring and blocking. Keywords: Classroom discourse; mathematics education; complexity

The ability to notice students’ mathematical thinking is key to better understanding student learning and effective teaching. Our professional development program utilized a Child Study Assignment ...

Results from an experiment in Fall 2013 of 902 incoming students at this university are reported. In this experiment, after students were given a basic math assessment to ensure they had the necessary math skills to take a principles of economics course, they were randomly allocated to a treatment or control group to test whether there was a significant impact of test format, calculator use, and calculator type on students’ scores. The interaction of calculator use/type and test format was also tested. The results from this experiment suggest that each treatment had a significant positive impact on students’ assessment scores, with much variation depending on the type of question asked and the level of performance. JEL Classifications: A22, C23

PurposeThis study aims to explore how the theories of professional capital and decisional capital can be extended to introduce “professional mathematics capital” and “decisional mathematics capital”.Design/methodology/approachProfessional development (PD) efforts in one school district in elementary mathematics education are described to illustrate these extensions and to contemplate ways to enhance teacher learning of mathematics pedagogy.FindingsBoth theoretical extensions provided useful frameworks for conceptualizing mathematics PD. Preliminary evidence suggests that participants demonstrated the emergence of professional and decisional mathematics capital.Research limitations/implicationsWhile there were observed and reported changes to teacher practice, further research is needed to explore the implications of these theoretical extensions on student learning.Originality/valueThis study serves to enhance the literature related to PD and teachers' mathematical content knowledge. The theoretical extensions of professional and decisional mathematics capital are a novel and promising concept that allows for a unique approach to be laid out for those designing PD in mathematics.

Several teaching moves have been suggested to support young children’s simple addition and subtraction performance, including use of a number path, directly modeling addition and subtraction, using...

Can a school or district improve student achievement simply by switching to a higher‐quality textbook or curriculum? We conducted the first multi‐textbook, multi‐state effort to estimate textbook efficacy following widespread adoption of the Common Core State Standards (CCSS) and associated changes in the textbook market. Pooling textbook adoption and student test score data across six geographically and demographically diverse U.S. states, we found little evidence of differences in average achievement gains for schools using different math textbooks. We found some evidence of greater variation in achievement gains among schools using pre‐CCSS editions, which may have been more varied in their content than post‐CCSS editions because they were written for a broader set of standards. We also found greater variation among schools that had more exposure to a given text. However, these differences were small. Despite considerable interest and attention to textbooks as a low‐cost, “silver bullet” intervention for improving student outcomes, we conclude that the adoption of a new textbook or set of curriculum materials, on its own, is unlikely to achieve this goal.

Professional noticing of children’s mathematical thinking (Jacobs et al. in J Res Math Educ 41(2):169–202, 2010) is a construct that is used frequently to understand the ways in which teachers attend to, interpret, and respond to children’s mathematical thinking. In this paper, we present our analysis of prospective elementary mathematics teachers’ (PTs’) responses to a pedagogical activity designed to engage them in an approximation (Grossman et al. in Teach Coll Rec 111(9): 2055–2100, 2009) of professional noticing of children’s mathematical thinking in the moment of teaching, with a focus on developing responses which extend the student’s thinking. PTs were provided two different examples of student work and a series of questions designed to elicit information about their ability to professionally notice student work. We present data and analysis of 73 PTs’ abilities to engage in the individual skills associated with noticing as well as their abilities to use the skills cohesively in concert. Our results demonstrate the type of representation used determined PTs’ success in all three facets of noticing, with a particular effect on interpreting. Further, our focus on a specific type of response move, along with the introduction of a scaffold for that response move, made a difference in PTs’ ability to successfully respond to student work when compared to a prior study with the same PTs (Tyminski et al. 2014). We unpack these results along with suggestions for pedagogical practice as well as directions for future research.

This paper explores peer interactions in an elementary mathematics classroom (ages 9–10) where the teacher intentionally shared authority with her students and supported them in learning to share authority with one another. Authors examine how students shifted between shared, concentrated, and contested social and intellectual authority relations in partner and small group work during a three-week unit on place value. Findings show that (a) students were able to share both social and intellectual authority, and did so often; (b) the distribution of social authority was more dynamic than that of intellectual authority; and (c) when groups shifted into shared intellectual authority, shifts were usually preceded by a student making some aspect of the collaborative task public. We connect these findings to research on authority in mathematics classrooms that serve racially and linguistically minoritized students and offer directions for future work.

Mathematics teacher educators can use video clips of children solving mathematics problems to help teacher candidates attend to nuanced aspects of teaching and learning mathematics. However, the pr...

The aim of this study is to determine the non-routine problem solving performances of mathematics teacher candidates. A descriptive survey model was used for this work and it was conducted with 50 teacher candidates studying elementary mathematics teaching in a medium-sized university in Turkey. To determine the non-routine problem solving performance of the teacher candidates, open ended non-routine problems were prepared according to an expert’s opinion. Firstly, the data obtained were examined with a holistic rubric to know the problem solving levels of the teacher candidates and secondly the levels of the teacher candidates for each problem solving step of Polya were evaluated with a two point scale. When the problem solving performances of the teacher candidates were examined in a holistic manner, it was concluded that their performance is low when the difficult level of problem is raised. From the results, it was determined that teacher candidates mostly tended to go through a solution by trying to use arithmetic operations to solve non-routine problems. As a result, it was suggested to examine teacher candidates’ problem solving knowledge and pedagogical content knowledge and to re-evaluate the results of the research with different question types. Key words: Non-routine problem, Mathematics teacher candidates, Mathematics education.

This case study explored Prospective Elementary Mathematics Specialists’ (PEMSs) pedagogical practices during a K-5 Mathematics Endorsement (K-5 ME) program, specifically focusing on the authentic residency with mentor sessions. Participants included nine PEMSs, with qualitative and quantitative data collected via individual interviews, professional portfolios, and observations of classroom practices. Upon completion of the K-5 ME program, all participants were implementing instructional practices learned about in the program in substantial ways. Participants were honing their skills for orchestrating effective discourse, and the application of those skills became more meaningful as they saw the impact it was having on student learning. This implementation and documentation program coursework was rigorous as PEMSs worked to develop themselves as mathematics teachers and teacher leaders. The collaborative support during the authentic residency and mentor sessions seem to have been significant for PEMSs in supporting implementation of newly learned instructional practices. Ultimately, PEMSs completed the program feeling more prepared as elementary mathematics teachers and teacher leaders.

This study compares web usage data with interviews from 41 participants, who are members of an online professional development site called the Everyday Mathematics Virtual Learning Community (VLC), to explore how elementary school teachers learn from classroom video. Web usage data reveal that the commentary surrounding video posted to the VLC is sparse and surface level, possibly indicating a lack of serious attention to the videos. Interview data, however, indicate that participants felt they learned from this resource. Participants reported that the videos provided them with the opportunity to view and reflect on model lessons, plan curricula, and consider student thinking, among other learning outcomes. Participants also identified key factors that prevented them from posting comments to the site to convey their learning. These results can be used to understand not only how teachers perceive their own learning from classroom video, but also to redesign online professional development experiences to promote expression of that learning.

In the present study, researchers used problem-posing instruction to examine elementary students’ understanding of multiplication. Students in fourth and fifth grade classrooms (n = 24) from a rura...

The Common Core State Standards for Mathematics (CCSS-M) aim to engage students in complex mathematical practices, including modeling, reasoning, and argumentation. Currently, little is known about how teachers’ daily instruction supports these practices. This study draws upon data from daily logs completed by third-, fourth-, and fifth-grade mathematics teachers from 39 states to learn about students’ engagement in standards-aligned mathematical practices. We find that there are both substantial fluctuations in students’ engagement in these practices and reported cognitive demand from day to day, as well as large differences across teachers. Practices in which students engage are related to teachers’ perceptions of student ability. These findings offer a broad perspective on how CCSS-M–based instruction unfolds across a range of states and policy environments.

In many discussions of the ways in which abstraction is applied in computer science (CS), researchers and advocates of CS education argue that CS students should be taught to consciously and explicitly move among levels of abstraction (Armoni Journal of Computers in Mathematics and Science Teaching, 32(3), 265–284, 2013; Kramer Communications of the ACM, 50(4), 37–42, 2007; Wing Communications of the ACM, 49(3), 33–35, 2006). In this paper, we describe one way that attention to levels of abstraction could also support learning in mathematics. Specifically, we propose a framework for using abstraction in elementary mathematics based on Armoni’s (2013) framework for teaching computational abstraction. We propose that such a framework could address an enduring challenge in mathematics for helping elementary students solve word problems with attention to context. In a discussion of implications, we propose that future research using the framework for instruction and teacher education could also explore ways that attention to levels of abstraction in elementary school mathematics may support later learning of mathematics and computer science.

The inclusion of alternative and multimodal methods for online interaction and knowledge construction in mathematics teacher education is still an incipient field. In this paper, we present a multiple case study of three blended courses in an elementary mathematics teacher education program at Western University. In these blended courses, the online component included the construction of collaborative mind maps. Through constructivist grounded theory methods, we analyzed teacher candidates’ mind maps as (a) final products, and (b) interaction processes. The resulting theory describes how pre-service mathematics teachers interact and construct knowledge while they engage in online collaborative mind mapping. The study provides insights into the ways that collaborative and multimodal technologies affect mathematics teacher education, and in turn, suggests how its implementation may be improved.

Although educational games have been used for a considerable time, their true potential for enhancing achievement and motivation is still being explored. We argue in this paper that we may get closer to realizing this potential if the theoretical underpinning of educational games is improved. We developed a simple interactive math game based on insights from cognitive load and game design theory, in which players solve mathematical problems competitively and creatively. To investigate the effects of the game on achievement and motivation, we ran an experiment with fifth- and sixth-grade students. Our results show that students who played the game achieved better math results than those who did not. We did not find any significant differences in math motivation. Another promising finding, albeit beyond the scope of our hypotheses, relates to the potential effects of math games on student behavior.

Drawing on a larger, cross-institutional study that examines equitable elementary mathematics education, this article reports initial findings related to tensions that emerged for preservice teache...

Teachers’ decision-making and pedagogical reasoning often become visible in their lesson planning sessions. This study explores how the professional learning opportunities presented by teacher-facilitator interactions in planning sessions. By tracing shifts in teachers’ discourse in planning sessions, we examine the development of their pedagogical reasoning. The findings of this study illustrate that these interactions create four kinds of professional learning opportunities: (1) reflecting on students’ learning in past lessons; (2) attending to the details of the complexity of teaching; (3) negotiating and adjusting lesson goals and activities by making direct and informed decisions for teaching; and (4) anticipating specific features of instruction. This study also illustrates how refining and elaborating teaching complexity supports teachers in re-conceptualizing and expanding their teaching knowledge.

This paper presents findings from a two-year qualitative study examining integration of computer science (CS) and computational thinking (CT) into elementary mathematics instruction. Integrated uni...

In this synthesis, we reviewed 65 studies involving elementary students (i.e., grades 1–5) identified with mathematics difficulty (MD) in which authors implemented a mathematics intervention. Of these studies, we identified 33 group designs, 9 quasi-experimental designs, and 23 single-case designs. We aimed to synthesize performance differences between students with MD with and without reading difficulty (RD). We identified three categories of students for analysis: Students with MD+RD, MD-alone, or MD-nonspecified (i.e., no reading information provided). Overall, 80% of studies included students with MD-nonspecified, and the interventions for these students demonstrated strong effects. For the limited number of studies with students with MD+RD or MD-alone, intervention effects were strong for students with MD+RD and variable for students with MD-alone. In the three studies directly comparing the performance of students with MD+RD versus MD-alone, we noted differential patterns of performance. To tailor interventions to student need, more research must be conducted to understand whether students with MD with variable reading profiles respond differentially to mathematics intervention.

This article focuses on conversations about gender and mathematics among other intersecting identities such as age, education level, and professional expertise. I used positioning theory to unpack a conversation at a science museum (between museum volunteer John, prospective teacher Ann, and myself) to share a story about gender and mathematics. I argue that the impact of this conversation from our perspectives as young women who do work in elementary mathematics education should be made visible to recognize and address inequities for women and girls within mathematics and mathematics education spaces. Implications for elementary teacher education include providing opportunities for prospective teachers to share their stories and gendered experiences with attention to intersections of age, gender, and connected disciplinary narratives (in this case, mathematics).

Informed by a constructivist-based, student-adaptive pedagogical approach, this study explores the benefits of teacher–learner discourse moves for the mathematics learning of students with learning disabilities (LD). During a constructivist teaching experiment for nurturing the multiplicative reasoning and problem solving of five third-grade students with school-identified LD, we analyzed the global trends and detailed dynamics of teacher–student interactions with statistical discourse analysis. We found that the teacher’s discourse moves to support each individual student’s problem solving helped engage them in mathematical reasoning, which improved their problem-solving performance. Thus, this study contributes to knowledge in the field of special education by (a) specifying ways in which discourse-oriented mathematics instruction can help each student with LD and (b) showcasing a novel statistical analysis of teacher–student discourse.

This article provides a concrete illustration of how teachers in a primary school in Singapore discuss students’ learning in a lesson study cycle and grew professionally as a community. Specificall...

This mixed-methods study explored the pedagogical practices of Prospective Elementary Mathematics Specialists (PEMSs) as they completed a university K-5 Mathematics Endorsement program. Participants were 13 elementary teachers at an urban, high-needs charter school. Data were collected via individual interviews, written reflections on enacted teaching practices, two observations of classroom teaching practices, and a 36-item Cognitively Guided Instruction Teacher Knowledge Assessment. The findings show the PEMSs were connecting their learning during program courses with instructional practices in their classrooms, as 85% were implementing standards-based learning environments (SBLEs) at a high level, with the classroom event of providing their students opportunities to make conjectures about mathematical ideas as a relative struggle. The PEMSs described pedagogical shifts across the program, providing insights into these changes, along with how particular program components contributed, with the emergent themes of skepticism, trying it on, shifters, and need more support.

Professional learning experiences (PLEs) provide teachers with opportunities to improve their understanding of mathematics content and teaching practices. However, PLEs are often conducted in person and in small groups—hence costly and localized. The purpose of the current study was to explore different ways for teachers to engage in PLEs and how these approaches might enable the field to scale up these efforts in a sustainable manner. We compared the impact of three PLE formats on the early algebra knowledge and teaching practices of elementary mathematics teachers: (1) a facilitated summer workshop, (2) a multimedia course completed on teachers’ own time, and (3) learning resources provided in the algebra curriculum unit that teachers used individually. Our findings suggest that all three formats can be mapped against a set of principles for quality professional learning. Analysis of pre- and post-treatment measures indicate that participating teachers’ knowledge of algebra content and best practices significantly increased, regardless of the PLE format with which they engaged. Interviews with a subset of the teachers from the three groups point to the key features of each of the formats that can be capitalized on by designers of PLEs.

This research utilized self-study methodology to examine my experience as a novice elementary mathematics teacher educator whose foundation was a high school mathematics teacher and graduat...

The role of language in mathematics teaching and learning is increasingly highlighted by standards and reform movements in the US. However, little is known about teachers’, and especially e...

This study examined how authors of four different elementary mathematics curriculum materials articulate the mathematical goals of the lesson and orient the activities toward the goals, as well as the extent to which teachers steered instruction toward the goals during enactment. Through document analysis, we identified four ways in which authors support teachers in identifying and orienting the lesson toward the goals. Analysis of the enacted lessons of 8 teachers suggests a correlation between the depth to which the goals were communicated across the four categories and the extent to which teachers steered the instruction towards the goals. The authors conclude with recommendations to curriculum developers for communicating mathematical goals in ergonomic ways.

The Steepest Descent (or Ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool is neither taught nor even mentioned in K12 education. We study whether it is feasible for elementary school students to learn this algorithm, while also aligning with the standard school curriculum. We also look at whether it can be used to create enriching activities connected to children’s real-life experiences, thus enhancing the integration of STEM and fostering Computational Thinking. To address these questions, we conducted an empirical study in two phases. In the first phase, we tested the feasibility with teachers. In a face-to-face professional development work-shop with 457 mathematics teachers actively participating using an online platform, we found that after a 10-minute introduction they could successfully apply the algorithm and use it in a couple of models. They were also able to complete two complex and novel tasks: selecting models and adjusting the parameters of a model that uses the steepest descent algorithm. In a second phase, we tested the feasibility with 90 fourth graders from 3 low Socioeconomic Status (SES) schools. Using the same introduction and posing the same questions, we found that they were able to understand the algorithm and successfully complete the tasks on the online platform. Additionally, we found that close to 75% of the students completed the two complex modeling tasks and performed similarly to the teachers.

The aim of this study was to analyse preservice elementary mathematics teachers' concept definitions of circle, circular region, and sphere concepts in geometrical terms. The research was conducted during the 2016-2017 academic year with 56 preservice mathematics teachers enrolled within a teacher education programme at a state university in Turkey. A test consisting of three open-ended questions regarding circle, circular region, and sphere was used as the study's data collection tool. The preservice teachers' test answers were investigated according to correctness and generalization criteria. Answers regarding each concept were compared with those of the two other concepts. Following the data analysis, semi-structured interviews were conducted with nine of the participant preservice teachers. The findings of the research revealed that the preservice teachers mostly experienced difficulty in defining the sphere. In addition, it was determined that most preservice teachers provided either insufficiently detailed or incorrect answers for the concepts of circle, circular region, and sphere. When the examples of the concepts were examined, it was determined that only a few of the preservice teachers gave appropriate examples of the related concepts.

In this chapter, the authors explore the experiences of K-12 teachers as they navigated an abrupt transition from a traditional face-to-face mathematics classroom to virtual learning. The authors used a survey to ask teachers to explain what effective mathematics instruction meant for their classroom. Their responses most closely aligned with four of the National Council of Teachers of Mathematics (NCTM) effective practices. The survey continued to prompt teachers to share their concerns for the transition, the most effective virtual tools they implemented, support they received, how their virtual classrooms would influence their return to face, and where they needed more support. The authors offer recommendations for supporting teachers as the virtual classroom currently remains in place for many and for transitioning back to the traditional face-to-face classroom. Technology use and digital competence continues to expand in K-12 education.

Derived math fact fluency becomes more imperative across all mathematical content areas during a students’ mathematics development. However, many of them struggle to automate the most basic math facts sufficiently and therefore are not able to deal with more complex mathematical problems. This leads to the fact that many of them are already left behind in the early years of their school careers whether they have diagnosed learning disabilities or not. In this single-case research project, we evaluated a peer-tutoring approach designed to extend the number of automated single-digit addition tasks for four struggling elementary students through a multicomponent motivational system including immediate correction of errors, graphical feedback on performance, positive reinforcement, direct instruction flashcards, and a racetrack game. A multiple-baseline design (ABE) across subjects was applied to assess the effects of the treatment. The results indicate significant and large effects of the intervention on the number of automated math facts for the participants. This substantiates the assumption that the math-fact recall performance of struggling students can be improved through the method of peer tutoring even with the limited resources available in everyday school life.

The computer science (CS) education field is exploring several instructional strategies for teaching CS to children in elementary school. Strong arguments have been made for integration--- constructing activities that not only teach CS, but use the CS to support learning in a core subject. Integrating CS materials into a specific curriculum is a non-trivial task that may unfairly burden elementary teachers, who are often generalists. Successful development and classroom implementation of integrated materials relies on many decisions about what, when, and how much subject matter to cover in relation to the main curriculum. In this paper, we describe the design of a collection of 3rd and 4th grade (8-10 years old) integrated math+CS lessons. Our instructional materials use Scratch as a programming language and employ a learning trajectory approach to integrate the CS concepts of sequence, decomposition, repetition, conditionals, variables, and debugging into fractions content in a popular elementary mathematics curriculum. The integrated lessons are inserted throughout the main mathematics curriculum, providing multiple, non-continuous exposures to CS content. In addition, we present preliminary data from selected activities, including teacher feedback about the structure and impact of the math+CS instructional materials on their students? work.

This article reviews research on the achievement outcomes of elementary mathematics programs; 87 rigorous experimental studies evaluated 66 programs in grades K–5. Programs were organized in six categories. Particularly positive outcomes were found for tutoring programs (effect size [ES] = +0.20, k = 22). Positive outcomes were also seen in studies focused on professional development for classroom organization and management (e.g., cooperative learning; ES = +0.19, k = 7). Professional development approaches focused on helping teachers gain in understanding of mathematics content and pedagogy had little impact on student achievement. Professional development intended to help in the adoption of new curricula had a small but significant impact for traditional (nondigital) curricula (ES = +0.12, k = 7), but not for digital curricula. Traditional and digital curricula with limited professional development, as well as benchmark assessment programs, found few positive effects.

This study intends to determine the statistical literacy levels of pre-service mathematics teachers and to evaluate the contribution of the statistics courses in the elementary mathematics education curriculum to statistical literacy. A mixed methods research design was adopted. The study group consisted of 202 pre-service mathematics teachers enrolled in the Statistics and Probability course. In the data collection process, a pre-test and post-test was administered to determine the pre-service teachers' statistical literacy before and after the statistical course, and classroom observations were performed to identify the contribution of the statistics course to statistical literacy. The Rasch model was used for validity-reliability analyses, and one-way ANOVA tests were used to analyze the quantitative data. Content analysis was utilized in the analysis of qualitative data, which revealed that statistical literacy levels of pre-service teachers are generally low, generally influencing the competence of pre-service teachers. The pre-service teachers failed in the sample selection component in the pretest and data interpretation in the post- test, while they were more successful with table and graphs in the pre-test and sample selection in the post-test. The comparative analysis of revealed statistically significant differences in favor of U4 in the pre- test, but in favor of U1 in the post-test. It was concluded that practices included in the statistics lessons could be effective on these differences.

Fostering fantasy play for young children through augmented reality has the potential to support 21st century learning activities by stimulating creativity, communication, and flexibility. We present a design exploration of MathMythos AR, an augmented reality card-based math addition game that enables children to engage in basic math tasks embedded in fantastical narratives. We provide insights into our design process, the effects of fantasy and everyday narratives, and discuss implications for AR card games that show potential to foster motivation for learning math. The presented insights are the foundation for the the next iteration of MathMythos AR, where we aim to create compelling and immersive AR narratives for learning.

This full research paper is concerned with structuring educational content for mobile learning. Mobile devices are present in various areas of society and, in the educational context, the available resources of mobility and connectivity have contributed to their growing adoption. However, the generation of educational content for mobile devices requires special attention to issues such as: (i) restrictions on mobile devices; and (ii) complexity of developing mobile applications, related to the variety of existing platforms. This paper presents Educom.ml, which is a modeling approach for mobile educational content supported by MDE (Model-Driven Engineering) and IMA-CID (Integrated Modeling Approach - Conceptual, Instructional, Di-dactic). Educom.ml proposes a modeling approach that involves creating models that structure educational content and models that model mobile platforms. In this context, MDE minimizes the complexity of developing cross-platform applications and the automatic generation of educational content. Meanwhile, IMA-CID is responsible for structuring and organizing educational content. To illustrate our ideas, a mobile app was generated based on modeling educational content in the field of elementary mathematics.

Matematik eğitimi ve öğretiminin nitelikli olabilmesi için eğitimin temel taşı olan öğretmenlerin matematik okuryazarlık öz-yeterlik (MOÖ)’lerinin yüksek olması ve sürekli geliştirilmesi gerekmektedir. Matematik öğretmen adaylarının MOÖ’lerinin yüksek olması için düşünme, sorgulama ve üretme yeteneklerin geliştirilmesi ilk sırada yer almalıdır. Bu nedenle, çalışmada ilköğretim matematik öğretmeni adaylarının MOÖ düzeylerinin belirlenmesi amaçlanmaktadır. Bu doğrultuda, bu çalışmanın amacını ilköğretim matematik öğretmeni adaylarının MOÖ düzeylerine yönelik sorulara verdikleri yanıtların aile eğitim durumlarına ve cinsiyetlerine göre farklılık gösterip göstermediğinin belirlenmesi oluşturmaktadır. Bu araştırma,2019-2020 eğitim-öğretim yılı güz döneminde Alanya Alaaddin Keykubat Üniversitesi Eğitim Fakültesi İlköğretim Matematik Öğretmenliği bölümünde öğrenim görmekte olan toplam 73 son sınıf öğrencisi öğretmen adayı ile yüz yüze anket tekniği kullanılarak yapılmıştır. Araştırmadan elde edilen veriler; ortalama, t-testi ve tek yönlü varyans analizi yardımıyla analiz edilmiştir. Araştırmada öğretmen adaylarının önemli bir bölümünün MOÖ’lerinin gelişmiş olduğu sonucuna ulaşılmıştır. Diğer taraftan, anne-baba eğitim durumu ile okuryazarlık öz-yeterlik puanları arasında anlamlı bir ilişkiye rastlanmamıştır. Anne-baba eğitim durumunun MOÖ düzeyine herhangi bir katkısının olmadığı saptanmıştır. Öğretmen adaylarının MOÖ puanları ile cinsiyetleri arasında anlamlı bir farklılık olduğu tespit edilmiştir. Erkek öğretmen adaylarının MOÖ puan ortalamasının, kadın öğretmen adaylarının MOÖ puan ortalamasından daha düşük olduğu sonucuna ulaşılmıştır. Okullarda matematik ders programı okuryazarlığı, mantıksal akıl yürütme, matematik öğretiminde kavram yanılgıları gibi derslere ağırlık verilmesi öğretmen adaylarının MOÖ’lerinin artmasına; düşünme, sorgulama ve üretme yeteneklerin gelişmesine katkı sağlayacaktır., In order to be qualified in mathematics education and training, mathematics literacy self-efficacy (MLSE) of teachers, which is the cornerstone of education, should be high and continuously developed. Developing thinking, questioning and producing skills should be the first priority for mathematics teacher candidates to have high MLSE. Therefore, it is aimed to determine the levels of MLSE of primary school mathematics teacher candidates. In this respect, the aim of this study is to determine whether primary mathematics teacher candidates' answers to the questions related to their levels of MLSE differ according to their parents’ educational status and gender. This research was carried out by using face - to - face questionnaire technique with 73 senior students- teacher candidates who are studying in Alanya Alaaddin Keykubat University Faculty of Education Elementary Mathematics Teaching Department in fall semester of 2019-2020 academic year. The data obtained from the study were analyzed by using mean, t-test and one-way analysis of variance. In the study, it has been concluded that a significant number of teacher candidates have developed MLSE. In the study, no significant relationship was found between the educational status of parents and literacy self-efficacy scores. It was found that the educational status of the parents did not contribute to the level of MLSE. There was a significant difference between the scores of teacher candidates' MLSE scores and gender. It was concluded that the mean score of MLSE of male students was lower than the mean score of MLSE of female students. Focusing on courses such as literacy of mathematics curriculum in schools, logical reasoning, misconceptions in mathematics teaching will contribute to the increase of teacher candidates' MLSE, development of thinking, questioning and producing abilities.