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In this paper we present the results of an investigation related to the developing of mathematical knowledge and skills by first semester university students when solving a Model Eliciting Activity [MEA] which involves quadratic function knowledge. This was a qualitative research. The theoretical framework was Models and Modeling Perspective [MMP]. The results show that the students used their mathematical knowledge and skills related to linear and quadratic functions to describe the situation; they moved from a quantitative cycle of understanding (associated with linear and quadratic behaviors), to an algebraic cycle of understanding (associated with quadratic behaviors). [For the complete proceedings, see ED629884.]

We present the results of a research project on arithmetic-algebraic thinking that was carried out jointly by a team in Mexico and another in Quebec. The project deals with the concepts of variable and covariation between variables in the sixth grade at the elementary level and the first, second, and third years of secondary school--namely, children from 11 to 14 years old. We target secondary students (first year or K7) in this article. Our objective relates to the development of a gradual generalization in arithmetic-algebraic thinking in a socio-cultural approach to the learning of mathematics. We experimented with investigative situations using a paper-and-pencil approach and technology. We analyze the emergence, in this context, of a visual abstraction, the production of institutional and non-institutional representations, a sensitivity to contradiction, and, finally, the concepts of variable and of covariation between variables. [For the complete proceedings, see ED629884.]

The design of the Cognitive Tutor Algebra I (CTA1) intelligent tutoring system assumes that students work through sections of material following a pre-specified order, and only move on from one section to the next after mastering the first section's skills. However, the software gives teachers the flexibility to override that structure, by reassigning students to different sections of the curriculum. Which students get reassigned? Does reassignment hurt student learning? Does it help? This paper used data from the treatment arm of a large effectiveness study of the CTA1 curriculum to estimate the effects of reassignment on students' scores on an Algebra I posttest. Since reassignment is not randomized, we used a multilevel propensity score matching design, along with assessments of sensitivity to bias from unmeasured confounding, to estimate the effects of reassignment. We found that reassignment reduces posttest scores by roughly 0.2 standard deviations--about the same as the overall CTA1 treatment effect--that unmeasured confounding is unlikely to completely explain this observed effect, and that the effect of reassignment may vary widely between classrooms. [For the full proceedings, see ED607784.]

This study aims to describe how subjects construct explicit warrant derived from implicit warrant when completing mathematical proof. This research was conducted on seventeen students of mathematics education study programs by providing tests on vector material in elementary linear algebra courses. The test results show that there are four students who can solve the evidentiary questions correctly using warrant, but there is only one student who can be the subject of research. The selection of subjects is based on students' ability to communicate verbally about the thought process carried out in constructing implicit warrant to explicit warrant when conducting proof. Data in this study were obtained from think aloud, tests, and interviews conducted by researchers to subjects. The results showed that the explicit warrant constructed by the subjects was obtained from an implicit warrant based on the thought process carried out. The subject constructs an explicit warrant derived from an implicit warrant through four steps, namely identifying problems,determining warrant, doing algebraic manipulation, and making conclusions. Warrant is a guarantor used to get the correct conclusions from a mathematical proof, thus further research needs to be done related to warrant. [This paper was published in: "AIP Conference Proceedings" v2215, p060005-1-060005-5, 2020. AIP Publishing (ISBN 978-0-7354-1968-1).]

Many studies have shown that visual representations can enhance student understanding of STEM concepts. However, prior research suggests that visual representations alone are not necessarily effective across a broad range of students. To address this problem, we created a novel, scaffolded form of diagrammatic self-explanation in which students "explain" their problem-solving steps in the form of diagrams. We used contrasting cases to support students' sense-making between algebraic equations and diagrams in the self-explanation activity. We conducted a classroom experiment with 41 students in grades 5 and 6 to test the effectiveness of this strategy when embedded in an Intelligent Tutoring System for algebra. We found that scaffolded diagrammatic self-explanation enhanced conceptual knowledge for students who did not have prior knowledge of formal equation-solving strategies. The study is the first experimental study showing that visual representations can enhance conceptual knowledge in early algebra. [This paper was published in: "ICLS 2020 Proceedings," ISLS, 2020, pp. 35-42.]

When designing an instructional tool and using it in pedagogical activities, it is essential that designers and users understand what pedagogical affordances and constraints the tool provides to support its successful integration into targeted pedagogical activities. Toward this end, we developed "Pedagogical Affordance Analysis (PAA)." PAA involves analyzing teachers' Pedagogical Content Knowledge and/or Technological Pedagogical Content Knowledge to elicit pedagogical affordances and constraints that are specific to a given instructional goal. Information obtained through PAA can help in designing, refining, and/or evaluating instructional tools. We present a case study in which we used PAA to successfully design a visual representation for middle-school algebra. To the best of our knowledge, PAA is the only available systematic method that leverages teachers' pedagogical knowledge in identifying pedagogical affordances and constraints. PAA can be used across a wide range of existing tools and prototypes of to-be-designed tools. [This paper was published in: "ICLS 2020 Proceedings," ISLS, 2020, pp. 1561-64.]

Verbal protocols were collected from math-anxious and math-comfortable college students while they solved algebra problems. These protocols were then examined for differences in problem-solving processes. Differences occurred in the use of two basic strategies: generating values and symbolic transformations. Math-anxious students generated more values; math-comfortable students made more symbolic transformations. The data suggest that for the math-anxious students the real problem is not numerical; rather, it is the inability to apply symbolic procedures. (MP)

Integrating visual representations in an interactive learning activity effectively scaffolds performance and learning. However, it is unclear whether and how "sustaining" or "interleaving" visual scaffolding helps learners solve problems efficiently and learn from problem solving. We conducted a classroom study with 63 middle-school students in which we tested whether sustaining or interleaving a particular form of visual scaffolding, called anticipatory diagrammatic self-explanation in an Intelligent Tutoring System, helps students' learning and performance in the domain of early algebra. Sustaining visual scaffolding during problem solving helped students solve problems efficiently with no negative effects on learning. However, in-depth log data analyses suggest that interleaving visual scaffolding allowed students to practice important skills that may help them in later phases of algebra learning. This paper extends scientific understanding that sustaining visual scaffold does not over-scaffold student learning in the early phase of skill acquisition in algebra. [This paper was published in: "Proceedings of the 44th Annual Conference of the Cognitive Science Society," edited by J. Culbertson et al., Cognitive Science Society, 2022, pp. 1751-58.]

Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The study reported here characterizes empirically developed progressions in Grades K-1 students' thinking about arguments concerning sums of evens and odds. Data are drawn from classroom lessons of an early algebra instructional sequence and interviews conducted at four timepoints during the implementation of the sequence. Overall, students transitioned from unfamiliarity with the concepts of even or odd prior to instruction in Kindergarten to making valid parity arguments at the conclusion of instruction in Grade 1. Results of this study align with other research that shows young learners can develop viable arguments to justify mathematical generalizations.

Gaming the system, a behavior in which learners exploit a system's properties to make progress while avoiding learning, has frequently been shown to be associated with lower learning. However, when we applied a previously validated gaming detector across conditions in experiments with an algebra tutor, the detected gaming was not associated with learning, challenging its construct validity. Our iterative exploratory data analysis suggested that some contextual factors that varied across and within conditions might contribute to this lack of association. We present a latent variable model, "item response theory-based gaming detection" (IRT-GD), that accounts for contextual factors and estimates latent gaming tendencies as the degree of deviation from normative behaviors across contexts. Item response theory models, widely used in knowledge assessment, account for item difficulty in estimating latent student abilities: students are estimated as having higher ability when they can get harder items correct than when they only get easier items correct. Similarly, IRT-GD accounts for contextual factors in estimating latent gaming tendencies: students are estimated as having a higher gaming tendency when they game in less commonly gamed contexts than when they only game in more commonly gamed contexts. IRT-GD outperformed the original detector on three datasets in terms of the association with learning. IRT-GD also more accurately revealed intervention effects on gaming and revealed a correlation between gaming and perceived competence in math. Our approach is not only useful for others wanting to apply a gaming assessment in their context but is also generally applicable in creating robust behavioral measures. [For the full proceedings, see ED623995.]

Problem solving and reasoning are two key components of becoming numerate. Reports obtained from international assessments show that Australian students' problem solving ability is in a long-term decline. There is little evidence that teachers are embracing problem solving as part of the classroom routine. In this study, we analyse 598 Year 7 to 10 students' responses to a measurement task using Sfard's commognition framework. Four implications lead to recommendations on how to support curriculum, assessment and pedagogical alignment.

This study reports on a professional learning (PL) initiative aimed at establishing a community of practice, through teacher working groups in which teachers can explore and develop their algebraic pedagogical content knowledge (PCK). Here we report on teachers' solutions to three differently represented algebraic problems and explore what the nature of their solutions tells us about their algebraic reasoning and their PCK. The findings showed that most participants favoured only one solution and provided useful insights for the value of teacher working groups in PL activities to develop teachers' algebraic reasoning, understanding, and extend their range of problem-solving strategies.

"Proceedings of International Conference on Education in Mathematics, Science and Technology" includes full papers presented at the International Conference on Education in Mathematics, Science and Technology (ICEMST) which took place on March 24-27, 2022 in Antalya, Turkey. The aim of the conference is to offer opportunities to share ideas, to discuss theoretical and practical issues and to connect with the leaders in the fields of education. The conference is organized annually by the International Society for Technology, Education, and Science (ISTES). The ICEMST invites submissions which address the theory, research or applications in all disciplines of education. The ICEMST is organized for: faculty members in all disciplines of education, graduate students, K-12 administrators, teachers, principals and all interested in education. After peer-reviewing process, all full papers are published in the Conference Proceedings. [Individual papers are indexed in ERIC.]

Worked examples have been shown to improve student learning in algebra. However, less is known about how to design worked examples to support student learning in online settings. We explore how college students react to worked examples that vary in their degree of extensiveness and dynamicness. In an online, within-subjects study, 109 college students viewed six worked example presentations: (1) static concise; (2) static extended; (3) sequential concise; (4) sequential extended; (5) dynamic history; and (6) dynamic no history. Students rated the helpfulness of each worked example and explained their rating. We found that students rated the static concise presentation as the most helpful and the dynamic no history presentation as the least helpful example. Responses were coded by researchers for common themes and revealed insights that may inform how researchers and teachers design worked examples for online environments. [For the complete proceedings, see ED630210.]

Asynchronous, online mathematics teacher professional development (PD) was designed to align with research on teacher professional learning as well as to support Communities of Inquiry (e.g., Garrison et al., 2000). The intervention included two actively facilitated formats and a structured independent condition, where facilitation was integrated into the design of the intervention. Participants' responses to intervention activities were analyzed using indicators of Garrison et al.'s Community of Inquiry framework, seeking to understand the ways in which the intervention enabled participant learning across facilitation formats. Analysis has implications for building the CoI framework into subsequent online asynchronous mathematics teacher PD as a way to increase teacher learning, build community, and effectively scale interventions. [For the complete proceedings, see ED630210.]

This study shares two frameworks for analyzing teacher actions that support students in generalizing and examines how those frameworks align with teacher questioning. One classroom teaching episode focused on the mathematical activity of generalizing is shared to illustrate effective generalizing promoting practices. We found several patterns of productive and unproductive generalizing promoting actions and questioning. Repeating generalizing promoting actions in succession were needed to produce student generalizations. Priming actions that set up for later generalizing promoting were helpful when students struggled to identify and state generalizations. Connection questions promoted generalizing, but justification and concept questions did not. Further research will explore the additional strategies to support teachers in fostering student-created generalizations. [For the complete proceedings, see ED630210.]

Research on dyscalculia has focused almost exclusively on elementary-aged students' deficits in speed and accuracy in arithmetic calculation. This case study expands our understanding of dyscalculia by documenting how one college student with dyscalculia understood algebra during a one-on-one design experiment. A detailed case study of 19 video recorded sessions revealed that she relied upon unconventional understandings of algebraic quantities and notation, which led to persistent difficulties. This exploratory case study provides new insights into the character of difficulties that arose and persisted for one student with dyscalculia in the context of algebra and suggests the utility of documenting the persistent understandings that students with dyscalculia rely upon, particularly in understudied mathematical domains, like algebra. [For the complete proceedings, see ED630210.]

Interest-driven activities, such as mathematical play, can support student agency, motivation, and engagement, and can foster dispositions that reflect authentic disciplinary engagement. However, the bulk of research on mathematical play investigates the mathematics that emerges in young children's natural play or in informal spaces such as video games. We introduce the term "playful math" to highlight the potential of playifying classroom-based activities, and we explore the nature of students' activity when engaged in playful math tasks in a teaching experiment. Our findings show that playful math tasks increased students' agency, authority, investment, and goal selection, as well as encouraged the development of creative, challenging ideas. We present a case of two students' playful engagement in the form of an Explore-Strategize Cycle and discuss implications of playful math for student engagement. [For the complete proceedings, see ED630210.]

Despite significant research exploring students' quantitative reasoning, few studies have explored the semiotic processes that mediate its development. In this report, we present a case study to show how one student constructed a semiotic chain for a quantity as he worked with a mathematical task. Importantly, we connect frameworks for quantitative reasoning and semiotics to make sense of this process. Our findings show how our case student constructed a sign for a chunk of change in a triangle to support his later construction of the quantity of amount of change of area. We also describe how the case student leveraged these signs to bolster his development of the quantity of total area. We emphasize the role of artifacts, such as physical manipulatives, a digital applet, and a diagram, in this process. Finally, we discuss the implications of this analysis for future studies that explore students' constructions of quantity. [For the complete proceedings, see ED630210.]

Isomorphism and homomorphism appear throughout abstract algebra, yet how algebraists characterize these concepts, especially homomorphism, remains understudied. Based on interviews with nine research-active mathematicians, we highlight new sameness-based conceptual metaphors and three new clusters of metaphors: sameness/formal definition, changing perspectives, and generalizations beyond algebra. Implications include a way to articulate a conceptual purpose for homomorphism beyond its relationship to isomorphism: namely, as a tool for changing perspectives when problem-solving. [For the complete proceedings, see ED630210.]

This research reports on the teacher language and gesture that contributed to shifts in thinking about the equal sign and equations observed in twenty kindergarteners who took part in an early algebra intervention. Our analysis revealed ways in which the teacher used language and gesture to support students in moving from describing and working with the equal sign operationally (i.e., as a signal to compute) to describing the symbol as indicating the equivalence of two amounts and successfully working with equations of various forms. We detail four kinds of language and two kinds of gesture specifically related to mathematical equivalence that we believe contributed to students' growth. [For the complete proceedings, see ED630210.]

By highlighting the curriculum modifications that lead to maintaining, or enhancing, the mathematical quality of an algebra lesson introducing the substitution method for solving systems of equations from an algebra textbook, we present an analysis of how a teacher and her students impact how the mathematical ideas unfold across the lesson and how they are experienced. Using a narrative-based analytical approach to write the stories of the written and enacted lessons, we found key similarities and differences in the lessons. In comparing the mathematical plots, we found evidence of how the teacher and students alter the unfolding story with the incorporation of more jamming than seen in the text and more questions developed based on the students' needs and their responses. [For the complete proceedings, see ED630210.]

This study aimed at exploring Senior High School Mathematic Teachers, Prospective Teachers and Student's conceptual misunderstanding on Senior High School algebra with an intent to uncover the errors they make as a result of conceptual misunderstanding. A test consisting of fourteen (14) tasks was used for data collection. A sample of 210 consisting of sixty (60) prospective senior high school mathematics Teachers from mathematics education department of University of Education Winneba forty (40) SHS mathematics teachers and one hundred and ten (110) senior high school students from four (4) selected senior high schools in Ashanti region of Ghana. The study employed convenience, purposive and simple random sampling as sampling techniques and descriptive survey design as the research design. The data collection tools used were test and semi structured interview guide. Constructivism and behaviourism theories were employed as the theoretical frame work for the study. The study identified seven (7) categories of conceptual misunderstanding in Senior High School algebra among the prospective teachers and the students' whiles six of these seven were also found among the teachers. The seven conceptual misunderstanding identified were on algebraic variables, algebraic expressions, algebraic equations and algebraic word problems. The study recommends that teachers, prospective teachers and students should be aware of the existence of conceptual misunderstanding in teaching and learning of algebraic concept. The study also recommends that, heads of schools should organize workshops and refresher courses for mathematics teachers on sensitive topics like conceptual misunderstandings in mathematics. [For the complete proceedings, see ED631021.]

Knowledge space theory (KST) is a mathematical framework for modeling and assessing student knowledge. While KST has successfully served as the foundation of several learning systems, recent advancements in machine learning provide an opportunity to improve on purely KST-based approaches to assessing student knowledge. As such, in this work we compare the performance of an existing KST-based adaptive assessment to that of a newly developed version--with this new version combining the predictive power of a neural network model with the strengths of existing KST-based approaches. Using a cluster randomized experiment containing data from approximately 140,000 assessments, we show that the new neural network assessment engine improves on the performance of the existing KST version, both on standard classification metrics, as well as on measures more specific to the student learning experience. [For the full proceedings, see ED623995.]

Previous research has shown that providing video recommendations to students in virtual learning environments implemented at scale positively affects student achievement. However, it is also critical to evaluate whether the treatment effects are heterogeneous, and whether they depend on contextual variables such as disadvantaged student status and characteristics of the school settings. The current study extends the evaluation of a novel video recommendation system by performing an exploratory search for sources of heterogeneity of treatment effects. This study's design is a multi-site randomized controlled trial with an assignment at the student level across three large and diverse school districts in the southeast United States. The study occurred in Spring 2021, when some students were in regular classrooms and others in online classrooms. The results of the current study replicate positive effects found in a previous field experiment that occurred in Spring 2020, at the onset of the COVID-19 pandemic. Then, causal forests were used to investigate the heterogeneity of treatment effects. This study contributes to the literature on content sequencing systems and recommendation systems by showing how these systems can disproportionally benefit the groups of students who had higher levels of previous algebra ability, followed more recommendations, learned remotely, were Hispanic, and received free or reduced-price lunch, which has implications for the fairness of implementation of educational technology solutions.

Any advanced class in Science, Technology, Engineering, and Mathematics fields requires prerequisite knowledge. Typically, different students will have different levels of knowledge in these prerequisite areas. A prerequisite (Linear Algebra for Machine Learning course) was implemented as an interactive online course using Jupyter Notebooks and nbgrader and compared with traditional classroom mode. Post-assessment test shows that traditional class provides a better level of understanding. However, a survey shows a preference by students and instructors for interactive implementation compared to traditional class. [For the full proceedings, see ED639633.]

"Wheel spinning" is the phenomenon in which a student fails to master a Knowledge Component (KC), despite significant practice. Ideally, an intelligent tutoring system would detect this phenomenon early, so that the system or a teacher could try alternative instructional strategies. Prior work has put forward several criteria for wheel spinning and has demonstrated that wheel spinning can be detected reasonably early. Yet the literature lacks systematic comparisons among the multiple wheel spinning criteria, features, and models that have been proposed, across multiple evaluation criteria (e.g., earliness, precision, and generalizability) and datasets. In our experiments, we constructed six wheel spinning detectors and compared their performance under two different wheel spinning criteria with three datasets. The results show that two prominent criteria for wheel spinning diverge substantially, and that a Random Forest model has the most consistent performance in early detection of wheel spinning across datasets and wheel spinning criteria. In addition, we found that a simple model overlooked by previous research (Logistic Regression trained on a single feature) is able to detect wheel spinning at an early stage with decent performance. This work brings us closer to unifying strands of prior work on wheel spinning (e.g., understanding how different criteria compare) and to early detection of wheel spinning in educational practice. [This paper was published in: Proceedings of the 12th International Conference on Educational Data Mining Montreal, QC, Canada, July 2-5, 2019.]

Systems of equations are an important topic in school mathematics. However, there is limited research examining productive ways of supporting students' understandings of systems of equations. In this paper, we first present a conceptual analysis of potential ways students may leverage their quantitative and covariational reasoning to graph systems of relationships. We then describe results from a design experiment in which we examined the potential of supporting middle-grades students in reasoning in ways compatible with this conceptual analysis. We highlight two different ways of reasoning students engaged in as they compared the relative magnitudes of two quantities with respect to a third quantity and leveraged this reasoning to graphically represent two relationships on the same coordinate system. We draw implications from these results for the teaching and learning of systems of equations. [For the complete proceedings, see ED606556.]

This paper provides evidence on how elementary school students from a Mexican public school move from using an operational sense, expressed in computational strategies, to a kind of relational thinking based on structure sense ideas and expressed by number decomposition. Even though the results are somewhat preliminary, they illustrate how students can leave behind their computational strategies and develop a more sophisticated mathematical reasoning regarding equivalence of numerical expressions and equalities; however the strategies they developed tended to be based on "ad hoc decomposition of one side and comparison with the initial form of the other side," rather than on compensation [For the complete proceedings, see ED606556.]

We study the usage of a self-guided online tutoring platform called Algebra Nation, which is widely by middle school and high school students who take the End-of-Course Algebra I exam at the end of the school year. This article aims to study how the platform contributes to increasing students' exam scores by examining users' logs over a three year period. The platform under consideration was used by more than 36,000 students in the first year, to nearly 67,000 by the third year, thus enabling us to examine how usage patterns evolved and influenced students' performance at scale. We first identify which Algebra Nation usage factors in conjunction with math overall preparation and socioeconomic factors contribute to the students' exam performance. Subsequently, we investigate the effect of increased teacher familiarity level with the Algebra Nation on students' scores across different grades through mediation analysis. The results show that the indirect effect of teacher's familiarity with the platform through increasing student's usage dosage is more significant in higher grades. [This paper was published in: "The 9th International Learning Analytics & Knowledge Conference (LAK19)" (Tempe, AZ, March 4-8, 2019). New York, NY: Association for Computing Machinery (ACM). (978-1-4503-6256-6).]

Research in both the New Zealand and international contexts identifies the need for New Zealand classrooms to foster culturally responsive and mathematical practices that align with Påsifika students' cultural values, backgrounds, interests and experiences. The aim of this study was to investigate how the use of culturally responsive tasks along with cultural practices can foster Påsifika students' participation and engagement in mathematics. Eleven Year 5 and 6 students used cameras to document their out-of-school mathematical experiences. These photographs were used to design culturally relevant tasks that were implemented in the classroom. In this paper, we analyse the students' perspectives and understandings of mathematics embedded within their lives beyond the classroom.

Understanding equivalence is fundamental to STEM disciplines, but many students struggle with the concept. We present a novel method for students to explore ideas of equivalence where students dynamically transform expressions from initial states to goal states in the web-based app Graspable Math. The structure of the goal state activities implies that any initial and goal state pair represent the same quantity (or varying quantity). We propose that for students, the physical experience of moving algebraic objects and observing how the initial state transforms into the goal state helps generalize notation mechanics. In fall of 2019, we will test this supposition in a randomized control trial of 1500 students in which student performance in pre- and post-tests will be compared to an online problem set control. [This paper was published in: "Proceedings of the forty-first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education," edited by S. Otten et al., University of Missouri, 2019, pp. 1738-43.]

Through a theoretical framework emphasizing the importance of fidelity of implementation (FOI), this paper explores how 3rd and 4th grade teachers implemented an early algebra intervention, and the extent to which the FOI related to student learning. The data for this report are taken from the first two years of an experimental research project. Videotaped classroom observations, our primary measure of FOI, were coded by adding to and adapting the Mathematical Quality of Instruction (MQI) instrument, and student performance was measured by overall score (correctness) on an algebra assessment. Results revealed a significant positive relationship between teachers' implementation and their students' performance. [This paper was published in: Galindo, E., & Newton, J., (Eds.), "Proceedings of the Thirty-Ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education" (pp. 299-302). Hoosier Association of Mathematics Teacher Educators.]

The results of educational research studies are only as accurate as the data used to produce them. Drawing on experiences conducting large-scale efficacy studies of classroom-based algebra interventions for community college and middle school students, I am developing practice-based data cleaning procedures to support scholars in conducting rigorous research. The paper identifies common sources of data errors in mathematics education research and offers a framework and related data cleaning process designed to address these errors. [This paper was published in: Weinberg, A., Rasmussen, C., Rabin, J., Wawro, M., and Brown, S. (Eds.), "Proceedings of the 20th Annual Conference on Research in Undergraduate Mathematics Education," p129-140. San Diego, CA (2017).]

We apply an advanced data visualization technique, "Sankey diagram," to explore how middle-school students (N = 343) solved problems in a game-based algebraic notation tool. The results indicate that there is a large variation in the types of students' strategies to solve the problems, with some approaches being more efficient than others. The findings suggest that Sankey diagrams can be used both in research and practice to unpack our understanding of variability in mathematical problem-solving. [This paper was published in: "Proceedings of the 15th International Conference of the Learning Sciences--ICLS 2021," 2021, pp. 887-888.]