Math Knowledge Research Articles

Examining the use of bilingual accommodations in digital math assessments: User perceptions

Digital math assessments with bilingual accommodations allow multilingual learners to use their entire linguistic repertoire to showcase their knowledge and skills. The bilingual accommodations, which include tools like language translation and audio prompts in both English and Spanish, are designed to be adaptable, giving multilingual learners the freedom to view or listen to the items in either language and to write or say their responses in either language or a combination of both. This study examined how 56 middle school emergent bilingual learners used these bilingual accommodations and explored the perceptions of teachers and students regarding these accommodations. This study provides evidence regarding using bilingual accommodation in math assessments for middle school emergent multilingual learners. The results showed how students used their full linguistic repertoire and language modalities to showcase their math knowledge and skills. Both teachers and students reported having positive perceptions of the bilingual accommodations, reinforcing its responsiveness to different learners’ needs and preferences.

Experience of interdisciplinary projects implementation in the training of pre-serviced IT-specialists

Abstract The problems of contemporary IT specialists’ training in terms of the high requirements to their mathematical and computational thinking skills as well as the urgency of raising their motivation to mastering math and algorithmization are discussed in the paper. It is pointed out that initial university courses should involve the students in the experiences that focus pre-service IT-specialists on the deep understanding of a mathematical backround and an algorithmic nature of any coding task, demonstrate them the role of math in the analysis of algorithm characteristics, and importance of math knowledge in for successful IT-career. One of such experiences presented by the authors is involving the pre-service IT-specialists into the work upon the interdisciplinary projects. The said activity is elaborated basing on the core didactic principles of PBL with the focus on the interdisciplinary project peculiarities. The goal, stages and results of the said PBL are described and analyzed in terms of its impact on the students’ awareness of mathematical knowledge value in their vocational activity. The levels of of formation of the IT-specialists’ awareness of mathematical knowledge value are established and determined. The survey and monitoring program were developed and realized which showed the changes in the distribution of pre-service IT-specialists by the levels of the said awareness for their future IT career. The prospects of further research are outlined in terms of holding the empirical research for the verification of the offered PBL activity impact on the motivation to IT-specialists’ learning mathThe software module’s core components are distinguished and the set of requirements in terms of their design are formulated according to the logic of the components work.

Complementary Worldviews Aligning: A Relational Approach to STEM Education

Abstract: Educators in Canada face federal and provincial mandates arising from the TRC Calls to Action (2012) to incorporate First Nations, Métis, and Inuit (FNMI) perspectives across the curriculum. Yet it is not uncommon to hear K–12 educators as well as some university faculty asking, "How do I incorporate Indigenous culture into science? Is it even possible?" This paper not only describes how it is possible but also explains why it is necessary, providing a theoretical framework and practical examples of how Western approaches to science, technology, engineering, and math (STEM) knowledge can be braided with Indigenous treatments of these knowledge categories and disciplines. Historically, Niitsitapi (Blackfoot) and other Indigenous worldviews have been systematically and systemically dismissed by the sciences and primarily confined to the humanities. Therefore, to move beyond merely learning about Indigenous cultures and lean into learning from them (i.e., learn through the lens of Indigenous cultures), we must (1) teach Niitsitapi and other Indigenous stories beyond the humanities classroom; (2) better engage the etiological, ontological, epistemological, axiological, and practical traditions of Niitsitapi and other Indigenous Peoples; and (3) operationalize pedagogical and methodological models that acknowledge, respect, and embody Indigenous ways of knowing and being in STEM education.

Augmented Reality as a Tool to Support the Connection Between Reality and Mathematical Knowledge: A Case for Teaching Parallel Relations of Planes in Space

In the 11th−grade Vietnamese Mathematics Curriculum, students learn about parallel relations between planes in space. This is cognitively challenging for many students. Studies have shown difficulties relating to limited spatial imagination and drawing representations. The teacher’s approach also causes difficulties for some students; for example, some teachers do not approach new knowledge from practice. These approaches lead students to learn math only in that class rather than to relate math knowledge to real life, whereas real-life objects can be good tools for illustrating knowledge of spatial geometry. This study uses an action research method using GeoGebra 3D Calculator software to design teaching situations about parallel relations of lines and planes in space. This study was conducted with 40 students in 11th grade in Long An Province, Vietnam. It was found that learning tasks can be designed to help students construct knowledge effectively and overcome difficulties. The results of this research show that AR software for 3D Geometry, in particular GeoGebra, creates a connection between reality and abstract knowledge about the parallel relations of lines and surfaces in space. The research also shows that the application of augmented reality in teaching helps students understand and test hypotheses, eliminate false hypotheses, and build new knowledge about parallel relations effectively.

Acquisition of math knowledge in digital and non-digital game-based learning classrooms: Impact of intrinsic motivation and cognitive load

Educational games, spanning a wide spectrum from digital games to non-digital games, have been considered as promising tools to facilitate math learning. However, previous studies focused more on digital game-based learning, few compared the differences between digital and non-digital games. We conducted a quasi-experiment to examine the effects of digital and non-digital games on math knowledge acquisition, intrinsic motivation and cognitive load in Chinese classrooms. Two equivalent versions of games (digital vs non-digital) focusing on coordinate knowledge acquisition were developed, and three groups (digital game, non-digital game and traditional teaching group) were assigned. The results reveal that students in the digital game group reported significantly higher intrinsic motivation and lower intrinsic and extraneous cognitive load than non-digital game group. While non-digital game group had better knowledge acquisition performance and germane cognitive load than digital game group. Our findings suggest that affordance of game technology influences students’ motivation and cognition, causing “false” high motivation and low cognitive engagement among students. Non-digital games could serve as cost-effective alternatives to enhance math learning performance within authentic classrooms, thus providing valuable insights into establishing a resilient and sustainable game-based learning environment.

The (in)effectiveness of training domain‐general skills to support early math knowledge

The (in)effectiveness of training domain‐general skills to support early math knowledge

“He’s Probably the Only Teacher I’ve Actually Learned From”: Marginalized Students’ Experiences With and Self-Perceptions of High School Mathematics

Understanding how marginalized students experience and perceive mathematics is critical to achieving the goal of inclusive and equitable math pedagogy. We report on 67 focus groups with 251 predominantly Black high schoolers experiencing economic marginalization in the Southern United States and attended to their achievement level and race-gender identities. Students often shared concerns about their teacher’s math knowledge for teaching and effectiveness in supporting academic success. Their self-perceptions of math identities varied, and students often did not value advanced math even when they expressed career interests that require advanced math. We discuss practical implications for supporting the math development of marginalized high schoolers, including centering the needs and strengths of Black girls, and propose an expanded inclusive and equitable pedagogical framework.

Improving students’ problem-solving abilities through answering questions in metaverse games: taking GOXR software as an example

In computer-based dialogue learning, students’ willingness to communicate and ability to interact is one of the important factors. Few studies have examined the testing of mobile metaverse teaching material systems built for interactive communication and learning courses. This study developed and designed course content for a virtual classroom, which is suitable for mobile learning on Android or iOS systems and can provide metaverse space for students to discuss homework using their mobile phones, as well as a system for online self-learning and testing. Students can participate in classes without time or space restrictions. In addition, questions related to life math knowledge and leveling up are included, such as the basic reproduction number of COVID-19, influenza, and enterovirus. There were 100 valid responses from two schools, which recognized the convenience and benefit of the virtual digital technology of the mobile self-learning system in the metaverse space as an auxiliary tool for learning, as it provides a more flexible and diversified educational learning mode. This system can be used for course teaching, after-class review, and testing to facilitate self-testing of learning results.

Your body tells how you engage in collaboration: Machine‐detected body movements as indicators of engagement in collaborative math knowledge building

AbstractCollaborative learning, driven by knowledge co‐construction and meaning negotiation, is a pivotal aspect of educational contexts. While gesture's importance in conveying shared meaning is recognized, its role in collaborative group settings remains understudied. This gap hinders accurate and equitable assessment and instruction, particularly for linguistically diverse students. Advancements in multimodal learning analytics, leveraging sensor technologies, offer innovative solutions for capturing and analysing body movements. This study employs these novel approaches to demonstrate how learners' machine‐detected body movements during the learning process relate to their verbal and nonverbal contributions to the co‐construction of embodied math knowledge. These findings substantiate the feasibility of utilizing learners' machine‐detected body movements as a valid indicator for inferring their engagement with the collaborative knowledge construction process. In addition, we empirically validate that these inferred different levels of learner engagement indeed impact the desired learning outcomes of the intervention. This study contributes to our scientific understanding of multimodal approaches to knowledge expression and assessment in learning, teaching, and collaboration.Practitioner notesWhat is already known about this topic Previous research emphasizes the importance of gestures as essential tools for constructing common ground and reflecting shared meaning‐making in learning and teaching contexts. The prior studies in multimodal learning analytics (MMLA) suggest that certain forms of body movements and postures can be differentiated based on the automatic detection of upper body joint locations. Empirical observations indicate that co‐thought gestures typically involve smaller hand or arms movement that are closer to the gesturer's body than co‐speech gestures used in interpersonal communication. What this paper adds This paper fills the research gap by examining the use of gestures in collaborative learning, offering insights into how individuals contribute verbally and nonverbally to collaborative knowledge construction. This paper introduces the concept of using machine‐detected body movements as a viable proxy for inferring learners' engagement in collaborative knowledge‐building activities. Leverages sensor technologies for automatic detection of body movements, the innovative approach in this work seeks to overcome the time‐intensive and laborious process of manually coding gestures. Implications for practice and/or policy By recognizing the potential significance of learners' body movements in indicating engagement levels with collaborative knowledge‐building activities, instructors can set up computer‐supported collaborative learning (CSCL) environments to enable capturing these movements. Given the crucial role of gestures in learning, teaching, and collaboration, educators can create more equitable formative assessment practices for linguistically diverse students by developing strategies that align with multimodal forms of knowledge expression. Research can expand beyond mathematics to explore the transferability of these findings to other subjects, helping educators create comprehensive pedagogical approaches that leverage multimodal interactions across disciplines.

Student profiles based on in‐game performance and help‐seeking behaviours in an online mathematics game

AbstractWell‐designed online educational games can improve students' math knowledge, skills and engagement; however, more research is needed to understand how to formatively assess components of students' mathematical understanding and learning as students solve problems in online educational games. In this study, we examined how 7th‐grade students' (N = 760) in‐game performance (ie, strategy efficiency, mathematical validity of the first action, mathematical errors) and help‐seeking behaviours (ie, hint requests) correlated with their algebraic knowledge in an online mathematics game. The k‐means cluster analysis identified four groups of students based on their in‐game metrics, and some variabilities in their in‐game performance were found. Although hint requests were available, only a few students showed a high percentage of hint requests during their gameplay. The regression analysis revealed that students' in‐game performance and help‐seeking behavioural patterns explained a significant amount of variance in students' algebraic knowledge above and beyond their prior knowledge. Our results suggest that how students interact with the online learning game is related to their later math performance, and qualitative aspects of student behaviours captured using log data provide meaningful information to students' algebraic understanding. Practitioner notesWhat is already known about this topic Well‐designed online educational games can improve students' math knowledge, skills, and engagement. Several studies found that some in‐game metrics, such as in‐game progress or correctness of tasks, are positively associated with learning outcomes. However, many studies used simple metrics like the correctness of each task or the number of problems completed to measure students' performance in the game. Few studies measured more in the moment or qualitative aspects of student in‐game performance, for example, how efficiently students solved problems in the game. What this paper adds In‐game metrics measuring more in the moment and qualitative aspects of students' problem‐solving explained a significant amount of variance in students' algebraic knowledge above and beyond students' prior knowledge. Students' strategy efficiency and strategic planning were positively associated with students' math problem‐solving performance. Although hints were available for almost all problems, only a few students exhibited a high level of help‐seeking behaviours, and the students with the lowest in‐game performance who needed help the most showed low help‐seeking behaviours. Implications for practice and/or policy Classifying students into profiles could provide ways to identify students with different levels of problem‐solving skills and help teachers provide more personalized instruction. Teachers could use this information as a formative assessment to identify the core areas of intervention needed, particularly for students struggling with math concepts taught in the game. Instructional strategies that make hints more appealing or engaging to students might be needed.

Money talks! The role of parents’ discussion of money for preschoolers’ math knowledge

Children’s participation in cultural, everyday practices and social interactions involving math and money can contribute to the development of their knowledge and skills in these domains. Further work is needed to uncover what features of these activities, such as aspects of the conversations that may occur (e.g., number and money talk), facilitate and/or are shaped by children’s understanding of money concepts and skills. The present study examined the extent to which parents engaged in conversations about numbers and money with their four-year-old children during pretend grocery play and the relations to children’s math skills. We found that talk about price labeling and exchanging currency or goods occurred most frequently and that money and number talk were not significantly related to children’s broader math skills. However, parents’ money talk was positively associated with children’s money-related math skills, and this association was driven by the co-occurrence of talk about money and numbers. Our results suggest that parent-child conversations in familiar contexts such as grocery shopping provide rich opportunities to discuss culturally relevant practices surrounding money and practice math skills in the context of monetary exchanges. Thus, it is critical to consider how existing family practices and everyday contexts support children’s early math learning.

Development of creative thinking via fractions and rhythm

In this study we follow the progress of fourth graders’ (N = 86) fractions knowledge and their fraction-related creative thinking, while utilizing a multi-disciplinary approach that combines mathematics and music with various teaching emphases. For the purpose of the study, an intervention program was implemented, focusing on fractions knowledge, rhythm patterns, and creative thinking. Three classes were taught the same MusiMath curriculum that explicitly connects mathematics and music. Moreover, these classes received additional instruction on fractions and rhythm, but with differing focuses: Creative Math class, Creative Music class, and Creative Math and Music class. A fourth class served as a control group, where standard mathematics and music were taught without any MusiMath lessons or creative intervention. Using a novel software, developed for the current study, students answered questions that had only one correct answer, as well as questions that invited diverse and original responses encouraging creative thinking. Pre- to post-intervention analyses indicated that the experimental groups outperformed the control group on fractions knowledge and creative thinking in both math and music, showing superiority of the Creative Math and Music instruction.

A study of mathematical understanding levels in set theory based on the APOS framework by using python programming language for secondary school students

This study used the APOS theoretical framework to assess secondary school pupils’ set math knowledge. Princess Chulabhorn Science College Lopburi randomly sampled 20 8<sup>th</sup> graders in the second semester of 2022. There are a total of six plans, with each plan comprising a 180-minute. The objectives are the instructional goals. Content is the topic. Learning materials include resources and tools. Last, activities include learning assignments and exercises. Assessment includes three subtests to assess set understanding and a test to assess mathematical comprehension. These activities increased secondary school students’ set comprehension. The result of the study indicated that they had demonstrated a strong<b> </b>conceptual understanding of set theory to pass the criteria over 60% of the total students with a statistical significance level of .01. Furthermore, delving into all four APOS theoretical levels we found similar impressive results, with over 60% of students exceeding expectations at each level (p<0.01).

Improving 5th Grade Mathematics Knowledge with Worked Examples and Self-Explanation Prompts

Prior short-term studies have shown the effectiveness of worked examples and self-explanation prompts in improving elementary students’ mathematics knowledge. However, year-long classroom-based interventions have been tested only with older students. The purpose of the current study was to explore the effectiveness of a year-long classroom intervention, MathByExample, which paired worked examples and self-explanation prompts with practice problems. We utilized a classroom-based experimental design where 5th-grade classrooms were randomly assigned to one of two conditions. Findings illustrate that intervention dosage impacts the effectiveness of the intervention in improving 5th graders’ grade-level mathematics knowledge. In addition, prior knowledge impacted the effectiveness of the intervention for two of the four outcome variables. This study expands the literature on the use of worked examples and self-explanation prompts in several ways. It provides evidence that this tool has the potential to improve elementary students’ learning. It included four different measures of math knowledge, which provides stronger support for the effectiveness of the intervention. Finally, it adds to the literature that shows the benefits of studying and explaining both correct and incorrect worked examples.

Investigating young children’s engineering construction and design in free outdoor play activities in Oman

ABSTRACT This study investigates children's engineering construction and design and math knowledge in play activities in a preschool setting in a hot country, Oman. It contributes to studies examining the relationships between play and STEM learning by showing that children experience engineering and mathematical concepts in play activities. The study draws on Vygotsky's (1967) notion of play as an imaginary situation to analyze children's strategies in play activities. It is situated within approaches that point to the link between imagination and cognitive development using ethnography as a research methodology and taking an interpretive paradigm to data analysis. The data included observation notes and video recordings of children's interactions in play activities. The findings indicate that free playtime enables children to express their ideas about constructions (building), measures, and functions of materials. It also highlights how teachers' conceptualization of play is shaped by contextual factors (hot weather). It suggests that teachers can develop children's conceptual development in math by taking an intentional teaching approach to playful activities.

Words matter: Effect of manipulating storybook texts on parent and child math talk

Children who experience greater math talk during home math activities demonstrate higher levels of math knowledge. The current study was designed to test whether the features of storybooks affect the amount and kind of extratextual math talk parents and preschool children produce during storybook reading. Parent-child dyads (N = 50) were randomly assigned to one of two conditions: implicit or explicit. The implicit condition involved a storybook with math elements embedded only in the illustrations; whereas, the explicit condition included the same set of illustrations as well as numeric and spatial words in the text. Both parents and children in the explicit condition produced more math-related utterances than those in the implicit condition. Among parents, the difference in quantity of talk was present across a range of different types of math talk. Mediation analyses showed that condition affected parent math talk via child math talk and child math talk via parent math talk. These results point to the bidirectional relation between parent and child math talk during storybook reading and the importance of the features of learning materials on that talk.

Preparedness of Students for Self-regulated Learning of Mathematics

This work aims to examine the relationship between general self-regulated learning abilities and students' general intellectual abilities, mathematical learning abilities, and academic achievement. A study was conducted with a sample of eighth-grade students (N=325). The research employed a survey and descriptive method, and the instruments used included a test of general intellectual abilities, a test of self-regulated learning abilities, a test to measure mathematical learning abilities, and a standardized math knowledge test. Based on the obtained results, we indicate those factors with high or moderately high correlations. Among the results obtained, there is a high correlation between general intellectual abilities and general self-regulated learning abilities (subtests for interpreting graphs and interpreting geographic maps). The results show a high correlation between the total score on the self-regulated learning abilities test and math achievement. A moderately high correlation was achieved between the test of general intellectual abilities and self-regulated learning abilities (subtests for finding necessary information, exploring new material, and the index of developed abilities and techniques for self-regulated learning). On the math learning ability test, various abilities are differentiated, including formalization of mathematical content, spatial abilities, imagination, flexibility, and critical thinking. Based on the research results, it is considered significant to investigate the effects of different innovative teaching systems and teaching methods on students' self-regulated learning abilities and mathematical learning abilities.

Research And Developing Mathematics Knowledge Child Development Perspectives, 2022

Proficiency in mathematics is critical to success academically, economically, and in life. Greater success in math is related to entering and completing college, earning more in adulthood, and making more optimal decisions concerning health. Knowledge of math begins to develop at a young age, and this early knowledge matters: Knowledge of math at or before school entry predicts outcomes in math and reading across primary and secondary school. More than one children struggle to learn math. For example, only 60% of fourth-grade and 55% of eighth-grade students in the United States performed at or above proficiency in math on the 2020 National Assessment of Educational Progress, and proficiency rates were even lower for African-American and Hispanic children and for children from low-income homes. More than one students do not master challenging math content. Developing strong knowledge about mathematics is important for success academically, economically, and in life, but more than one children fail to become proficient in math. Research on the developmental relations between conceptual and procedural knowledge of math provides insights into the development of knowledge about math. First, competency in math requires children to develop conceptual knowledge, procedural knowledge, and procedural flexibility. Second, conceptual and procedural knowledge often develop in a bidirectional, iterative fashion, with improvements in one type of knowledge supporting improvements in the other, as well as procedural flexibility. Third, learning techniques such as comparing, explaining, and exploring promote more than one type of knowledge about math, indicating that each is an important learning process. Researchers need to develop and validate measurement tools, devise more comprehensive theories of math development, and bridge more between research and educational practice.

Multiplying Success: Small-Group Instruction in an Early College High School Mathematics Class

The study was conducted in an early college high school’s 9th-grade Precalculus class and focused on how differentiated small-group math centers impact students’ course grades and overall math progress. Students’ math journals were evaluated on how effective students find the Precalculus math centers to improve their math progress and grade. A paired sample t-test showed that students significantly improved their course grades and overall math knowledge over twelve weeks of instruction. However, students’ views about the small group instruction differed greatly. Working in small group math centers is an effective instructional method. Advanced students can move through the curriculum faster and work on enrichment, while others are given extra time and support to reach proficiency. It is, however, significantly more time-consuming than the traditional lecture/practice method. Capitalizing on the effectiveness of small group instruction is only possible after finding a way to reduce the time it takes to prepare for the centers.

Large Field Surveys and Short Items Sets: Estimating Reasoning Skills among Distinct Samples in Malawi and Zambia

Raven’s Progressive Matrices measure logical reasoning and are often included in large multi-topic surveys in low and middle-income countries. The matrices are image-based items that do not require formal knowledge of language or math to complete. As such, they are attractive items to measure logical reasoning in international development contexts. Many of these large field surveys include short item Raven’s sets because space is too limited to fit a full suite. However, short sets can result in restricted variation in terms of test scores. In this paper, we use a nominal response model (NRM) form of item response theory (IRT) to uncover hidden variation in right and wrong answers using short-item Raven’s tests from two large field surveys in Malawi and Zambia. We also analyze relationships between a set of other variables, comparing performance of different versions of the logical reasoning scores as both independent and dependent variables, checking the validity of the new scores. The new NRM-estimated logical reasoning scores follow a more normal distribution in both samples. Validity checks suggest that when relationships are less strong, NRM-estimated scores can capture more nuance than summed scores or even 2 parameter logistic IRT-estimated scores. NRM can uncover differences that are not apparent when using simple summed scores.