• Research in Mathematical Education
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• v.27 no.3
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• pp.335-365
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• 2024

Learning mathematics in a student-centered, problem-based classroom requires students to develop mathematical understanding and reasoning collaboratively with others. Despite its critical role in students' collaborative learning in groups and classrooms, evidence of student thinking has rarely been perceived and utilized as a resource for planning and teaching. This is in part because teachers have limited access to student work in paper-and-pencil classrooms. As an alternative approach to making student thinking visible and accessible, a digital collaborative platform embedded with a problem-based middle school mathematics curriculum is developed through an ongoing design-based research project (Edson & Phillips, 2021). Drawing from a subset of data collected for the larger research project, we investigated how students generated mathematical inscriptions during small group work, and how teachers used evidence of students' solution strategies inscribed on student digital workspaces. Findings show that digital flexibility and mobility allowed students to easily explore different strategies and focus on developing mathematical big ideas, and teachers to foreground student thinking when facilitating whole-class discussions and planning for the next lesson. This study provides insights into understanding mathematics teachers' interactions with digital curriculum resources in the pursuit of students' meaningful engagement in making sense of mathematical ideas.

• Journal of The Korean Association For Science Education
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• v.30 no.7
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• pp.920-932
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• 2010

Many topics in science, especially, abstract concepts, relationships, properties, entities in invisible ranges, are described in mathematical representations such as formula, numbers, symbols, and graphs. Although the mathematical representation is an essential tool to better understand scientific phenomena, the mathematical element is pointed out as a reason for learning difficulty and losing interests in science. In order to further investigate the relationship between mathematics knowledge and science understanding, the current study examined 793 high school students' understanding of the pH value. As a measure of the molar concentration of hydrogen ions in the solution, the pH value is an appropriate example to explore what a student mathematical structure of logarithm is and how they interpret the proportional relationship of numbers for scientific explanation. To the end, students were asked to write their responses on a questionnaire that is composed of nine content domain questions and four affective domain questions. Data analysis of this study provides information for the relationship between student understanding of the pH value and related mathematics knowledge.

• Journal of The Korean Association For Science Education
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• v.25 no.7
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• pp.728-735
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• 2005

In this study, relationships between student the cognitive affective characteristics and conceptual understanding from individual computer-assisted instruction were investigated. Tests regarding field dependence-independence, learning strategy, self-regulated ability, visual learning preference, goal orientation, self-efficacy on ability, and computer attitude were administered. After having been taught by means of a CAl program, a conception test on molecular motion was administered. It was found that student conceptual understanding was significantly related to field independence, learning strategy, self-regulated ability among the cognitive characteristics and visual learning preference, goal orientation, self-efficacy on ability among the affective characteristics. Multiple regression analysis of the cognitive characteristics on conceptual understanding found that field dependence-independence was the most significant predictor. Self-regulated ability and a deep learning strategy were also found to have predictive power. Lastly, analysis of the affective characteristics, visual learning preference and self-efficacy on ability exposed them to be significant predictors of student conceptual understanding.

• Journal of the Korean School Mathematics Society
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• v.15 no.4
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• pp.719-745
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• 2012

This research is a study on student's understanding fundamental conception of mathematical curriculum, especially in geometry domain. The goal of researching is to analyze student's wrong conception about that domain and get the mathematical teaching method. We developed various questions of descriptive assessment. Then we set up the term, procedure of research for the understanding student's knowledge of geometry. And we figured out the student's understanding extent through analysing questions of descriptive assessment in geometry. In this research, we concluded that most of students are having difficulty with defining the fundamental conception of mathematics, especially in geometry. Almost all the students defined the fundamental conceptions of mathematics obscurely and sometimes even missed indispensable properties. Prior to this study, we couldn't identify this problem. Here are some suggestions. First, take time to reflect on your previous mathematics method. And then compile some well-selected questions of descriptive assessment that tell us more about student's understanding in geometry.

• Journal of The Korean Association For Science Education
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• v.25 no.1
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• pp.41-56
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• 2005

Assessing students' knowledge can be a challenging endeavor, as researchers attempt to capture the full complexity and potential development of children's ideas. In this study, the Dynamic Science Assessment (DSA) method (Magnusson, Templin, and Boyle, 1997) was employed to investigate 9-12 year old students' understandings of light, while engaging in multiple tasks with a flashlight with various reflectors and mirrors. The results showed that DSA was effective in providing an opportunity to establish a Zone of Proximal Development, in addition to diagnosing a student's prior understanding. Throughout the interview, a student showed a conceptual model of light as being a solid single entity whose shape can be determined by the shape of the casing of a flashlight. However, as DSA provided phenomena that could not be explained by his unitary model, the student began to re-examine his original conceptual model, and attempted to revise it. This study addressed how Dynamic Science Assessment can help us better understand, not only students' current state of understanding, but also a potential development of understanding in their ZPD. In that sense, this study argues that we should pay more attention to the instructive role of classroom assessment that can promote and support further development of students' deeper understandings.

• East Asian mathematical journal
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• v.36 no.2
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• pp.317-330
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• 2020

The purpose of this action research project was to study the effects of incorporating coding into the middle school math classroom affected student dispositions with math and their understanding of mathematical concepts. The project, involving a total of 107 US middle school students, used five data sources to examine these effects: a survey, a chart measuring student engagement, a pre- and post-assessment before and after the coding project, and teacher observation with reflection forms. After analyzing the data, it was found that incorporating coding into the middle school math classroom could have a positive impact on student math dispositions and their understanding of math concepts.

• Research in Mathematical Education
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• v.24 no.3
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• pp.255-278
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• 2021

Proof serves a critical role in mathematical practices as well as in fostering student's mathematical understanding. However, the research literature accumulates results that there are not many opportunities available for students to engage with proving-related activities and that students' understanding about proof is not promising. This unpromising state of instruction of proof calls for a novel approach to address the aforementioned issues. This study investigated an instruction of proof to explore a pedagogy to teach how to prove. The teacher utilized the way of problem posing to make proving a routine part of everyday lesson and changed the classroom culture to support student proving. The study identified the teacher's support for student proving, the key pedagogical changes that embraced proving as part of everyday lesson, and what changes the teacher made to cultivate the classroom culture to be better suited for establishing a supportive community for student proving. The results indicate that problem posing has a potential to embrace proof into everyday lesson.

• Research in Mathematical Education
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• v.9 no.1 s.21
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• pp.47-58
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• 2005

Although student-centered teaching practices have been advocated in mathematics education reform, implementing them at the classroom level remains challenging. This exploratory case study examined two unevenly successful student-centered approaches to see how teachers understand and characterize reform, and to articulate issues in implementing reform ideas. The comparison and contrast between the classrooms showed similar classroom social norms but dramatically different mathematical practices. This affords the possibility of exploring the challenges of reform for teachers and other personnel who are attempting to move teaching practices towards the student-centered ideals.

• Journal of Science Education
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• v.33 no.2
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• pp.346-352
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• 2009

The purpose of this research was to analyze the chinese chemistry terminology in chemistry unit of 7th grade science textbooks in 7th curriculum and find relationship between student understanding and difficulty index for chinese preferred students and non-chinese preferred students. The chinese terminology in 7th curriculum was reduced less than that of 6th curriculum but still was over 70%. Students had difficulties in understanding of abstract terminologies and science terms but thought easily the concrete, common terminologies. The tendency of student understanding was similar to that of difficulty index. For chinese chemistry terminology, understanding of chinese preferred students was higher than that of non-chinese preferred students. For easily translated chemistry terminology, there was no significant difference but both were showed the improved understanding. Therefore student understanding should be improved in science if science textbooks would be written by easily translated chemistry terminology.

• Research in Mathematical Education
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• v.11 no.2
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• pp.127-141
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• 2007

This paper compares and analyzes mathematics teachers' understanding of students' mathematical comprehension after experiences with the Cognitively Guided Instruction (CGI) or the Development of Mathematical Ideas (DMI) teaching strategies. This report sheds light on current issues confronted by the educational system in the context of mathematics teaching and learning. In particular, the declining rate of mathematical literacy among adolescents is discussed. Moreover, examples of CGI and DMI teaching strategies are presented to focus on the impact of these teaching styles on student-centered instruction, teachers' belief, and students' mathematical achievement, conceptual understanding and word problem solving skills. Hence, with a gradual enhancement of reformed ways of teaching mathematics in schools and the reported increase in student achievement as a result of professional development with new teaching strategies, teacher professional development programs that emphasize teachers' understanding of students' mathematical comprehension is needed rather than the currently dominant traditional pedagogy of direct instruction with a focus on teaching problem solving strategies.