Hangil Kim

DOI: Vol.27(No.2) 157-173, 2024

Researchers continue to emphasize the centrality of proof in the context of school mathematics and the importance of proof to student learning of mathematics is well articulated in nationwide curricula. However, researchers reported that students’ performance in proving tasks is not promising and students are not likely to see the need to prove a proposition even if they learned mathematical proof previously. Research attributes this issue to students’ tendencies to accept an empirical argument as proof for a mathematical proposition, thus not being able to recognize the limitation of an empirical argument as proof for a mathematical proposition. In Korea, there is little research that investigated high school students’ views about the need for proof in mathematics and their understanding of the limitation of an empirical argument as proof for a mathematical generalization. Sixty-two 11th graders were invited to participate in an online survey and the responses were recorded in writing and on either a four- or five-point Likert scale. The students were asked to express their agreement with the need of proof in school mathematics and to evaluate a set of mathematical arguments as to whether the given arguments were proofs. Results indicate that a slight majority of students were able to identify a proof amongst the given arguments with the vast majority of students acknowledging the need for proof in mathematics.

school students’ perceptions, mathematical argument, proof validation, survey

Amanda J. Meiners , Angel Luis Figueroa-rosado

DOI: Vol.27(No.2) 175-193, 2024

In K-12 education, reassessment is a common practice, providing students with opportunities to enhance their understanding through low-stakes assignments. However, reassessment is underutilized in higher education, including during the challenges posed by the COVID-19 pandemic. Our study advocates for expanding the use of reassessment in university settings to promote holistic learning and focus on what shifts of change were made by students in an initial mathematics content course as they sought to gain licensure for teaching in a birth (daycare/pre-K setting) to eighth-grade classrooms. Our study took place during COVID-19 semesters and aimed to examine how using a reassessment approach early on in a gateway course for Prospective Teachers (PTs) affected the pass rate of the course. Results showed significant differences between the PTs who engaged with the test recovery and those who did not. We propose recovery opportunities like ours provide the necessary guidance to support early degree necessary classes that are typically gatekeeping and, as another, likely cause too few students within the courses because they were able to advance into the teacher pipeline and out into the field. Future studies may consider how the reassessment could be done more before the official summative assessment of a unit or chapter to continue the shifts in teaching practices and pedagogy that are constant within the K-12 education systems at the university level.

mathematics education, prospective teachers, reassessment

Hangil Kim

DOI: Vol.27(No.2) 195-210, 2024

Researchers and curricula continue to call for proof to serve a central role in learning of mathematics throughout kindergarten to grade 12 and beyond. Despite its prominence and recognition gained during past decades, proof is still a stumbling block for both teachers and students. Research efforts have been made to address issues related to teaching and learning of proof. An area in which such research efforts have been made is analysis of curriculum material (i.e. textbook analysis) with a focus on proof. This study is another research effort in this area of research through investigating the guidance offered in curriculum materials with the following research question: What is the nature (e.g., kinds of content knowledge, pedagogical content knowledge) of guidance is offered for teachers to implement proof tasks in grade 8 geometry textbooks? Results indicate that the guidance offered for proof tasks are concerned more with content knowledge about the content-specific instructional goals than with pedagogical content knowledge which supports teachers in preparing in-class interactions with students to teach proof.

guidance, proof, teacher learning, textbook analysis

Tye G. Campbell , Sindura Kularajan

DOI: Vol.27(No.2) 211-221, 2024

What is the aim of mathematics education? Current aims of mathematics education often lack the multidimensionality needed to account for a successful experience in mathematics. In this short paper, we argue for a multidimensional aim of mathematics education via the construct of flourishing. Flourishing is derived from the notion of eudaimonia, which broadly refers to achieving the “highest good,” or living a well-lived life. Building on prior research, we operationalize flourishing as an aggregate of several positive affective, behavioral, cognitive, and social traits, all of which contribute to students’ propensities to achieve the “highest good” in mathematics. In particular, we propose five traits which contribute to students’ propensities to achieve the “highest good” (i.e., flourish) in mathematics: (1) positive emotions toward mathematics; (2) engagement in mathematics; (3) community in mathematics; (4) meaning in mathematics; (5) perceived competence in mathematics. Thus, we argue that one productive aim of mathematics education is to support students in fulfilling each of these traits, which ultimately leads to flourishing in mathematics. To supplement our theoretical stance, we offer suggestions for measuring flourishing as an aim. We close this short paper by describing the implications that such an aim might suggest for pedagogy, policy, and research.

flourishing, mathematics education, aims of mathematics education

Yujin Lee , Ali Bicer , Ji Hyun Park

DOI: Vol.27(No.2) 223-239, 2024

The integration of coding and mathematics education, known as coding-integrated mathematics education, has received much attention due to the strength of Artificial Intelligence-based Science, Technology, Engineering, Arts, and Mathematics (AI-based STEAM) education in improving students’ affective domain. The present study investigated the effectiveness of coding-integrated mathematics education on students’ development of affective mathematics engagement. Participants in this study were 86 middle and high school students who attended the coding-integrated mathematics program. Surveys of students’ affective mathematics engagement were administered before and after the intervention period. The results showed that students’ affective mathematics engagement was statistically significantly improved through coding-integrated mathematics education. In particular, students exhibited increased positive affective mathematics engagement in terms of mathematical attitude, emotion, and value. These findings indicate the positive influence of coding-integrated mathematics education on students’ learning in mathematics.

affective mathematics engagement, affect, attitude, emotion, value, coding, STEAM education

Sunghwan Hwang

DOI: Vol.27(No.2) 241-251, 2024

Mathematics educators have examined mathematical modeling, where students tackle authentic real-life problems and develop problem-solving strategies with a sense of agency. However, few empirical studies have been conducted to illuminate the developmental process of teachers’ competencies in mathematical modeling, particularly for elementary school teachers. Scholars have noted that elementary mathematics teachers can effectively teach mathematical modeling by designing tasks that consider students' abilities and preferences. In this vein, this review paper introduces a study conducted by Jung (2023), which examines the developmental process of an elementary school mathematics teacher's competencies in mathematical modeling and how she overcame related challenges.

mathematical modeling, teacher education, professional development, task development