This paper examines the field of mathematics education and the divisions within this domain. It presents a comparison from two websites, The Science of Math and The Science of Mathematics, and discusses their similarities and differences as they describe and define the field of mathematics education.
This paper describes a structured approach to engaging preservice teachers in professional mathematics education conferences through a combination of presentation or volunteer opportunities. We detail a small-scale program implemented at Author’s University that removes financial barriers to conference participation while providing scaffolded support and mentorship. The program design emphasizes building a community through shared experiences and structured reflection. We offer practical guidance for teacher preparation programs seeking to implement similar initiatives, including timeline considerations, mentoring structures, and assessment strategies.
This study discusses how teaching K-8 preservice teachers (PSTs) about the measures of central tendency through the context of the voting process impacted their learning about mathematics as well as the voting process and issues that may arise. Being a well-informed citizen, especially for people who will be teaching in the next few years, is important as they will influence many children in the future. Findings show changes in the PSTs' perspectives on the voting process, voting issues, and learning center measures. Additionally, PSTs indicated they enjoyed learning about the measures of central tendency through context of the voting process and the issue of voter suppression. Furthermore, researchers found teaching through this context had long-term implications, as one PST reached out during the most recent election, which was more than a year after the course ended.
The Georgia Numeracy Project Individual Knowledge Assessment of Number (IKAN) written assessment is a video-based assessment used in Georgia to assess Grades 4-8 numeracy mastery. IKAN written pre/post assessment data were collected spring and fall 2021 and spring 2022 semesters at a Georgia instituion of higher education in a Foundations of Numbers and Operations course to assess K-8 preservice teachers mathematics numeracy knowledge. Students' numeracy knowledge increased during the course but almost all students did not complete the course with the highest possible stage scores. These data support the assertation a content course can positively impact student knowledge. These data also show that more focused work is needed in content courses that prepare future K-8 preservice teachers in order for these teachers to teach Grades 4-8 numeracy knowledge.
The following autoethnography is completed by a group of mathematics teacher educators (MTEs) after transitioning their mathematics content courses for K-8 Preservice Teachers (PSTs) from face-to-face to online due to COVID-19 in Spring 2020. The MTEs present their perceptions of the shift to online teaching and learning by describing (a) how they typically teach their classes, (b) how they redesigned classes to support student learning when the pandemic started, (c) their PSTs' perceptions of which course components we effective (or not) in helping them adjust to the new online learning environment, and (d) next steps in teaching and research.
This paper reports the benefits and challenges of incorporating a paired-placement model at four different post-secondary teacher preparation programs in secondary mathematics education. The paired-placement model places two secondary mathematics clinical teachers with one mentor (or cooperating) teacher during their internship experience. Benefits exhibited were increased collaboration, more knowledgeable cooperating teachers, increased sense of community, teaming, pedagogical risk-taking, increased reflective practice, established natural professional learning communities, Plan-Do-Study-Act Cycle (PDSA), and increased accountability. Challenges found through the PDSA cycle include personnel issues, number of days teaching, perceived classroom management preparation, preparing university supervisors, mentors, and teacher candidates, and support for collaboration afterward.
Mathematical Education of Teachers II (METII), echoed by the American Statistical Association publication, Statistical Education of Teachers, recommended teacher preparation programs support future teachers in developing deep understandings of mean and median, such that middle grades teachers may use them to “summarize, describe, and compare distributions” (Conference Board of Mathematical Sciences, 2012, p. 44; Franklin et al., 2015). Georgia Standards of Excellence require statistical reasoning from students beginning as early as 6-7 years old, including interpretation of measures of center and statistical reasoning about best measures of center (Georgia Department of Education, 2015). This level of understanding and interpretation of measures of center, however, has been a persistent struggle for students and their teachers (e.g., Jacobbe & Carvalho, 2011). Jacobbe and Carvalho argued that an over-reliance on computation with little focus on conceptual understanding has created these barriers to statistical reasoning. To impact students’ understanding, a starting point is to address teachers’ understanding, particularly by supporting conceptual understanding of measures of center in teacher preparation programs (Jacobbe & Carvalho, p. 207). Our research question was: What conceptual understandings of mean and median do preservice teacher candidates (PSTs) exhibit when presented with a mean and median statistical task? We present findings from a two-part study, comparing PSTs’ responses to a task written to elicit conceptual understandings and statistical reasoning in one semester, with PSTs’ responses to a revised task in a second semester, both given at the end of a senior-level Statistics for K-8 Teachers course.
National Council of Teachers of Mathematics (NCTM) has long supported the use of children’s literature, writing, and manipulatives to improve conceptual understanding of mathematics (2000). In a professional learning community for K-2 teachers, professional development was designed and implemented on ways to incorporate literacy and manipulatives into a mathematics lesson. The teachers were charged with collaboratively planning lessons that included multiple components: the standard(s), a mathematics activity, manipulatives, a writing task, and children’s literature. As the data were analyzed, it became apparent that while most of the lessons were well connected, this did not happen for all of the lessons. In addition, we observed that there were cases of teacher misconceptions. We feel these misconceptions contributed to the lack of connectedness in some of the lessons.
As mathematics teacher educators, we have a responsibility to prepare as many people as we can, to teach mathematics in ways that foster a deeper understanding of the content. We do this by teaching current and future teachers in college programs and providing professional development to in-service teachers. A less explored way is to prepare these “students” to present ideas they have learned to colleagues at their school, other schools in their district, and conferences. In this paper, I share my experience of helping students go through the process of preparing to present over the last two years at our state K-12 mathematics conference and include some of their reflections through this process.
Creative writing in the mathematics classroom promotes mathematical applications in the real world, constructivist learning, embodied learning, transfer of mathematical ideas, and student engagement. When students are allowed to write about mathematical concepts creatively, they are able to take concepts that they have learned and put them into their world or even create a situation where the mathematical concept applies. Applying mathematical concepts to other environments helps learners transfer mathematical concepts. Learners are able to take the mathematics content and contextualize it outside of the classroom. Writing in mathematics also is a way for students to embody learning. Because writing involves some kind of physical action, connecting mathematics through physical means allows for active and embodied learning. Additionally, creative writing can help students to reformulate their thinking about a concept or can allow for review of mathematics material. As teachers and learners, we see the value in creative writing in the mathematics classroom. Writing can transform us and help to deepen understanding of mathematical concepts. In the classroom, we can use creative writing to aid in students’ understanding of mathematical concepts. Creative writing is also engaging and allows students the freedom to reformulate and review their mathematical thinking in their own ways.
In the mathematics classroom, most preservice mathematics teachers possess basic skills to use technology as an instructional strategy in communicating content standards. However, today’s demands for preservice teachers to engage in a variety of “best teaching practices” in their preservice teaching and edTPA requirements can oftentimes place the acquisition of technical skills and integration of new technology in content curriculum far from the forefront of their minds. Ertmer, Conklin, Lewandowski, Osika, Selo, and Wignall (2003) acknowledged preservice teachers’ desires to gain the adequate technical skills necessary to use technology in teachers’ daily tasks of facilitating and managing their classrooms. They suggested that “in order to translate these skills into practice, teachers need specific ideas about how to use these skills to achieve meaningful learning outcomes under normal classroom conditions” (p. 96). Preservice teachers need guidance and information about “how, as well as why, to use technology in meaningful ways” so they can “develop their own visions for, or ideas about, meaningful technology use” (p. 96). Thus, the instructional aid of technology integration in the mathematics classroom must look to address specific uses of technology to help preservice mathematics teachers build awareness and confidence to implement innovative teaching approaches to enhance student learning.
A lesson study cycle is a professional development process that integrates research and reflection through collaboration. The cycle allows a group to refine a lesson based on these collaboration efforts such as interaction with students and the post-lesson discussion. Secondary pre-service teachers in a mathematics methods course engaged in a lesson study cycle through collaboration between in-service teachers, Georgia College professors, and students in a local high school classroom. We systematically investigated this process to determine that through preparing, enacting and reflecting on their practice, Pre-service Teachers (PST) developed insight, reasoning, and understanding of the mathematics that they taught.
Despite some gains, improving mathematics instruction remains an area of concern in the United States. The implementation of the Common Core Standards and the challenge of teaching the 21st Century student require mathematics teachers to examine their pedagogy to determine if they need to change or improve their practices. This paper provides a personal account of my journey when determining my identity as a mathematics teacher and how constructing my identity helped in changing and improving my practices as a mathematics teacher. The study was done using autoethnography, a burgeoning research method, and identity theory. This study has the goals of giving “voice” to the classroom teacher and providing a practical method for improving instruction. The findings indicate that my identity is composed of many facets, and my identity is a key factor underlying who I am as a mathematics teacher. The findings also resulted in the development of the Math Madness Model (M3) Instrument, which can facilitate self-studies by other mathematics classroom teachers and educators with the purpose of improving their practices.
College students often ask questions such as, “Why do I have to take this class? Is there a point to it?” For Early Childhood Education (ECE) majors these questions may often take on a slightly different form, wondering, “How can I incorporate this information into my classroom?” or “Do I understand this well enough to teach this to my students?” It is especially important for pre- service teachers to feel confident working with the mathematical content that they are learning and for them to believe that they can successfully teach that same information to a group of students. Swackhamer, Koellner, Basile, and Kimbrough (2009) have called for additional research concerning “how content knowledge can support teacher efficacy along with increasing the knowledge of students” (page 75). The number of mathematics content courses provided to support the development of early childhood education majors understanding of mathematics varies across universities. Some wonder whether it is necessary to have a series of four mathematics content courses or if a fewer number of courses would suffice. This study is intended to determine if there is a significant difference in how pre-service teachers think about teaching mathematics at each stage of a progression of four-course content courses, as well as to determine if there seems to be a ceiling effect when students no longer feel these courses are continuing to improve their content knowledge and subsequent teaching ability. Cohen and Hill (2001) describe teacher beliefs as, “Teachers’ ideas about mathematics teaching and learning” and note that these beliefs may shape their teaching. One aspect of a teacher’s beliefs includes her sense of self-efficacy. Researchers have recognized teacher’s sense of self-efficacy as an important attribute of effective teaching which is related to positive teacher and student outcomes (Tschannen-Moran, Woolfolk Hoy, & Hoy; 1998). In this study we explore the effects of a series of four mathematics content courses on pre-service teachers’ beliefs about teaching mathematics and their own self efficacy beliefs. These classes were designed to improve understanding and self-efficacy in a subject that many students have the most difficulty with. Our study provides a snapshot of students from each of the four content courses in the series by exploring their beliefs about teaching mathematics and their own self-efficacy and beliefs they hold at the end of each course. References: Cohen, D. & Hill, H. (2001). Learning policy: When state education reform works. New Haven, CT: Yale University Press. Swackhamer, L.E., Koellner, K., Basile, C., & Kimbrough, D. (2009). Increasing the self- efficacy of inservice teachers through content knowledge. Teacher Education Quarterly, Spring, 63-78. Tschannen-Moran, M., Woolfok-Hoy, A., & Hoy, W. K. (1998). Teacher efficacy: Its meaning and measure. Review of Educational Research, 68(2), 202-248.
Eight assessments were developed for CAEP (formerly NCATE) and NCTM recognition of our secondary mathematics program. These assessments include internship work samples, field evaluations, and candidate portfolios addressing content knowledge, pedagogical methods, and mathematics technology. Based on data collected from these assessments, alongside ongoing evaluation of the program, several curriculum and program revisions were implemented, including: 1) development of mathematics content-specific courses in classroom management, assessment, and secondary curriculum; 2) restructuring of a senior seminar course in mathematics education; and 3) an increased content focus in probability and statistics. The adoption of new NCTM standards in the CAEP review process then provided an opportunity to significantly revise these assessments. We describe the original assessments, the results of assessment data analysis, subsequent program changes, assessment revisions now in progress, challenges encountered, and additional program enhancements envisioned.
The availability and familiarity of online discussion tools create new instructional options that teacher educators can use to foster prospective teachers’ understanding of mathematics. In particular, online discussion blogs provide an avenue through which teacher educators can press prospective teachers to explore mathematical concepts and share their mathematical reasoning with peers. Furthermore, by incorporating visual stimulations as a design component of these discussion blogs, prospective teachers can make sense of and respond to others’ ideas about mathematical concepts with greater clarity. This paper shares preliminary findings of a research study that examined the extent to which the design of a series of visually-aided online discussion prompts facilitated prospective elementary teachers’ (PSTs) use of mathematical reasoning in a geometry and measurement course. Results suggest that (a) the wording of discussion prompts influences the nature of mathematical justifications that PSTs focus on in their responses and (b) social norms for communicating in online forums may influence the ways in which PSTs interact with peers in an online discussion blog about their mathematical reasoning.
Many teachers have trouble transitioning their students between natural recursive thinking about the data and algebraic notation for representing linear functions (Zazkis & Liljedahl, 2002). In this study, we interviewed eighteen middle school students to see how they used prior instruction to think about a geometric pattern and construct its corresponding linear equation. All students were given the same task to complete and were questioned about their thinking during the interview. We found that the recording of pattern recognition plays a substantial part in helping students recognize and write explicit patterns. By having students decompose the total perimeter into how they saw the pattern growing, students were more successful in making the connection to the numeric representation of growth. In addition, they were better able to explain how they set up the equation, and the connection of each part of the equation to the original pattern. As teachers work with their students in developing a conceptual understanding of linear equations, it is critical that students are exposed to geometric patterns. The results of this study will help mathematics teacher educators better prepare teachers to develop their students’ develop rich and connected mathematical understanding. References: Zazkis, R. & Liljedahl, P. (2002a, March). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49, 379-402. Zazkis, R. & Liljedahl, P. (2002b). Arithmetic sequence as a bridge between conceptual fields. Canadian Journal of Science, Mathematics and Technology Education, 2(1), 93-120.
