Draw a picture of yourself learning math: What pre-service teachers’ self-portraits illustrate about their complex relationships with mathematics

Access the online Pressbooks version of this article here. The purpose of this study was to examine factors that may influence pre-service teachers’ relationships with mathematics. Elementary pre-service teachers who were enrolled in a mathematics methods course (n = 52) wrote a letter to math and drew a picture of themselves learning math. The self-portraits were analyzed by a team of undergraduate student researchers and teacher educators to identify themes related to the types of emotions, experiences, and situations displayed. The results of the self-portrait analysis indicated a higher percentage of negative emotions as compared to positive and neutral emotions. Additionally, the portraits indicated the influence of early elementary experiences on developing the participants’ math identity and relationships with mathematics. Implications for teacher preparation coursework and elementary mathematics pedagogy are discussed

The Landscape of US Elementary Mathematics Teacher Education: Course Requirements for Mathematics Content and Methods

The adequate preparation of future teachers of mathematics is critical, requiring sufficient opportunities to develop both pedagogical skill and content knowledge. Yet, despite new recommendations for mathematics teacher preparation, we know little about the landscape of course-based learning opportunities in US elementary teacher education programs. To what extent do US elementary teacher education programs meet the Standards for Preparing Teachers of Mathematics outlined by the Association of Mathematics Teacher Educators (AMTE) for mathematics content and methods courses? Based on an a priori power analysis, we gathered a random sample of 291 higher education institutions. Within these institutions, we analyzed 736 programs, including Bachelor’s, Master’s, and Credential programs. We found that overwhelmingly US elementary teacher education programs do not meet the aspirations outlined in the AMTE standards, with Master’s and Credential programs and those covering all elementary grades particularly falling short. Potential explanations for these challenges and implications for teacher education program design are discussed

What pre-service teachers want “Math” to know: Examining self-identified relationships and critical experiences with mathematics

This study examines the self-reported critical experiences that undergraduate pre-service teachers (PSTs) choose to share when writing a letter directly to “Math” and creating a self-portrait of a math learning experience. The letters sought to initiate a personification of math and the self-portraits to further explore math learning experiences of the PSTs. The letters and portraits were examined to understand the types of math relationships and critical events PSTs reported and their impact on PST identity and agency as a future teacher. Portraits were analyzed by PST research partners. The relationship between the categories of critical events and mindset was explored

A Fourth Grade Teaching Experiment on Fraction Magnitude: Investigating Student Reasoning Through Mathematical Discourse and Design Research

Abstract Students in the United States continue to struggle with fraction mastery despite the fact that understanding fractions is essential for further progress in mathematics (NAEP, 2008). This research project investigated the potential of using high-press mathematical discourse (Kazemi & Stipek, 2008) to investigate fourth graders’ emerging understanding of fraction magnitude. Fraction magnitude refers to the measurement quality of the fraction, or how much of a given unit the fraction represents. Students who understand the properties of fraction magnitude have demonstrated a more promising trajectory for fraction mastery and for success in algebra (Fuchs et al., 2014; Schneider, Grabner, & Paetsch, 2009; Siegler, Fazio, Bailey, & Zhou, 2012). This study investigated fourth graders’ reasoning about the measurement construct of fractions that emerged during a whole-class teaching experiment (Lamberg & Middleton, 2009; Lamberg, 2007; McKenney & Reeves, 2013). Students participated in solving tasks which involved fraction magnitude, measurement, and density. Design research methodology was used to carefully analyze the learning ecology (Cobb, Confrey, diSessa, Lehrer, & Schauble, 2003). The domain specific understanding of fraction magnitude was investigated using flexible design revisions based on student work and discourse which emerged during the unit. This was used to produce a fraction magnitude unit reflecting an actual learning trajectory of fourth grade students (Lamberg & Middleton, 2009; McKenney & Reeves, 2013). An instructional unit based on developing fraction magnitude and measurement understanding was created and used in this study. The developed unit incorporated research-based findings on using the measurement construct for instruction (e.g., Fuchs et Al., 2014: Schneider et al., 2009; Siegler et al., 2012) as well as research based curriculum, such as the Rational Number Project (Behr, Cramer, Harel, Lesh, & Post, 1979). Data was collected from each teaching episode. The lessons were video recorded, student work was documented and analyzed, and teacher/researcher interviews, as well as student interviews, were recorded, transcribed, and evaluated. An iterative design was implemented in which the data collected from one lesson informed changes made in the following lesson. The purpose of the iterative design was to test emerging theories and hypotheses of what was being understood and observed (Gravemeijer & Cobb, 2006; Lamberg & Middleton, 2009) The teaching experiment provided insights into students’ reasoning during fraction magnitude tasks and how episodes of whole class mathematics discourse supported both teacher insight and student understanding. The realized learning trajectory along with mathematical mindset norms that emerged are documented. Implications for curriculum development and teaching fraction magnitude are discussed

A Framework for Reflective Practice

Teaching involves making constant choices and orchestrating interventions that impact purposeful teaching and learning. Finding time to collect information and develop solutions for a teaching challenge can be problematic. Teachers may feel pressure to shift instructional practices without incorporating purposeful reflection. We developed a reflection framework and tested it in a middle grades classroom over a two-week period, and employed practitioner research to investigate the potential of allowing for deep reflection within the middle school structure. We investigated how the framework impacted the teacher’s ability to reflect and adjust based on student learning in the classroom. We conclude that sophisticated reflection in a social context is crucial to making conscious instructional modifications

Tension Between Objectivism and Constructivism in Organizing and Enacting Student Learning in Online STEM Education

Tensions between constructivist learning theories and objectivist learning theories in online courses implicate a need for a theoretical balance. This article describes organizing and enacting tasks that elicit constructivist learning of mathematics in an online mathematics teacher education course. The results focus on a conceptual framework that was developed to explicate this balance and show how the learning goal, evidence of student learning, and the teaching that occurs are built on the teaching philosophy tenet