In this dissertation I explore instructors' work with instructional tasks as they plan to introduce various representations of derivatives. Drawing on the notion of "framing" from sociology, I adopt a situative lens to study calculus instructors' planning of instructional tasks. I rely on Herbst and Chazan's (2012) notion of…

Context: Research has demonstrated the importance of teacher quality for student achievement above all other school-based factors (Aaronson et al., 2007; Goldhaber, 2002; Rivkin et al., 2005; Rockoff, 2004). Yet while states and districts have allocated significant resources toward professional learning (PL) aimed at improving instruction (Jacob…

The problem addressed through this study was the inconsistent implementation of online formative assessment to inform instruction by high school mathematics teachers in a Northeast Regional High School District (NRHSD). The purpose of this basic qualitative study was to investigate how high school mathematics teachers in a NRHSD use online…

The calls for reasoning and proof to have a prominent place in secondary mathematics classrooms raise the question of knowledge that teachers need to support student learning of reasoning and proof. Several conceptualizations of Mathematical Knowledge for Teaching Proof (MKT-P) have been proposed over the years, yet some key questions about the…

In 2 experiments, I studied the effects of an Equivalence Based Instruction (EBI) math intervention on the emergence of untaught selection responses and abstraction to production responses. In Experiment I, using a multiple baseline design, I implemented the EBI intervention among a group of 17 first grade participants with varying levels of math…

Preparing prospective mathematics teachers to become teachers who recognize and respond to students' mathematical needs is challenging. In this study, we use the construct of critical incident as a tool to support prospective mathematics teachers' reflection on their authentic fieldwork activities, notice students' thinking, and link it to the…

The home numeracy environment (HNE) is an essential factor to explain family engagement in relation to numeracy. Research in this field has mostly focused on English-speaking families and has not taken into consideration cultural differences that contextualize the home environment. Measuring HNE in more ethnically diverse samples might counter…

Assembly Bill (AB) 1705 seeks to improve California community college students' progress in Science, Technology, Engineering and Math (STEM) programs. The law ensures that students begin math in the course that best positions them to complete their calculus requirement. A college has this obligation to all STEM students, regardless of their…

We investigated how teachers' narratives about their histories as learners provided insight into how they enacted rough drafting and revising -- a form of ambitious mathematics instruction. We interviewed 32 teachers in the U.S.A who reported using rough drafting and revising in their mathematics teaching. Teachers spoke about positive, negative,…

Mathematical reasoning, a fundamental aspect of human cognition, poses significant challenges for artificial intelligence (AI) systems. Despite recent advancements in natural language processing (NLP) and large language models (LLMs), AI's ability to replicate human-like reasoning, generalization, and efficiency remains an ongoing research…

Because the failure rate for college algebra is large and sometimes up to 50%, college algebra serves as a gatekeeper to STEM fields and degree completion. Therefore, it is critical to examine students who are at risk of dropping, withdrawing, and failing college algebra help-seeking behavior. The purpose of this mixed methods study was to focus…

This article reports on a project implemented to help middle school teachers provide evidence-based instruction and intervention to students with mathematics learning disabilities (MLD) and mathematics difficulties (MD). Multiple sources--interviews, surveys, and field notes from formal and informal observations--were used to gather data on…

In primary education, a variety of teaching methods, such as enhanced and discovery learning, have had a significant influence on student achievement, particularly in mathematics. Several studies have discussed the positive effects of the appropriate use of technology in the classroom on student achievement. The main purpose of the current study…

As remote learning technologies play an increasingly larger role in education, clear evidence of effectiveness is needed for widely used online learning technologies, such as Assessment and LEarning in Knowledge Spaces (ALEKS). By adapting to individual students' knowledge states and personalizing interactive practice and feedback, ALEKS may…

The relationship between teacher interventions and students' mathematical thinking has been the subject of inquiry for quite some time. Using the Pirie-Kieren theory for dynamic growth in mathematical understanding, this study documents teacher interventions that support students' growth toward developing a general understanding of a mathematical…