This project researches ways to increase the use of quantitative reasoning in the teaching and learning of mathematics.
Today, quantitative reasoning is needed in virtually all academic fields as well as in everyday life. And yet it remains largely absent from teaching and learning mathematics. As a result, K-12 students are often unprepared for future studies in science, technology, engineering and mathematics fields. These teachers are also not sufficiently trained to support their students' quantitative reasoning. But through this project, Kevin Moore hopes to redesign the current mathematics education course to focus more on developing future teachers' quantitative reasoning.
The project, titled "Advancing Secondary Mathematics Teachers' Quantitative Reasoning," is supported by an NSF Early Career Grant under award No. DRL-1350342.
Over the past 20 years, researchers and policy documents, including the Common Core State Standards for Mathematics (CCSSM), have directed mathematics educators at all levels to increase emphasis on quantitative reasoning. Unfortunately, quantitative reasoning still remains mostly absent from the teaching and learning of mathematics, particularly at the secondary level. A byproduct of this absence is that students are not being prepared for continued studies in mathematics and other STEM fields. Complicating the matter, teachers are not being sufficiently prepared to support their students' quantitative reasoning.
The proposed 5-year project, referred to as Advancing Reasoning, addresses the aforementioned situation by investigating pre-service secondary mathematics teachers' (PSTs') quantitative reasoning in the context of secondary mathematics concepts including function and algebra. Specifically, the project will extend prior work in the area of quantitative reasoning in order to develop differentiated instructional experiences and curriculum that support PSTs' quantitative reasoning and produce transformational shifts in their knowledge. Three interrelated research questions guide the project: (i) What aspects of quantitative reasoning provide support for PSTs' understanding of major secondary mathematics concepts such as function and algebra? (ii) How can instruction support PSTs' quantitative reasoning in the context of the teaching and learning of major secondary mathematics concepts such as function and algebra? (iii) How do the understandings PSTs hold upon entering a pre-service program support or inhibit their quantitative reasoning?
Advancing Reasoning addresses these questions by enacting an iterative, multi-phase study with PSTs enrolled in a secondary mathematics education content course. The main phase of the study implements a series of classroom design experiments that will produce knowledge on central aspects of PSTs' quantitative reasoning and the instructional experiences that support such reasoning. By drawing this knowledge from a classroom setting, Advancing Reasoning will contribute research-based and practice-driven deliverables that improve the teaching and learning of mathematics.
Advancing Reasoning will contribute important knowledge to the area of quantitative reasoning, which forms a CCSSM Standard for Mathematical Practice and a conceptual underpinning of secondary mathematics. More specifically, the project will advance research and practice oriented knowledge of differentiated approaches to supporting PSTs' quantitative reasoning. The generated products will fill a pressing need for concrete materials at the pre-service level that embody research-based knowledge in the area of quantitative reasoning. The PI's work in the areas of quantitative reasoning, curriculum development, and both pre-service and in-service professional development provides research and instructional experiences to assure that the proposed work will lead to new knowledge and mechanisms that realize dramatic improvements in future secondary teachers' ability to prepare the mathematical and scientific thinkers of tomorrow.
In addition to providing transformational experiences for 200 PSTs over the course of the project, Advancing Reasoning will influence the PSTs' future students and those teachers that they collaborate with professionally. The establishment of research-based curricular materials in the University of Georgia secondary mathematics education program will influence all future program PSTs. Advancing Reasoning will form relationships with in-service teachers who represent a range of school settings (e.g., urban, rural, and underrepresented populations) through the implementation of summer workshops. The project generated knowledge and products will be disseminated to the broader educational communities through an active social media presence, a project website hosting all project artifacts, and scholarly publications and presentations geared toward both research and practitioner communities. The accessible collection of research and educational products will provide a model program for transforming PSTs' quantitative reasoning that is adoptable at other institutions. Due to the understandably vague nature of the CCSSM Standards for Mathematical Practice, concrete examples of PSTs' quantitative reasoning and differentiated approaches to supporting such reasoning will be of important use to mathematics educators at all levels.