New Thoughts about the Feeble-Minded

Abstract

An experimental social science curriculum with the express intent of developing inquiry skills was tested in a controlled experiment against an established conventional curriculum. The new curriculum involved inquiry skill objectives as well as knowledge objectives for each unit; readings stressed source material. Post-experiment testing showed that students who followed the experimental program developed inquiry skills to a significantly greater degree than students in the control group.     

Acting Like a Mathematician: A Project to Encourage Inquiry Early in the Math Major

Abstract

Inquiry is promoted as a way to engage students so that they learn more deeply; inquiry is also an end in itself, introducing students to the research process and the behaviors of a mathematician. This article reflects on an individual exploratory project used in a sophomore-level number theory course, examining how it supported student inquiry and integrated with departmental efforts to encourage productive mathematical dispositions. Additional attention is given to the choice of topics, focus on process rather than product, and student reflections in supporting the goal of student inquiry.     

Reflections on Transformative Experiences with Mathematical Inquiry: The Case of Christine

Abstract

We present a first-hand, longer-term account of one student’s (Christine’s) experiences in and after a mathematics inquiry course. In this course, students actively posed problems, conducted their own mathematical explorations, and wrote journal entries about their experiences. During the course, Christine found that inquiry helped her develop mathematical content knowledge and a deeper understanding of the nature of research. After the course, Christine became a mathematics education faculty member in a mathematics department and reports that the course impacted the way she teaches mathematics. This provides an illustrative case of the potential long-lasting benefits of an inquiry course.     

Teaching Inquiry to High School Teachers Through the Use of Mathematics Action Research Projects

Abstract

This paper describes the use of Mathematics Action Research Projects (ARPs) as a capstone experience in lieu of a Master’s Thesis in a Master’s program for in-service secondary teachers. The ARPs include two primary components: (i) each teacher participant conducts mathematical research that is new to them on a topic that is connected in some way to the material they teach in one of their classes; and (ii) each teacher participant also creates an in-class innovation related to the mathematical research they have been doing, and implements it in their own classroom. Ten teacher participants have completed such ARPs with the author over the last 3 years. In completing their ARPs, teacher participants not only learn how to conduct mathematical inquiry themselves, but also most often choose to implement some kind of inquiry-based classroom innovation that allows them to share some of this experience with their own students. This course structure has had the effect of encouraging teachers to decide to try more inquiry-based teaching methods, and at the same time, has given them the knowledge and tools to be successful in doing so.     

Mathematical Flexibility: Aspects of a Continuum and the Role of Prior Knowledge

Abstract

Psychologists and mathematics educators have long viewed flexibility as critical to students’ mathematical development. In this paper, we focused on the multidimensional nature of flexibility to better understand how preference, knowledge, and use of effective methods for solving algebra problems are related. In Study 1, we identified research-based aspects of flexibility with algebra and assessed students on them following a two-step equations unit. Results indicated that certain aspects of flexibility develop prior to others and that prior knowledge of algebra plays a significant role in that development. Study 2 confirmed and elaborated on these results using a larger sample size. Implications for theory and for supporting flexibility in classrooms are discussed.     

‘Let your data tell a story:’ climate change experts and students navigating disciplinary argumentation in the classroom

ABSTRACT

Science education trends promote student engagement in authentic knowledge in practice to tackle personally consequential problems. This study explored how partnering scientists and students on a social media platform supported students’ development of disciplinary practice knowledge through practice-based learning with experts during two pilot enactments of a project-based curriculum focusing on the ecological impacts of climate change. Through the online platform, scientists provided feedback on students' infographics, visual argumentation artifacts that use data to communicate about climate change science. We conceptualize the infographics and professional data sets as boundary objects that supported authentic argumentation practices across classroom and professional contexts, but found that student generated data was not robust enough to cross these boundaries. Analysis of the structure and content of the scientists’ feedback revealed that when critiquing argumentation, scientists initiated engagement in multiple scientific practices, supporting a holistic rather than discrete model of practice-based learning. While traditional classroom inquiry has emphasized student experimentation, we found that engagement with existing professional data sets provided students with a platform for developing expertise in systemic scientific practices during argument construction. We further found that many students increased the complexity and improved the visual presentation of their arguments after feedback.     

Constructing an Inquiry Orientation from a Learning Theory Perspective: Democratizing Access through Task Design

Abstract

It is widely accepted in the mathematics education community that pedagogies oriented toward inquiry are aligned with a constructivist theory of learning, and that these pedagogies effectively support students’ learning of mathematics. In order to promote such an orientation, we first separate the idea of inquiry from its conception as a collection of methods. Then, by grounding those methods in a generally accepted theory of learning, we construct an inquiry-oriented pedagogy from a constructivist perspective. We then discuss the implications of this pedagogy for the design of mathematical tasks that democratize student access to inquiry. This work has implications for educators who wish to enact an inquiry-oriented pedagogy in their classroom in order to support their students’ problem solving and problem posing.     

The preparation experiences of elementary mathematics specialists: examining influences on beliefs,content knowledge,and teaching practices

Many in the field of mathematics education call for elementary schools to have elementary mathematics specialists (EMSs) who provide needed mathematical expertise and support for children and teachers. EMSs serve as a reasonable, immediate alternative to the challenges generated by elementary teachers needing improved mathematical knowledge for teaching in the classroom. However, limited inquiry has explored how to best prepare EMSs and how program features and learning activities influence their development. This mixed-method study identifies some of the interrelated benefits from a K-5 Mathematics Endorsement Program designed to prepare EMSs through examining changes in mathematical beliefs, specialized content knowledge (SCK), and classroom teaching practices during the program. Data (n = 32) were collected over the 2-semester program via belief surveys, a content knowledge assessment, observations of teaching practices, and individual interviews from elementary teachers participating in the program. The findings show some changes in beliefs can be made relatively quickly, other shifts in beliefs take more time and continued support, and changes in SCK and adoption of various aspects of standard-based pedagogy require considerably greater opportunities to learn. The described program features and learning experiences provided a context for these changes and offer considerations for EMS preparation programs.     

Expanding and sustaining arts-based educational research as practitioner inquiry

ABSTRACT

As practitioner inquiry is now established as a widely-recognized research tradition and flourishing movement for educational change, we might consider ways that practitioner inquiry could be conceptualized and executed to broaden implementation, deepen understanding, and sustain inquiry within teacher education. Arts-based research may be an ideal methodology for the extension and sustainment of such inquiry as its visual, performative orientation lends itself to participant engagement and provides access in the representation and dissemination of results. This article will put forth models for advancing arts-based practitioner inquiry within the field of teacher education, by drawing from multiple cycles of a dual-layered, ABER study. This vision of arts-based practitioner inquiry is that of inclusion, increasing the number of those who conduct and interact with research; collaboration, blurring boundaries between the inquiries of teacher educators and pre-service teachers; accessibility, tapping into the power of the arts to engage and communicate in ways that scientific language cannot; and continued engagement, using learning from one cycle to inform inquiry in the next.     

Navigating Mandates and Working toward Coherence: Our Journey with a High-Stakes Teacher Performance Assessment

Abstract

This article details the experiences of four teacher education faculty members as we navigated the consequential implementation of a state-mandated high stakes teacher performance assessment in our educator preparation program. By shifting our perspective from simply complying with an assessment mandate to considering how we can leverage implementation of high stakes performance assessment as a vehicle for program inquiry, we were able to gain significant insight into our practice.     

The Spectrum of Dynamic Inquiry Teaching Practices

The Israeli high school biology curriculum comprises the Biomind program, in which students are engaged in an open inquiry learning process. The dynamic features of open inquiry often pose challenges to teachers in implementing the Biomind program. The current qualitative research shows that facilitating students in a dynamic open inquiry process is multidimensional. Teaching practices cover a wide range of methods, from structured inquiry through guided inquiry to open inquiry. An individual teacher’s profile can be elucidated on the basis of this spectrum. In addition, we realised that teachers often encounter several difficulties in implementing open dynamic inquiry: A dearth of teachers’ scientific knowledge, students’ lack of scientific knowledge and skills, and a restrictive time-frame. This study suggests several areas which should be considered while implementing an on going professional development support for teachers who are engaged in open inquiry teaching.     

Making inquiry-based science learning visible: the influence of CVS and cognitive skills on content knowledge learning in guided inquiry

ABSTRACT

Many science curricula and standards emphasise that students should learn both scientific knowledge and the skills associated with the construction of this knowledge. One way to achieve this goal is to use inquiry-learning activities that embed the use of science process skills. We investigated the influence of scientific reasoning skills (i.e. conceptual and procedural knowledge of the control-of-variables strategy) on students’ conceptual learning gains in physics during an inquiry-learning activity. Eighth graders (n?=?189) answered research questions about variables that influence the force of electromagnets and the brightness of light bulbs by designing, running, and interpreting experiments. We measured knowledge of electricity and electromagnets, scientific reasoning skills, and cognitive skills (analogical reasoning and reading ability). Using structural equation modelling we found no direct effects of cognitive skills on students’ content knowledge learning gains; however, there were direct effects of scientific reasoning skills on content knowledge learning gains. Our results show that cognitive skills are not sufficient; students require specific scientific reasoning skills to learn science content from inquiry activities. Furthermore, our findings illustrate that what students learn during guided inquiry activities becomes visible when we examine both the skills used during inquiry learning and the process of knowledge construction. The implications of these findings for science teaching and research are discussed.     

The role of academic developers in embedding high-impact undergraduate research and inquiry in mainstream higher education: twenty years’ reflection

Abstract

The focus of this article is on the role of academic developers in supporting and influencing undergraduate research and inquiry, a high-impact activity. We examine the levels at which academic developers can influence undergraduate research and inquiry practices by distinguishing between staff and student practices; disciplinary and departmental practices and policies; institutional practices and policies; and national and international practices and policies. Drawing on our experiences over the last 20 years, we discuss the widening of academic development practice and consider who are the academic developers when it comes to embedding undergraduate research and inquiry in mainstream higher education.     

Using the inquiry-based learning approach to enhance student innovativeness: a conceptual model

ABSTRACT

Individual innovativeness has become one of the most important employability skills for university graduates. In this paper, we focus on how students could be better prepared to be innovative in the workplace, and we argue that inquiry-based learning (IBL) – a pedagogical approach in which students follow the inquiry-based processes used by scientists to construct knowledge – can be effective for this purpose. Drawing on research which examines the social and cognitive micro-foundations of innovative behavior, we develop a conceptual model that links IBL and student innovativeness, and introduce three teacher-controlled design elements that can influence the strength of this relationship, namely whether an inquiry is open or closed, discovery-focused or information focused and individual or team-based. We argue that an open, discovery-focused and team-based inquiry offers the greatest potential for enhancing students’ skills in innovation. This paper has several implications for higher education research and practice.     

RETHINKING FOOD UTILIZED AS MATERIALS FOR ART

ABSTRACT

Teaching mathematics in an early childhood program requires mathematical content knowledge and teacher self-efficacy, yet research has shown that early childhood educators often have negative attitudes towards mathematics and feel underprepared to teach mathematical concepts. The study reported here documents the reconceptualization of a graduate, preservice teacher education program, a program designed to address teacher anxiety and increase capacity to teach mathematics in a play-based early childhood setting. The study aimed to investigate: (1) the effectiveness of the mathematics component of the course in equipping teacher candidates to teach mathematics in early childhood, and (2) whether participation in the mathematics component of the course changed teacher candidates’ self-efficacy regarding mathematics. Findings show that both self-efficacy and content knowledge improved when teacher candidates had the opportunity to engage with play-based learning experiences that embed mathematical concepts. Furthermore, the focus on a learning trajectories approach supports the identification of developmental progression points in children’s emerging mathematical understanding, assisting with teacher candidates’ fine-grained observations, assessment of children’s learning, and authentic, individualized planning for learning.     

Education the Handmaid of Philosophy

Abstract

This article addresses how we might teach for global citizenship in world history classrooms. Despite the name, secondary world history courses in the United States have not consistently focused on global interconnections, multiple perspectives, and inquiry into global issues. We explore why this might be, as well as suggest specific learning activities and curricular topics in world history that could help meet global citizenship goals.     

Using Games to Engage Students in Inquiry

Abstract

This paper discusses the author’s experiences of getting advanced undergraduate math students to engage in mathematical inquiry by using games as a vehicle for exploration. The students explored the mathematics behind SET^®1, Spot it!^®2, Blokus^®3, and Six^®4. Specifically, we present the experience of the instructor and students and how the games were used to promote and incite inquiry.     

A theory of planned behaviour-based analysis of TIMSS 2011 to determine factors influencing inquiry teaching practices in high-performing countries

ABSTRACT

Given the abundance of literature describing the strong relationship between inquiry-based teaching and student achievement, more should be known about the factors impacting science teachers’ classroom inquiry implementation. This study utilises the theory of planned behaviour to propose and validate a causal model of inquiry-based teaching through analysing data relating to high-performing countries retrieved from the 2011 Trends in International Mathematics and Science Study assessments. Data analysis was completed through structural equation modelling using a polychoric correlation matrix for data input and diagonally weighted least squares estimation. Adequate fit of the full model to the empirical data was realised. The model demonstrates that the extent the teachers participated in academic collaborations was positively related to their occupational satisfaction, confidence in teaching inquiry, and classroom inquiry practices. Furthermore, the teachers’ confidence with implementing inquiry was positively related to their classroom inquiry implementation and occupational satisfaction. However, perceived student-generated constraints demonstrated a negative relationship with the teachers’ confidence with implementing inquiry and occupational satisfaction. Implications from this study include supporting teachers through promoting collaborative opportunities that facilitate inquiry-based practices and occupational satisfaction.     

Provoking contingent moments: Knowledge for ‘powerful teaching’ at the horizon

Background: Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define the knowledge needed by teachers to teach mathematics effectively. A plethora of terms, such as mathematical content knowledge, pedagogical content knowledge, horizon content knowledge and specialised content knowledge, have been used to describe aspects of such knowledge.

Purpose: This paper proposes a model for teacher knowledge in mathematics that embraces and develops aspects of earlier models. It focuses on the notions of contingent knowledge and the connectedness of ‘big ideas’ of mathematics to enact what is described as ‘powerful teaching’. It involves the teacher’s ability to set up and provoke contingent moments to extend children’s mathematical horizons. The model proposed here considers the various cognitive and affective components and domains that teachers may require to enact ‘powerful teaching’. The intention is to validate the proposed model empirically during a future stage of research.

Sources of evidence: Contingency is described in Rowland’s Knowledge Quartet as the ability to respond to children’s questions, misconceptions and actions and to be able to deviate from a teaching plan as needed. The notion of ‘horizon content knowledge’ (Ball et al.) is a key aspect of the proposed model and has provoked a discussion in this article about students’ mathematical horizons and what these might comprise. Together with a deep mathematical content knowledge and a sensibility for students and their mathematical horizons, these ideas form the foundations of the proposed model.

Main argument: It follows that a deeper level of knowledge might enable a teacher to respond better and to plan and anticipate contingent moments. By taking this further and considering teacher knowledge as ‘dynamic’, this paper suggests that instead of responding to contingent events, ‘powerful teaching’ is about provoking contingent events. This necessarily requires a broad, connected content knowledge based on ‘big mathematical ideas’, a sound knowledge of pedagogies and an understanding of common misconceptions in order to be able to engineer contingent moments.

Conclusions: In order to place genuine problem-solving at the heart of learning, this paper argues for the idea of planning for contingent events, provoking them and ‘setting them up’. The proposed model attempts to represent that process. It is anticipated that the new model will become the framework for an empirical research project, as it undergoes a validation process involving a sample of primary teachers.