Inquiry-Based Learning and the Art of Mathematical Discourse

Abstract

Our particular flavor of inquiry-based learning (IBL) uses mathematical discourse, conversations, and discussions to empower students to deepen their mathematical thinking, building on strengths of students in the humanities. We present an organized catalog of powerful questions, discussion prompts, and talk moves that can help faculty facilitate a classroom focused on mathematical discourse. The paper brings this discourse alive through classroom vignettes and explores various teacher moves and their impacts. The mathematical theme of the classroom investigations, Maypole dance patterns, stems from the learning guide “Discovering the Art of Mathematics: Dance.” Both authors are part of the NSF-funded project “Discovering the Art of Mathematics,” which provides IBL materials for mathematics for liberal arts courses, see www.artofmathematics.org.     

Exploring the pedagogical features of integrating essential competencies of scientific inquiry in classroom teaching

ABSTRACT

Background: As inquiry-based instruction is not universally implemented in science classrooms, it is crucial to introduce instructional strategies through the use of contextualized learning activities to allow students with different background knowledge and abilities to learn the essential competencies of scientific inquiry and promote their emotional perception and engagement.

Purpose: This study explores how essential scientific competencies of inquiry can be integrated into classroom teaching practices and investigates both typical and gifted secondary students’ emotional perception and engagement in learning activities.

Sample: A case teacher along with 226 typical and 18 gifted students from a suburban secondary school at Taiwan participated in this study.

Design and methods: After attending twelve 3-hour professional development workshops that focused on scientific inquiry teaching, the case teacher voluntarily developed and elaborated her own teaching activities through the discussions and feedback that she received from workshop participants and science educators. Quantitative and qualitative data were collected through activity worksheet, questionnaire, video camera, and tape recorders. Frequency distribution, Mann-Whitney U test, and discourse analysis were used for data analyses.

Results: Case teacher’s teaching activities provide contextual investigations that allow students to practice making hypotheses, planning investigations, and presenting and evaluating findings. Students’ learning outcomes reveal that typical students can engage in inquiry-based learning with positive emotional perception as well as gifted students regardless of their ability level. Both gifted and typical students’ positive emotional perception of and active engagement in learning provide fresh insight into feasible instructions for teachers who are interested in inquiry-based teaching but have little available time to implement such instructions into their classrooms.

Conclusions: The results of our work begin to address the critical issues of inquiry-based teaching by providing an exemplary teaching unit encompassing essential scientific competencies     

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.     

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.     

Investigation of effective strategies for developing creative science thinking

The purpose of this study was to explore the effectiveness of the creative inquiry-based science teaching on students’ creative science thinking and science inquiry performance. A quasi-experimental design consisting one experimental group (N?=?20) and one comparison group (N?= 24) with pretest and post-test was conducted. The framework of the intervention focused on potential strategies such as promoting divergent and convergent thinking and providing an open, inquiry-based learning environment that are recommended by the literature. Results revealed that the experimental group students outperformed their counterparts in the comparison group on the performances of science inquiry and convergent thinking. Additional qualitative data analyses from classroom observations and case teacher interviews identified supportive teaching strategies (e.g. facilitating associative thinking, sharing impressive ideas, encouraging evidence-based conclusions, and reviewing and commenting on group presentations) for developing students’ creative science thinking.     

Inquiry-based science education: scaffolding pupils’ self-directed learning in open inquiry

ABSTRACT

This paper describes a multiple case study on open inquiry-based learning in primary schools. During open inquiry, teachers often experience difficulties in balancing support and transferring responsibility to pupils’ own learning. To facilitate teachers in guiding open inquiry, we developed hard and soft scaffolds. The hard scaffolds consisted of documents with explanations and/or exercises regarding difficult parts of the inquiry process. The soft scaffolds included explicit references to and additional explanations of the hard scaffolds. We investigated how teacher implementation of these scaffolds contributed to pupils’ self-directed learning during open inquiry. Four classes of pupils, aged 10–11, were observed while they conducted an inquiry lesson module of about 10 lessons in their classrooms. Data were acquired via classroom observations, audio recordings, and interviews with teachers and pupils. The results show that after the introduction of the hard scaffolds by the teacher, pupils were able and willing to apply them to their investigations. Combining hard scaffolds with additional soft scaffolding promoted pupils’ scientific understanding and contributed to a shared guidance of the inquiry process by the teacher and her pupils. Our results imply that the effective use of scaffolds is an important element to be included in teacher professionalisation.     

The relationship among elementary teachers’ content knowledge,attitudes, beliefs,and practices

This study investigated 481 in-service elementary teachers’ level of mathematical content knowledge, attitudes toward mathematics, beliefs about the effectiveness of inquiry-based instruction, use of inquiry-based instruction and modeled the relationship among these variables. Upper elementary teachers (grades 3–5) were found to have greater content knowledge and more positive attitudes toward mathematics than primary teachers (grades K-2). There was no difference in teachers’ beliefs about effective instruction, but primary level teachers were found to use inquiry-based instruction more frequently than upper elementary teachers. Consistent with Ernest’s [Ernest (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–33] model of mathematics teaching, content knowledge, attitudes, and beliefs were all found to be related to teachers’ instructional practice. Furthermore, beliefs were found to partially mediate the effects of content knowledge and attitudes on instructional practice. Content knowledge was found to be negatively related to beliefs in the effectiveness of inquiry-based instruction and teachers’ use of inquiry-based instruction in their classrooms. However, overall, teachers with more positive attitudes toward mathematics were more likely to believe in the effectiveness of inquiry-based instruction and use it more frequently in their classroom. Teacher beliefs were found to have the strongest effect on teachers’ practice. Implications for the goals and objectives of elementary mathematics methods courses and professional development are discussed.

Science in Silence: How Educators of the Deaf and Hard-of-Hearing Teach Science

Science learning is inextricably tied to two aspects of students’ lives: literacy and culture. While English Learners (ELs) who speak a non-English native language are typically the focus in this line of scholarly inquiry, deaf and hard-of-hearing (DHH) students occupy a distinct space in this conversation. For DHH learners, literacy levels can be hindered by an early dependence on a more survival-based language learning model that postpones basic scientific inquiry. The vocabulary for curiosity is limited, which in turn affects the educational culture. DHH learners have a unique culture that demands an appropriate science curriculum, which thus far has not been explored or attempted for either DHH learners or their educators. Data collected consisted of interviews with teachers of DHH students, as well as observational data collected from a high-minority urban K-8 school for DHH students. The analysis revealed that, first, many of the teachers had limited preparation to teach science content. Second, DHH teachers used inconsistent instructional strategies ranging from drawing pictures to building models. Third, the modifications provided to DHH science learners were mostly limited to visual support and repetition. Implications for teacher education programs include instruction focused on specific supports for DHH students and co-teaching methods, and deeper investigation of inquiry-based science practices. Implications for classroom practices include providing hands-on, inquiry-based instruction, working closely with parents, and developing students’ and teachers’ understanding of scientific inquiry.

     

Environment–attitude relationships: girls in inquiry-based mathematics classrooms in the United Arab Emirates

Girls’ attitudes towards mathematics can impact their achievement and career choices in STEM fields. Can the introduction of inquiry-based learning (IBL) in mathematics classes generate positive associations between girls’ perceptions of the learning environment and their attitudes towards mathematics? Based in the United Arab Emirates, this study provided important information about the relationships between learning environment factors central to an inquiry method and student engagement. Data collection involved administering two surveys to female mathematics students (N?=?291) in four schools: one to assess students’ perceptions of the learning environment and another to assess students’ attitudes towards mathematics. Positive and statistically-significant (p?<?.01) associations emerged between learning environment factors important to an inquiry approach and students’ attitudes. These findings provide important information about how IBL might improve girls’ attitudes towards mathematics classes and whether IBL environments are related to their attitudes.

     

Inquiry-Based Whole-Class Teaching with Computer Simulations in Physics

In this study we investigated the pedagogical context of whole-class teaching with computer simulations. We examined relations between the attitudes and learning goals of teachers and their students regarding the use of simulations in whole-class teaching, and how teachers implement these simulations in their teaching practices. We observed lessons presented by 24 physics teachers in which they used computer simulations. Students completed questionnaires about the lesson, and each teacher was interviewed afterwards. These three data sources captured implementation by the teacher, and the learning goals and attitudes of students and their teachers regarding teaching with computer simulations. For each teacher, we calculated an Inquiry-Cycle-Score (ICS) based on the occurrence and order of the inquiry activities of predicting, observing and explaining during teaching, and a Student-Response-Rate (SRR) reflecting the level of active student participation. Statistical analyses revealed positive correlations between the inquiry-based character of the teaching approach and students’ attitudes regarding its contribution to their motivation and insight, a negative correlation between the SRR and the ICS, and a positive correlation between teachers’ attitudes about inquiry-based teaching with computer simulations and learning goal congruence between the teacher and his/her students. This means that active student participation is likely to be lower when the instruction more closely resembles the inquiry cycle, and that teachers with a positive attitude about inquiry-based teaching with computer simulations realize the importance of learning goal congruence.     

Zen and the art of neriage: Facilitating consensus building in mathematics inquiry lessons through lesson study

One danger of integrating inquiry-based problem-solving activities into mathematics lessons is that different strategies could be accepted without in-depth discussions on the cogency and efficiency of the strategies. To overcome this issue, Japanese teachers typically go through a series of lesson-study-based teacher learning sessions and learn how to help students build consensus on the best mathematical strategy and think deeply about problem solving (neriage in Japanese). Assuming that this can also be an effective model in other cultural contexts, a video-based lesson study was conducted for a group of US teachers to effectively incorporate consensus building discussions in their mathematical inquiry lessons. Through the lesson study, the teachers learned to release control of class discussions to their students and help them discuss and examine different strategies. This article concludes with various aspects that the teachers learned for effectively implementing neriage in their lessons.     

CONTENT ANALYSIS OF 1998–2012 EMPIRICAL STUDIES IN SCIENCE READING USING A SELF-REGULATED LEARNING LENS

In this study, we investigated the impact of teaming school-based instructional coaches with science or mathematics middle school teachers to build a community of practice around inquiry instruction. This professional development model began with a 2-week summer institute and continued with four follow-up sessions during the academic school year for the teacher and instructional coach participants. The teachers’ participation in this professional development program with (1) content instruction through inquiry lessons, (2) practice teaching to middle school students, and (3) coach-led reflection improved their understanding of inquiry-based practices and the quality of their classroom inquiry implementation. Professional development experiences that prepare teachers and coaches simultaneously in inquiry and content may help build a shared language for reform and accelerate inquiry instructional changes.     

It is All About Inquiry: A Cross-Disciplinary Conversation About the Shared Foundations for Teaching

Abstract

This paper brings together general principles for teaching inquiry across disciplines with those generally employed in mathematics classrooms. It describes some broad principles of teaching inquiry to first-year writing students and shows how these can be employed in the context of a course on game theory in popular culture. Although undergraduate mathematics may seem miles away from undergraduate writing, especially in first-year courses, we show how common educational practices in inquiry-based mathematics courses are easily adapted to teaching a writing course and how these pedagogical methods can be used to encourage students to develop habits of inquiry.     

‘Just Be Quiet and Listen to Exactly What He's Saying': Conceptualising power relations in inquiry-oriented classrooms

Interest in inquiry-based science education (IBSE) often pays little heed to the complex power relations that exist within classrooms. A common obstacle to inquiry is that it strongly diverges from current classroom culture and hence, is outside the sphere of teachers' and students' experiences. Teachers and students bring expectations to the classroom that are entrenched in traditional practices and influenced by dynamics of power that exist within all teacher–student relationships. This study, which emerged during a wider study of the use of a Virtual Chemistry Lab in supporting IBSE, explores how classroom discourse constructs and maintains power relations that either stifle or facilitate inquiry-based approaches in two science lessons. Research methods included teacher interviews, student focus groups, video-recorded lessons, and student self-assessments. Findings indicate distinctive features of power inside the classroom that impact on inquiry-based instruction, such as predominant teacher monitoring on task completion over task understanding, lack of student engagement in ownership of scientific ideas, and prevailing norms of what effective teacher questioning is. We discuss implications for IBSE change efforts, highlighting that well-established power relations currently represent an important limiting factor in the capacity of teachers' IBSE implementation.     

The meaning of student inquiry questions: A teacher's beliefs and responses

This research explores an American high school chemistry teacher's perspective on the meaning of student questions that originate from curiosity and engagement with subject matter. Ethnographic analysis of a teacher's reflective processes and decision-making approach suggests that questions hold contradictory meanings as powerful, conflicting pressures come to play in the everyday patterns of classroom discourse. Although thoughtful intellectual questions are valued as indicators of student attitudes and understandings, they nonetheless create an interruption to the normal flow of things. To the teacher, such interruptions pose threats to his control of classroom events and his ability to cover the content of his course. Although science educators might enthusiastically endorse the idea that classrooms should be characterized by a spirit of inquiry in which student questions are encouraged and respected, findings suggest that it can be difficult for this to happen in actual schools where particular teachers face specific institutional curricular pressures.     

Building undergraduate STEM majors’ capacity for delivering inquiry-based mathematics and science lessons: An exploratory evaluation study

Recruiting and preparing STEM majors for teaching has become one of the major efforts at improving mathematics and science teacher quality at secondary level. One question is whether STEM majors who have not had the chance to experience active learning in mathematics and science classes as secondary students themselves know what inquiry pedagogy is. Secondly, it is unclear whether those who experienced inquiry in their college introductory discipline courses will be able to utilize the pedagogy in teaching secondary content. We address these questions through studying an undergraduate research methods course designed to improve STEM majors’ capacity for delivering inquiry-based mathematics and science lesson. Analysis of data from pre-and-post course surveys and students’ written research reports including students’ reflection on their inquiry projects suggests that offering future STEM teachers opportunities to conduct inquiry and reflect explicitly on how inquiry can be used to teach secondary content is important and beneficial.     

学习性评价在小学科学探究式教学中的运用

探究既是科学学习的目标,又是科学学习的方式。它不仅关注学生的动手能力,更关注学生的思维发展。教师应在课堂上通过各种方式促进学生思维的发展,如在观察的基础上了解学生,从而对他们提出质疑,为他们设置挑战,对他们的科学记录内容予以反馈等,所有这些都具有学习性评价的特征。在小学科学课上,如何运用学习性评价来促进学生的探究活动及他们的思维发展是一个非常值得探讨的问题。     

Keeping their attention: Classroom practices associated with behavioral engagement in first grade mathematics classes in China and the United States

This study investigated variation in students’ behavioral engagement across mathematics classes in China and the United States. Student behavioral engagement was examined along with two aspects of the classroom (group size and teacher instructions given about classroom behavior). Video observational data were collected and coded over 1051 time intervals in 35-minute mathematics sessions in Chinese classrooms (n = 8) and comparable American classrooms (n = 7). Latent growth analyses revealed that overall, behavioral engagement declined over time, although the drop-off was dramatically sharper in American classrooms relative to Chinese classrooms. In addition, larger group size and the timing of teacher instructions (given before versus after the behavior) were significantly associated with increased engagement. This study revealed compelling cultural differences as well as patterns in student and teacher behaviors associated with students engaging in on-task behaviors in the classroom. Implications for ways to promote effective classroom behavior are discussed.