Teacher candidates' growth in designing mathematical tasks as exhibited in their lesson planning

Abstract

In order to gain insight into preservice teachers' beliefs about planning for mathematics instruction, a study was carried out involving K‐8 teacher candidates enrolled in an elementary mathematics methods course. Doyle's (1992) notion of academic task and the research on pedagogical content knowledge served as the theoretical framework for this study. The teacher candidates submitted lesson plans at three intervals during a semester‐long methods course; the lesson plans were then coded based on candidates' planned uses of academic tasks. Analyses of the data revealed trends in these teacher candidates' design of academic tasks over the course of the semester. Recommendations and implications are pre‐sented highlighting the benefits of incorporating the knowledge base on academic task into a mathematics methods course as a means to con‐tribute to teacher candidates' developing pedagogical content knowledge via their designing of academic tasks in lesson planning.     

The Relationship between Pre-service Mathematics Teachers’ Focus on Student Thinking in Lesson Analysis and Lesson Planning Tasks

This study explored whether pre-service teachers’ (PSTs’) lesson analysis skills during a teacher education course in the country of Turkey were related to their skills of lesson planning. PSTs’ lesson analysis skills during fieldwork were assessed by their attention to and interpretation of student thinking and learning, and how it is influenced by the teachers’ instructional decisions. The PSTs’ lesson analysis scores were significantly and positively correlated with scores in lesson planning task focusing on student thinking. The findings contribute to the literature on whether PSTs’ lesson analysis skills may be transferred to one of the core activities of teaching.     

Understanding Preservice Teacher Skills to Construct Lesson Plans

This study examined preservice teachers’ (PSTs) capacity for lesson planning in a university-based teacher preparation program in the USA Participants (n?=?126) wrote lesson plans in three approaches: synthesis, creation, and modification. Findings indicate that PSTs who modified preexisting lesson plans produced better lesson plans than their peers and reported higher efficacy in their use of the lesson plan in their field experiences. This study supports the notion that the efficacy of first-year teaching lies more appropriately in the area of enacting curriculum than in the area of designing curriculum. With respect to career-long learning, PSTs’ abilities to do curriculum work are likely to improve, as they grow more familiar with students and existing excellent curricula over years. Although the study presents a snapshot of U.S. preservice teachers’ capacity for curriculum design, the findings may serve to inform the literature on the developmental aspect of curriculum design for teacher education systems across the world.     

Examining the Effectiveness of an Academic Language Planning Organizer as a Tool for Planning Science Academic Language Instruction and Supports

To engage in the practices of science, students must have a strong command of science academic language. However, content area teachers often make academic language an incidental part of their lesson planning, which leads to missed opportunities to enhance students’ language development. To support pre-service elementary science teachers (PSTs) in making language planning an explicit part of their science lessons, we created the Academic Language Planning Organizer (ALPO). The purpose of this study was to determine the effectiveness of the ALPO on two levels: first, by examining participants’ interactions with the ALPO as they identified academic language features, objectives and supports; and second, by exploring the ways that participants translated identified language supports to planned science activities. Findings indicated that, when using the ALPO, PSTs identified clear language functions and relevant vocabulary terms, and also frequently developed clear, observable and measurable language objectives. When lesson planning, PSTs were largely successful in translating previously identified language supports to their lesson plans, and often planned additional language supports beyond what was required. We also found, however, that the ALPO did not meet its intended use in supporting PSTs in identifying discourse and syntax demands associated with specific academic language functions, suggesting that revisions to the ALPO could better support PSTs in identifying these academic language demands. Implications for supporting PSTs’ planning for and scaffolding of science academic language use are presented.     

The best laid plans: Educational innovation in elementary teacher generated integrated STEM lesson plans

ABSTRACT

Students need to be prepared for the 21st century by developing the literacy skills necessary for participating in the age of synthesis—an age that requires a progressive set of skills and knowledge. The authors identified nine educational innovations that are perceived to be effective for preparing students for the 21st century age of synthesis society. They coded a collection of 39 teacher-generated Grade 3–5 science, technology, engineering, and mathematics (STEM) lesson plans to document the extent to which the teachers included these nine educational innovations their STEM lesson planning. The authors found practices such as project-based and student-centered learning (which are common established approaches to teaching STEM) to be strongly represented in the plans, whereas practices such as family involvement and place-based learning (which have not been traditionally used in STEM instruction) were less evident in the plans. In their discussion they explore the implications for STEM teaching, and potential directions for future research.     

Investigating peer-assessment strategies for mathematics pre-service teacher learning on formative assessment

Formative assessment practices for secondary mathematics have been advocated as valuable for students, but difficult for teachers to learn. There have been calls in the literature to increase the emphasis on formative assessment in mathematics teacher preparation courses. This study explored the use of peer-assessment strategies for helping pre-service secondary mathematics teachers (PSTs) cultivate formative assessment principles and practices for assessing school students. Twenty-seven PSTs participated in a peer-assessment cycle comprised of: sourcing a rich mathematics task; constructing an assessment rubric for it; and collecting and analysing a selection of secondary student responses to the task. Each PST then provided written and verbal feedback to a peer on his/her rubric and student solution assessments. We draw on theoretical conceptions of Teacher Assessment Literacy in Practice to characterize the PSTs’ perceptions of their experience of formative assessment processes for learning to assess school students, in terms of cognitive and affective dimensions of their conceptions of assessment. The cohort evidenced a wide range of levels of confidence with the various aspects of formative assessment practices but on average less confidence in assessing school student task responses themselves than in assessing peer work. In addition to highlighting specific changes to different types of assessment knowledge, the PSTs also evidenced an awareness of shifts in their attitudes, in coming to view student task responses with more appreciation and humility.

     

Prospective elementary teachers’ responses to unanticipated incorrect solutions to problem-solving tasks

Eliciting and responding to student thinking are high-leverage practices that have powerful implications for student learning. However, they are difficult to enact effectively, particularly for novices, and more research is needed to understand how teacher education can support teachers in developing these skills. This study examined ways prospective elementary teachers (PSTs) responded to unanticipated incorrect student solutions to high-demand problem-solving tasks and how their responses changed over a 6-week field experience embedded in a practiced-based mathematics methods course. Data were collected in 6 weekly cycles of planning (written plans), enactment (video of problem-solving sessions with students), and reflection (written reflections on video). Problem-solving task implementations were analyzed using cognitive demand and math-talk frameworks. Of the three collaborating PST groups, two groups improved at responding to unanticipated incorrect solutions, but these two groups also developed a tendency to shut down anticipated solutions. The third group showed no patterns in their responses to unanticipated incorrect solutions, but did maintain the cognitive demand when responding to anticipated solutions. I present a case of one group of collaborating PSTs who made improvements in responding to unanticipated incorrect solutions in terms of the pedagogical moves they employed, cognitive demand associated with their responses, and how their responses changed over time. Implications for teacher education are discussed.     

Lesson Planning Practices of Special Education Teachers

This study reports the results of a survey of special education teachers regarding: (a) how special education teachers organize and develop their lesson plans, (b) which lesson plan components special education teachers include in their lesson planning activities and how each component is planned, and (c) what lesson plan components special education teachers recommend that beginning teachers include in written lesson plans. As indicated by the results, the majority of the special education teachers who participated in this study did not write out lesson plans for each lesson they taught. They indicated that, even though most of the planning prior to instruction was unwritten, it was often "consciously" planned, or planning was unnecessary because the component was performed by habit or instinct. A substan- tial majority indicated that they did not use any expert's lesson planning format, such as Hunter's (1984) or a format suggested in preservice teacher training. None of the 14 components regularly included in preservice lesson plans and instructional design models were written out by a majority of the teachers; only 3 of the 14components were written out by over one third of the respondents. Conversely, this study demonstrated that, although these teachers did not write out detailed lesson plans, they strongly recommended that beginning teachers do so. All 14 components were recommended by at least one third of the respondents, with 8 recommended by a majority. Limitations, questions for future investigation, and implications for teacher preparation are discussed.     

The role of lesson analysis in pre-service teacher education: an empirical investigation of teacher learning from a virtual video-based field experience

A video-based program on lesson analysis for pre-service mathematics teachers was implemented for two consecutive years as part of a teacher education program at the University of Lazio, Italy. Two questions were addressed: What can preservice teachers learn from the analysis of videotaped lessons? How can preservice teachers’ analysis ability, and its improvement, be measured? Two groups of preservice teachers (approximately 140 in total) participated in the program. A three-step lesson analysis framework was applied to three lesson videos: (1) goal(s) and parts of the lesson; (2) student learning; and, (3) teaching alternatives. Preservice teachers’ ability to analyze lessons was measured through an open-ended pre- and post-assessment. In the assessment, preservice teachers were asked to mark and comment on events (in a lesson not included in the program) that they found interesting for: teachers’ actions/decisions; students’ behavior/learning; and, mathematical content. A coding system was developed based on five criteria: elaboration, mathematics content, student learning, critical approach, and alternative strategies. In both studies, the ability to analyze instruction improved significantly on all five criteria. These data suggest promising directions for the development of both an instrument to measure lesson analysis abilities and a model for teacher learning.     

Pre-service mathematics teachers’ learning and teaching of activity-based lessons supported with spreadsheets

In this study, 12 pre-service mathematics teachers worked in teams to develop their knowledge and skills in using teacher-led spreadsheet demonstrations to help students explore mathematics concepts, stimulate discussions and perform authentic tasks through activity-based lessons. Pre-service teachers’ lesson plans, their instruction of the lessons designed, experiences and lesson enactment outcomes were examined. The pre-service teachers in the study were able to develop and demonstrate their knowledge and skill adequately in designing and enacting activity-based mathematical lessons supported with spreadsheets. The results also showed that the pre-service teachers’ use of the spreadsheet as an instructional tool promoted student in-depth mathematical concept formation and an activity-based learning approach to make lessons less teacher centred and more interactive.     

Coach learning to help teachers learn to enact conceptually rich,student-focused mathematics lessons

The past decade has witnessed a strong, standards-based call for improving what mathematics is taught and how it is taught. In the USA, districts have hired instructional coaches to help teachers shift their teaching from algorithm-based instruction to instruction that is more student-centered and conceptually focused. The purpose of this study was to contribute to the field’s understanding of (a) the specific coaching practices that help teachers enact more conceptual-based forms of instruction; and (b) how coaches learn to enact those practices. Using a design-based implementation research approach, we trained coaches using a particular model for one-on-one coaching (Content-Focused Coaching); the coaches then worked with teachers to plan lessons aligned with the coaching model. Data consisted of videotapes of pre-lesson conferences that were transcribed and coded according to the model. Analyses of 32 coaches’ practice over a 2-year period suggest that each of the three components of our coaching model (attention to student thinking, pedagogy, and mathematics) demonstrated statistically significant improvement over time. An illustrative analysis of five coaching sessions of one coach revealed a progression over five sessions from planning discussions that stayed at the level of general strategies to more specific conversations about teaching a particular task and then to deeper discussions that integrate attention to mathematical concepts, student thinking, and pedagogical moves. We view this delineation of coach learning as an important first step in laying the groundwork for the design of future coach training.

     

Using Activity Theory to Examine How Teachers' Lesson Plans Meet Students' Learning Needs

How is lesson planning useful? This research study used Cultural Historical Activity Theory and intersubjectivity to answer this questions. This research explored to what extent teacher candidates' lesson plans (i.e., alignment among objectives, assessment, and instruction), and analyses of assessment data mediate their thinking about students' learning needs. Four to five daily lesson plans with corresponding videos and commentaries from 10 elementary school (K–6) teacher candidates were used in this study. Qualitative analyses revealed that teacher candidates seldom considered their students' learning needs and seldom anticipated how instructional activities facilitated students' thinking. One teacher candidate, however, used assessment data to consider students' learning needs and to plan future lessons to meet students' learning needs. The implication of research findings suggest that teacher education programs must improve in developing teacher candidates' skills of aligning lesson plan features and using assessment data as tools to mediate their thinking about students' learning needs.     

Professional knowledge or motivation? Investigating the role of teachers’ expertise on the quality of technology-enhanced lesson plans

In an expertise study with 94 mathematics teachers varying in their relative teacher expertise (i.e., student teachers, trainee teachers, in-service teachers), we examined effects of teachers' professional knowledge and motivational beliefs on their ability to integrate technology within a lesson plan scenario. Therefore, we assessed teachers' professional knowledge (i.e., content knowledge, pedagogical content knowledge, technological knowledge), and their motivational beliefs (i.e., self-efficacy, utility-value). Furthermore, teachers were asked to develop a lesson plan for introducing the Pythagorean theorem to secondary students. Lesson plans by advanced teachers (i.e., trainee teachers, in-service teachers) comprised higher levels of instructional quality and technology exploitation than the ones of novice teachers (i.e., pre-service teachers). The effect of expertise was mediated by teachers' perceived utility-value of educational technology, but not by their professional knowledge. These findings suggest that teachers’ motivational beliefs play a crucial role for effectively applying technology in mathematics instruction.     

Learning to teach in a context of education reform: liberal studies student teachers' decision‐making in lesson planning

Liberal studies is a new subject in the new senior secondary curriculum in Hong Kong. This study attempted to identify factors that shape liberal studies student teachers' decisions in lesson planning. Based on interview data and lesson plans developed by the student teachers, this article maintains that four factors interacted with the subject features of liberal studies to shape the student teachers' planning decisions, namely, teacher knowledge, curriculum requirements, materials and resources, and interaction with equal and more capable partners. This paper further looks into how teacher knowledge expresses itself at different stages of lesson planning. The findings suggest that to facilitate enquiry learning in students, liberal studies teachers need to adopt an enquiry stance in lesson planning. This paper argues that the limitations of liberal studies student teachers' content knowledge need to be addressed in teacher preparation programmes and suggests teacher networking as one way to strengthen novice liberal studies teachers' content preparation. The implications for teacher education are discussed.     

Part of the assignment: student–teachers’ planning instruction within/across activity systems

ABSTRACT

Looking closely at lesson plans as mediating tools, this study examines preservice teacher learning. By using activity theory in our analysis of lesson plans and other data collected in a student-teaching course, we uncovered tensions within/across the contexts of university teacher education program and secondary school field placements. This study serves to further understandings of how new teachers learn to appropriate the genres of teaching and to explore contradictions between a university preparation program and secondary school contexts. Findings provide an account of the student–teachers’ lesson planning and an explanation of how disruptions in those plans provided insight into points of tension. By viewing these tensions as contradictions within/across activity systems, we identify them as opportunities to better understand teacher learning and ways we might support new teachers in navigating tensions in their classrooms and schools.     

Defining Differentiation in Cyber Schools: What Online Teachers Say

Online education has grown over the last ten years and with it has been an increase in diverse learners. In an effort to understand how online teachers meet the needs of diverse learners, researchers surveyed teachers in two cyber schools. 118 participants were asked their definition of differentiation and how differentiation is seen in their practice. After the survey was collected, NVivo qualitative software was used to continually reduce the data through constant comparison. The results from the survey data revealed that online teachers defined differentiation from two distinct perspectives: a) why a student needs differentiation, and b) what a student needs differentiated. Online teachers stated learning styles as their primary reason for differentiation. This result was not only different from findings in face-to-face classrooms, but does not support research on what impacts student achievement. Online teachers also cited when they differentiate, they adjust content, product, and process (63% coverage). Finally, noticeably absent from the data were references to using assessments in the classroom to inform differentiation. Future research should consider how online teachers differentiate in their learning environments and how they make day-to-day decisions as they adjust instruction to meet the needs of their learners.     

Prospective teacher learning: recognizing evidence of conceptual understanding

This study examined prospective teachers’ (PSTs) ability to recognize evidence of children’s conceptual understanding of mathematics in three content areas before and after an instructional intervention designed to support this ability. It also investigates the role PSTs’ content knowledge plays in their ability to recognize children’s mathematical understanding. Results of content knowledge assessments administered at the beginning of the study revealed that content knowledge did seem to support PSTs’ analyses of children’s understanding when the child’s response demonstrated understanding or demonstrated a misconception. Content knowledge did not seem to support PSTs’ analyses of children’s procedural responses, as many PSTs with good content knowledge initially characterized procedural solutions as evidence of conceptual understanding. Similarly, content knowledge did not seem to support PSTs’ analyses of children’s responses with features commonly associated with understanding but not evidence of understanding. After the instructional intervention consisting of three multifaceted lessons in which PSTs examined many examples of student thinking, they showed improved ability to analyze responses with conceptual features and no evidence of conceptual understanding and responses demonstrating procedural knowledge. Results suggest that content knowledge is not sufficient for supporting PSTs’ analysis of children’s thinking, and that building activities such as the intervention into content courses may help develop this ability. Implications for teacher education programs and future research are considered.     

Use of comics to enhance students’ learning for the development of the twenty-first century competencies in the mathematics classroom

Abstract

This paper discusses the use of comics in teaching mathematics in the secondary mathematics classroom. We explicate how the use of comics in teaching mathematics can prepare students for the twenty-first century competencies. We developed an alternative teaching package using comics for two lower secondary mathematics topics. This alternative teaching package consists of (1) several sets of comic strips expounding all related mathematical concepts in a lively way; (2) tiered practice questions for learning reinforcement; and (3) a set of proposed lesson outlines with suggestions on how to use the comics for mathematics teaching. We also report how one of the teachers in our study used this teaching package in her mathematics lessons. Her lessons were video-recorded and 11 students were interviewed to help us understand how the mathematics comics lessons were enacted and the students’ perception of comics as instruction. We identified instances in which the teacher tweaked the provided resource to further enhance student learning and incorporated elements of the twenty-first century competencies during her lessons. Through selected student interviews, we also identified instances in which students commented on their gain from the new approach from the perspective of the twenty-first century competencies.