50 mathematics lessons : rich and engaging ideas for secondary Mathematics.

Es una colección de cincuenta lecciones de matemáticas que requieren poco tiempo de preparación y que resultan idóneas para profesores de secundaria muy ocupados y con varias clases en el mismo día.

Promoting Student Collaboration in a Detracked, Heterogeneous Secondary Mathematics Classroom

Detracking and heterogeneous groupwork are two educational practices that have been shown to have promise for affording all students needed learning opportunities to develop mathematical proficiency. However, teachers face significant pedagogical challenges in organizing productive groupwork in these settings. This study offers an analysis of one teacher’s role in creating a classroom system that supported student collaboration within groups in a detracked, heterogeneous geometry classroom. The analysis focuses on four categories of the teacher’s work that created a set of affordances to support within group collaborative practices and links the teacher’s work with principles of complex systems.

Supporting Whole-Class Collaborative Inquiry in a Secondary Mathematics Classroom

Recent mathematics education reform efforts call for the instantiation of mathematics classroom environments where students have opportunities to reason and construct their understandings as part of a community of learners. Despite some successes, traditional models of instruction still dominate the educational landscape. This limited success can be attributed, in part, to an underdeveloped understanding of the roles teachers must enact to successfully organize and participate in collaborative classroom practices. Towards this end, an in-depth longitudinal case study of a collaborative high school mathematics classroom was undertaken guided by the following two questions: What roles do these collaborative practices require of teacher and students? How does the community’s capacity to engage in collaborative practices develop over time? The analyses produced two conceptual models: one of the teacher’s role, along with specific instructional strategies the teacher used to organize a collaborative learning environment, and the second of the process by which the class’s capacity to participate in collaborative inquiry practices developed over time.

Secondary mathematics. I-

Mode of access: Internet.

An online community of practice for pre-service and beginning teachers of secondary mathematics

The aim of this study was to investigate how a community of practice focused on learning to teach secondary mathematics was created and sustained by pre-service and beginning teachers. Bulletin board discussions of one pre-service cohort are analysed in terms of Wenger’s (1998) three defining features of a community of practice: mutual engagement, joint enterprise, and a shared repertoire. The study shows that the emergent design of the community contributed to its sustainability in allowing the pre-service teachers to define their own professional goals and values. Sustainability was also related to how the participants expanded, transformed, and maintained the community during the pre-service program and after graduation.

Understanding technology integration in secondary mathematics: Theorising the role of the teacher

Previous research on computers and graphics calculators in mathematics education has examined effects on curriculum content and students’ mathematical achievement and attitudes while less attention has been given to the relationship between technology use and issues of pedagogy, in particular the impact on teachers’ professional learning in specific classroom and school environments. This observation is critical in the current context of educational policy making, where it is assumed – often incorrectly – that supplying schools with hardware and software will increase teachers’ use of technology and encourage more innovative teaching approaches. This paper reports on a research program that aimed to develop better understanding of how and under what conditions Australian secondary school mathematics teachers learn to effectively integrate technology into their practice. The research adapted Valsiner’s concepts of the Zone of Proximal Development, Zone of Free Movement and Zone of Promoted Action to devise a theoretical framework for analysing relationships between factors influencing teachers’ use of technology in mathematics classrooms. This paper illustrates how the framework may be used by analysing case studies of a novice teacher and an experienced teacher in different school settings.

The relationship between the secondary mathematics curriculum, college persistence, and success at an urban community college

According to Venezia, Kirst, and Antonio (2003) and Barth’s 2002 Thinking K16 Ticket to Nowhere report, the disconnect between K-12 and postsecondary education was a contributing factor to high attrition rates. Since mathematics emerged as a primary concern for college readiness, Barth (2002) called for improving student transitions from K-12 to postsecondary institutions through the use of state or local data. The purpose of the present study was to analyze mathematics course-taking patterns of secondary students in a local context and to evaluate high school characteristics in order to explore their relationships with Associate degree attainment or continuous enrollment at an urban community college. Also, this study extended a national study conducted by Clifford Adelman (The Toolbox Revisited, 2006) as it specifically focused on community college students that were not included his study. Furthermore, this study used the theoretical framework that human capital, social capital, and cultural capital influence habitus—an individual’s or a group’s learned inclination to behave within the parameters of the imposed prevailing culture and norms. Specifically, the school embedded culture as it relates to tracking worked as a reproduction tool of ultimate benefit for the privileged group (Oakes, 1994). ^ Using multilevel analysis, this ex post facto study examined non-causal relationships between math course-taking patterns and college persistence of public high school graduates who enrolled at the local community college for up to 6 years. One school-level variable (percent of racial/ethnic minorities) and 7 student-level variables (community college math proportion, remedial math attempts, race, gender, first-year credits earned, socioeconomic status, and summer credits earned) emerged as predictors for college persistence. Study results indicated that students who enter higher education at the community college may have had lower opportunities to learn and therefore needed higher levels of remediation, which was shown to detract students from degree completion. Community college leaders are called to partner with local high schools with high percentages of racial/ethnic minorities to design academic programs aimed at improving the academic preparation of high school students in mathematics and promote student engagement during the first year and summers of college. ^

EXAMINING SECONDARY MATHEMATICS TEACHER CANDIDATES’ LEARNING AND ENACTMENT OF MATHEMATICS TEACHING PRACTICES: A MULTIPLE CASE STUDY

This qualitative case study explored three teacher candidates’ learning and enactment of discourse-focused mathematics teaching practices. Using audio and video recordings of their teaching practice this study aimed to identify the shifts in the way in which the teacher candidates enacted the following discourse practices: elicited and used evidence of student thinking, posed purposeful questions, and facilitated meaningful mathematical discourse. The teacher candidates’ written reflections from their practice-based coursework as well as interviews were examined to see how two mathematics methods courses influenced their learning and enactment of the three discourse focused mathematics teaching practices. These data sources were also used to identify tensions the teacher candidates encountered. All three candidates in the study were able to successfully enact and reflect on these discourse-focused mathematics teaching practices at various time points in their preparation programs. Consistency of use and areas of improvement differed, however, depending on various tensions experienced by each candidate. Access to quality curriculum materials as well as time to formulate and enact thoughtful lesson plans that supported classroom discourse were tensions for these teacher candidates. This study shows that teacher candidates are capable of enacting discourse-focused teaching practices early in their field placements and with the support of practice-based coursework they can analyze and reflect on their practice for improvement. This study also reveals the importance of assisting teacher candidates in accessing rich mathematical tasks and collaborating during lesson planning. More research needs to be explored to identify how specific aspects of the learning cycle impact individual teachers and how this can be used to improve practice-based teacher education courses.

The effects of teaching a mathematics problem solving strategy on the problem solving ability of grade nine students

Forty grade 9 students were selected from a small rural board in southern Ontario. The students were in two classes and were treated as two groups. The treatment group received instruction in the Logical Numerical Problem Solving Strategy every day for 37 minutes over a 6 week period. The control group received instruction in problem solving without this strategy over the same time period. Then the control group received the treat~ent and the treatment group received the instruction without the strategy. Quite a large variance was found in the problem solving ability of students in grade 9. It was also found that the growth of the problem solving ability achievement of students could be measured using growth strands based upon the results of the pilot study. The analysis of the results of the study using t-tests and a MANOVA demonstrated that the teaching of the strategy did not significaritly (at p s 0.05) increase the problem solving achievement of the students. However, there was an encouraging trend seen in the data.

Teaching and aligning upper level mathematics classes to Michigan high school content expectations in an alternative education setting : approaches and issues

After teaching regular education secondary mathematics for seven years, I accepted a position in an alternative education high school. Over the next four years, the State of Michigan adopted new graduation requirements phasing in a mandate for all students to complete Geometry and Algebra 2 courses. Since many of my students were already struggling in Algebra 1, getting them through Geometry and Algebra 2 seemed like a daunting task. To better instruct my students, I wanted to know how other teachers in similar situations were addressing the new High School Content Expectations (HSCEs) in upper level mathematics. This study examines how thoroughly alternative education teachers in Michigan are addressing the HSCEs in their courses, what approaches they have found most effective, and what issues are preventing teachers and schools from successfully implementing the HSCEs. Twenty-six alternative high school educators completed an online survey that included a variety of questions regarding school characteristics, curriculum alignment, implementation approaches and issues. Follow-up phone interviews were conducted with four of these participants. The survey responses were used to categorize schools as successful, unsuccessful, and neutral schools in terms of meeting the HSCEs. Responses from schools in each category were compared to identify common approaches and issues among them and to identify significant differences between school groups. Data analysis showed that successful schools taught more of the HSCEs through a variety of instructional approaches, with an emphasis on varying the ways students learned the material. Individualized instruction was frequently mentioned by successful schools and was strikingly absent from unsuccessful school responses. The main obstacle to successful implementation of the HSCEs identified in the study was gaps in student knowledge. This caused pace of instruction to also be a significant issue. School representatives were fairly united against the belief that the Algebra 2 graduation requirement was appropriate for all alternative education students. Possible implications of these findings are discussed.

Motivation and Learning in Mathematics Pre-service Teachers

Based on a review of literature of conceptual and procedural knowledge in relation to intrinsic and extrinsic motivation, the purpose of this study was to test the relationship between conceptual and procedural knowledge and intrinsic and extrinsic motivation. Thirty-eight education students with a mathematics focus (elementary or secondary) in their junior, senior, or fifth year completed a survey with a Likert scale measuring their preference to learning (conceptual or procedural) and their motivation type (intrinsic or extrinsic). Findings showed that secondary mathematics focused students were more likely to prefer learning mathematics conceptually than elementary mathematics focused students. However, secondary and elementary mathematics focused students showed an equal preference for learning mathematics procedurally and sequentially. Elementary and secondary students reported similar intrinsic and extrinsic motivation. Extrinsically motivated students preferred procedural learning more than conceptual learning. While there was no statistically significant preference with intrinsically motivated students, there was a trend favoring preference of conceptual learning over procedural learning. These results tend to support the hypothesis that mathematics focused students who prefer conceptual learning are more intrinsically motivated, and mathematics focused students who prefer procedural learning are more extrinsically motivated.

Development of prospective mathematics teachers’ professional noticing in a specific domain: proportional reasoning

The aim of this research is to identify aspects that support the development of prospective mathematics teachers’ professional noticing in a b-learning context. The study presented here investigates the extent to which prospective secondary mathematics teachers attend and interpret secondary school students’ proportional reasoning and decide how to respond. Results show that interactions in an on-line discussion improve prospective mathematics teachers’ ability to identify and interpret important aspects of secondary school students’ mathematical thinking.

Why do we study mathematics: a philosophical and historical retrospect ...

"Address delivered before the Secondary mathematics section of the National education association, Boston, July 8, 1910."