Algebra Classroom Research Articles

基于问题解决的线性代数课堂学习环境设计的探究

基于问题解决的线性代数课堂学习环境设计的探究

Whole-Class Implementation of the Self-Determined Learning Model of Instruction in Inclusive High School Mathematics Classes

Abstract Skills associated with self-determination (e.g., self-regulation, problem solving, goal-setting, planning) are infused throughout all secondary content standards, including career and college readiness standards for which all students are responsible. Given research demonstrating the link between self-determination and positive school and post-school outcomes, there is a need to examine the implementation and outcomes of instruction related to self-determination in inclusive general education classrooms. This article reports findings of a one-group, pretest-posttest design examining the impact of the Self-Determined Learning Model of Instruction (SDLMI), a model of instruction designed to be implemented by teachers to support students to learn skills associated with self-determination, on goal achievement of adolescents with and without disabilities in inclusive high school Algebra classrooms. Findings suggest that participants with and without disabilities attained educationally-relevant goals related to math following intervention. Directions for future research and practice are discussed.

General thinking activities in the algebra classroom

General thinking activities in the algebra classroom

The Adoption of Variation Theory in the Classroom: Effect on Students’ Algebraic Achievement and Motivation to Learn

Introduction. Analysis of lessons held in East Asia regions that perform well in Trends in International Mathematics and Science Studies such as; South Korea, Hong Kong and Japan, demonstrated teachers in mathematics classroom enacted features of the content systematically with consideration of variation within students’ capabilities. Recent studies found that integration of variation theory in classroom instruction improve students’ performance significantly. Considering the prior successes in integration of variation theory in classroom in other countries, it is imperative to examine the effect of variation theory based strategy in the teaching and learning of the algebra in schools in Malaysia.Method. The study used quasi-experimental non-equivalent control group research design and involved 58 Form Two (Grade 8th) students in two classes (30 in experimental group, 28 in control group) in Malaysia The first class of students went through algebra class taught with Variation Theory Based Strategy (VTBS) while the class of students experienced Conventional Teaching Strategy (CTS). The instruments used for the study were a 24-item Algebra Test and 46-item Instructional Materials Motivation Interest Survey.Results. Result from Analysis of Covariance indicated that experimental group students achieved significantly better test scores than control group. However, result of Multivariate Analysis of Variance did not show evidence of significant effect of VTBS on experimental group students’ overall motivation in all the five subscales; attention, relevance, confidence, satisfaction, and interest.Discussion and Conclusion. These results suggested the adoption of VTBS in the algebra classroom is effective on students’ algebraic performance but not on students’ motivation to learn. Futher investigations of the impact of VTBS on students’ affective outcomes are recommended.

The effect of providing instructional facilitation on student college readiness

We investigated the impacts of a peer-facilitated instructional intervention in mathematics on progress towards readiness for college among 10th graders who facilitated instruction for 9th graders in algebra classrooms in urban secondary schools. A goal of the intervention is to promote readiness for college by placing middle-performing students in the role of instructional facilitators. The program draws on theory that holds that instructional facilitation helps facilitators enhance their content knowledge and develop in metacognitive and social-emotional domains. We used propensity score matching to evaluate the program’s impact on facilitators’ achievement of outcomes that represent early high school “on-track for college” benchmarks, benchmarks for college readiness, and college entry without need for remediation. Acting as a 10th grade instructional facilitator increased students’ likelihood of meeting near-term, intermediate, and long-term indicators of college readiness. These results indicate that intensive long-term interventions in early high school that draw on students as resources can having lasting impacts on real-world metrics for college-readiness.

Using The Internet In Teaching Algebra To Middle School Students: A Study Of Teacher Perspectives And Attitudes

During the past decades, technological resources have been improved to support the teaching of mathematics. While the improvement of technological resources, the World Wide Web provides teachers and students many resources that engage students in rich mathematics experiences. There are a vast number of educational resources available through the Internet for students and teachers, which should be implemented in the classroom to support and improve algebra instructions. This study seeks to identify the extent of the middle school teacher’s awareness of using the Internet to teach and develop students’ learning of algebra. The participant’s teachers in this study are teaching in schools located in a rural Appalachian region of a Midwestern state in the United States. The study found that the Internet’s function in the algebra classroom within this particular group of middle childhood teachers are used for purposes that do not contribute to algebra instruction.

Inequalities in Math: Using the Algebra Classroom as a Site for Social Justice

This article examines what can happen when issues of Social Justice and Equity are explored in a 7th grade Algebra classroom. While the project was met with resistance along the way and it was clear that there was not a great deal of support from other teachers or administration, my classroom became a place of rich dialogue, critical inquiry and vibrant discussion. Work like this is indispensable to providing students with a framework for social justice and equity in their own lives.

Making a Success of “Algebra for All”

In 2003, Chicago launched “Double-Dose Algebra,” requiring students with pretest scores below the national median to take two periods of math–algebra and supplemental coursework. In many schools, assignment to Double Dose changed the peer composition of the algebra classroom. Using school-specific instrumental variables within a regression-discontinuity design (RDD), we find that attending a lower skill classroom reduced math achievement for median-skill students. As a result, the Double-Dose policy had little or no effect for median-skill students in schools that exposed them to low-skill classrooms. However, the effects of Double Dose were substantially positive in schools that did not do so. We consider policy implications and interpretations of the results from RDDs.

Flipping an Algebra Classroom: Analyzing, Modeling, and Solving Systems of Linear Equations

The present study investigated whether flipping an algebra classroom led to a stronger focus on conceptual understanding and improved learning of systems of linear equations for 54 seventh- and eighth-grade students using teacher journal data and district-mandated unit exam items. Multivariate analysis of covariance was used to compare scores on three factors, analyze, model, and solve systems of linear equations. We found comparable statistically significant learning gains in both treatment groups. We found that the focus on conceptual understanding was similar in the flipped and control classrooms, and the learning gains were statistically significant and similar in both groups. Explicit attention to the substance of the at-home videos and in-class activities is needed to use the flipped classroom model to successfully shift the instructional focus from procedural to conceptual understanding.

Repeated Square Roots

An inquiry-oriented investigation illustrates how students in algebra classrooms may explore limit meaningfully.

“Can You Tell Me More?” Student Journaling and Reasoning

Using journals in an algebra classroom encourage students to develop mathematical reasoning, sense making, and discourse.

Learning Algebra by Example in Real-World Classrooms

Math and science textbook chapters invariably supply students with sets of problems to solve, but this widely used approach is not optimal for learning; instead, more effective learning can be achieved when many problems to solve are replaced with correct and incorrect worked examples for students to study and explain. In the present study, the worked example approach is implemented and rigorously tested in the natural context of a functioning course. In Experiment 1, a randomized controlled study in ethnically diverse Algebra classrooms demonstrates that embedded worked examples can improve student achievement. In Experiment 2, a larger randomized controlled study demonstrated that improvement in posttest scores as a result of the assignments varies based on students’ prior knowledge; students with low prior knowledge tend to improve more than higher knowledge peers.

The impact of technology-enhanced curriculum on learning advanced algebra in US high school classrooms

We report on two large studies conducted in advanced algebra classrooms in the US, which evaluated the effect of replacing traditional algebra 2 curriculum with an integrated suite of dynamic interactive software, wireless networks and technology-enhanced curriculum on student learning. The first study was a cluster randomized trial and the second was a quasi-experimental replication study using a subset of the original treatment teachers. Both studies demonstrated significant impact on student learning of core algebra concepts including both procedural and conceptual problems. Various variables were modeled to understand the impact of such an intervention including demographic factors and class level. We found that being in an honors class significantly predicts learning gains but being in a non-honors SimCalc class significantly predicts learning gains versus all other groups. We also found significant effects of treatment on difference scores for problems which demanded simple procedural approaches and those that demanded complex conceptual understanding.

From Getting “Fired” to Becoming a Collaborator: A Case of the Coconstruction of Identity and Engagement in a Project-Based Mathematics Classroom

This article investigates the coconstruction of student identity and engagement in the case of a 9th grader in a project-based algebra classroom that afforded students a great deal of autonomy. The focal student, Terrance, utilized classroom resources to serve both project-related and social functions as he interacted with his peers during multiweek projects. As a result, his positioning within his group and patterns of engagement in the mathematics projects shifted dramatically across the academic year. The article ends with a discussion of student autonomy as a potentially powerful feature of hybrid classrooms.

Exploring how teacher-related factors relate to student achievement in learning advanced algebra in technology-enhanced classrooms

In this study, we examine the relationship between contextual variables related to teachers and student performance in Advanced Algebra classrooms in the USA. The data were gathered from a cluster-randomized study on the effects of SimCalc MathWorlds®, a curricular and technological intervention as a replacement for Algebra 2 curriculum, on student learning of Algebra 2 content. Conditional measures (teacher background characteristics) and instructional measures (self-reported instructional preferences, stances, and classroom practices) were subjected to a variety of empirical analyses to discern their relationship to student learning. Researchers examined both the overall effect of teacher contextual variables on student learning and the specific effect of SimCalc on both teacher instructional measures and student performance. There is evidence to support that teachers who use the SimCalc curriculum value classroom communication, deep understanding of math concepts, and support for both routine and non-routine problems.

Teacher Change in Teaching Practices Towards Developing Students' Reasoning in Mathematics

Research shows that formative assessment has a more powerful effect on student learning than summative assessment. This case study of an 8th grade algebra classroom focuses on how the implementation of Formative Assessment Lessons (FALs) and the participation in teacher learning communities related to FALs changed in the teacher`s instructional practices, over the course of a year, to promote students` mathematical reasoning and justification. Two classroom observations are analyzed to identify how the teacher elicited and built on students` mathematical reasoning, and how the teacher prompted students to respond to and develop one another`s mathematical ideas. Findings show that the teacher solicited students` reasoning more often as the academic year progressed, and students also began developing mathematical reasoning in meaningful ways, such as articulating their mathematical thinking, responding to other students` reasoning, and building on those ideasleading by the teacher. However, findings also show that teacher change in teaching practices is complicated and intertwined with various dimensions of teacher development. This study contributes to the understanding of changes in teaching practices, which has significant implications for teacher professional development and frameworks for investigating teacher learning.

The Instructional Challenge in Improving Teaching Quality: Lessons from a Classroom Observation Protocol

Background/Context Teacher evaluation is a major policy initiative intended to improve the quality of classroom instruction. This study documents a fundamental challenge to using teacher evaluation to improve teaching and learning. Purpose Using an observation instrument (CLASS-S), we evaluate evidence on different aspects of instructional practice in algebra classrooms to consider how much scores vary, how well observers are able to judge practice, and how well teachers are able to evaluate their own practice. Participants The study includes 82 Algebra I teachers in middle and high schools. Five observers completed almost all observations. Research Design Each classroom was observed 4–5 times over the school year. Each observation was coded and scored live and by video. All videos were coded by two independent observers, as were 36% of the live observations. Observers assigned scores to each of 10 dimensions. Observer scores were also compared with master coders for a subset of videos. Participating teachers also completed a self-report instrument (CLASS-T) to assess their own skills on dimensions of CLASS-S. Data Collection and Analysis For each lesson, data were aggregated into three domain scores, Emotional Support, Classroom Organization, and Instructional Support, and then averaged across lessons to create scores for each classroom. Findings/Results Classroom Observation scores fell in the high range of the protocol. Scores for Emotional Support were in the midlevel range, and the lowest scores were for Instructional Support. Scores for each domain were clustered in narrow ranges. Observers were more consistent over time and agreed more when judging Classroom Organization than the other two domains. Teacher ratings of their own strengths and weaknesses were positively related to observation scores for Classroom Organization and unrelated to observation scores for Instructional Support. Conclusions/Recommendations This study identifies a critical challenge for teacher evaluation policy if it is to improve teaching and learning. Aspects of teaching and learning in the observation protocol that appear most in need of improvement are those that are the hardest for observers to agree on, and teachers and external observers view most differently. Reliability is a marker of common understanding about important constructs and observation protocols are intended to provide a common language and structure to inform teaching practice. This study suggests the need to focus our efforts on the instructional and interactional aspects of classrooms through shared conversations and clear images of what teaching quality looks like.

A modified approach to team-based learning in linear algebra courses

This paper documents the author’s adaptation of team-based learning (TBL), an active learning pedagogy developed by Larry Michaelsen and others, in the linear algebra classroom. The paper discusses the standard components of TBL and the necessary changes to those components for the needs of the course in question. There is also an empirically controlled analysis of the effects of TBL on the student learning experience in the first year of TBL use.

Learning from comparison in algebra

Mastery of algebra is an important yet difficult milestone for students, suggesting the need for more effective teaching strategies in the algebra classroom. Learning by comparing worked-out examples of algebra problems may be one such strategy. Comparison is a powerful learning tool from cognitive science that has shown promising results in prior small-scale studies in mathematics classrooms. This study reports on a yearlong randomized controlled trial testing the effect of an Algebra I supplemental comparison curriculum on students’ mathematical knowledge. 141 Algebra I teachers were randomly assigned to either implement the comparison curriculum as a supplement to their regular curriculum or to be a ‘business as usual’ control. Use of the supplemental curriculum was much less frequent than requested for many teachers, and there was no main effect of condition on student achievement. However, greater use of the supplemental curriculum was associated with greater procedural student knowledge. These findings suggest a role for comparison in the algebra classroom but also the challenges of supporting teacher integration of new materials into the curriculum.

Linear equations and rap battles: how students in a wired classroom utilized the computer as a resource to coordinate personal and mathematical positional identities in hybrid spaces

This paper draws on the constructs of hybridity, figured worlds, and cultural capital to examine how a group of African-American students in a technology-driven, project-based algebra classroom utilized the computer as a resource to coordinate personal and mathematical positional identities during group work. Analyses of several vignettes of small group dynamics highlight how hybridity was established as the students engaged in multiple on-task and off-task computer-based activities, each of which drew on different lived experiences and forms of cultural capital. The paper ends with a discussion on how classrooms that make use of student-led collaborative work, and where students are afforded autonomy, have the potential to support the academic engagement of students from historically marginalized communities.